A famous urban legend states that a penny dropped from the top of the Empire State Building will punch a hole in the sidewalk below. Given the height of the building and the hardness of the penny, that seems like a reasonable possibility. Whether it's true or not is a matter that can be determined scientifically. Before we do that, though, let's get some background.
Falling rocks can be dangerous and, the farther they fall, the more dangerous they become. Falling raindrops, snowflakes, and leaves, however, are harmless no matter how far they fall. The distinction between those two possibilities has nothing to do with gravity, which causes all falling objects to accelerate downward at the same rate. The difference is entirely due to air resistance.
Air resistance—technically known as drag—is the downwind force an object experiences as air moves passed it. Whenever an object moves through the air, the two invariably push on one another and they exchange momentum. The object acts to drag the air along with it and the air acts to drag the object along with it, action and reaction. Those two aerodynamic forces affect the motions of the object and air, and are what distinguish falling snowflakes from falling rocks.
Two types of drag force affect falling objects: viscous drag and pressure drag. Viscous drag is the friction-like effect of having the air rub across the surface of the object. Though important to smoke and dust particles in the air, viscous drag is too weak to affect larger objects significantly.
In contrast, pressure drag is strongly affects most large objects moving through the air. It occurs when airflow traveling around the object breaks away from the object's surface before reaching the back of the object. That separated airflow leaves a turbulent wake behind the object—a pocket of air that the object is effectively dragging along with it. The wider this turbulent wake, the more air the object is dragging and the more severe the pressure drag force.
The airflow separation occurs as the airflow is attempting to travel from the sides of the object to the back of the object. At the sides, the pressure in the airflow is especially low due as it bends to arc around the sides. Bernoulli's equation is frequently invoked to help explain the low air pressure near the sides of the object. As this low-pressure air continues toward the back of the object, where the pressure is much greater, the airflow is moving into rising pressure and is pushed backward. It is decelerating.
Because of inertia, the airflow could be expected to reach the back of the object anyway. However, the air nearest the object's surface—boundary layer air—rubs on that surface and slows down. This boundary layer doesn't quite make it to the back of the object. Instead, it stops moving and consequently forms a wedge that shaves much of the airflow off of the back of the object. A turbulent wake forms and the object begins to drag that wake along with it. The airflow and object are then pushing on one another with the forces of pressure drag.
Those pressure drag forces depend on the amount of air in the wake and the speed at which the object is dragging the wake through the passing air. In general, the drag force on the object is proportional to the cross sectional area of its wake and the square of its speed through the air. The broader its wake and the faster it moves, the bigger the drag force it experiences.
We're ready to drop the penny. When we first release it at the top of the Empire State Building, it begins to accelerate downward at 9.8 meters-per-second2—the acceleration due to gravity—and starts to move downward. If no other force appeared, the penny would move according to the equations of motion for constant downward acceleration, taught in most introductory physics classes. It would continue to accelerate downward at 9.8 meters-per-second2, meaning that its downward velocity would increase steadily until the moment it hit sidewalk. At that point, it would be traveling downward at approximately 209 mph (336 km/h) and it would do some damage to the sidewalk.
That analysis, however, ignores pressure drag. Once the penny is moving downward through the air, it experiences an upward pressure drag force that affects its motion. Instead of accelerating downward in response to its weight alone, the penny now accelerates in response to the sum of two force: its downward weight and the upward drag force. The faster the penny descends through the air, the stronger the drag force becomes and the more that upward force cancels the penny's downward weight. At a certain downward velocity, the upward drag force on the penny exactly cancels the penny's weight and the penny no longer accelerates. Instead, it descends steadily at a constant velocity, its terminal velocity, no matter how much farther drops.
The penny's terminal velocity depends primarily on two things: its weight and the cross sectional area of its wake. A heavy object that leaves a narrow wake will have a large terminal velocity, while a light object that leaves a broad wake will have a small terminal velocity. Big rocks are in the first category; raindrops, snowflakes, and leaves are in the second. Where does a penny belong?
It turns out that a penny is more like a leaf than a rock. The penny tumbles as it falls and produces a broad turbulent wake. For its weight, it drags an awful lot of air behind it. As a result, it reaches terminal velocity at only about 25 mph (40 km/h). To prove that, I studied pennies fluttering about in a small vertical wind tunnel.
Whether the penny descends through stationary air or the penny hovers in rising air, the physics is the same. Of course, it's much more convenient in the laboratory to observe the hovering penny interacting with rising air. Using a fan and plastic pipe, I created a rising stream of air and inserted a penny into that airflow.
At low air speeds, the penny experiences too little upward drag force to cancel its weight. The penny therefore accelerated downward and dropped to the bottom of the wind tunnel. At high air speeds, the penny experienced such a strong upward drag force that it blew out of the wind tunnel. When the air speed was just right, the penny hovered in the wind tunnel. The air speed was then approximately 25 mph (40 km/h). That is the terminal velocity of a penny.
The penny tumbles in the rising air. It is aerodynamically unstable, meaning that it cannot maintain a fixed orientation in the passing airstream. Because the aerodynamic forces act mostly on the upstream side of the penny, they tend to twist that side of the penny downstream. Whichever side of the penny is upstream at one moment soon becomes the downstream side, and the penny tumbles. As a result of this tumbling, the penny disturbs a wide swath of air and leaves a broad turbulent wake. It experiences severe pressure drag and has a low terminal velocity.
The penny is an example of an aerodynamically blunt object—one in which the low-pressure air arcing around its sides runs into the rapidly increasing pressure behind it and separates catastrophically to form a vast wake. The opposite possibility is an aerodynamically streamlined object—one in which the increasing pressure beyond the object's sides is so gradual that the airflow never separates and no turbulent wake forms. A penny isn't streamlined, but a ballpoint pen could be.
Almost any ballpoint pen is less blunt than a penny and some pens are approximately streamlined. Moreover, pens weigh more than pennies and that fact alone favors a higher terminal velocity. With a larger downward force (weight) and a smaller upward force (drag), the pen accelerates to a much greater terminal velocity than the penny. If it is so streamlined that it leaves virtually no wake, like the aerofoil shapes typical of airplane components, it will have an extraordinarily large terminal velocity—perhaps several hundred miles per hour.
Some pens tumble, however, and that spoils their ability to slice through the air. To avoid tumbling, a pen must "weathervane"—it must experience most of its aerodynamic forces on its downstream side, behind its center of mass. Arrows and small rockets have fletching or fins to ensure that they travel point first through the air. A ballpoint pen can achieve that same point-first flight if its shape and center of mass are properly arranged.
Almost any ballpoint pen dropped into my wind tunnel plummeted to the bottom. I was unable to make the air rise fast enough to observe hovering behavior in those pens. Whether they would tend to tumble in the open air was difficult to determine because of the tunnel's narrowness. Nonetheless, it's clear that a heavy, streamlined, and properly weighted pen dropped from the Empire State Building would still be accelerating downward when it reached the sidewalk. Its speed would be close to 209 mph at that point and it would indeed damage the sidewalk.
As a final test of the penny's low terminal velocity, I built a radio-controlled penny dropper and floated it several hundred feet in the air with a helium-filled weather balloon. On command, the dropper released penny after penny and I tried to catch them as they fluttered to the ground. Alas, I never managed to catch one properly in my hands. It was a somewhat windy day and the ground at the local park was uneven, but that's hardly an excuse—I'm simply not good at catching things in my hands. Several of the pennies did bounce off my hands and one even bounced off my head. It was fun and I was more in danger of twisting my ankle than of getting pierced by a penny. The pennies descended so slowly that they didn't hurt at all. Tourist below the Empire State Building have nothing fear from falling pennies. Watch out, however, for some of the more streamlined objects that might make that descent.
If by smart meters you mean the devices that monitor power usage and possibly adjust power consumption to periodically, then I don't see how they can affect health. Their communications with the smart grid are of no consequence to human health and having the power adjusted on household devices is unlikely to be a health issue (unless they cut off your power during a blizzard or a deadly heat wave).
The radiated power from all of these wireless communications devices is so small that we have yet to find mechanisms whereby they could cause significant or lasting injury to human tissue. If there is any such mechanism, the effects are so weak that the risk associated with it are dwarfed by much more significant risks of wireless communication: the damage to traditional community, the decline of ordinary human interaction, and the surge in distracted driving.
The Japanese did stop the chain reactions in the Fukushima Daiichi reactors, even before the tsunami struck the plant. The problem that they're having now is not the continued fissioning of uranium, but rather the intense radioactivity of the uranium daughter nuclei that were created while the chain reactions were underway. Those radioactive fission fragments are spontaneously decaying now and there is nothing that can stop that natural decay now. All they can do now is to try to contain those radioactive nuclei, keep them from overheating, and wait for them to decay into stable pieces.
The uranium atom has the largest naturally occurring nucleus in nature. It contains 92 protons, each of which is positively charged, and those 92 like charges repel one another ferociously. Although the nuclear force acts to bind protons together when they touch, the repulsion of 92 protons alone would be too much for the nuclear force—the protons would fly apart in almost no time.
To dilute the electrostatic repulsion of those protons, each uranium nucleus contains a large number of uncharged neutrons. Like protons, neutrons experience the attractive nuclear force. But unlike protons, neutrons don't experience the repulsive electrostatic force. Two neutron-rich combinations of protons and neutrons form extremely long-lived uranium nuclei: uranium-235 (92 protons, 143 neutrons) and uranium-238 (92 protons, 146 neutrons). Each uranium nucleus attracts an entourage of 92 electrons to form a stable atom and, since the electrons are responsible for the chemistry of an atom, uranium-235 and uranium-238 are chemically indistinguishable.
When the thermal fission reactors of the Fukushima Daiichi plant were in operation, fission chain reactions were shattering the uranium-235 nuclei into fragments. Uranium-238 is more difficult to shatter and doesn't participate much in the reactor's operation. On occasion, however, a uranium-238 nucleus captures a neutron in the reactor and transforms sequentially into neptunium-239 and then plutonium-239. The presence of plutonium-239 in the used fuel rods is one of the problems following the accident.
The main problem, however, is that the shattered fission fragment nuclei in the used reactor fuel are overly neutron-rich, a feature inherited from the neutron-rich uranium-235 nuclei themselves. Midsize nuclei, such as iodine (with 53 protons), cesium (with 55 protons), and strontium (with 38 protons), don't need as many neutrons to dilute out the repulsions between their protons. While fission of uranium-235 can produce daughter nuclei with 53 protons, 55 protons, or 38 protons, those fission-fragment versions of iodine, cesium, and strontium nuclei have too many neutrons and are therefore unstable—they undergo radioactive decay. Their eventual decay has nothing to do with chain reactions and it cannot be prevented.
How quickly these radioactive fission fragment nuclei decay depends on exactly how many protons and neutrons they have. Three of the most common and dangerous nuclei present in the used fuel rods are iodine-131 (8 days half-life), cesium-137 (30 year half-life), and strontium-90 (29 year half-life). Plutonium-239 (24,200 year half-life) is also present in those rods. When these radioactive nuclei are absorbed into the body and then undergo spontaneous radioactive decay, they damage molecules and therefore pose a cancer risk. Our bodies can't distinguish the radioactive versions of these chemical elements from the nonradioactive ones, so all we can do to minimize our risk is to avoid exposure to them or to encourage our bodies to excrete them by saturating our bodies with stable versions.
By asking me to "neglect possible discharges," you're asking me to neglect what actually happens. There will be a discharge, specifically a phenomenon known as "field emission". Neglect that discharge, then yes, the sphere can in principle store an unlimited amount of charge. But on route to infinity, I will have had to ignore several other exotic discharges and then the formation of a black hole.
What will really happen is a field emission discharge. The repulsion between like charges will eventually become so strong that those charges will push one another out of the metal and into the vacuum, so that charges will begin to stream outward from the metal sphere.
Another way to describe that growing repulsion between like charges involves fields. An electric charge is surrounded by a structure in space known as an electric field. An electric field exerts forces on electric charges, so one electric charge pushes on other electric charges by way of its electric field.
As more and more like charges accumulate on the sphere, their electric fields overlap and add so that the overall electric field around the sphere becomes stronger and stronger. The charges on the sphere feel that electric field, but they are bound to the metal sphere by chemical forces and it takes energy to pluck one of them away from the metal.
Eventually, the electric field becomes so strong that it can provide the energy needed to detach a charge from the metal surface. The work done by the field as it pushes the charge away from sphere supplies the necessary energy and the charge leaves the sphere and heads out into the vacuum. The actually detachment process involves a quantum physics phenomenon known as tunneling, but that's another story.
The amount of charge the sphere can store before field emission begins depends on the radius of the sphere and on whether the charge is positive or negative. The smaller that radius, the faster the electric field increases and the sooner field emission starts. It's also easier to field-emit negative charges (as electrons) than it is to field-emit positive charges (as ions), so a given sphere will be able to hold more positive charge than negative charge.
Modern brushless DC motors are amazing devices that can handle torque reversals instantly. In fact, they can even generate electricity during those reversals!
Instant reversals of direction, however, aren't physically possible (because of inertia) and aren't actually what your friend wants anyway. I'll say more about the distinction between torque reversals and direction reversals in a minute.
In general, a motor has a spinning component called the rotor that is surrounded by a stationary component called the stator. The simplest brushless DC motor has a rotor that contains permanent magnets and a stator that consists of electromagnets. The magnetic poles on the stator and rotor can attract or repel one another, depending on whether they like or opposite poles—like poles repel; opposite poles attract.
Since the electronics powering the stator's electromagnets can choose which of the stator's poles are north and which are south, those electronics determine the forces acting on the rotor's poles and therefore the direction of torque on the rotor. To twist the rotor forward, the electronics make sure that the stator's poles are always acting to pull or push the rotor's poles in the forward direction so that the rotor experiences forward torque. To twist the rotor backward, the electronics reverses all those forces.
Just because you reverse the direction of torque on the rotor doesn't mean that the rotor will instantly reverse its direction of rotation. The rotor (along with the rider of the scooter) has inertia and it takes time for the rotor to slow to a stop and then pick up speed in the opposite direction. More specifically, a torque causes angular acceleration; it doesn't cause angular velocity. During that reversal process, the rotor is turning in one direction while it is being twisted in the other direction. The rotor is slowing down and it is losing energy, so where is that energy going? It's actually going into the electronics which can use this electricity to recharge the batteries. The "motor" is acting as a "generator" during the slowing half of the reversal!
That brushless DC motors are actually motor/generators makes them fabulous for electric vehicles of all types. They consume electric power while they are making a vehicle speed up, but they generate electric power while they are slowing a vehicle down. That's the principle behind regenerative braking—the vehicle's kinetic energy is used to recharge the batteries during braking.
With suitable electronics, your friend's electric scooter can take advantage of the elegant interplay between electric power and mechanical power that brushless DC motors make possible. Those motors can handle torque reversals easily and they can even save energy in the process. There are limits, however, to the suddenness of some of the processes because huge flows of energy necessitate large voltages and powers in the motor/generators and their electronics. The peak power and voltage ratings of all the devices come into play during the most abrupt and strenuous changes in the motion of the scooter. If your friend wants to be able to go from 0 to 60 or from 60 to 0 in the blink of eye, the motor/generators and their electronics will have to handle big voltages and powers.
Although that sounds like a simple question, it has a complicated answer. Gravity does affect light, but it doesn't affect light's speed. In empty space, light is always observed to travel at "The Speed of Light." But that remark hides a remarkable result: although two different observers will agree on how fast light is traveling, they may disagree in their perceptions of space and time.
When those observers are in motion relative to one another, they'll certainly disagree about the time and distance separating two events (say, two firecrackers exploding at separate locations). For modest relative velocities, their disagreement will be too small to notice. But as their relative motion increases, that disagreement will become substantial. That is one of the key insights of Einstein's special theory of relativity.
But even when two observers are not moving relative to one another, gravity can cause them to disagree about the time and distance separating two events. When those observers are in different gravitational circumstances, they'll perceive space and time differently. That effect is one of the key insights of Einstein's general theory of relativity.
Here is a case in point: suppose two observers are in separate spacecraft, hovering motionless relative to the sun, and one observer is much closer to the sun than the other. The closer observer has a laser pointer that emits a green beam toward the farther observer. Both observers will see the light pass by and measure its speed. They'll agree that the light is traveling at "The Speed of Light". But they will not agree on the exact frequency of the light. The farther observer will see the light as slightly lower in frequency (redder) than the closer observer. Similarly, if the farther observer sends a laser pointer beam toward the closer observer, the closer observer will see the light as slightly higher in frequency (bluer) than the farther observer.
How can these two observers agree on the speed of the beams but disagree on their frequencies (and colors)? They perceive space and time differently! Time is actually passing more slowly for the closer observer than for the farther observer. If they look carefully at each others' watches, the farther observer will see the closer observer's watch running slow and the closer observer will see the farther observer's watch running fast. The closer observer is actually aging slightly more slowly than the farther observer.
These effects are usually very subtle and difficult to measure, but they're real. The global positioning system relies on ultra-precise clocks that are carried around the earth in satellites. Those satellites move very fast relative to us and they are farther from the earth's center and its gravity than we are. Both difference affect how time passes for those satellites and the engineers who designed and operate the global positioning system have to make corrections for the time-space effects of special and general relativity.
Liquid water can evaporate to form gaseous water (i.e., steam) at any temperature, not just at its boiling temperature of 212 F. The difference between normal evaporation and boiling is that, below water's boiling temperature, evaporation occurs primarily at the surface of the liquid water whereas at or above water's boiling temperature, bubbles of pure steam become stable within the liquid and water can evaporate especially rapidly into those bubbles. So boiling is a just a rapid form of evaporation.
What you are actually seeing when raindrops land on warm surfaces is tiny water droplets in the air, a mist of condensation. Those droplets happen in a couple of steps. First, the surface warms a raindrop and speeds up its evaporation. Second, a small portion of warm, especially moist air rises upward from the evaporating raindrop. Third, that portion of warm moist air cools as it encounters air well above the warmed surface. The sudden drop in temperature causes the moist air to become supersaturated with moisture—it now contains more water vapor than it can retain at equilibrium. The excess moisture condenses to form tiny water droplets that you see as a mist.
This effect is particularly noticeable when it's raining because the humidity in the air is already very near 100%. The extra humidity added when the warmed raindrops evaporate is able to remain gaseous only in warmed air. Once that air cools back to the ambient temperature, the moisture must condense back out of it, producing the mist.
Solid ice is less dense than liquid water, meaning that a liter of ice has less mass (and weighs less) than a liter of water. Any object that is less dense than water will float at the surface of water, so ice floats.
That lower-density objects float on water is a consequence of Archimedes' principle: when an object displaces a fluid, it experiences an upward buoyant force equal in amount to the weight of the displaced fluid. If you submerge a piece of ice completely in water, that piece of ice will experience an upward buoyant force that exceeds the ice's weight because the water it displaces weighs more than the ice itself. The ice then experiences two forces: its downward weight and the upward buoyant force from the water. Since the upward force is stronger than the downward force, the ice accelerates upward. It rises to the surface of the water, bobs up and down a couple of times, and then settles at equilibrium.
At that equilibrium, the ice is displacing a mixture of water and air. Amazingly enough, that mixture weighs exactly as much as the ice itself, so the ice now experiences zero net force. That's why its at equilibrium and why it can remain stationary. It has settled at just the right height to displace its weight in water and air.
As for why ice is less dense than water, that has to do with the crystal structure of solid ice and the more complicated structure of liquid water. Ice's crystal structure is unusually spacious and it gives the ice crystals their surprisingly low density. Water's structure is more compact and dense. This arrangement, with solid water less dense than liquid water, is almost unique in nature. Most solids are denser than their liquids, so that they sink in their liquids.
The electric circuit that powers your lamp extends only as far as a nearby transformer. That transformer is located somewhere near your house, probably as a cylindrical object on a telephone pole down the street or as a green box on a side lawn a few houses away.
A transformer conveys electric power from one electric circuit to another. It performs this feat using several electromagnetic effects associated with changing electric currents—changes present in the alternating current of our power grid. In this case, the transformer is moving power from a high-voltage neighborhood circuit to a low-voltage household circuit.
For safety, household electric power uses relatively low voltages, typically 120 volt in the US. But to deliver significant amounts of power at such low voltages, you need large currents. It's analogous to delivering hydraulic power at low pressures; low pressures are nice and safe, but you need large amounts of hydraulic fluid to carry much power. There is a problem, however, with sending low voltage electric power long distances: it's inefficient because wires waste power as heat in proportion to the square of the electric current they carry. Using our analogy again, sending hydraulic power long distances as a large flow of hydraulic fluid at low pressure is wasteful; the fluid will rub against the pipes and waste power as heat.
To send electric power long distances, you do better to use high voltages and small currents (think high pressure and small flows of hydraulic fluid). That requires being careful with the wires because high voltages are dangerous, but it is exactly how electric power travels cross-country in the power grid: very high voltages on transmission lines that are safely out of reach.
Finally, to move power from the long-distance high-voltage transmission wires to the short-distance low-voltage household wires, they use transformers. The long-distance circuit that carries power to your neighborhood closes on one side of the transformer and the short-distance circuit that carries power to your lamp closes on the other side of the transformer. No electric charges pass between those two circuits; they are electrically insulated from one another inside the transformer. The electric charges that are flowing through your lamp go round and round that little local circuit, shuttling from the transformer to your lamp and back again.
The f-number of a lens measures the brightness of the image that lens casts onto the camera's image sensor. Smaller f-numbers produce brighter images, but they also yield smaller depths of focus.
The f-number is actually the ratio of the lens' focal length to its effective diameter (the diameter of the light beam it collects and uses for its image). Your zoom lens has a focal length that can vary from 70 to 300 mm and a minimum f-number of 5.6. That means the when it is acting as a 300 mm telephoto lens, its effective light gathering surface is about 53 mm in diameter (300 mm divided by 5.6 gives a diameter of 53 mm).
If you examine the lens, I think that you'll find that the front optical element is about 53 mm in diameter; the lens is using that entire surface to collect light when it is acting as a 300 mm lens at f-5.6. But when you zoom to lower focal lengths (less extreme telephoto), the lens uses less of the light entering its front surface. Similarly, when you dial a higher f-number, you are closing a mechanical diaphragm that is strategically located inside the lens and causing the lens to use less light. It's easy for the lens to increase its f-number by throwing away light arriving near the edges of its front optical element, but the lens can't decrease its f-number below 5.6; it can't create additional light gathering surface. Very low f-number lenses, particularly telephoto lenses with their long focal lengths, need very large diameter front optical elements. They tend to be big, expensive, and heavy.
Smaller f-numbers produce brighter images, but there is a cost to that brightness. With more light rays entering the lens and focusing onto the image sensor, the need for careful focusing becomes greater. The lower the f-number, the more different directions those rays travel and the harder it is to get them all to converge properly on the image sensor. At low f-numbers, only rays from a specific distance converge to sharp focus on the image sensor; rays from objects that are too close or too far from the lens don't form sharp images and appear blurry.
If you want to take a photograph in which everything, near and far, is essentially in perfect focus, you need to use a large f-number. The lens will form a dim image and you'll need to take a relatively long exposure, but you'll get a uniformly sharp picture. But if you're taking a portrait of a person and you want to blur the background so that it doesn't detract from the person's face, you'll want a small f-number. The preferred portrait lenses are moderately telephoto—they allow you to back up enough that the person's face doesn't bulge out at you in the photograph—and they have very low f-numbers—their large front optical elements gather lots of light and yield a very shallow depth of focus.
Both the fork and the food are almost certainly safe. While the microwave oven is operating, electric current will flow through the fork and electric charge will accumulate momentarily on the tips of the fork's tines. However, most forks are thick enough to handle the current without becoming noticeably hot and have tines that are dull enough to accumulate the charge without sparking. The end result is that the fork doesn't do much while the oven is operating; it reflects the microwaves and therefore alters the cooking pattern slightly, but you probably won't be able to tell. Once the cooking is over, the fork is just as it was before you put it in the oven and the food is basically just microwaved food.
If a fork has particularly sharp tines, however, then you should be careful not to put in the microwave oven. Sharp metal objects can and do spark in the microwave oven. Those sparks are probably more of a fire hazard than a food safety hazard—they can ignite the food or its container and start a fire.
Yes. My solution is to fill the well hole with objects that are dense enough and hydrodynamically streamlined enough to descend by gravity alone through the upward flow of oil. As they accumulate in the 3+ mile deep well hole, those objects will impede the flow until it becomes a trickle. Large steel balls (e.g., cannonballs) should do the trick. If they are large enough, they will have a downward terminal velocity, even as they move through the upward flowing oil. Because they descend, they will eventually accumulate at the bottom of the well hole and form a coarse "packed powder." That powder will use its enormous weight and its resistance to flow to stop the leak. Most importantly, building the powder doesn't require any seals or pressurization at the top of the well hole, so it should be easy to do.
The packed powder will exert downward drag forces on the upward flow of oil and gas, slowing its progress and decreasing its pressure faster than gravity alone. With 3+ miles of hole to fill, the dense steel objects should impede the flow severely. As the flow rate diminishes, the diameters of the metal spheres can be reduced until they are eventually only inches or even centimeters in diameter. The oil and gas will then be forced to flow through fine channels in the "powder," allowing viscous drag and pressure drag to extract all of the pressure potential energy from the flow and convert that energy into thermal energy. The flow will, in effect, be attempting to lift thousands of pounds of metal particles and it will fail. It will ooze though the "packed powder" at an insignificant rate.
Another way to think about my technique is that it gradually increases the average density of the fluid in the well hole until that column of fluid is so heavy that the high pressure at the bottom of the hole is unable to lift it. The liquid starts out as a light mixture of oil and gas, but it gradually transforms into a dense mixture of oil, gas, and iron. Viscous forces and drag forces effectively couple the materials phases together to form a single fluid. Once that fluid is about 50% iron by volume, its average density will be so high (4 times the density of water) that it will stop flowing upward. If iron isn't dense enough (7.8 times water), you could use silver cannonballs (10.5 times water). Then you could say that "silver bullets" stopped the leak! The failed "top kill" concept also intended to fill the well hole with a dense fluid: heavy mud. But it required pushing the oil and gas down the well hole to make room for the mud. That displacement process proved to be impossible because it required unobtainable pressures and pumping power. My approach takes no pressurization or pumping at all because it doesn't actively displace the oil and gas.
Including deformable lead spheres in the mixture will further plug the upward flow. The lead will deform under the weight of metal overhead and will fill voids and narrow channels. Another refinement of this dense-fill concept would be to drop bead chains down the well hole. The first large ball in such a chain would be a "tug boat" that is capable of descending against the upward flow all by itself. It would be followed by progressively smaller balls that need to draft (travel in the wake of) the balls ahead of them in order to descend into the well. Held together by steel or Kevlar cord, those bead chains would accumulate at the bottom of the well and impede the flow more effectively than individual large balls. Especially streamlined (non-spherical) objects such as steel javelins, darts, rods, and rebar could also be dropped into the well at the start of the filling process. In fact, sturdy sacks filled with junk steel objects—nuts and bolts—might even work. Anything that descends into the well hole is good and smaller particles are better. The point is not to form a seal, since the enormous pressure that will develop beneath any seal will blow it upward. The point is always to form narrow channels through which the oil and gas will struggle to flow.
A video of this idea appears at: http://www.youtube.com/watch?v=8H29H_1vTHo and a manuscript detailing this idea appears on the Physics ArXiv: http://arxiv.org/abs/1006.0656. I'm trying to find a home for it in the scientific literature, but so far Applied Physics Letters, Physic Review E (which includes the physics of fluids), and PLoS (Public Library of Science) One have turned it down—they want articles with new physics in them, not articles applying old physics to new contexts, no matter how important those contexts. It's no wonder that the public views science as arcane and irrelevant.
As the candle burns, its wax melts into a liquid, that liquid "wicks" up the wick (like water flowing up into a paper towel), and then the extreme heat of the flame vaporizes the wax (it is become gaseous wax). Once the wax is a gas, it burns in much the same way that natural gas burns — it reacts with oxygen in the air to become water and carbon dioxide. That reaction released chemical potential energy as thermal energy.
One important difference between a candle flame and a natural gas flame: whereas the flame of a well-adjusted natural gas burner emits very little light (a dim blue glow), the flame of a candle is quite visible. That's because the wax vapor in a candle flame isn't mixed well with air before it begins to burn. Instead of burning quickly and completely, as natural gas does in a burner that premixes the gas with air, the wax vapor in a candle flame burns gradually as it continues to mix with air. The partially burned wax forms tiny carbon particles. Those carbon particles are so hot that they glow yellow-hot — they emit thermal radiation. In other words, they are "incandescent". It's those glowing carbon particles that produce the candle's yellowish light. Eventually the carbon particles burn away to carbon dioxide.
Our eyes sense color by measuring the relative brightnesses of the red, green, and blue portions of the light spectrum. When all three portions of the spectrum are present in the proper amounts, we perceive white.
The color sensing cells in our eyes are known as cone cells and they can detect only three different bands of color. One type of cone cell is sensitive to light in the red portion of the spectrum, the second type is sensitive to the green portion of the spectrum, and the third type is sensitive to the blue portion of the spectrum.
Their sensitivities overlap somewhat, so light in the yellow and orange portions of the spectrum simultaneously affects both the red sensitive cone cells and the green sensitive ones. Our brains interpret color according to which of three cone cells are being stimulated and to what extent. When both our red sensors and our green sensors are being stimulated, we perceive yellow or orange.
That scheme for sensing color is simple and elegant, and it allows us to appreciate many of the subtle color variations in our world. But it means that we can't distinguish between certain groups of lights. For example, we can't distinguish between (1) true yellow light and (2) a carefully adjusted mixture of true red plus true green. Both stimulate our red and green sensors just enough to make us perceive yellow. Those groups of lights look exactly the same to us.
Similarly, we can't distinguish between (3) the full spectrum of sunlight and (4) a carefully adjusted mixture of true red, true green, and true blue. Those two groups stimulate all three types of cone cells and make us perceive white. They look identical to us.
That the primary colors of light are red, green, and blue is the result of our human physiology and the fact that our eyes divide the spectrum of light into those three color regions. If our eyes were different, the primary colors of light would be different, too.
Many things in our technological world exploit mixtures of those three primary colors to make us see every possible color. Computer monitors, televisions, photographs, and color printing all make us see what they want us to see without actually reproducing the full light spectrum of the original. For example, if you used a light spectrum analyzer to study a flower and a photograph of that flower, you'd discover that their light spectra are different. Those spectra stimulate our eyes the same way, but the details of the spectra are different. We can't tell them apart.
Most four-tube fluorescent fixtures are effectively two separate two-tube units. They share the same ballast, but otherwise each pair of tubes is independent of the other. Removing one of those pairs from the fixture will save nearly half the energy and expense, and is a good idea if you don't need the extra illumination.
The two tubes within a pair operate in series: current flowing as a discharge through the gas in one tube also flows through the gas in the other tube. That's why they both go out simultaneously. Only one of them is actually dead, but since the dead one has lost its ability to sustain a discharge, it can't pass any current on to its partner. Replacing the dead tube is usually enough to get the pair working again, at least for while.
Leaving dead tubes in a fixture isn't the same as removing unnecessary tubes. Tubes often die slow, lingering deaths during which they sustain weak or flickering discharges that consume some energy without providing much light. Also, most fluorescent fixtures heat the electrodes at the ends of the tubes to start the discharge. During startup, the ballast runs an electric current through each electrode (hence the two metal contacts at each end of the tube) and the heated electrodes introduces electric charges into the gas so the discharge can start.
That heating current is only necessary during starting, but if the discharge never starts then the ballast may continue to heat the electrodes for days, weeks, or years. If you look at the ends of a tube that fails to start, you may see the electrodes glowing red hot. Because of that heater current, leaving a failed fluorescent tube in a fixture can be waste of energy and money. Be careful removing those tubes from the fixture—although they produce no light, they can still be hot at their ends.
Polymers are simply giant molecules that were formed by sticking together a great many small molecules. The properties of a given polymer depend on which small molecules it contains and how those molecules were assembled. To help your students visualize this idea, I'd go right to two familiar models: snap-together beads ("pop beads") and spaghetti.
Snap-together beads are a perfect model for many polymers. As individual beads, you can pour them like a liquid and move your hand through them easily. But once you begin snapping them together into long chains, they develop new properties that weren't present in the beads themselves. For example, they get tangled together and don't flow so easily any more.
That emergence of new properties is exactly what happens in many polymers. For example, ethylene is a simple gas molecule, but if you stick ethylene molecules together to form enormous chains, you get polyethylene (more specifically, high-density polyethylene, recycling number 2, milk-jug plastic). Ethylene molecules are called "monomers" and the giant chains that are made from them are called "polymers".
Polyethylene retains some of the chemical properties of its monomer units, namely that it doesn't react with most other chemicals and almost nothing sticks to it. But polyethylene also has properties that the monomer units didn't have: polyethylene is a sturdy, flexible solid. You can stretch it without breaking it. That happens because you can make its polymer molecules slide across one another, but you can't untangle the tangles.
To get an idea of what it's like to work with molecules that can slide through each other but may not be able to untangle themselves, shift over to cooked and drained spaghetti. If you dice the spaghetti up into tiny pieces, it's like the monomers—nothing to tangle. You can pour the tiny pieces like a liquid. But trying doing that with a bowl of long spaghetti noddles. They're so tangled up that they can't do much. In fact, if you let the water dry up to some extent, the stuff will become a sturdy, flexible solid, just like HDPE!
There is much more to say about polymers, for example, they're not all simple straight chains and some of them cross-link so that they can't untangle no matter what you do. But this should be a good start. Polymer molecules are everywhere, including in paper and hair. Paper is primarily cellulose, giant molecules built out of sugar molecules. Hair is protein polymer, giant molecules built out of protein monomer units. They're both sturdy, stretchy, flexible solids and they're both softened by water—which acts as a molecular lubricant for the polymer molecules. Not all polymers are sturdy, or stretchy, or flexible, but a good many are.
The door of a microwave oven is carefully designed to reflect microwaves so that they can't escape from the oven. That mesh that you see in the door isn't plastic, it's metal. Metal surfaces reflect microwaves and, even though the mesh has holes in it to allow you to observe the food, it acts as a perfect mirror for the microwaves. Basically, the holes are so much smaller than the 12.2-cm wavelength of the 2.45-GHz microwave that the microwave cannot propagate through the holes. Electric currents flow through the metal mesh as the microwave hits it and those currents re-radiate the microwave in the reflected direction. Since the holes aren't big enough to disrupt that current flow, the mesh reflects the microwaves as effectively as a solid metal surface would.
As for how your cell phone and the cell tower can communicate for miles despite all the intervening stuff, it's actually a challenge. The microwaves from your phone and the tower are partly absorbed and partly reflected each time they encounter something in your environment, so they end up bouncing their way through an urban landscape. That's why cell towers have multiple antennas and extraordinarily sophisticated transmitting and receiving equipment. They are working like crazy to direct their microwaves at your phone as effectively as possible and to receive the microwaves from your phone even though those waves are very weak and arrive in bits and pieces due to all the scattering events they experience during their passage. Indoor cell phone reception is typically pretty poor unless the building has its own internal repeaters or microcells.
There are times when you don't get any reception because the microwaves from the cell phone and tower are almost completely absorbed or reflected. For example, if you were to stand in a metalized box, the microwaves from your cell phone would be trapped in the box and would not reach the cell tower. Similarly, the microwaves from the cell tower would not reach you. Moreover, the box doesn't have to be fully metalized; a metal mesh or a transparent conductor is enough to reflect the microwaves. Transparent conductors are materials that conduct relatively low-frequency currents but don't conduct currents at the higher frequencies associated with visible light. They're used in electronic displays (e.g., computer monitors and digital watches) and in energy-conserving low-E windows. I haven't experimented with cell phone reception near low-E windows, but I'm eager to give it a try. I suspect that a room entirely walled by low-E windows will have lousy cell phone reception.
Incandescent lightbulbs will be phased out beginning with 100-watt bulbs in 2012 and ending with 40-watt bulbs in 2014. The reason for this phase out is simple: incandescent lightbulbs are horribly energy inefficient.
Light is a form of energy, so you can compare the visible light energy emitted by any lamp to the energy that lamp consumes. According to that comparison, an incandescent lightbulb is roughly 5% efficient—a 100-watt incandescent bulb emits about 5 watts of visible light. In contrast, a fluorescent lamp is typically about 20% energy efficient—a 25-watt fluorescent lamp emits about 5 watts of visible light.
Another way to compare incandescent and fluorescent lamps is via their lumens per watt. The lumen is a standard unit of usable illumination and it incorporates factors such as how sensitive our eyes are to various colors of light. If you divide a light source's light output in lumens by its power input in watts, you'll obtain its lumens per watt.
For the incandescent lightbulb appearing at the left of the photograph, that calculation yields 16.9 lumens/watt. For the "long life" bulb at the center of the photograph, it give only 15.3 lumens/watt. And for the color-improved bulb on the right of the photograph, the value is only 12.6 lumens/watt. Our grandchildren will look at this photograph of long forgotten incandescent bulbs and be amazed that we could squander so much energy on lighting.
The fluorescent lamp in the other photograph is far more efficient. It produces more useful illumination than any of the three incandescent bulbs, yet it consumes just over a quarter as much power. Dividing its light out in lumens by its power consumption in watts yields 64.6 lumens/watts. It is 4 times as energy efficient as the best of the incandescent lightbulbs. Some fluorescent lamps are even more efficient than that.
Another feature to compare is life expectancy. Even the so-called "long life" incandescent predicts a 1500 hour life, which is only 15% of the predicted life for the fluorescent lamp (10,000 hours). Although the fluorescent costs more, it quickly pays for itself in energy use and less frequent replacement. You should recycle a fluorescent lamp because it does contain a tiny amount of mercury, but overall it's a much more environmentally friendly light source.
Adding salt to water won't make everything float, but it will work for an object that just barely sinks in pure water. A hard-boiled egg is the most famous example: the egg will sink in pure water, but float in concentrated salt water. To explain why that happens, I need to tell you about the two forces that act on the egg when it's in the water.
First, the egg has its weight—it's being pulled downward by gravity. That weight force tends to make the egg sink. Second, the egg is being pushed upward by the water around it with a force known as "the buoyant force." The buoyant force tends to make the egg float. It's a battle between those two forces and the strongest one wins.
The buoyant force exists because the water that is now surrounding the egg used to be surrounding an egg-shaped blob of water and it was pushing up on that blob of water just hard enough to support the blob's weight. Now that the egg has replace the egg-shaped blob of water, the surrounding water is still pushing up the same amount as before and that upward force on the egg is the buoyant force.
Since the buoyant force on the egg is equal in amount to the weight of the water that used to be there, it can support the egg only if the egg weighs no more than the egg-shaped blob of water. If the egg is heavier than that blob of water, the buoyant force will be too weak to support it and the egg will sink.
It so happens that a hard-boiled egg weighs slightly more than an egg-shaped blob of pure water, so it sinks in pure water. But that egg weighs slightly less than an egg-shaped blob of very salty water. Adding salt to the water increases the water's weight significantly while having only a small effect on the water's volume. Salt water is heavier, cup for cup, than fresh water and it produces stronger buoyant forces.
In general, any object that weighs more than the fluid it displaces sinks in that fluid. And any object that weighs less than the fluid it displaces floats. You are another good example of this: you probably sink in fresh water, particularly after letting out all the air in your lungs. But you float nicely in extremely salty water. The woman in this photograph is floating like a cork in the ultra-salty water of the Dead Sea.
When you use a microwave oven to heat water in a glass or glazed container, the water will have difficulty boiling properly. That's because boiling is an accelerated version of evaporation in which water vapor evaporates not only from the water's upper surface, but also through the surface of any water vapor bubbles the water happens to contain. I use the phrase "happens to contain" because that is where all the trouble lies.
Below water's boiling temperature, bubbles of water vapor are unstable—they are quickly crushed by atmospheric pressure and vanish into the liquid. At or above water's boiling temperature, those water vapor bubbles are finally dense enough to withstand atmospheric pressure and they grow via evaporation, rise to the surface, and pop. At that point, I'd probably call the water vapor by its other name: steam. But where do those steam or water vapor bubbles come from in the first place?
Forming water vapor bubbles in the midst of liquid water, a process called nucleation, is surprisingly difficult and it typically happens at hot spots or non-wetted defects (places where the water doesn't completely coat the surface and there is trapped air). When you boil water in a metal pot on the stove, there are hot spots and defects galore and nucleating the bubbles is not a problem. When you boil water in a glass or glazed container using a microwave oven, however, there are no significant hot spots and few non-wetted defects. The water boils fitfully or not at all. The "not at all" possibility can lead to disaster.
Water that's being heated in a metal pot on the stove boils so vigorously that the stove is unable to heat it more than tiny bit above its boiling temperature. All the heat that's flowing into the water is consumed by the process of transforming liquid water into gaseous water, so the water temperature doesn't rise. Water that's being heated in a glass container in a microwave oven boils so fitfully that you can heat it above its boiling temperature. It's simply not able to use up all the thermal energy it receives via the microwaves and its temperature keeps rising. The water becomes superheated.
Most of the time, there are enough defects around to keep the water boiling a bit and it superheats only a small amount. When you remove the container of water from the microwave oven and toss in some coffee powder or a teabag, thus dragging air bubbles below the surface, the superheated water boils into those air bubbles. A stream of bubbles suddenly appears on the surface of the water. Most people would assume that those bubbles had something to do with the powder or teabag, not with the water itself. Make no mistake, however, the water was responsible and those bubbles are mostly steam, not air.
Occasionally, though, the water fails to boil at all or stops boiling after it manages to wet the last of the defects on the glass or glazed surface. I've made this happen deliberately many times and it's simply not that hard to do. It can easily happen by accident. With no bubbles to assist evaporation, the water's only way to get rid of heat is via evaporation from its top surface. If the microwave oven continues to add thermal energy to the water while it is having such difficulty getting rid of that energy, the water's temperature will skyrocket and it will superheat severely.
Highly superheated water is explosive. If something causes nucleation in that water, a significant fraction of the water will flash to steam in the blink of an eye and blast the remaining liquid water everywhere. That boiling-hot water and steam are a major burn hazard and the blast can break the container or blow it across the room. I've heard from a good number of people who have been seriously hurt by exploding superheated water produced accidentally in microwave ovens. It's a hazard people should take seriously.
After that long introduction, it's time to answer your question. Yes, I believe that the microwave makers are responsible for advising people of this hazard. Moreover, they know that they are responsible for doing it. If you look at any modern microwave oven user manual, you will find a discussion of superheating or overheating. Look at your manual, I'll bet it's in there.
But that discussion will almost certainly be buried in the middle of an long list of warnings. For example, in one manual, the discussion of overheated water appears as item 17 of 22, after such entries as "4. Install or locate this appliance only in accordance with the provided installation instructions" and "12. Do not immerse cord or plug in water". To be fair to the manufacturer, warning 17 is longest of the bunch and it suggests mostly reasonable precautions (although I'm not so happy with recommendation 17a: "Do not overheat the liquid."). No Duh.
I think the issue is this: most product warnings are provided not out of any sincere concern for the consumer, but out of fear of litigation. A manufacturer's goal when providing those warnings is therefore to be absolutely comprehensive so that they can point to a line in a user manual in court and claim to have fulfilled their responsibility. The number and order of the warnings makes no difference; they just have to be in there somewhere.
So all those warnings you ignore in product literature aren't really about consumer safety, they're about product liability. You ignore them because everything now comes with a thousand of them, ranging from the reasonable to the ridiculous. For my research, I ordered 99.999% pure sodium chloride (i.e., ultrapure table salt). It came with a 6-page Material Safety Data Sheet that identifies it as an "Xi Irritant", noting that it is "Irritating to eyes, respiratory system and skin" and recommending first aid measures that include:
"After inhalation: supply fresh air. If required, provide artificial respiration. Keep patient warm. Seek immediate medical advice.So much for swimming in the ocean...
By design and by accident, our society has lost the ability to distinguish real risk from imaginary risk. We treat all risks as equal and spend way too much time worrying about the wrong ones. If you want to be safer around your cell phone, for example, you should worry more about driving with it in your hand than about the microwave radiation it emits. The current evidence is that your risk of injury or death due to a cell-phone related accident far outweighs your risk from cell-phone microwave exposure. Even if further research proves that cell phone microwave exposure is injurious, we should be acting according to our best current assessments of risk, not according to fears and beliefs.
That said, I'd like to see product literature rank their warnings according to risk and put the real risks in a separate place where they can't be overlooked or ignored. Put the real consumer safety stuff where the consumers will see it and put the product liability stuff somewhere else where the lawyers can find it. For a microwave oven, there are probably about half a dozen real risks that people should know about. Several of them are relatively obvious (e.g., don't heat sealed containers) and some are not obvious (e.g., liquids heated in the microwave can become superheated and explode).
Maybe we'll get a handle on risk someday. In the meantime, inform your friends and children that they should be careful about heating liquids in the microwave, particularly in glass or glazed containers. Just knowing that superheating is possible would probably halve the number of burns and other injuries that result from superheating accidents.
When you run a microwave oven without any food inside, there is nothing to absorb the microwaves and they build up inside the cooking chamber. Eventually, something has to absorb them and that something is the oven's microwave source—its magnetron. The magnetron isn't good at handling excessive power that returns to it from the cooking chamber and it can be damaged as a result.
In all my years of experimenting with microwave ovens, I've only killed a magnetron once. But then again, I haven't run a microwave oven for more than a minute or two without anything inside it. If the oven works again after cooling down, then you're probably OK. The oven may have thermal interlocks in its microwave source to prevent that source from overheating and becoming a fire hazard. If the oven fails to work after an hour of cooling off, then you're probably out of luck. The magnetron and/or its power supply are likely to be fried and in need of replacement.
High heeled shoes can produce enormous pressures on a wooden floor and dent it permanently. To understand why that happens, let's start with a pair of flat-heeled shoes and consider the forces and pressures in that situation.
When a women stands on the floor, the floor must support her weight. Specifically, she isn't accelerating so the net force on her must equal zero. That implies that the floor must exert an upward force on her that exactly cancels her downward weight. She is motionless and stays motionless because there is no overall force on her.
Because the floor is pushing upward on her shoes, her shoes must be pushing downward on the floor. It's an example of the famous "action and reaction" principle known as Newton's third law: if you push on something, it pushes back equally hard in the opposite direction. Anyway, her shoes are pushing down hard on the floor.Now for the pressure part of the story. Because she is wearing flats, her shoes are pushing against a large area of the floor and the pressure—the force per area—she produces on the floor is relatively small. For example, if she weighs 130 pounds (580 newtons) and her shoes have a contact area of 10 square inches (65 square centimeters), then the pressure she exerts on the floor is about 13 pounds-per-square-inch (9 newtons-per-square-centimeter or 90,000 pascals). That's a gentle pressure that won't permanently dent most woods. It might dent cork or balsa, but that's about it.
But when she wears high heels, most of her weight is supported by a very small area of flooring. If the heels are narrow spikes with a contact area of 0.1 square inches (0.65 square centimeters) and she puts all of her weight briefly on one of the heels, she may exert a pressure of 1300 pounds-per-square-inch (9000 newtons-per-square-centimeter or 90 million pascals) on the floor. That's an enormous pressure that will permanently dent most wooden floors.
You can experiment with these ideas simply by supporting the weight of your right hand with the open palm of your left hand. If you lay your right fist on your left palm, you won't feel any discomfort in your left hand. The pressure on your left palm is very small. But if you instead point right index finger into your left palm and use that finger to support the entire weight of your right hand, it won't feel so comfortable. If you shift all of the weight to your fingernail, it'll start to hurt your left palm. What you're doing is reducing the area of your left palm that is supporting your right hand and as that area gets smaller, the pressure on your left palm increases. Beyond a certain pressure, it feels uncomfortable. Long before your palm dents permanently, you'll decide to stop the experimenting.
The cable would indeed lengthen when you pulled it. In fact, you would produce a wave of stretching motion that travels along the cable at the speed of sound in that cable. That's because you can't directly influence the cable beyond what you can touch. You can only pull on your end of the cable, causing it to accelerate and move, and let it then pull on the portion of cable adjacent to it.
Each portion of cable responds to being pulled by accelerating, moving, and consequently pulling on the portion of cable adjacent to it. There will be a long series of actions—pulling, accelerating, moving, and pulling again—that propagates your influence along the cable. A wave will travel along the cable, a wave consisting of a local reduction in the cable's density. It's a stretching wave. In that respect, the wave is a type of sound wave—a density fluctuation that propagates through a medium.
How quickly the density wave travels along the cable depends on how stiff the cable is and on its average mass density. The stiffer the cable, the more strongly each portion can influence its neighboring portions and the faster the density wave will travel. The greater the cable's mass density, the more inertia it has and the slower it respond to pulls, so the density wave will travel slower.
A cable made from a stiff, low-density material carries sound faster than a soft, high-density material. A steel cable should carry your wave at about 6100 meters/second (3.8 miles/second). But a diamond cable would reach 12000 meters/second (7.5 miles/second) because of its extreme stiffness and a beryllium cable would approach 13000 meters/second (8.0 miles/second) because of its extremely low mass density.
Regardless of which material you choose, you're clearly not going to be able to send any signals faster than the speed of light. It would take a density wave more than 100,000 years to travel the 5-light year length of your cable. And sadly, friction-like dissipation effects in the cable would turn the density wave's energy into thermal energy in a matter of seconds, so it would barely get started on its journey before vanishing into randomness.
While I'm sorry to hear that your dog isn't well, I doubt that electromagnetic fields are responsible for her infirmities. The fields from the telephone adapter are too weak to have any significant effect and 60-Hz electromagnetic fields don't appear to be dangerous even at considerably stronger levels.
To begin with, plug-in power adapters are designed to keep their electromagnetic fields relatively well contained. They're engineered that way not because of safety concerns but because their overall energy efficiencies would diminish if they accidentally conveyed power to their surroundings. Keeping their fields inside keeps their energy inside, where it belongs. Moreover, any electric and magnetic fields emerging from an adapter probably don't propagate as waves and instead fall off exponentially with distance. As a result, it should be fairly difficult to detect electric or magnetic fields more than a few inches from the adapter.
Even if the adapter did project significant electric and magnetic fields all the way to where your dog sleeps, it's still unlikely that they would cause any harm. For years, researchers have been looking for a correlation between high-voltage electric power lines and a variety of human illnesses, notably childhood cancers such as leukemia. As far as I know, no such correlation has ever been demonstrated. In all likelihood, if there are any risks to being near 60-Hz electric or magnetic fields, those risks aren't large enough to be easily recognized.
In contrast to power adapters, cell phones deliberate emit electric and magnetic fields in order to communicate with distant receivers on cell phone towers. Those fields are woven together to form electromagnetic waves that propagate long distances and definitely don't vanish inches from a cell phone. Any electromagnetic hazard due to a power adapter pales in comparison to the same for cell phones.
Furthermore, cell phone operate at much higher frequencies than the alternating current power line. A typical cell phone frequency is approximately 1 GHz (1,000,000,000 Hz), while ordinary alternating current electric power operates at 60 Hz (50 Hz in Europe). Higher frequencies carry more energy per quanta or "photon" and are presumably more dangerous. But even though cell phones are held right against heads and radiate microwaves directly into brain tissue, they still doen't appear to be significantly dangerous. As unfond as I am of cell phones, I can't condemn them because of any proven radiation hazard. Their biggest danger appears to be driving with them; I don't understand why they haven't been banned from the hands of drivers.
Lastly, there are no obvious physical mechanisms whereby weak to moderate electric and magnetic fields at 60-Hz would cause damage to human or canine tissue. We're essentially non-magnetic, so magnetic fields have almost no effect on us. And electric fields just push charges around in us but that alone doesn't cause any obvious trouble. Research continues into the safety of electromagnetic fields at all frequencies, but this low-frequency stuff (power lines and cell phones) doesn't seem to be unsafe.
Although yours isn't a physics question, it's one that's interesting to me and easy to answer. The person who sets up the website gets to choose the domain. That's all there is to it. As long as the complete domain name hasn't already been registered, you can pay a fee and register it. For example, I chose to register this website as www.howeverythingworks.org because I feel more like an organization (of one person) than a commercial enterprise. I could have registered it as www.howeverythingworks.in, but that would imply I'm in India and I'm not. The only exception that I know of is .edu, which is restricted to educational institutions. I would not be allowed to register this website as www.howeverythingworks.edu.
Actually, I could have registered this website as www.howeverythingworks.com, but I would have had to purchase that domain name from someone else. It is registered to a cybersquatter—someone who registers a domain name in hopes of selling it at a profit to someone else. Cybersquatting was hugely popular during the internet bubble, when companies were paying vast amounts of money for particular domain names. But these days, who wants to pay thousands of dollars for a name? I'm totally happy to be www.howeverythingworks.org and I'll let someone else pay the big bucks to purchase www.howeverythingworks.com. In the meantime, that domain is just a link to advertising and an offer to sell the domain name.
The glass window itself isn't important to the microwave oven's operation, but the metal grid associated with that window certainly is. The grid forms the sixth side of the metal box that traps the microwaves so they cook food effectively. In principle, you can remove all the glass and still cook food, but I think that would be a bad idea. The grid isn't very sturdy on its own and if it develops cuts or holes, it will allow microwaves to leak out of the oven. You want those microwaves to stay inside the box to cook the food and not to escape to cook you.
Even if the oven door has multiple layers of glass, those layers are there for your protection. If you touch the outside of the metal grid while the oven is on or get close enough to it through the last layer of glass, you'll be able to absorb some microwave power and it'll probably hurt. That's because while the holes in the grid are too small to allow the microwaves to propagate through them and truly escape from the oven, they do allow an "evanescent wave" to exist just outside each hole in the grid. That evanescent wave dies off exponentially with distance beyond the hole, so it won't travel around the room. But you don't want to put your finger in it.
For inexpensive microwave ovens, you're probably best off simply recycling the oven. I'm not happy about the modern everything-is-disposable state of appliances and equipment, but I can't say that it's cost effective to repair an oven that costs less than about $100. For more expensive microwave ovens, you can usually replace the window or the door. We have had a GE combination microwave and convection oven over our stove top for about 10 years and the door started to come apart about 18 months ago. I purchased a replacement microwave oven door over the web for $140 and installed it myself. It works beautifully. If you're not handy or are concerned about microwave leaks, you should probably have it replaced professionally. But you can look up the parts themselves online at a number of web sites and get an idea of what the cost will be.
As long you shutdown the computer first, turning off the power strip is fine. Essentially all modern household computer devices are designed to shut themselves down gracefully when they lose electrical power and that's exactly what they down when you turn off the power strip.
In fact, turning off the power strip is likely to save energy as well. Many computer devices have two different "off" switches: one that stops them from doing their normal functions and one that actually cuts off all electrical power. Computers in particular don't really turn off until you reach around back and flip the real power switch on the computer's power supply. The same is true of television monitors and home theater equipment.
In general, any device that has a remote control or that can wake itself up to respond to a pretty button or to some other piece of equipment is never truly off until you shut off its electrical power. Our homes are now filled with electronic gadgets that are always on, waiting for instructions. Keeping them powered up even at a low level consumes a small amount of electrical power and it adds up. Last I heard, this always-on behavior of our gadgets consumes something on the order of 1% of our electrical power. Whatever it is, it's too much. So by turning off your power strip and completely stopping the flow of power to your computer, your speakers, your monitor, etc., you are saving energy. You lose the convenience of being able to turn everything on from your couch with a remote, but who cares. Energy is too precious to waste for such nonessential conveniences.
Unlike sound waves or ocean waves, radios waves do not travel in a material. Radio waves are a class of electromagnetic waves and consist of nothing more than electric and magnetic fields. Since they don't require any medium through which to travel, they can go right through empty space. That's why we're able to see the stars, after all.
The idea of a wave that travels through space itself was a rather disorienting notion to scientists in the late 1800s. They were used to the idea that waves are disturbances in a tangible material or "medium": fluctuations in the density of air, ripples on the surface of water, vibrations of a taut string. Having observed that light and radio waves are electromagnetic waves, they set about looking for the medium that supported those waves. They were expecting to find this "luminiferous aether" but they failed. In fact, the absence of an aether led in part to Einstein's theory of special relativity.
The structure of a radio wave, or any electromagnetic wave, is quite simple. It consists only of a fluctuating electric field and a fluctuating magnetic field. An electric field is a structure in space that affects electric charge; it pushes on charge and causes that charge to accelerate. Similarly, a magnetic field is a structure that affects magnetic pole. Remarkably, changing electric fields produce magnetic fields and changing magnetic fields produce electric fields. That interrelatedness allows the wave's fluctuating electric field to produce its fluctuating magnetic field and vice verse. The wave's electric and magnetic fields endless recreate one another. Although electric charge or magnetic pole is needed to emit or receive a radio wave, that wave can travel perfectly well for billions of light years without involving any charge or pole. It travels through space itself.
Because the oven's microwave frequency is more than 20 times higher than anything a normal radio receives, I'd be surprised if the radio would notice even a pretty severe microwave leak. What you describe doesn't sound like it's caused by the microwaves. It sounds like it's caused by an electrical problem in the oven's high-voltage power supply.
An older oven would have used a heavy transformer, a capacitor, and a diode to convert ordinary household AC power to high-voltage DC power for its magnetron microwave tube. But since your oven was made recently, it probably uses a switching power supply to produce that high voltage. That supply contains a much more sophisticated electronic switching system to convert household AC power to high-voltage DC power. The new approach is cheaper and lighter, so it's taking over in microwave ovens. Just because it's more sophisticated, however, doesn't mean it's more reliable.
My guess is that the unit in your oven has a problem. If it has an intermittent contact in it or if there is a conducting path that is sparking somewhere in the power supply or in the unit as whole, they'll be randomly fluctuating currents present in the oven and those current fluctuations will produce radio waves. A sparking wire or carbonized patch on the power supply will start and stop the flow of current erratically and that can easily cause interference on the AM band. Ordinary AM radio is very susceptible to radio-frequency interference at around 1 MHz and sparking stuff tends to produce such radio waves. A car with a bad ignition system, a lawn mower, and a thunderstorm all interfere beautifully with AM reception. And I suspect that you've got a similar electrical problem in your oven. I doubt that your oven is a microwave hazard, but you should probably have a repair person to take a look at it. It shouldn't have anything sparking inside it.
It probably won't work and it's definitely not safe. Instead of tricking your friends, you risk cooking them. Here is why I think you'd better leave your plan as a thought experiment only.
Those YouTube videos were complete fakes; they didn't pop any popcorn while the camera was rolling. To make it appear that the cell phones were popping the corn, the people who produced the videos dropped already prepared popcorn into the frame and then photoshopped away the unpopped kernels. When you watch the video, it looks like the kernels are popping, but they're really just disappearing via video editing as precooked popcorn is sprinkle onto the set from above.
The reason they had to use video trickery is pretty clear: to pop popcorn with microwaves, those microwaves have to be extremely intense. Each kernel contains only a tiny amount of water and it's the water that heats up when the kernel is exposed to microwaves. If the microwaves aren't intense enough, the heat they deposit in the kernel's water will flow out to the rest of the kernel and into the environment too quickly for the kernel's water to superheat and then flash to steam.
Even when you put popcorn kernels in a closed microwave oven, it takes a minute or two for the kernels to accumulate enough thermal energy to pop. In that closed microwave oven, the microwaves bounce around inside the metal cooking chamber and their intensity increases dramatically. It's like sending the beam from a laser pointer into a totally mirrored room—the light energy in that room will build up until it is extremely bright in there. In the closed cooking chamber of the oven, the microwave energy also builds up until the microwave intensity is enough to pop the corn. How intense? Well, a typical microwave oven produces 700 watts of microwave power. Since the cooking chamber is nearly empty when you're popping popcorn, the cooking chamber accumulates a circulating power of very roughly 50,000 watts.
Although that power is spread out over the cross section of the oven, the microwaves are still seriously intense -- thousands of watts per square inch. To put that in perspective, a cell phone transmits a maximum of 2 watts and that power is spread out over at least 5 square inches so the intensity is less than 1 watt per square inch. When I saw those videos in Summer 2008, I realized that there was no way cell phones were ever going to pop popcorn. They certainly wouldn't do it while they are ringing, because that's when they are primarily receiving microwaves, not when they're transmitting them. It's when you're talking that your cell phone is regularly producing microwaves. It was all obviously just fun and games.
So what about your disassembled microwave oven? Since there is no metal box to trap the microwaves and accumulate energy, they'll only have one shot at popping the corn kernels. The microwaves will emerge from the magnetron's waveguide at high intensity, but they'll spread out quickly once there is nothing to guide them. You could probably pop kernel right at the mouth of the magnetron but not a few inches away. Unless you use microwave optics to focus those microwaves, they'll have spread too much by the time they get through the table and reach the kernels of popcorn and the kernels will probably never pop.
If that were the whole story, the worst that would happen with your experiment would be that it wouldn't cook popcorn. But there is a real hazard here. Sending about 700 watts of microwaves into the room isn't exactly safe. It's something like having a red hot coal emitting 700 watts of infrared light, except that you won't see anything with your eyes and this microwave "light" is coherent (i.e., laser-like) so it can focus really tightly. You'd hate to have some metal structure in the room or even inside the walls of the room focus the microwaves onto you. You absorb microwave much better than the corn kernels and you'll "pop" long before they do. Actually, your eyes are particularly sensitive to microwave heating and you might not notice the damage until too late. Without instruments to observe the pattern of microwaves in the room when the magnetron is on, I wouldn't want to be in the room.
A basketball depends on pressurized air for its bounciness. When the ball hits the court, it compresses that air and the air stores energy in its compression. The ball's rebound is powered by the air returning to its original characteristics. The ball's skin, on the other hand, isn't all that bouncy and doesn't store energy well. To bounce well, the basketball needs to store energy in its air during the bounce, not in its skin. That's why it's important to have an air pump so that you can keep your basketball properly inflated.
When you cool a basketball, however, you reduce the pressure of its air. That's because the air molecules have less thermal energy at colder temperatures and thermal energy is responsible for air pressure. A basketball that was properly inflated at warm temperature becomes under-inflated when you cool it down. At the same time, the basketball's skin becomes less elastic and more leathery at cool temperatures. So the basketball suffers from under-inflation and from a leathery, not-very-bouncy skin.
If you cool a basketball to low enough temperature, its skin will freeze and become brittle. Just how low the temperature has to go depends on the material used in to make the basketball. I've never seen a basketball shatter on the court, even in pretty cold weather, so I doubt you can "freeze" one in a household freezer. But I'm sure that a dip in liquid nitrogen at -395 °F would do the trick. I often freeze rubber handballs in liquid nitrogen for my class and then shatter them on the floor.
To help you visualize how a string can vibrate at several frequencies at once, I wrote a flash program that shows you what a vibrating string looks like. That program should appear below this note. It allows you to adjust eight parameters: the amplitudes of the string's four simplest vibrational modes (its fundamental vibration through its fourth harmonic vibration) and the phases of those modes. The program starts with a pure fundamental vibration of the string, which is easy to visualize. But you can turn on the second, third, and fourth harmonic vibrations to whatever extent you like. What you'll observe is that a string that's vibrating at several frequencies at once has a complicated shape, but doesn't look all that unfamiliar. It's simply a mixture of several standing waves that evolve at different rates. As a result, it exhibits a fancy rippling shape that you've probably see on a jump rope or a clothesline.
If you look carefully at the string while it's vibrating in a mixture of several harmonics, you'll see that it has only one shape at any moment in time. It's just a jiggling string, after all. The parts of that shape, however, are evolving at different rates in time and those parts are actually the different harmonics going through their individual motions at their own frequencies.
The speed of light in vacuum, as denoted by the letter c, is truly a constant of nature and one of its most influential constant at that. Even if light didn't exist, the speed of light in vacuum would. It is a key component of the relationship between space and time known as special relativity.
But while the speed of light in vacuum is a constant, the speed of light in matter isn't. Light is an electromagnetic wave and consists of electric and magnetic fields. Electric fields push on electric charge and matter contains electric charges, so light and matter interact. That interaction normally slows light down; the light gets delayed by the process of shaking the electric charges. In air, this slowing effect is tiny, less than 1 part in a thousand. In glass, plastic, or water, light is slowed by about 30 or 40%. In diamond, the interaction is strong enough to slow light by 60%. In silicon solar cells, light is slowed by 70%. And so it goes.
To really slow light down, however, you need to choose a specific frequency of light and let it interact with a material that is resonant with that light. Because a resonant material responds extremely strongly to the light's electric field, it delays the light by an enormous amount. And by choosing just the right wavelength of light to match a particular collection of resonant atoms, Lene Hau and her colleagues managed to bring light essentially to a halt. The light lingers nearly forever with the atoms in their apparatus and it barely makes any headway.
Yes, you can tell how fully you have consolidated a powder by the extent to which it scatters light. The more perfect the packing, the more transparent the powder becomes. It's a matter of homogeneity: the more perfect the packing, the more homogeneous the material and the easier it is for light to travel straight through it.
To understand why light scatter depends on homogeneity, consider what happens when light pass through clear particles. Even though they are clear, light still interacts with them, as evidenced by rainbows, clouds, and even the blue sky. How best to think about that interaction depends on the size of the particles. If the particles are large, like smooth beads of glass or plastic, then they exhibit the familiar refraction and reflection effects of window panes and lenses. If the particles are small, like air molecules and tiny water droplets, then they exhibit a more antenna-like interaction with light. In effect, those tiny particles occasionally absorb and reemit the light waves, particularly at the short-wavelength (i.e., blue) end of the light spectrum.
Both types of interactions are quite familiar to us. Large particles scatter light about without any color bias and exhibit a white appearance. The more surface area a collection of particles has, the more light that collection scatters. For example, a large ice crystal is clear but crushed ice or snow is white. Similarly, a bowl of water is clear but a mist of water droplets is white. Lastly, a bowl of air is clear, but a froth of air bubbles in water is white. As you can see, the transparent particles don't have to be solids or liquids to scatter light, they can even be gases!
On the other hand, truly tiny particles scatter light about according to wavelength and color. In most cases, shorter-wavelength (blue) light scatters more than longer-wavelength (red) light. That effect, known as Rayleigh scattering, is responsible for the blue sky and the red sunset.
In a nutshell then, large transparent particles appear white and tiny transparent particles appear colored (typically bluish). And the more particles there are, the more light is scattered.
Returning to your question, a loose powder of transparent particles scatters light like crazy and appears white or possible colored, depending on particle size. As you pack the powder more and more tightly together, its surfaces join together and it starts to lose the ability to scatter light; it becomes less white and more translucent. When the consolidation is almost complete, the material acquires a slightly hazy look due to scattering by the occasional voids left inside the otherwise transparent material. Finally, when the material is fully consolidated and there is no internal surface left in the powder, it is homogeneous and clear. So sending light through a packed transparent powder and measuring the amount and color of the scattered light tells you a lot about how well consolidated that powder is.
Yes, the temperature of the gas will rise as you shake it. It's a subtle effect, so insulating the container by putting it in vacuum is probably a good idea. As you shake the container, its moving walls bat the tiny gas molecules around, sometimes adding energy to them and sometimes taking it away. On average however, those moving walls add energy to the gas molecules and thereby increase the gas's temperature.
A simple way to see why that's the case is to picture the gas as composed of many little bouncing balls inside the container. Those balls are perfectly elastic so they rebound from a stationary wall without changing their speeds at all. But the walls of the container aren't stationary, they move back and forth as you shake the container. Because of the moving walls, the balls change their speeds as they rebound. A ball that bounces off a wall that is moving toward it gains speed during its bounce, like a pitched ball rebounding from a swung bat. On the other hand, a ball that bounces off a wall that is moving away from it loses speed during its bounce, like a pitched ball rebounding from a bat during a bunt. If both types of bounces were equally common in every way then, on average, the balls (or actually the gas molecules) would neither gain nor lose speed as the result of bounces off the walls and the gas temperature would remain unchanged.
But the bounces aren't equally common. It's more likely that a moving ball will hit a wall that is moving toward it than that it will hit a wall that is moving away from it. It's a geometry problem; you get wet faster when you run toward a sprinkler than when you run away from the sprinkler. So, on average, the balls (or gas molecules) gain speed as the result of bounces off the walls and the gas temperature increases.
How large this effect is depends on the relative speeds of the gas molecules and the walls. The effect becomes enormous when the walls move as fast or faster than the gas molecules but is quite subtle when the gas molecules move faster than the walls. Since air molecules typically move at about 500 meters per second (more than 1000 mph) at room temperature, you'll have to shake the container pretty violently to see a substantial heating of the gas.
You're right that DC (direct current) power transmission has some important advantages of AC (alternating current) power transmission. In alternating current power transmission, the current reverses directions many times per second and during each reversal there is very little power being transmitted. With its power surging up and down rhythmically, our AC power distribution system is wasting about half of its capacity. It's only using the full capacity of its transmission lines about half of each second. Direct current power, in contrast, doesn't reverse and can use the full capacity of the transmission lines all the time.
DC power also avoids the phase issues that make the AC power grid so complicated and fragile. It's not enough to ensure that all of the generators on the AC grid are producing the correct amounts of electrical power; those generators also have to be synchronized properly or power will flow between the generators instead of to the customers. Keeping the AC power grid running smoothly is a tour-de-force effort that keeps lots of people up at night worrying about the details. With DC power, there is no synchronization problem and each generating plant can concentrate on making sure that their generators are producing the correct amounts of power at the correct voltages.
Lastly, alternating currents tend to flow on the outsides of conductors due to a self-interaction between the alternating current and its own electromagnetic fields. For 60-cycle AC, this "skin effect" is about 1 cm for copper and aluminum wires. That means that as the radius of a transmission line increases beyond about 1 cm, its current capacity stops increasing in proportion to the cross section of the wire and begins increasing in proportion to the surface area of the wire. For very thick wires, the interior metal is wasted as far as power delivery is concerned. It's just added weight and cost. Since direct current has no skin effect, however, the entire conductor can be carry current and there is no wasted metal. That's a big plus for DC power distribution.
The great advantage of AC power transmission has always been that it can use transformers to convey power between electrical circuits. Transformers make it easy to move AC power from a medium-voltage generating circuit to an ultrahigh-voltage transmission line circuit to a medium-voltage city circuit to a low-voltage neighborhood circuit. DC power transmission can't use transformers directly because transformers need alternating currents to move power from circuit to circuit. But modern switching electronics has made it possible to convert electrical power from DC to AC and from AC to DC easily and efficiently. So it is now possible to move DC power between circuits by converting it temporarily into AC power, sending it through a transformer, and returning it to DC power. They can even use higher frequency AC currents and consequently smaller transformers to move that power between circuits. It's a big win on all ends. While I haven't followed the developments in this arena closely, I would not be surprised if DC power transmission started to take hold in the United State as we transition from fossil fuel power plants to renewable energy sources. Using those renewable sources effectively will require that we handle long distance transmission better than we do now and we'll have to develop lots of new transmission infrastructure. It might well be DC transmission.
A traditional fluorescent lamp needs a ballast to limit the current flowing through its gas discharge. That's because gas discharges have strange electrical characteristics, most notably a regime of "negative" electrical resistance: the voltage drop across the discharge actually decreases as the current in the discharge increases. If you connect a gas discharge lamp to a voltage source without anything to limit the current and start the discharge, the current flowing through the lamp will rise essentially without limit and the lamp will quickly destroy itself. As a kid, I blew up several small neon lamps by connecting them directly to the power line without any current limiter. That was not a clever or safe idea, so don't try it!
The standard current limiter for fluorescent lamps and other discharge lamps that are powered from 60-cycle (or 50-cycle) alternating current has been an electromagnetic coil known as a ballast. When that coil is in series with the discharge, the coil's self-inductance limits how quickly the current flowing through the lamp can rise and therefore how much power the lamp can consume before the alternating current reverses direction. The discharge winks on and off with each current reversal and never draws more current than it can tolerate. Unfortunately, the lamp's light also winks on and off and some people can see that flicker, especially with their peripheral vision.
Actually, the ballast usually has another job to do in a traditional fluorescent lamp: it acts as a transformer to provide the current needed to heat the electrode filaments at the ends of the lamp. Heating those electrodes helps drive electrons out of the metal and into the lamp's gas so that the gas becomes electrically conducting. In total then, the ballast receives alternating current electric power from the power line and prepares it so that all the lamp filaments are heated properly and a limited current flows through the lamp from one electrode to the other.
In modern fluorescent lamps with heated electrodes, however, the role of the ballast has been usurped by a more sophisticated electronic power conditioning device. That device converts 60-cycle alternating current electric power into a series of electrical energy pulses, typically at about 40,000 pulses per second, and delivers them to the lamp. The lamp's flicker is almost undetectable because it is so fast and the limited energy in each pulse prevents the discharge from consuming too much power. It's a much better system. Compact fluorescent lamps use it exclusively.
So where might high voltage fit into this story? Well, there are some fluorescent lamps that don't heat their electrodes with filaments. They rely on the discharge itself to drive electrons out of the electrodes and into the gas to sustain the discharge. But that begs the question: "how does such a lamp start its discharge?" It uses high voltage. Because of cosmic rays and natural radioactivity, gases always have some electric charges in them: ions and electrons. When the voltage difference between the two ends of the lamp becomes very large, the electric field in the lamp propels those naturally occurring ions and electrons into the constituents of the lamp violently enough to start the lamp's discharge. The voltages needed to start these "cold cathode" lamps are typically in the low thousands of volts. For example, the cold cathode fluorescent lamps used in laptop computer displays start at about 2000 volts and then operate at much lower voltages.
When you carry the firewood up the hill, you transfer energy to it and increase its gravitational potential energy. When you then burn the wood, you seem to make this energy disappear. After all, there doesn't appear to be any difference between burning wood in the valley and burning wood on the top of the hill. The wood is gone either way.
But appearances can be deceiving. Since energy is a conserved quantity, the energy that you invest in the firewood can't disappear. It simply becomes difficult to find because it is dispersed in the burned gases that were once the wood.
To find that energy, imagine compressing the burned gases into a small container to make their weight more noticeable and reduces buoyant effects due to the atmosphere. You could then carry those burned gases, which include all of the firewood's atoms, back down the hill. As you descended, the container of burned gases would transfer its gravitational potential energy to you.
I've swept a number of details under the rug, such as the fact that many of the oxygen atoms in your container were originally part of the atmosphere rather than the log. But even when all those details are taken into account, the answer is the same: the firewood's gravitational energy doesn't disappear, it just gets more difficult to find.
No, those gases don't absorb microwaves significantly regardless of frequency. Diatomic molecules are nearly oblivious to long wavelength electromagnetic waves. In fact, that's why they don't contribute to the "greenhouse effect." Oxygen does have an unusual absorption band in the near infrared, but that's about it.
It's quite possible that the pattern of microwaves inside your oven is more intense at some places than in others — that's why most microwaves have carousels in them to move the food around. I don't think that the pattern will change much with age, but it's possible that your oven isn't producing as much microwave power as it once did and you notice the low-intensity regions more than before. It's not a true "fault", but it is a nuisance. If you get tired of putting up with it, you should probably replace the oven. It used to be that you could purchase carousel inserts for the ovens, but I don't see them for sale anymore.
Since light carries energy, a laser beam can't simply disappear after a couple of feet — something would have to absorb it and its energy. Since the atmosphere is extremely transparent to visible light, it won't do the trick.
Since eye safety requires limiting the amount of laser power that can enter a person's eye, you can make a laser more eye-safe by enlarging its beam. Even a powerful laser can be eye-safe if only a small fraction of the laser light can enter a person's iris and focus on their retina.
Although it's natural to think of a laser beam as a narrow pencil of light that stays narrow forever, that's not really the case. The diameter of a laser beam changes with distance from its source. The beams from typical lasers, including laser pointers, start relatively narrow and widen as gradually as the physics of light propagation will allow. But with the help lenses, you can change that widening process dramatically. For example, if you send a typical laser beam through a converging lens that has a focal length of 1 foot, the laser beam will converge to a very narrow "beam waist" 1 foot beyond the lens and will then spread relatively quickly with distance. It will return to its original diameter 1 foot beyond its waist and to 10 times its original diameter 10 feet beyond its waist. With its light spread out by a factor of 10 in both height and width, it will have only 1/100th the intensity (power per unit area) of the original beam. Because of its large size, only a fraction of the beam and its light power will now enter a person's iris and focus on their retina.
Using this scheme, you can have a beam that is extremely intense for the first 2 feet, including a super-intense waist at the 1-foot mark. But beyond that point, the beam spreads quickly and soon becomes so wide that it is no longer a eye hazard.
The problem for planes isn't the temperature, it's the humidity. When the air reaches 100% relative humidity, moisture in that air begins to condense on objects such as plane wings. The moisture can also condense into rain, snow, or sleet and then fall onto those plane wings.
If the temperature of overly moist air is 32 F or below, planes preparing for takeoff can accumulate heavy burdens of ice. When water vapor condenses as ice directly onto the wings themselves, that condensation process is called deposition and is familiar to you as frost. Deposition is a relatively slow process, so most of the trouble for planes occurs when it is actually snowing or sleeting. Removing the ice then requires either heat or chemicals.
When the plane is flying at high altitudes, however, the air is extremely dry. Even though the air temperature is far below the freezing temperature of water, the fraction of water molecules in the air is nearly zero and the relative humidity is much less than 100%. That means that an ice cube suspended in that dry air would actually evaporate away to nothing. Technically, that "evaporation" of ice directly into water vapor is call sublimation and you've seen it before. Think of all the foods that have experienced freezer burn in your frost-free (i.e., extremely dry air) refrigerator or the snow that has mysteriously disappeared from the ground during a dry spell even though the temperature has never risen above freezing. Both are cases of sublimation — where water molecules left the ice to become moisture in the air.
Since our eyes are only sensitive to light that's in the visible range, any "smart" optical system would have to present whatever it detects as visible light. That means it has to either shift the frequencies/wavelengths of non-visible electromagnetic radiation into the visible range or image that non-visible radiation and present a false-color reproduction to the viewer. Let's consider both of these schemes.
The first approach, shifting the frequencies/wavelengths, is seriously difficult. There are optical techniques for adding and subtracting optical waves from one another and thereby shifting their frequencies/wavelengths, but those techniques work best with the intense waves available with lasers. For example, the green light produced by some laser pointers actually originated as invisible infrared light and was doubled in frequency via a non-linear optical process in a special crystal. The intensity and pure frequency of the original infrared laser beam makes this doubling process relatively efficient. Trying to double infrared light coming naturally from the objects around you would be extraordinarily inefficient. In general, trying to shift the frequencies/wavelengths of the various electromagnetic waves in your environment so that you can see them is pretty unlikely to ever work as a way of seeing the invisible portions of the electromagnetic spectrum.
The second approach, imaging invisible portions of the electromagnetic spectrum and then presenting a false-color reproduction to the viewer, is relatively straightforward. If it's possible to image the radiation and detect it, it's possible to present it as a false-color reproduction. I'm talking about a camera that images and detects invisible electromagnetic radiation and a computer that presents a false-color picture on a monitor. Imaging and detecting ultraviolet and x-ray radiation is quite possible, though materials issues sometimes makes the imaging tricky. Imaging and detecting infrared light is easy in some parts of the infrared spectrum, but detection becomes problematic at long wavelengths, where the detectors typically need to be cooled to extremely low temperatures. Also, the resolution becomes poor at long wavelengths.
Camera systems that image ultraviolet, x-ray, and infrared radiation exist and you can buy them from existing companies. They're typically expensive and bulky. There are exceptions such as near-infrared cameras — silicon imaging chips are quite sensitive to near infrared and ordinary digital cameras filter it out to avoid presenting odd-looking images. In other words, the camera would naturally see farther into the infrared than our eyes do and would thus present us with images that don't look normal.
In summary, techniques for visualizing many of the invisible portions of the electromagnetic spectrum exist, but making them small enough to wear as glasses... that's a challenge. That said, it's probably possible to make eyeglasses that image and detect infrared or ultraviolet light and present false-color views to you on miniature computer monitors. Such glasses may already exist, although they'd be expensive. As for making them small enough to wear as contact lenses... that's probably beyond what's possible, at least for the foreseeable future.
During wine making, the amount of dissolved carbon dioxide (and possibly oxygen gas) can easily exceed its equilibrium concentration. That means that the liquid contains more dissolved gas than it would have if exposed to the atmosphere for a long period of time and had thereby reached its equilibrium concentration of the gas. Having too much dissolved gas does not, however, mean that this gas will leave quickly. For example, when you open a bottle of carbonated beverage the carbon dioxide is out of equilibrium. Although the gas was in equilibrium at the high pressure of the sealed bottle, it instantly became out of equilibrium when the bottle was opened and the density of gaseous carbon dioxide suddenly decreased. Nonetheless, it can take days for the excess carbon dioxide to come out of solution and leave. You've probably noticed that carbonated beverages take hours or days to "go flat."
Part of the reason why it takes so long for the dissolved gases to come out of solution is that the gas can only leave through the exposed surface of the liquid. In an open bottle of carbonated beverage that may be only a few square inches or a few dozen square centimeters. The dissolved gas has to find its way to that exposed surface and break free of the liquid. That's a slow process. The same thing is happening in your wine: the dissolve carbon dioxide and oxygen gases must normally find their way to the top of the tank and then break free to enter the gaseous region at the top of the tank — another slow processes. To speed the escape of dissolved gases, you can enlarge the exposed surface of the liquid by bubbling an inert gas through the liquid. Here, inert gas is any gas that doesn't dissolve significantly in the liquid and that doesn't affect the liquid if it does dissolve. Nitrogen is great for wine because it doesn't interact chemically with the wine. As you let bubbles of nitrogen float upward through the wine, you provide exposed surface within the body of the liquid wine and allow carbon dioxide and oxygen to break free of the liquid and enter those bubbles.
The spherical interface between the gas bubble and the surrounding liquid is a busy, active place — gas molecules are moving between the gas and liquid in both directions. Because carbon dioxide is over-concentrated in the liquid, it is statistically more likely for a carbon dioxide molecule to leave the liquid and enter the bubble's gas than the other way around. It takes a little energy to break those carbon dioxide molecules free of the liquid and that need for energy affects the balance between dissolved carbon dioxide and gaseous carbon dioxide at equilibrium. The harder it is for the carbon dioxide molecules to obtain the energy they need to escape from the liquid, the greater the equilibrium concentration of dissolved carbon dioxide — the saturated concentration. But your wine is supersaturated, containing more than the equilibrium concentration of dissolved carbon dioxide, so carbon dioxide molecules go from liquid to gas more often than the other way around.
When the degree of supersaturation (excess gas concentration) is high, the transfer of gas molecules from liquid to gas bubble can be fast enough to make the bubbles grow in size significantly as they float up through the wine. You can see this type of rapid bubble growth in a glass of freshly poured soda, beer, or champagne. In beer, champagne, and your wine, however, the liquid surface of the bubble contains various natural chemicals that alter the interface with the gas and affect bubble growth. The "tiny bubbles" of good champagne reflect that influence.
Another way to provide the extra exposed surface in the wine and thereby allow the supersaturated dissolved gases to come out of solution would be to agitate the wine so violently that empty cavities open up within the wine. Although that approach would provide lots of extra surface, it would probably not be good for the wine. Bubbling gas through the wine is a much more gentle.
The exact choice of gas barely matters as long as it is chemically inert in the wine. Argon or helium would be just as effective, but they're more expensive (and in the case of helium, precious). The temperature of the gas doesn't matter significantly, but the temperature of the wine does. The cooler the wine, the higher the concentration of dissolved carbon dioxide and oxygen it will contain at equilibrium so you'll remove more of those gases if you do your bubbling while the wine is relatively warm.
Most likely, the ant never left the floor or walls of the microwave oven, where it was as close as possible to those metal surfaces. The six sides of the cooking chamber in a microwave oven are made from metal (or painted metal) because metal reflects microwaves and keeps them bouncing around inside the chamber.
Metals are good conductors of electricity and effectively "short out" any electric fields that are parallel to their surfaces. Microwaves reflect from the metal walls because those walls force the electric fields of the microwaves to cancel parallel to their surfaces and that necessitates a reflected wave to cancel the incident wave. Because of that cancellation at the conducting surfaces, the intensity of the microwaves at the walls is zero or very close to zero.
The ant survived by staying within a tiny fraction of the microwave wavelength (about 12.4 cm) of the metal surfaces, where there is almost zero microwave intensity. Had the ant ventured out onto your cup, it would have walked into real trouble. Once exposed to the full intensity of the microwaves, it would not have fared so well.
I think that you've rediscovered an experiment in which people cut a grape almost in half, open the two halves like a book and lay it flat on a plate. In the microwave, the thin bridge between the halves carbonizes and than emits flames. Basically, the fruit pieces or berries are acting as antennas for the microwaves, which drive electric currents through the narrow bridges between parts. The berries aren't great conductors, but they're not true insulators either. Those bridges overheat (like an overloaded extension cord) and burn up. The flames come from the burning bridges.
If you let the flames go on long enough and enough carbon develops, you'll probably start getting plasma balls in the oven (lots of fun, but not great for the oven... you can scorch its top surface because those plasma balls rise and skittle around the ceiling of the oven). Anyway, you can probably find the carbon areas if you look closely enough, but they're no worse than a little burnt toast.
Yours is actually a complicated question. After you open the soda, the CO2 dissolved in the soda is no longer in equilibrium with the gas above soda. When you cap the bottle, CO2 will gradually escape from the liquid until it forms a dense gas so that CO2 molecules from that gas return to the liquid solution as often as they leave the solution for the gas. In other words, the equilibrium between dissolved CO2 and gaseous CO2 has to be reestablished.
By shrinking the volume of gas over the soda, your boyfriend reduces the number of CO2 molecules that must enter the gas phase in order to reestablish that equilibrium. BUT, when dense gas develops in the squeezed bottle, the high pressure of that gas will reinflate the bottle to its original size. The benefits of shrinking the gas volume will thus be lost.
To succeed in keeping more of the CO2 molecules in solution, you have to make sure that the squeezed bottle stays squeeze. That's hard to do. You're probably better off pouring the soda gently into a smaller bottle, one that just barely holds all of the liquid. That smaller bottle won't expand as a dense gas of CO2 forms above the liquid soda and the soda will reestablish its equilibrium without losing too many of its dissolved CO2 molecules.
When you watch something move, what you really notice is the change in the angle at which see you it. Nearby objects don't have to be traveling fast to make you turn your head quickly to watch them go by so you perceive them as moving rapidly. An object that is heading directly toward you or away from you doesn't appear to be moving nearly as quickly because its change in angle is much smaller.
When you watch a distant object move, you don't see it change angles quickly so you perceive it as moving relatively slowly. Take the moon for example: it is moving thousands of miles an hour yet you can't see it move at all. It's just so far away that you see no angular change. And when you look down from a high-flying jet, the distant ground is changing angles slowly and therefore looks like it's not moving fast.
In principle, the brownie would heat up faster by radiation in a hot environment and cool off faster by radiation in a cold environment. A black object is better at both absorbing thermal radiation and emitting thermal radiation, so the brownie would soak up more thermal radiation in the hot environment and give off more thermal radiation in the cold environment.
In practice, however, most of the radiation involved in baking these desserts and letting them cool on a kitchen counter is in the infrared and it's hard to tell just what color a brownie or cake is in the infrared. It's likely that both are pretty dark when viewed in infrared light. Basically, even things that look white to your eye are often gray or black in the infrared. Thus I suspect that both the brownie and cake absorb most of the thermal radiation they receive while being baked and emit thermal radiation efficienty while they're cooling on the counter.
Light has no charge at all. It consists only of electric and magnetic field, each endlessly recreating the other as the pair zip off through empty space at the speed of light.
The fact that light waves can travel in vacuum, and don't need any material to carry them, was disturbing to the physicists who first studied light in detail. They expected to find a fluid-like aether, a substance that was the carrier of electromagnetic waves. Instead, they found that those waves travel through truly empty space. One thing led to another, and soon Einstein proposed that the speed of light was profoundly special and that space and time were interrelated by way of that speed of light.
What you propose to do is far more difficult than you imagine. Determining the chemical contents of food is hard, even with a well-equipped laboratory and permission to destroy the food in order to study it. The idea of analyzing a casserole in detail simply by beaming microwaves at it is science fiction. Think how much easier airport security would be if they could chemically analyze everything that came in the front door just by beaming microwaves at it.
That said, however, let me make two comments. First, the question quickly turns to computer interface issues, as though the chemical analysis part is trivial in comparison to computer presentation part. Physical science and computer science are truly different fields and not everything in the scientific domain can be reduced to a software package. Physics and chemistry haven't disappeared with the advent of computers and there will never be a firmware upgrade for your microwave oven that will turn it into a nutritional analysis laboratory. As a society, we've gone a bit too far in replacing science education with technology education, particularly computer software.
Second, while remote chemical analysis isn't easy, it can be done in certain cases with the clever use of physics and chemistry. One of my friends here at Virginia, Gaby Laufer, has developed an instrument that studies the infrared light transmitted by the air and can determine whether that air contains any of a broad variety of toxic or dangerous gases in a matter of seconds. Air's relative transparency makes it easier to analyze than an opaque casserole, but even when you can see through something it's not trivial to see what it contains. Gaby's instrument does a phenomenal job of fingerprinting the gas's absorption features and identifying trouble.
Note added: a reader informed me that there are now microwave ovens that can read bar codes and adjust their cooking to match the associated food. A scale in the base of the oven can determine the food's weight and cook it properly. Another reader suggested that a microwave oven might be able to measure the food's microwave absorption and weight in order to adjust cooking power and time. While that's also a good possibility, ovens that sense food temperature or the humidity inside the oven can achieve roughly the same result by turning themselves off at the appropriate time.
That's exactly right! Coasting and zero net force go hand-in-hand: when an object is experiencing zero net force, it doesn't accelerate and thus it coasts. A coasting object is an inertial object, meaning that it moves at a steady pace along a straightline path. And if the coasting object is at rest, it stays at rest.
To clarify the term "net force," note that when an object is experiencing several separate forces, it doesn't accelerate in response to each one individually. Instead, it accelerates in response to the sum of all the forces acting on it: the net force. Remember that forces have directions associated with them (forces are vector quantities), so when you sum them you must consider their directions carefully. The proper force to consider in Newton's second law is actually the net force on the object. If you know both the net force on the object and the object's mass, you can predict the object's acceleration. And if the net force is zero, then the object doesn't accelerate at all — it coasts.
I figure that some day, we'll turn to our landfills as resources for precious elements like copper and gold. That assumes, of course, that we survive global warming. In the meantime, we'll just keep throwing stuff out.
Despite the scary title "microwave radiation," a microwave oven is basically just another household electronic device. It is an extremely close relative of a convention cathode-ray-tube television set. If you're OK with putting CRT televisions and computer monitors in the landfill, you should have no problems with putting microwave ovens there, too. Even when the microwave oven is on, all it has inside it is microwave radiation and that's just not a big deal. The instant you turn it off, it doesn't even have those microwaves in it. It's just boring inert electronic parts and they'll sit in the landfill for generations, rusting and decaying like every other abandoned electronic gadget. I'd rather see it go to a recycling center and have its precious materials returned to the resource bin, but as landfill junk goes, it's not all that bad. Given that toxic chemicals are the primary concern with landfills, microwave ovens are probably rather innocuous. They have no radioactive contents and although the high-voltage capacitor might have oil in it, that oil can no longer be the toxic PCBs that were common a few decades ago. Even when that oil leaks into the environment, it's probably not going to do much.
So there you have it, microwave ovens go to their graves no more loudly or dangerously than old televisions or computers or cell phones.
In fact, I might start calling cell phones "microwave phones" because that's exactly what they are. They communicate with the base unit by way of microwave radiation. Given the number of people who have cell phones semi-permanently installed in their ears, concerns about microwave radiation should probably be redirect from microwave ovens to "microwave phones." Think about it next time your six-year-old talks for an hour with her best friend on that "microwave phone."
While it's easy to push on water, it's hard to pull on water. When you drink soda through a straw, you may feel like you're pulling on the water, but you're not. What you are actually doing is removing some air from the space inside the straw and above the water, so that the air pressure in that space drops below atmospheric pressure. The water column near the bottom of the straw then experiences a pressure imbalance: the usual atmospheric pressure below it and less-than-atmospheric pressure above it. That imbalance provides a modest upward force on the water column and pushes it up into your mouth.
So far, so good. But if you make that straw longer, you'll need to suck harder. That's because as the column of water gets taller, it gets heavier. It needs a more severe pressure imbalance to push it upward and support it. By the time the straw and water column get to be about 40 feet tall, you'll need to suck every bit of air out from inside the straw because the pressure imbalance needed to support a 40-foot column of water is approximately one atmosphere of pressure. If the straw is taller than 40 feet, you're simply out of luck. Even if you remove all the air from within the straw, the atmospheric pressure of the water below the straw won't be able to push the water up the straw higher than about 40 feet.
To get the water to rise higher in the straw, you'll need to install a pump at the bottom. The pump increases the water pressure there to more than 1 atmosphere, so that there is a bigger pressure imbalance available and therefore the possibility of supporting a taller column of water.
OK, so returning to your question: once a well is more than about 40 feet deep, getting the water to the surface requires a pump at the bottom. That pump can boost the water pressure well above atmospheric and thereby push the water to the surface despite the great height and weight of the water column. Suction surface pumps are really only practical for water that's a few feet below the surface; after that, deep pressure pumps are a much better idea.
Your daughter's question is a cute one. I like it because it highlights the distinction between the speed of light and all other speeds. The speed of light is unimaginably special in our universe. Strange though it may sound, even if light didn't exist there would still be the speed of light and it would still have the same value. The speed of light is part of the geometry of space-time and the fact that light travels at "the speed of light" is almost a cosmic afterthought. Gravity and the so-called "strong force" also travel at that speed.
OK, so there is actually a multi-way tie for first place in the speed rankings. Your daughter's question is what comes next? The actual answer is that it's a many-way tie between everything else. With enough energy, you can get anything moving at just under the speed of light, at least in principle. For example, subatomic particles such as electrons, protons, and even atomic nuclei are routinely accelerated to just under the speed of light in sophisticated machines around the world. The universe itself has natural accelerators that whip subatomic particles up until they are traveling so close to the speed of light that it's hard to tell that they aren't quite at the speed of light. Nonetheless, I assure you that they're not. The speed of light is so special that nothing that has any mass at all can possibly travel at the speed of light. Only the ephemeral non-massive particles such as light particles (photons), gravity particles (gravitons), and strong force particles (gluons) can actually travel at the speed of light. In fact, once photons, gravitons, and gluons begin to interact with matter, they don't travel at the speed of light either. It's sort of a guilt-by-association: as soon as these massless particles leave the essential emptiness of the vacuum and begin to interact with matter, even they can't travel at the speed of light anymore.
That said, I can still offer the likely second place finisher on the speed list. I'm going to skip over light, gravity, and the strong force traveling in extremely dilute matter because that's sort of cheating — if you take something that naturally travels at the speed of light and slow it down the very, very slightest bit, of course it will come ridiculously close to the speed of light. In real second place are almost certainly cosmic ray particles. These cosmic rays are actually subatomic particles that are accelerated to fantastic energies by natural processes in the cosmos. How such accelerators work is still largely a mystery but some of the cosmic ray particles that reach our atmosphere have truly astonishing energies — once in a while a single cosmic ray particle that is smaller than an atom will carry enough energy with it that it is capable of moving small ordinary objects around. Even if it carries the energy of a fly, that's a stupendous amount of energy for an atomic fragment. Those cosmic ray particles are traveling so close to the speed of light that it would be a photo-finish with light itself.
As a general observation, the bottleneck in scientific research and technological innovation is almost always the ideas, not the equipment. Occasionally, a revolutionary piece of equipment comes on the scene and makes a whole raft of developments possible overnight. But a commercial superconducting magnet isn't revolutionary; you can buy one off the shelf. As a result, all the innovations that were waiting for magnets like that to become available were mopped up long ago and any new innovations will take new ideas.
Coming up with good ideas is hard work and if I had them, I'd have gotten hold of such a magnet myself. Although science is often taught as formulas and factoids, it's really about thinking and observing, and good ideas are nearly always more important than good equipment. Good ideas don't linger unstudied for long when commercial equipment is all it takes to pursue them.
Like a camera, your eye collects light from the scene you're viewing and tries to form a real image of that scene on your retina. The eye's front surface (its cornea) and its internal lens act together to bend all the light rays from some distant feature toward one another so that they illuminate one spot on your retina. Since each feature in the scene you're viewing forms its own spot, your eye's cornea and lens are forming a real image of the scene in front of you. If that image forms as intended, you see a sharp, clear rendition of the objects in front of you. But if your eye isn't quite up to the task, the image may form either before or after your retina so that you see a blurred version of the scene.
The optical elements in your eye that are responsible for this image formation are the cornea and the lens. The cornea does most of the work of converging the light so that it focuses, while the lens provides the fine adjustment that allows that focus to occur on your retina.
If you're farsighted, the two optical elements aren't strong enough to form an image of nearby objects on your retina so you have trouble getting a clear view while reading. Your eye needs help, so you wear converging eyeglasses. Those eyeglasses boost the converging power of your eye itself and allow your eye to form sharp images of nearby objects on your retina.
If you're nearsighted, the two optical elements are too strong and need to be weakened in order to form sharp images of distant objects on your retina. That's why you wear diverging eyeglasses.
People are surprised when I tell them that they're nearsighted or farsighted. They wonder how I know. My trick is simple: I look through their eyeglasses at distant objects. If those objects appear enlarged, the eyeglasses are converging (like magnifying glasses) and the wearer must be farsighted. If those objects appear shrunken, the eyeglasses are diverging (like the security peepholes in doors) and the wearer is nearsighted. Try it, you'll find that it's easy to figure out how other people see by looking through their glasses as they wear them.
Those touch pads are sensing your presence electronically, not mechanically. More specifically, electric charge on the pad pushes or pulls on electric charge on your finger and the pad's electronics can tell that you are there by how charge on the pad reacts to charge on your finger.
Because your finger and your body conduct electricity, the pad's electric charge is actually interacting with the electric charge on your entire body. In contrast, a straw is insulating, so the pad can only interact with charge at its tip, and while your car keys are conducting, they are too small to have the effect that your body has on that pad.
There are at least two ways for a pad and its electronics to sense your body and its electric charges. The first way is for the electronics to apply a rapidly alternating electric charge to the pad and to watch for the pad's charge to interact with charge outside the pad (i.e., on your body). When the pad is by itself, the electronics can easily reverse the pad's electric charge because that charge doesn't interact with anything. But when your hand is near the pad or touching it, it's much harder for the electronics to reverse the pad's electric charge. If you're touch the pad, the electronics has to reverse your charge, too, so the electronics sense a new sluggishness in the pad's response to charge changes. Even when you're not quite touching the pad, the electronics has some add difficulty reversing the pad's charge. That's because the pad's charge causes your finger and body to become electrically polarized: charges opposite to those on the pad are attracted onto your finger from your body so that your finger becomes electrically charged opposite to the charge of the pad. When the electronics then tries to withdraw the charge from the pad in order to reverse the pad's charge, your finger's charge acts to make that withdrawal difficult. The electronics finds that it must struggle to reverse the pad's charge even though you're not in direct contact with the pad. Overall, your finger complicates the charge reversals whenever it's near or touching the pad.
The second way for the pad's electronics to sense your presence is to let your body act as an antenna for electromagnetic influences in the environment. We are awash in electric and magnetic fields of all sorts and the electric charge on your body is in ceaseless motion as a result. You've probably noticed that touching certain input wires of a stereo amplifier produces lots of noise in the speakers; that's partly a result of the electromagnetic noise in our environment showing up as moving charge on your body. The little pad on the soda dispenser picks up a little of this electromagnetic noise all by itself. When you approach or touch the pad, however, you dramatically increase the amount of electromagnetic noise in the pad. The pad's electronics easily detect that new noise.
In short, soda dispenser pads are really detecting large electrically conducting objects. Their ability to sense your finger even before it makes contact is important because they need to work when people are wearing gloves. I first encountered electrical touch sensors in elevators when I was a child and I loved to experiment with them. Conveniently, they'd light up when they detected something and there was no need to clean up spilled soda. We'd try triggering them with elbows and noses, and a whole variety of inanimate objects. They were already pretty good, but modern electronics has made touch pads even better. The touch switches used by some lamps and other appliances function in essentially the same way.
What thrills me about your question is that while we've all noticed this effect, we're never taught why it happens. Let me ask your question in another way: we know that opening a window makes the clothes dry faster, but how do the clothes know that the window is open? Who tells them?
The explanation is both simple and interesting: the rate at which water molecules leave the cloths doesn't depend on whether the window is open or closed, but the rate at which water molecules return to the cloths certainly does. That return rate depends on the air's moisture content and can range from zero in dry air to extremely fast in damp air. Air's moisture content is usually characterized by its relative humidity, with 100% relative humidity meaning that air's water molecules land on surfaces exactly as fast as water molecules in liquid water leave its surface. When you expose a glass of water to air at 100% relative humidity, the glass will neither lose nor gain water molecules because the rates at which water molecules leave the water and land on the water are equal. Below 100% relative humidity, the glass will gradually empty due to evaporation because leaving will outpace landing. Above 100% relative humidity, the glass will gradually fill due to condensation because landing will outpace leaving.
The same story holds true for wet clothes. The higher the air's relative humidity, the harder it becomes for water to evaporate from the cloths. Landing is just too frequent in the humid air. At 100% relative humidity the clothes won't dry at all, and above 100% relative humidity they'll actually become damper with time.
When you dry clothes in a room with the window open and the relative humidity of the outdoor air is less than 100%, water molecules will leave the clothes more often than they'll return, so the clothes will dry. But when the window is closed, the leaving water molecules will remain trapped in the room and will gradually increase the room air's relative humidity. The drying process will slow down as the water-molecule return rate increases. When the room air's relative humidity reaches 100%, drying will cease altogether.
Water "plasticizes" the cotton. A plasticizer is a chemical that dissolves into a plastic and lubricates its molecules so that they can move across one another more easily. Cotton is almost pure cellulose, a polymer consisting of sugar molecules linked together in long chains. Since sugar dissolves easily in water, water dissolves easily in cellulose. Even though cellulose scorches before it melts, it can be softened by heat and water. When you iron cotton pants, the steam dissolves into the cellulose molecules and allows the fabric to smooth out beautifully.
You're right. Whether the microwave oven is grounded or not makes no difference on its screen's ability to prevent microwave leakage. In fact, the whole idea of grounding something is nearly meaningless at such high frequencies. Since electrical influences can't travel faster than the speed of light and light only travels 12.4 cm during one cycle of the oven's microwaves, the oven can't tell if it's grounded at microwave frequencies; its power cord is just too long and there just isn't time for charge to flow all the way through that cord during a microwave cycle.
When you ground an appliance, you're are making it possible for electric charge to equilibrate between that appliance and the earth. The earth is approximately neutral, so a grounded appliance can't retain large amounts of either positive or negative charge. That's a nice safety feature because it means that you won't get a shock when you touch the appliance, even if one of its power wires comes loose and touches the case. Any charge that the power wire tries to deposit on the case will quickly flow to the earth as the appliance and earth equilibrate.
But charge can't escape from the appliance through the grounding wire instantly. Light takes about 1 nanosecond to travel 1 foot and electricity takes a little longer than that. For charge to leave your appliance for the earth might well require 50 nanoseconds or more. That's not a problem for ordinary power distribution, so grounding is generally a great idea. Each cycle of the 60-Hz AC power in the U.S. takes 18 milliseconds to complete, so the appliance and earth have plenty of time to equilibrate with one another. But a cycle of the microwave power in the oven takes less about 0.4 nanoseconds to complete and there's just no time for the appliance and earth to equilibrate. At microwave frequencies, the electric current flowing through a long wire is wavelike, meaning that at one instant in time the wire has both positive and negative patches, spaced half a wavelength apart along its length. It's carrying an electromagnetic ripple.
The metal screen on the oven's door has to reflect the microwaves all by itself. It does this without a problem because the holes are so much smaller than 12.4 centimeters that currents easily flow around them during a cycle of the microwaves. Those currents are able to compensate for the holes in the screens and cause the microwaves to reflect perfectly.
No. Birds do this all the time. What protects the bird is the fact that it doesn't complete a circuit. It touches only one wire and nothing else. Although there is a substantial charge on the power line and some of that charge flows onto the bird when it lands, the charge movement is self-limiting. Once the bird has enough charge on it to have the same voltage as the power line, charge stops flowing. And even though the power line's voltage rises and falls 60 times a second (or 50 times a second in some parts of the world), the overall charge movement at 10,000 volts just isn't enough to bother the bird much. At 100,000 volts or more, the charge movement is uncomfortable enough to keep birds away, so you don't see them landing on the extremely high-voltage transmission lines that travel across vast stretches of countryside.
The story wouldn't be the same if the bird made the mistake of spanning the gap from one wire to another. In that case, current could flow through the bird from one wire to the other and the bird would run the serious risk of becoming a flashbulb. Squirrels occasionally do this trick when they accidentally bridge a pair of wires. Some of the unexpected power flickers that occur in places where the power lines run overhead are caused by squirrels and occasionally birds vaporizing when they let current flow between power lines.
If both of you were electrically neutral before the kiss, nothing would happen. Evidently, one of you has developed a net charge and that charge is suddenly spreading itself out onto the other person during the kiss. That charge flow is an electric current and you feel currents flowing through your body as a shock.
Most likely, one of you has been in contact with a insulating surface that has exchanged charge with you. For example, if you walked across wool carpeting in rubber-soled shoes, that carpeting has probably transferred some of its electrons to your shoes and your shoes have then spread those electrons out onto you. Rubber binds electrons more tightly than wool and so your shoes tend to steal a few of electrons from wool whenever it gets a chance. If you walk around a bit or scuff your feet, you'll typically end up with quite a large number of stolen electrons on your body. When you then go and kiss Uncle Al, about half of those electrons spread suddenly onto him and that current flow is shocking!
You have it exactly right. Water itself is burned hydrogen, and the energy required to separate water into hydrogen and oxygen is equal to the energy released when the hydrogen subsequently burns back into water. Energy in and energy out. Just as in bicycling, if you want to roll downhill, you have to pedal uphill first.
Anyone who claims to be able to extract useful energy through a process that starts with water and ends with water is a charlatan. Either they aren't producing any useful energy or it's coming from some other source. In these sorts of frauds, there is usually some electrical component that is supposedly needed to keep a minor part of the apparatus functioning. That component isn't insignificant at all; it's what actually keeps the entire apparatus functioning!
Hydrogen has such a mythical aura to it, but in the context of energy, it's just another fuel. Actually, it's more of any energy storage medium than a basic fuel. That's because hydrogen doesn't occur naturally on earth and can only be produced by consuming another form of energy. There is so much talk about "the hydrogen economy"Âť and the notion that hydrogen will rescue us from our dependence on petroleum. Sadly, politicians who promote hydrogen as the energy panacea neither understand science nor respect those who do. Since it takes just as much energy to produce hydrogen from water as is released when that hydrogen burns back into water, hydrogen alone won't save us.
As we grow progressively more desperate for useable energy, the amount of fraud and misinformation will only increase. There are only a few true sources for useable energy: solar energy (which includes wind power, hydropower, and biomass), fossil fuels (which include petroleum and coal), geothermal energy, and nuclear fuels. Hydrogen is not among them; it can be produced only at the expense of one of the others. Even ethanol, which is touted as an environmentally sound replacement for petroleum, has its problems; producing a gallon of ethanol can all too easily consume a gallon of petroleum.
Where energy is concerned, watch out for fraud, hype, PR, and politics. If we survive the coming energy and climate crises, it will be because we've learned to conserve energy and to obtain it primarily from solar and perhaps nuclear sources. It will also be because we've learned to set politics and self-interest aside long enough to make accurate analyses and sound decisions.
The watt is a unit of power, equivalent to the joule-per-second. One joule is about the amount of energy it takes to raise a 12 ounce can of soda 1 foot. A 60 watt lightbulb uses 60 joules-per-second, so the power it consumes could raise a 24-can case of soda 2.5 feet each second. Most tables are about 2.5 feet above the floor. Next time you leave a 60-watt lightbulb burning while you're not in the room, imagine how tired you'd get lifting one case of soda onto a table every second for an hour or two. That's the mechanical effort required at the generating plant to provide the 60-watts of power you're wasting. If don't need the light, turn off lightbulb!
What a great question! I love it. The answer is no, but there's much more to the story.
I'll begin to looking at how dust settles in calm air near the ground. That dust experiences its weight due to gravity, so it tends to descend. Each particle would fall like a rock except that it's so tiny that it experiences overwhelming air resistance. Instead of falling, it descends at an incredibly slow terminal velocity, typically only millimeters per second. It eventually lands on whatever is beneath it, so a room's floor gradually accumulates dust. But dust also accumulates on vertical walls and even on ceilings. That dust is held in place not by its weight but by electrostatic or chemical forces. When you go into an abandoned attic, most of the dust is on the floor, but there's a little on the walls and on the ceiling.
OK, now to the space shuttle. The shuttle is orbiting the earth, which means that although it has weight and is falling freely, it never actually reaches the earth because it's heading sideways so fast. Without gravity, its inertia would carry it horizontally out into space along a straight line path. Gravity, however, bends that straight line path into an elliptical arc that loops around the earth as an orbit.
So far no real surprises: dust near ground level settles in calm air and the shuttle orbits the earth. The surprise is that particles of space dust particles also orbit the earth! The shuttle orbits above the atmosphere, where there is virtual no air. Without air to produce air resistance, the dust particles also fall freely. Those with little horizontal speed simply drop into the atmosphere and are lost. But many dust particles have tremendous horizontal speeds and orbit the earth like tiny space shuttles or satellites.
Whether they are dropping toward atmosphere or orbiting the earth, these space dust particles are typically traveling at velocities that are quite different in speed or direction from the velocity of the space shuttle. The relative speed between a dust particle and the shuttle can easily exceed 10,000 mph. When such a fast-moving dust particle hits the space shuttle, it doesn't "settle."Âť Rather, it collides violently with the shuttle's surface. These dust-shuttle collisions erode the surfaces of the shuttle and necessitate occasional repairs or replacements of damaged windows and sensors. Astronauts on spacewalks also experience these fast collisions with space dust and rely on their suits to handle all the impacts.
Without any air to slow the relative speeds and cushion the impacts, its rare that a particle of space dust lands gracefully on the shuttle's surface. In any case, gravity won't hold a dust particle in place on the shuttle because both the shuttle and dust are falling freely and gravity doesn't press one against the other. But electrostatic and chemical attractions can hold some dust particles in place once they do land. So the shuttle probably does accumulate a very small amount of accumulated space dust during its travels.
The #2-pencil requirement is mostly historical. Because modern scantron systems can use all the sophistication of image sensors and computer image analysis, they can recognize marks made with a variety of materials and they can even pick out the strongest of several marks. If they choose to ignore marks made with materials other than pencil, it's because they're trying to be certain that they're recognizing only marks made intentionally by the user. Basically, these systems can "see" most of the details that you can see with your eyes and they judge the markings almost as well as a human would.
The first scantron systems, however, were far less capable. They read the pencil marks by shining light through the paper and into Lucite light guides that conveyed the transmitted light to phototubes. Whenever something blocked the light, the scantron system recorded a mark. The marks therefore had to be opaque in the range of light wavelengths that the phototubes sensed, which is mostly blue. Pencil marks were the obvious choice because the graphite in pencil lead is highly opaque across the visible light spectrum. Graphite molecules are tiny carbon sheets that are electrically conducting along the sheets. When you write on paper with a pencil, you deposit these tiny conducting sheets in layers onto the paper and the paper develops a black sheen. It's shiny because the conducting graphite reflects some of the light waves from its surface and it's black because it absorbs whatever light waves do manage to enter it.
A thick layer of graphite on paper is not only shiny black to reflected light, it's also opaque to transmitted light. That's just what the early scantron systems needed. Blue inks don't absorb blue light (that's why they appear blue!), so those early scantron systems couldn't sense the presence of marks made with blue ink. Even black inks weren't necessarily opaque enough in the visible for the scantron system to be confident that it "saw" a mark.
In contrast, modern scantron systems used reflected light to "see" marks, a change that allows scantron forms to be double-sided. They generally do recognize marks made with black ink or black toner from copiers and laser printers. I've pre-printed scantron forms with a laser printer and it works beautifully. But modern scantron systems ignore marks made in the color of the scantron form itself so as not to confuse imperfections in the form with marks by the user. For example, a blue scantron form marked with blue ink probably won't be read properly by a scantron system.
As for why only #2 pencils, that's a mechanical issue. Harder pencil leads generally don't produce opaque marks unless you press very hard. Since the early scantron machines needed opacity, they missed too many marks made with #3 or #4 pencils. And softer pencils tend to smudge. A scantron sheet filled out using a #1 pencil on a hot, humid day under stressful circumstances will be covered with spurious blotches and the early scantron machines confused those extra blotches with real marks.
Modern scantron machines can easily recognize the faint marks made by #3 or #4 pencils and they can usually tell a deliberate mark from a #1 pencil smudge or even an imperfectly erased mark. They can also detect black ink and, when appropriate, blue ink. So the days of "be sure to use a #2 pencil" are pretty much over. The instruction lingers on nonetheless.
One final note: I had long suspected that the first scanning systems were electrical rather than optical, but I couldn't locate references. To my delight, Martin Brown informed me that there were scanning systems that identified pencil marks by looking for their electrical conductivity. Electrical feelers at each end of the markable area made contact with that area and could detect pencil via its ability to conduct electric current. To ensure enough conductivity, those forms had to be filled out with special pencils having high conductivity leads. Mr. Brown has such an IBM Electrographic pencil in his collection. This electrographic and mark sense technology was apparently developed in the 1930s and was in wide use through the 1960s.
Power outages come in a variety of types, one of which involves a substantial decrease in the voltage supplied to your home. The most obvious effect of this voltage decrease is the dimming of the incandescent lights, which is why it's called a "brownout." The filament of a lightbulb is poor conductor of electricity, so keeping an electric charge moving through it steadily requires a forward force. That forward force is provided by the voltage difference between the two wires: the one that delivers charges to the filament and the one that collects them back from the filament. As the household voltage decreases, so does the force on each charge in the filament. The current passing through the filament decreases and the filament receives less electric power. It glows dimly.
At the risk of telling you more than you ever want to know, I'll point out that the filament behaves approximately according to Ohm's law: the current that flows through it is proportional to the voltage difference between its two ends. The larger that voltage difference, the bigger the forces and the more current that flows. This ohmic behavior allows incandescent lightbulbs to survive decreases in voltage unscathed. They don't, however, do well with increases in voltage, since they'll then carry too much current and receive so much power that they'll overheat and break. Voltage surges, not voltage decreases, are what kill lightbulbs.
The other appliances you mention are not ohmic devices and the currents that flow through them are not simply proportional to the voltage supplied to your home. Motors are a particularly interesting case; the average current a motor carries is related in a complicated way to how fast and how easily it's spinning. A motor that's turning effortlessly carries little average current and receives little electric power. But a motor that is struggling to turn, either because it has a heavy burden or because it can't obtain enough electric power to overcome starting effects, will carry a great deal of average current. An overburdened or non-starting motor can become very hot because it's wiring deals inefficiently with the large average current, and it can burn out. While I've never heard of a refrigerator motor dying during a brownout, it wouldn't surprise me. I suspect that most appliance motors are protected by thermal sensors that turn them off temporarily whenever they overheat.
Modern electronic devices are also interesting with respect to voltage supply issues. Electronic devices operate on specific internal voltage differences, all of which are DC — direct current. Your home is supplied with AC — alternating current. The power adapters that transfer electric power from the home's AC power to the device's DC circuitry have evolved over the years. During a brownout, the older types of power adapters simply provide less voltage to the electronic devices, which misbehave in various ways, most of which are benign. You just want to turn them off because they're not working properly. It's just as if their batteries are worn out.
But the most modern and sophisticated adapters are nearly oblivious to the supply voltage. Many of them can tolerate brownouts without a hitch and they'll keep the electronics working anyway. The power units for laptops are a case in point: they can take a whole range of input AC voltages because they prepare their DC output voltages using switching circuitry that adjusts for input voltage. They make few assumptions about what they'll be plugged into and do their best to produce the DC power required by the laptop.
In short, the motors in your home won't like the brownout, but they're probably protected against the potential overheating problem. The electronic appliances will either misbehave benignly or ride out the brownout unperturbed. Once in a while, something will fail during a brownout. But I think that most of the damage is down during the return to normal after the brownout. The voltages bounce around wildly for a second or so as power is restored and those fluctuations can be pretty hard some devices. It's probably worth turning off sensitive electronics once the brownout is underway because you don't know what will happen on the way back to normal.
That tear in the window screen presents three potential problems: microwave leakage, evanescent waves, and arcing. As long as the hole is small, less than a centimeter or so, it's not likely to allow much microwave leakage. The oven's microwaves have a wavelength of 12.4 centimeters and they'll reflect from conducting surfaces with holes much smaller than that wavelength. A foot from your oven, there probably won't be any significant microwave intensity, although the only way to be sure is with a microwave leakage meter.
The evanescent wave problem is more likely. When any electromagnetic wave reflects from a conducting surface that has small holes in it, there is what is known as an evanescent wave extending into and somewhat beyond each hole. It's as though the wave is trying to figure out whether or not it can pass through the opening and so it tries. Even when it discovers that the hole is far too small for it pass through (i.e., much smaller than its wavelength), it still offers electromagnetic intensity in the region just beyond the hole. The extent of the evanescent wave increases with the size of the hole. The microwave oven's screen has very small holes and it is located inside the glass window. The evanescent waves associated with those holes cut off so quickly that you can hold your hand against the glass and not expose your skin to significant microwaves. But once you've torn a larger hole in the screen, the evanescent waves can extend farther through that screen and perhaps out beyond the surface of the glass window. If you press your hand against the window just in front of the tear while the microwave oven is on, you may burn your hand.
Finally, there is the issue of arcing. To reflect the microwaves, the conducting screen must carry electric currents. The microwaves' electric fields push electric charge back and forth in the conducting screen and it is that moving charge (i.e., electric current) that ultimately redirects the microwaves back into the cooking chamber as a reflection. Those electric currents in the screen are real and they're not going to take kindly to that tear. It's a weak spot in the conducting surface through which they flow. Weak electrical paths can heat up like lightbulb filaments when they carry currents. Moreover, charge that should flow across the torn region can accumulate on sharp edges and leap through the air as an arc. If either of these processes happens, it may scorch the window and the screen, and cause increasing trouble.
You could be lucky: the leakage could be zero, the evanescent waves could remain far enough inside the window to never cause injury, and the tear could never heat up or arc. But the risk of operating this damaged microwave oven is not insignificant. Since it's an installed unit, I'd suggest replacing the screen or the door. There are a number of websites that sell replacement parts for microwave ovens and I have used them to replace the door on our microwave oven.
There is nothing hypothetical about the earth orbiting the moon; it's as real as the moon orbiting the earth. The earth and the moon are simply two huge balls in otherwise empty space and though the mass of one is 81 times the mass of the other, they're both in motion. More specifically, they're in orbit around their combined center of mass — the effective location of the earth-moon system.
Since the earth is so much more massive than the moon, their combined center of mass is 81 times closer to the middle of the earth than it is to the middle of the moon. In fact, it's inside the earth, though not at the middle of the earth. As a result, the earth's orbital motion takes the form of a wobble rather than a more obvious looping path. Nonetheless, the earth is orbiting.
I hope that you can see that there is no reason why the earth should be fixed in space while the moon orbits about it. You've been sold a bill of goods. The mistaken notion that the moon orbits a fixed earth is a wonderful example of the "factoid science" that often passes for real science in our society.
Because thinking and understanding involve hard work, people are more comfortable when the thought and understanding have been distilled out of scientific issues and they've been turned into memorizable sound bites. Those sound bites are easy to teach and easy to test, but they're mostly mental junk food. A good teacher, like a good scientist, will urge you to question such factoids until you understand the science behind them and why they might or might not be true.
When my children were young, I often visited their schools to help teach science. In third grade, the required curriculum had them categorizing things into solutions or mixtures. Naturally, I showed them a variety of things that are neither solutions nor mixtures. It was a blast. Science is so much more interesting than a collection of 15-second sound bites.
I'll assume that by "bigger lens" you mean one that is larger in diameter and that therefore collects all the light passing through a larger surface area. While a larger-diameter lens can project a brighter image onto the image sensor or film than a smaller-diameter lens, that's not the whole story. Producing a better photo or video involves more than just brightness.
Lenses are often characterized by their f-numbers, where f-number is the ratio of effective focal length to effective lens diameter. Focal length is the distance between the lens and the real image it forms of a distant object. For example, if a particular converging lens projects a real image of the moon onto a piece of paper placed 200 millimeters (200 mm) from the lens, then that lens has a focal length of 200 mm. And if the lens is 50 mm in diameter, it has an f-number of 4 because 200 mm divided by 50 mm is 4.
Based on purely geometrical arguments, it's easy to show that lenses with equal f-numbers project images of equal brightness onto their image sensors and the smaller the f-number, the brighter the image. Whether a lens is a wide-angle or telephoto, if it has an f-number of 4, then its effective focal length is four times the effective diameter of its light gathering lens. Since telephoto lenses have long focal lengths, they need large effective diameters to obtain small f-numbers.
But notice that I referred always to "effective diameter" and "effective focal length" when defining f-number. That's because there are many modern lenses that are so complicated internally that simply dividing the lens diameter by the distance between the lens and image sensor won't tell you much. Many of these lenses have zoom features that allow them to vary their effective focal lengths over wide ranges and these lenses often discard light in order to improve image quality and avoid dramatic changes in image brightness while zooming.
You might wonder why a lens would ever choose to discard light. There are at least two reasons for doing so. First, there is the issue of image quality. The smaller the f-number of a lens, the more precise its optics must be in order to form a sharp image. Low f-number lenses are bringing together light rays from a wide range of angles and getting all of those rays to overlap perfectly on the image sensor is no small feat. Making a high-performance lens with an f-number less than 2 is a challenge and making one with an f-number of less than 1.2 is extremely difficult. There are specialized lenses with f-numbers below 1 and Canon sold a remarkable f0.95 lens in the early 1960's. The lowest f-number camera lens I have ever owned is an f1.4.
Secondly, there is the issue of depth-of-focus. The smaller the f-number, the smaller the depth of focus. Again, this is a geometry issue: a low-f-number lens is bringing together light rays from a wide range of angles and those rays only meet at one point before separating again. Since objects at different distances in front of the lens form images at different distances behind the lens, it's impossible to capture sharp images of both objects at once on a single image sensor. With a high-f-number lens, this fact isn't a problem because the light rays from a particular object are rather close together even when the object's image forms before or after the image sensor. But with a low-f-number lens, the light rays from a particular object come together acceptably only at one particular distance from the lens. If the image sensor isn't at that distance, then the object will appear all blurry. If a zoom lens didn't work to keep its f-number relatively constant while zooming from telephoto to wide angle, its f-number would decrease during that zoom and its depth-of-focus would shrink. To avoid that phenomenon, the lens strategically discards light so as to keep its f-number essentially constant during zooming.
In summary, larger diameter lenses tend to be better at producing photographic and video images, but that assumes that they are high-quality and that they can shrink their effective diameters in ways that allow them to imitate high-quality lenses of smaller diameters when necessary. But flexible characteristics always come at some cost of image quality and the very best lenses are specialized to their tasks. Zoom lenses can't be quite as good as fixed focal length lenses and a large-diameter lens imitating a small-diameter lens by throwing away some light can't be quite as good as a true small-diameter lens.
As for my sources, one of the most satisfying aspects of physics is that you don't always need sources. Most of the imaging issues I've just discussed are associated with simple geometric optics, a subject that is part of the basic toolbox of an optical physicist (which I am). You can, however, look this stuff up in any book on geometrical optics.
Yes, but it's not a good idea. Depending on the type of plate, you can either damage your microwave oven or damage the plate.
If a plate is "microwave safe," it will barely absorb the microwaves and heat extremely slowly. In effect, the microwave oven will be operating empty and the electromagnetic fields inside it will build up to extremely high levels. Since the walls of the oven are mirrorlike and the plate is almost perfectly transparent to microwaves, the electromagnetic waves streaming out of the oven's magnetron tube bounce around endlessly inside the oven's cooking chamber. The resulting intense fields can produce various types of electric breakdown along the walls of the cooking chamber and thereby damage the surface with burns or arcs. Furthermore, the intense microwaves in the cooking chamber will reflect back into the magnetron and can upset its internal oscillations so that it doesn't function properly. Although magnetrons are astonishingly robust and long-lived, they don't appreciate having to reabsorb their own emitted microwaves. In short, your plates will heat up slowly and you'll be aging your microwave oven in the process. You could wet the plates before putting them in the microwave oven to speed the heating and decrease the wear-and-tear on the magnetron, but then you'd have to dry the plates before use.
If a plate isn't "microwave safe," then it will absorb microwaves and heat relatively quickly. If it absorbs the microwaves uniformly and well, then you can probably warm it to the desired temperature without any problems as long as you know exactly how many seconds it takes and adjust for the total number of plates you're warming. If you heat a plate too long, bad things will happen. It may only amount to burning your fingers, but some plates can't take high temperatures without melting, cracking, or popping. Unglazed ceramics that have soaked up lots of water will heat rapidly because water absorbs microwaves strongly. Water trapped in pores in such ceramics can transform into high-pressure steam, a result that doesn't seem safe to me. And if a plate absorbs microwaves nonuniformly, then you'll get hotspots or burned spots on the plate. Metalized decorations on a plate will simply burn up and blacken the plate. Cracks that contain water will overheat and the resulting thermal stresses will extend the cracks further. So this type of heating can be stressful to the plates.
You can only go a few feet under water before you'll no longer be able to draw air into your lungs through that hose. It's a pressure problem. The water pressure outside your chest increases rapidly as you go deeper, but the air pressure inside the hose and your mouth barely changes at all. Pretty soon, you'll have so much more pressure outside your lungs than inside them that you won't be able to draw in any more air. Your muscles just won't be strong enough.
The water pressure increases quickly with depth because each layer of water must support the weight of all the water layers above it. Since water is dense, heavy stuff, the weight piles on quickly and it takes only 10 meters (34 feet) of descent to increase the water pressure from atmospheric to twice atmospheric. In contrast, the air in the hose is light, fluffy stuff, so its pressure increases rather slowly with depth. Even though each layer of air has to support the weight of all the layers of air above it, the rise in pressure is extremely gradual. It takes miles of atmosphere above the earth for the air pressure to build up to atmospheric pressure near the ground. The air pressure in your hose is therefore approximately unchanged by your descent into the water.
With the water pressure outside rising quickly as you go deeper and the air pressure in your mouth rising incredibly slowly as you go deeper, you quickly find it hard to breathe. Your muscles can push your chest outward against a modest pressure imbalance between outside and inside. But by the time you're a few feet below the surface, you just can't draw air into your lungs through that hose anymore. You need pressurized air, such as that provided by a scuba outfit or a deep-sea diver's compressor system.
Despite the freezer's low temperature and the motionlessness of all the frozen foods inside it, there is still plenty of microscopic motion going on. Every surface inside the freezer is active, with individual molecules landing and leaving all the time. Whenever a molecule on the surface of a piece of food manages to gather enough thermal energy from its neighbors, it will break free of the surface and zip off into the air as a vapor molecule. And whenever a vapor molecule in the air collides with the surface of another piece of food, it may stick to that surface and remain there indefinitely.
Since the freezer has a nearly airtight seal, the air it contains remains inside it for a long time. That means that the odor molecules that occasionally break free of a pungent casserole at one end of the freezer have every opportunity to land on and stick to an ice cube at the other end. With time, the ice cube acquires the scent of the casserole and becomes unappealing.
To stop this migration of molecules, you should seal each item in the freezer in its own container. That way, any molecules that leave the food's surface will eventually return to it. Since ice cubes are normally exposed to the air in the freezer, keeping the odor molecules trapped in their own sealed containers keeps the freezer air fresh and the ice cubes odor-free.
No, there is no square-peg in round-hole effect going on in microwave ovens. Microwaves reflect from conducting surfaces, just as light waves reflect from shiny metals, and they can't pass through holes in conducting surfaces if those holes are substantially smaller than their wavelengths. The holes in the conducting mesh covering the microwave oven's window are simply too small for the microwaves and the microwaves are reflected by that mesh.
Microwaves themselves have no well-defined shape but they do have firm rules governing their overall structures. Books usually draw microwaves (and all other electromagnetic waves) as wavy lines, as though something was truly going up and down in space. From that misleading representation, it's easy for people to suppose that electromagnetic waves can't get through certain openings.
In reality, electromagnetic waves consist of electric and magnetic fields (influences that push on electric charge and magnetic pole, respectively) that point up and down in a rippling fashion, but nothing actually travels up and down per say. The spatial structures of these fields are governed by Maxwell's equations, a set of four famous relationships that bind electricity and magnetism into a single, unified classical theory. Maxwell's equations dictate the structures of electromagnetic waves and predict that electromagnetic waves on one side of a conducting surface can't propagate through to the other side of that surface. Even if there are small holes in the conducting surface, holes that are much smaller that the wavelength of the waves, those waves can't propagate through the surface. More specifically, the fields die off exponentially as they try to penetrate through the holes and the waves don't propagate on the far side.
The choice of round holes in the oven mesh is simply a practical one. You can pack round holes pretty tightly in a surface while leaving their conducting boundaries relatively robust. And round holes treat all electromagnetic waves equally because they have no wide or narrow directions.
Paper consists mostly of cellulose, a natural polymer (i.e. plastic) built by stringing together thousands of individual sugar molecules into vast chains. Like the sugars from which it's constructed, cellulose's molecular pieces cling tightly to one another at room temperature and make it rather stiff and brittle. Moreover, cellulose's chains are so entangled with one another that it couldn't pull apart even if its molecular pieces didn't cling so tightly. These effects are why it's so hard to reshape cellulose and why wood or paper don't melt; they burn or decompose instead. In contrast, chicle — the polymer in chewing gum — can be reshaped easily at room temperature.
Even though pure cellulose can't be reshaped by melting, it can be softened with water and/or heat. Like ordinary sugar, cellulose is attracted to water and water molecules easily enter its chains. This water lubricates the chains so that the cellulose becomes somewhat pliable and heat increases that pliability. When you iron a damped cotton or linen shirt, both of which consist of cellulose fibers, you're taking advantage of that enhanced pliability to reshape the fabric.
But even when dry, fibrous materials such as paper, cotton, or linen have some pliability because thin fibers of even brittle materials can bend significantly without breaking. If you bend paper gently, its fibers will bend elastically and when you let the paper relax, it will return to its original shape.
However, if you bend the paper and keep it bent for a long time, the cellulose chains within the fibers will begin to move relative to one another and the fibers themselves will begin to move relative to other fibers. Although both of these motions can be facilitated by moisture and heat, time along can get the job done at room temperature. Over months or years in a tightly rolled shape, a sheet of paper will rearrange its cellulose fibers until it adopts the rolled shape as its own. When you then remove the paper from its constraints, it won't spontaneously flatten out. You'll have to reshape it again with time, moisture, and/or heat. If you press it in a heavy book for another long period, it'll adopt a flat shape again.
The rear window of a car is made of tempered glass — the glass is heated approximately to its softening temperature and then cooled abruptly to put its surface under compression, leaving its inside material under tension. That tempering process makes the glass extremely strong because its compressed surface is hard to tear. But once a tear does manage to propagate through the compressed surface layer into the tense heart of the glass, the entire window shreds itself in a process called dicing fracture — it tears itself into countless little cubes.
The stresses frozen into the tempered glass affect its polarizability and give it strange characteristics when exposed to the electromagnetic fields in light. This stressed glass tends to rotate polarizations of the light passing through it. As a result, you see odd reflections of the sky (skylight is polarized to some extent). Those polarization effects become immediately apparent when you wear polarizing sunglasses.
Mercury does expand with temperature; moreover, it expands more rapidly with temperature than glass goes. That's why the column of mercury rises inside its glass container. While both materials expand as they get hotter, the mercury experiences a larger increase in volume and must flow up the narrow channel or "capillary" inside the glass to find room for itself. Mercury is essentially incompressible so that, as it expands, it pushes as hard as necessary on whatever contains it in order to obtain the space it needs. That's why a typical thermometer has an extra chamber at the top of its capillary. That chamber will receive the expanding mercury if it rises completely up the capillary so that the mercury won't pop the thermometer if it is overheated. In short, the force pushing mercury up the column can be enormous.
The force pushing mercury back down the column as it cools is tiny in comparison. Mercury certainly does contract when cooled, so that the manufacturer is telling you nonsense. But just because the mercury contracts as it cools doesn't mean that it will all flow back down the column. The mercury needs a push to propel it through its narrow channel.
Mercury is attracted only weakly to glass, so it doesn't really adhere to the walls of its channel. However, like all liquids, mercury has a viscosity, a syrupiness, and this viscosity slows its motion through any pipe. The narrower the pipe, the harder one has to push on a liquid to keep it flowing through that pipe. In fact, flow through a pipe typically scales as the 4th power of that pipe's radius, which is why even modest narrowing of arteries can dramatically impair blood flow in people. The capillaries used in fever thermometers are so narrow that mercury has tremendous trouble flowing through them. It takes big forces to push the mercury quickly through such a capillary.
During expansion, there is easily enough force to push the mercury up through the capillary. However, during contraction, the forces pushing the mercury back down through the capillary are too weak to keep the column together. That's because the only thing above the column of liquid mercury is a thin vapor of mercury gas and that vapor pushes on the liquid much too feebly to have a significant effect. And while gravity may also push down on the liquid if the thermometer is oriented properly, it doesn't push hard enough to help much.
The contracting column of mercury takes hours to drift downward, if it drifts downward at all. It often breaks up into sections, each of which drifts downward at its own rate. And, as two readers (Michael Hugh Knowles and Miodrag Darko Matovic) have both pointed out to me in recent days, there is a narrow constriction in the capillary near its base and the mercury column always breaks at that constriction during contraction. Since the top portion of the mercury column is left almost undisturbed when the column breaks at the constriction, it's easy to read the highest temperature reached by the thermometer.
Shaking the thermometer hard is what gets the mercury down and ultimately drives it through the constriction so that it rejoins into a single column. In effect, you are making the glass accelerate so fast that it leaves the mercury behind. The mercury isn't being pushed down to the bottom of the thermometer; instead, the glass is leaping upward and the mercury is lagging behind. The mercury drifts to the bottom of the thermometer because of its own inertia.
You're right that the glass tube acts as a magnifier for that thin column of mercury. Like a tall glass of water, it acts as a cylindrical lens that magnifies the narrow sliver of metal into a wide image.
As long as the oven's metal bottom is sound underneath the rust, there isn't a problem. The cooking chamber walls are so thick and highly conducting that they reflect the microwaves extremely well even when they have a little rust on them. However, if the metal is so rusted that it loses most of its conductivity in the rust sites, you'll get local heating across the rusty patches and eventually leakage of microwaves. If you're really concerned that there may be trouble, run the microwave oven empty for about 20 seconds and then (carefully!) touch the rusty spots. If they aren't hot, then the metal underneath is doing its job just fine.
The salesperson you spoke to was simply wrong. If you'll allow me to stand on my soapbox for a minute, I'll tell you that this is a perfect example of how important it is for everyone to truly learn basic science while they're in school and not to simply suffer through the classes as a way to obtain a degree. The salesperson is apparently oblivious to the differences between types of "radiation," to the short- and long-term effects of those radiations, and to the importance of intensity in radiation.
Let's start with the differences in types of radiation. Basically, anything that moves is radiation, from visible light, to ultraviolet, to X-rays, to microwaves, to alpha particles, to neutrons, and even to flying pigeons. These different radiations do different things when they hit you, particularly the pigeons. While "ionizing radiations" such as X-rays, ultraviolet, alpha particles, and neutrons usually have enough localized energy to do chemical damage to the molecules they hit, "non-ionizing radiation" such as microwaves and pigeons do not damage molecules. When you and your organic friend worry about toxic changes in food or precancerous changes in your tissue, what really worry you are molecular changes. Microwaves and pigeons don't cause those sorts of changes. Microwaves effectively heat food or tissue thermally, while pigeons bruise food or tissue on impact.
Wearing a lead apron while working around ionizing radiation makes sense, although a simple layer of fabric or sunscreen is enough to protect you from most ultraviolet. To protect yourself against pigeons, wear a helmet. And to protect yourself against microwaves, use metal. The cooking chamber of the microwave oven is a metal box (including the screened front window). So little microwave "radiation" escapes from this metal box that it's usually hard to detect, let alone cause a safety problem. There just isn't much microwave intensity coming from the oven and intensity matters. A little microwaves do nothing at all to you; in fact you emit them yourself!
If you want to detect some serious microwaves, put that microwave detector near your cellphone! The cellphone's job is to emit microwaves, right next to your ear! Before you give up on microwave ovens, you should probably give up on cellphones. That said, I think the worst danger about cellphones is driving into a pedestrian or a tree while you're under the influence of the conversation. Basically, non-ionizing radiation such as microwaves is only dangerous if it cooks you. At the intensities emitted by a cellphone next to your ear, it's possible that some minor cooking is taking place. However, the cancer risk is almost certainly nil.
Despite all this physics reality, salespeople and con artists are still more than happy to sell you protection against the dangers of modern life. I chuckle at the shields people sell to install on your cellphones to reduce their emissions of harmful radiation. The whole point of the cellphone is to emit microwave signals to the receiving tower, so if you shield it you spoil its operation! It would be like wrapping an X-ray machine in a lead box to protect the patient. Sure, the patient would be safe but the X-ray machine would barely work any more.
Returning to the microwave cooking issue, once the food comes out of the microwave oven, there are no lingering effects of its having been cooked with microwaves. There is no convincing evidence of any chemical changes in the food and certain no residual cooking microwaves around in the food. If you're worried about toxic changes to your food, avoid broiling or grilling. Those high-surface-temperature cooking techniques definitely do chemical damage to the food, making it both tasty and potentially a tiny bit toxic. One of the reasons why food cooked in the microwave oven is so bland is because those chemical changes don't happen. As a result, microwave ovens are better for reheating than for cooking.
No, you cannot store charged gases in any simple container. If you try to store a mixture of positively and negatively charge gas particles in a single container, those opposite charges will attract and neutralize one another. And if you try to store only one type of charge in a container, those like charges will repel and push one another to the walls of the container. If the container itself conducts electricity, the charges will escape to the outside of the container and from there into the outside world. And if the container is insulating, the charges will stick to its inside surface and you'll have trouble getting them to leave. Moreover, you'll have trouble putting large numbers of those like-charged gas particles into the container in the first place because the ones that enter first will repel any like charges that follow.
I like to view problems like this one in terms of momentum: when it reaches the pavement, a falling egg has a large amount of downward momentum and it must get rid of that downward momentum gracefully enough that it doesn't break. The whole issue in protecting the egg is in extracting that momentum gracefully.
Momentum is a conserved physical quantity, meaning that it cannot be created or destroyed. It can only be passed from one object to the other. When you let go of the packaged egg and it begins to fall, the downward momentum that gravity transfers into the egg begins to accumulate in the egg. Before you let go, your hand was removing the egg's downward momentum as fast as gravity was adding it, but now the egg is on its own!
Because momentum is equal to an object's mass times its velocity, the accumulating downward momentum in the egg is reflected in its increasing downward speed. With each passing second, the egg receives another dose of downward momentum from the earth. By the time the egg reaches the pavement, it's moving downward fast and has a substantial amount of downward momentum to get rid of. Incidentally, the earth, which has given up this downward momentum, experiences an opposite response—it has acquired an equal amount of upward momentum. However, the earth has such a huge mass that there is no noticeable increase in its upward speed.
To stop, the egg must transfer all of its downward momentum into something else, such as the earth. It can transfer its momentum into the earth by exerting a force on the ground for a certain amount of time. A transfer of momentum, known as an impulse, is the product of a force times a time. To get rid of its momentum, the egg can exert a large force on the ground for a short time or a small force for a long time, or anything in between. If you let it hit the pavement unprotected, the egg will employ a large force for a short time and that will be bad for the egg. After all, the pavement will push back on the egg with an equally strong but oppositely directed force and punch a hole in the egg.
To make the transfer of momentum graceful enough to leave the egg intact, the protective package must prolong the momentum transfer. The longer it takes for the egg to get rid of its downward momentum, the smaller the forces between the egg and the slowing materials. That's why landing on a soft surface is a good start: it prolongs the momentum transfer and thereby reduces the peak force on the egg.
But there is also the issue of distributing the slowing forces uniformly on the egg. Even a small force can break the egg if it's exerted only on one tiny spot of the egg. So spreading out the force is important. Probably the best way of distributing the slowing force would be to float the egg in the middle of a fluid that has the same average density as the egg. But various foamy or springy materials will distribute the forces nearly as well.
In summary, (1) you want to bring the egg to a stop over as long as period of time as possible so as to prolong the transfer of momentum and reduce the slowing forces and (2) you want to involve the whole bottom surface of the egg in this transfer of momentum so that the slowing forces are exerted uniformly on the egg's bottom surface. As for the actual impact force on the egg, you can determine this by dividing the egg's momentum just before impact (its downward speed times its mass) by the time over which the egg gets rid of its momentum.
I'm beginning to think that movies and television do a huge disservice to modern society by blurring the distinction between science and fiction. So much of what appears on the big and little screen is just fantasy.
The walls of your home are simply hard to look through. They block visible, infrared, and ultraviolet light nearly perfectly and that doesn't leave snoopers many good options. A person sitting outside your home with a thermal camera—a device that "sees" the infrared light associated with body-temperature objects—or a digital camera is going to have a nice view of your wall, not you inside. There are materials that, while opaque to visible light, are relatively transparent to infrared light, such as some plastics and fabrics. However, typical wall materials are too thick and too opaque for infrared light to penetrate. Sure, someone can put a camera inside your home and access it via an optical fiber or radio waves, but at that point, they might as well just peer through your window.
The only electromagnetic waves that penetrate walls well are radio waves, microwaves, and X rays. If someone builds an X ray machine around your home, they'll be able to see you, or at least your bones. Don't forget to wave. And, in principle, they could use the radar technique to look for you with microwaves, but you'd be a fuzzy blob at best and lost in the jumble of reflections from everything else in your home.
As for using a laser to monitor your conversations from afar, that's a real possibility. Surfaces vibrate in the presence of sound and it is possible to observe those vibrations via reflected light. But the technical work involved is substantial and it's probably easier to just put a bug inside the house or on its surface.
Since I first posted this answer, several people have pointed out to me that terahertz radiation also penetrates through some solid surfaces and could be used to see through the walls of homes. In fact, the whole low-frequency end of the electromagnetic spectrum (radio, microwaves, terahertz waves) can penetrate through electrically insulating materials in order to "observe" conducting materials inside a home and the whole high-frequency end of that spectrum (X-rays and gamma rays) can penetrate through simple atoms (low atomic number) in order to "observe" complex atoms inside a home. Still, these approaches to seeing through walls require the viewers to send electromagnetic waves through the house and those waves can be detected by the people inside. They're also not trivial to implement. I suppose that people could use ambient electromagnetic waves to see what's happening in a house, but that's not easy, either. Where there's a will, there's a way: stealth aircraft have been detected by way of the dark spot they produce in the ambient radio spectrum and the insides of the pyramids have been studied by looking at cosmic rays passing through them. Nonetheless, I don't think that many of us need worry about being studied through the walls of our homes.
While it may seem as though there is some grand conspiracy among physicists to deny validation to those inventors, nothing could be farther from the truth. Physicists generally maintain a healthy skepticism about whatever they hear and are much less susceptible to dogmatic conservativism than one might think. However, physicists think long and deep about the laws that govern the universe, especially about their simplicity and self-consistency. In particular, they learn how even the slightest disagreement between a particular law and the observed behavior of the universe indicates either a problem with that law (typically an oversimplification, but occasionally a complete misunderstanding) or a failure in the observation. The law of energy conservation is a case in point: if it actually failed to work perfect even one time, it would cease to be a meaningful law. The implications for our understanding of the universe would be enormous. Physicists have looked for over a century for a failure of energy conservation and have never found one; not a single one. (Note: relativistic energy conservation involves mass as well as energy, but that doesn't change the present story.)
The laws of both energy conservation and thermodynamics are essentially mathematical laws—they depend relatively little on the specific details of our universe. Just about the only specific detail that's important is time-translation symmetry: as far as we can tell, physics doesn't change with time—physics today is the same as it was yesterday and as it will be tomorrow. That observation leads, amazingly enough, to energy conservation: energy cannot be created or destroy; it can only change forms or be transferred between objects. Together with statistical principals, we can derive thermodynamics without any further reference to the universe itself. And having developed energy conservation and the laws of thermodynamics, the game is over for free-energy motors and generators. They just can't work. It's not a matter of looking for one special arrangement that works among millions that don't. There are exactly zero arrangements that work.
It's not a matter of my bias, unless you consider my belief that 2 plus 2 equals 4 to be some sort of bias. You can look all you like for a 2 that when added to another 2 gives you a 5, but I don't expect you to succeed.
About once every month or two, someone contacts me with a new motor that turns for free or a generator that creates power out of nowhere. The pattern always repeats: I send them the sad news that their invention will not work and they respond angrily that I am not listening, that I am biased, and that I am part of the conspiracy. Oh well. There isn't much else I can do. I suppose I could examine each proposal individually at length to find the flaw, but I just don't have the time. I'm a volunteer here and this is time away from my family.
Instead, I suggest that any inventor who believes he or she has a free-energy device build that device and demonstrate it openly for the physics community. Take it to an American Physical Society conference and present it there. Let everyone in the audience examine it closely. Since anyone can join the APS and any APS member can talk at any major APS conference, there is plenty of opportunity. If someone succeeds in convincing the physics community that they have a true free-energy machine, more power to them (no pun intended). But given the absence of any observed failure of time-translation symmetry, and therefore the steadfast endurance of energy conservation laws, I don't expect any successful devices.
You're both right about temperature being associated with kinetic energy in molecules: the more kinetic energy each molecule has, the hotter the substance (e.g. a person) is. But not all kinetic energy "counts" in establishing temperature. Only the disordered kinetic energy, the tiny chucks of kinetic energy that belong to individual particles in a material contributes to that material's temperature. Ordered kinetic energy, such as the energy in a whole person who's running, is not involved in temperature. Whether an ice cube is sitting still on a table or flying through the air makes no difference to its temperature. It's still quite cold.
Friction's role with respect to temperature is in raising that temperature. Friction is a great disorderer. If a person running down the track falls and skids along the ground, friction will turn that person's ordered kinetic energy into disordered kinetic energy and the person will get slightly hotter. No energy was created or destroyed in the fall and skid, but lots of formerly orderly kinetic energy became disordered kinetic energy—what I often call "thermal kinetic energy."
The overall story is naturally a bit more complicated, but the basic idea here is correct. Once energy is in the form of thermal kinetic energy, it's stuck... like a glass vase that has been dropped and shattered into countless pieces, thermal kinetic energy can't be entirely reconstituted into orderly kinetic energy. Once energy has been distributed to all the individual molecules and atoms, getting them all to return their chunks of thermal kinetic energy is hopeless. Friction, even at the molecular level, isn't important at this point because the energy has already been fragmented and the most that any type of friction can do is pass that fragmented energy about between particles. So friction creates thermal kinetic energy (out of ordered energies of various types)... in effect, it makes things hot. It doesn't keep them hot; they do that all by themselves.
As the snow settles and becomes denser, it may feel "heavier", but its total weight doesn't change much. The same water molecules are simply packing themselves into a smaller space. So while each shovel-full of the dense stuff really does weigh more than a shovel-full of the light stuff, the total number of water molecules present on your deck and their associated weight is still the same.
In actually, some of the water molecules have almost certainly left via a form of solid-to-gas evaporation known technically as "sublimation." You have seen this conversion of ice into gas when you have noticed that old ice cubes in your freezer are smaller than they used to be or when you see that the snow outside during a cold spell seems to vanish gradually without ever melting. Sublimation is also the cause of "freezer burn" for frozen foods left without proper wrapping.
Not surprisingly, no "free electricity" machines are ever released to real scientists for testing. That's because the results of such testing are certain: those machines simply can't work for very fundamental and incontrovertible reasons.
Like so many "scientific" conmen, the purveyors of this particular scam claim to be victims of a hostile scientific establishment, which refuses to accept their brilliant discoveries. They typically attack the deepest and most central tenets of science and claim that a conspiracy is perpetuating belief on those tenets. Their refusal to submit their work to scientific peer review is supposedly based on a fear that such review will be biased and subjective, controlled by the conspiracy.
The sad reality is that the "scientific establishment" is more than willing to examine the claims, but those claims won't survive the process of inspection. In some cases, the authors of the claims are truly self-deluded and are guilty only of pride and ignorance. But in other cases, the authors are real conmen who are out to make a buck at public expense. They should be run out of town on a rail. >
What a remarkable story! As much as I like to think I can predict what should happen in many cases, there is just nothing like a good experiment to bring some reality to the situation. Your microwave evidently sent a significant fraction of its 900 watts of microwave radiation through that crack between cooking chamber and door and roasted your finger instantly. This is a good cautionary tale for those who are careless or curious with potentially dangerous household gadgets. While I continue to think that serious injuries are unlikely even in a leaky microwave oven, you have shown that there are cases of real danger. Fortunately, you had time to snap you finger away. It's like Class 3 lasers, which are now common in the form of laser pointers and supermarket checkout systems: they can damage your vision if you stare into them, but your blink reflex is fast enough to keep you from suffering injury. Thanks for the anecdote and I'm glad your finger recovered.
I suspect that the air inside the car is vibrating the way it does inside an organ pipe or in a soda bottle when you blow carefully across the bottle's lip. This resonant effect is common in cars when one rear passenger window is opened slightly. In that case, air blowing across the opening in the window is easily deflected into or out of the opening and drives the air in the passenger compartment into vigorous vibration. In short, the car is acting like a giant whistle and because of its enormous size, its pitch is too low for you to hear. Instead, you feel the vibration as a sickening pulsation in the air pressure.
For the one-open-window problem, the solution is simple: open another window. That shifts the resonant frequency of the car's air and also helps to dampen the vibrations. Alternatively, you can close the opened window. In your case, the resonance appears to involve a less visible opening into the car, perhaps near the rear bumper. If you can close that leak, you may be able to stop the airflow from driving the air in the car into resonance. If you are unable to find the leak, your best bet is to do exactly what you've done: open another window.
Assuming that the wearer doesn't let the helmet move and that the object that hits the helmet is rigid, my answer is approximately yes. If a 20-pound rigid object hits the hat from a height of 2 feet, that object will transfer just over 40 foot-pounds of energy to the helmet in the process of coming to a complete stop. The "just over" has to do with the object's continued downward motion as it dents the hat and the resulting release of additional gravitational potential energy. Also, the need for a rigid dropped object lies in a softer object's ability to absorb part of the impact energy itself; a dropped 20-pound sack of flour will cause less damage than a dropped 20-pound anvil.
However, the true meaning of the "40 foot-pound" specification is that the safety helmet is capable of absorbing 40 foot-pounds of energy during an impact on its crown. This energy is transferred to the helmet by doing work on it: by pushing its crown downward as the crown dents downward. The product of the downward force on the crown times the distance the crown moves downward gives the total work done on the helmet and this product must not exceed 40 foot-pounds or the helmet may fail to protect the wearer. Since the denting force typically changes as the helmet dents, this varying force must be accounted for in calculating the total work done on the helmet. While I'm not particularly familiar with safety helmets, I know that bicycle helmets don't promise to be useable after absorbing their rated energies. Bicycle helmets contain energy-absorbing foam that crushes permanently during severe impacts so that they can't be used again. Some safety helmets may behave similarly.
Finally, an object dropped from a certain height acquires an energy of motion (kinetic energy) equal to its weight times the height from which it was dropped. As long as that dropped object isn't too heavy and the helmet it hits dents without moving overall, the object's entire kinetic energy will be transferred to the helmet. That means that a 20-pound object dropped from 2 feet on the helmet will deposit 40 found-pounds of energy in the helmet. But if the wearer lets the helmet move downward overall, some of the falling object's energy will go into the wearer rather than the helmet and the helmet will tolerate the impact easily. On the other hand, if the dropped object is too heavy, the extra gravitational potential energy released as it dents the helmet downward will increase the energy transferred to the helmet. Thus a 4000-pound object dropped just 1/100th of a foot will transfer much more than 40 foot-pounds of energy to the helmet.
Stirring the coffee involves a transfer of energy from you to the coffee. That's because you are doing physical work on the coffee by pushing it around as it moves in the direction of your push. What began as chemical energy in your body becomes thermal energy in the coffee. That said, the amount of thermal energy you can transfer to the coffee with any reasonable amount of stirring is pretty small and you'd lose patience with the process long before you achieved any noticeable rise in coffee temperature. I think that the effect you notice is more one of mixing than of heating. Until you mix the milk into the coffee, you may have hot and cold spots in your cup and you may notice the cold spots most strongly.
Stealth aircraft are designed to absorb most of the microwave radiation that hits them and to reflect whatever they don't absorb away from the microwave source. That way, any radar system that tries to see the aircraft by way of its microwave reflection is unlikely to detect anything returning from the aircraft. In effect, the stealth aircraft is "black" to microwaves and to the extent that it has any glossiness to its surfaces, those surfaces are tipped at angles that don't let radar units see that glossiness. Since most radar units emit bright bursts of microwaves and look for reflections, stealth aircraft are hard to detect with conventional radar. Just as you can't see a black bat against the night sky by shining a flashlight at it, you can't see a stealth aircraft against the night sky by shining microwaves at it.
Like any black object, the stealth aircraft will heat up when exposed to intense electromagnetic waves. But trying to cook a stealth aircraft with microwaves isn't worth the trouble. If someone can figure out where it is enough to focus intense microwaves on it, they can surely find something better with which to damage it.
As for detecting the stealth aircraft with the help of cell phones, that brings up the issue of what is invisibility. Like a black bat against the night sky, it's hard to see a stealth aircraft simply by shining microwaves at it. Those microwaves don't come back to you so you see no difference between the dark sky and the dark plane. But if you put the stealth aircraft against the equivalent of a white background, it will become painfully easy to see. Cell phones provide the microwave equivalent of a white background. If you look for microwave emission near the ground from high in the sky, you'll see microwaves coming at you from every cell phone and telephone tower. If you now fly a microwave absorbing aircraft across that microwave-rich background, you'll see the dark image as it blocks out all these microwave sources. Whether or not this effect was used in the Balkans, I can't say. But it does point out that invisibility is never perfect and that excellent camouflage in one situation may be terrible in another.
As I discussed previously, the sky is blue because tiny particles in the atmosphere (dust, clumps of air molecules, microscopic water droplets) are better at deflecting shorter wavelength blue light than they are at deflecting longer wavelength red light. As sunlight passes through the atmosphere, enough blue light is deflected (or more technically Rayleigh scattered) by these particles to give the atmosphere an overall blue glow. The sun itself is slightly reddened by this process because a fraction of its blue light is deflected away before it reaches our eyes.
But at sunrise and sunset, sunlight enters our atmosphere at a shallow angle and travels a long distance before reaching our eyes. During this long passage, most of the blue light is deflected away and virtually all that we see coming to us from the sun is its red and orange wavelengths. The missing blue light illuminates the skies far to our east during sunrise and to our west during sunset. When the loss of blue light is extreme enough, as it is after a volcanic eruption, so little blue light may reach your location at times that even the sky itself appears deep red. The particles in air aren't good at deflecting red wavelengths, but if that's all the light there is they will give the sky a dim, red glow.
A bicycle is my favorite example of a dynamically stable object. Although the bicycle is unstable at rest (statically unstable), it is wonderfully stable when moving forward (dynamically stable). To understand this distinction, let's start with the bicycle motionless and then start moving forward.
At rest, the bicycle is unstable because it has no base of support. A base of support is the polygon formed by an object's contact points with the ground. For example, a table has a square or rectangular base of support defined by its four legs as they touch the floor. As long as an object's center of gravity (the effective location of its weight) is above this base of support, the object is statically stable. That stability has to do with the object's increasing potential (stored) energy as it tips-tipping a statically stable object raises its center of gravity and gravitational potential energy, so that it naturally accelerates back toward its upright position. Since a bicycle has only two contact points with the ground, the base of support is a line segment and the bicycle can't have static stability.
But when the bicycle is heading forward, it automatically steers its wheels underneath its center of gravity. Just as you can balance a broom on you hand if you keep moving your hand under the broom's center of gravity, a bicycle can balance if it keeps moving its wheels under its center of gravity. This automatic steering has to do with two effects: gyroscopic precession and bending of the bicycle about its steering axis.
In the gyroscopic precession steering, the spinning wheel behaves as a gyroscope. It has angular momentum, a conserved quantity of motion associated with spinning, and this angular momentum points toward the left (a convention that you can understand by pointing the curved fingers of your right hand around in the direction of the tire's motion; your thumb will then point to the left). When the bicycle begins to lean to one side, for example to the left, the ground begins to twist the front wheel. Since the ground pushes upward on the bottom of that wheel, it tends to twist the wheel counter-clockwise according to the rider. This twist or torque points toward the rear of the bicycle (again, when the fingers of your right hand arc around counterclockwise, your thumb will point toward the rear). When a rearward torque is exerted on an object with a leftward angular momentum, that angular momentum drifts toward the left-rear. In this case, the bicycle wheel steers toward the left. While I know that this argument is difficult to follow, since angular effects like precession challenge even first-year physics graduate students, but the basic result is simple: the forward moving bicycle steers in the direction that it leans and naturally drives under its own center of gravity. You can see this effect by rolling a coin forward on a hard surface: it will automatically balance itself by driving under its center of gravity.
In the bending effect, the leaning bicycle flexes about its steering axis. If you tip a stationary bicycle to the left, you see this effect: the bicycle will steer toward the left. That steering is the result of the bicycle's natural tendency to lower its gravitational potential energy by any means possible. Bending is one such means. Again, the bicycle steers so as to drive under its own center of gravity.
These two automatic steering effects work together to make a forward moving bicycle surprisingly stable. Children's bicycles are designed to be especially stable in motion (for obvious reasons) and one consequence is that children quickly discover that they can ride without hands. Adult bicycles are made less stable because excessive stability makes it hard to steer the bicycle.
The "ink dots on a balloon" idea provides the answer to your question. In that simple analogy, the ink dots represent stars and galaxies and the balloon's surface represents the universe. Inflating the balloon is then equivalent to having the universe expand. As the balloon inflates, the stars and galaxies drift apart so that an ant walking on the surface of the balloon would have to travel farther to go from one "star" to another. A similar situation exists in our real universe: everything is drifting farther apart.
The ant lives on the surface of the balloon, a two-dimensional world. The ant is unaware of the third dimension that you and I can see when we look at the balloon. The only directions that the ant can move in are along the balloon's surface. The ant can't point toward the center of the balloon because that's not along the surface that the ant perceives. To the ant, the balloon has no center. It lives in a continuous, homogeneous world, which has the weird property that if you walk far enough in any direction, you return to where you started.
Similarly, we see our universe as a three-dimensional world. If there are spatial dimensions beyond three, we are unaware of them. The only directions that we can move in are along the three dimensions of the universe that we perceive. The overall structure of the universe is still not fully understood, but let's suppose that the universe is a simple closed structure like the surface of a higher-dimensional balloon. In that case, we wouldn't be able to point to a center either because that center would exist in a dimension that we don't perceive. To us, the universe would be a continuous, homogeneous structure with that same weird property: if you traveled far enough in one direction, you'd return to where you started.
While "centrifugal force" is something we all seem to experience, it truly is a fictitious force. By a fictitious force, I mean that it is a side effect of acceleration and not a cause of acceleration.
There is no true outward force acting on an object that's revolving around a center. Instead, that object's own inertia is trying to make it travel in a straight-line path that would cause it to drift farther and farther away from the center. The one true force acting on the revolving object is an inward one-a centripetal force. The object is trying to go straight and the centripetal force is pulling it inward and bending the object's path into a circle.
To get a feel for the experiences associated with this sort of motion, let's first imagine that you are the revolving object and that you're swinging around in a circle at the end of a rope. In that case, your inertia is trying to send you in a straight-line path and the rope is pulling you inward and deflecting your motion so that you go in a circle. If you are holding the rope with your hands, you'll feel the tension in the rope as the rope pulls on you. (Note that, in accordance with Newton's third law of motion, you pull back on the rope just as hard as it pulls on you.) The rope's force makes you accelerate inward and you feel all the mass in your body resisting this inward acceleration. As the rope's force is conveyed throughout your body via your muscles and bones, you feel your body resisting this inward acceleration. There's no actual outward force on you; it's just your inertia fighting the inward acceleration. You'd feel the same experience if you were being yanked forward by a rope-there would be no real backward force acting on you yet you'd feel your inertia fighting the forward acceleration.
Now let's imagine that you are exerting the inward force on an object and that that object is a heavy bucket of water that's swinging around in a circle. The water's inertia is trying to make it travel in a straight line and you're pulling inward on it to bend its path into a circle. The force you exert on the bucket is quite real and it causes the bucket to accelerate inward, rather than traveling straight ahead. Since you're exerting an inward force on the bucket, the bucket must exert an inward force on you (Newton's third law again). It pulls outward on your arm. But there isn't anything pulling outward on the bucket, no mysterious "centrifugal force." Instead, the bucket accelerates in response to an unbalance force on it: you pull it inward and nothing pulls it outward, so it accelerates inward. In the process, the bucket exerts only one force on its surroundings: an outward force on your arm.
As for the operation of a centrifuge, it works by swinging its contents around in a circle and using their inertias to make them separate. The various items in the centrifuge have different densities and other characteristics that affect their paths as they revolve around the center of the centrifuge. Inertia tends to make each item go straight while the centrifuge makes them bend inward. The forces causing this inward bending have to be conveyed from the centrifuge through its contents and there's a tendency for the denser items in the centrifuge to travel straighter than the less dense items. As a result, the denser items are found near the outside of the circular path while the less dense ones are found near the center of that path.
During the defrost cycle, the microwave oven periodically turns off its magnetron so that heat can diffuse through the food naturally, from hot spots to cold spots. These quiet periods allow frozen parts of the food to melt the same way an ice cube would melt if you threw it into hot water. While the magnetron is off, it isn't emitting any microwaves and the food is just sitting there spreading its thermal energy around.
A transformer's current regulation involves a beautiful natural feedback process. To begin with, a transformer consists of two coils of wire that share a common magnetic core. When an alternating current flows through the primary coil (the one bringing power to the transformer), that current produces an alternating magnetic field around both coils and this alternating magnetic field is accompanied by an alternating electric field (recall that changing magnetic fields produce electric fields). This electric field pushes forward on any current passing through the secondary coil (the one taking power out of the transformer) and pushes backward on the current passing through the primary coil. The net result is that power is drawn out of the primary coil current and put into the secondary coil current.
But you are wondering what controls the currents flowing in the two coils. The circuit it is connected to determines the current in the secondary coil. If that circuit is open, then no current will flow. If it is connected to a light bulb, then the light bulb will determine the current. What is remarkable about a transformer is that once the load on the secondary coil establishes the secondary current, the primary current is also determined.
Remember that the current flowing in the secondary coil is itself magnetic and because it is an alternating current, it is accompanied by its own electric field. The more current that is allowed to flow through the secondary coil, the stronger its electric field becomes. The secondary coil's electric field opposes the primary coil's electric field, in accordance with a famous rule of electromagnetism known as Lenz's law. The primary coil's electric field was pushing backward on current passing through the primary coil, so the secondary coil's electric field must be pushing forward on that current. Since the backward push is being partially negated, more current flows through the primary coil.
The current in the primary coil increases until the two electric fields, one from the primary current and one from the secondary current, work together so that they extract all of the primary current's electrostatic energy during its trip through the coil. This natural feedback process ensures that when more current is allowed to flow through the transformer's secondary coil, more current will flow through the primary coil to match.
As far as anyone has been able to determine so far, the wattage is so small that this microwave radiation doesn't affect us. Not all radiations are the same, and radio or microwave radiation is particularly nondestructive at low intensities. It can't do direct chemical damage and at low wattage can't cause significant RF (radio frequency) heating. At present, there is thus no plausible physical mechanism by which these phones can cause injury. I don't think that one will ever be found, so you're probably just fine.
Paper towels are made out of finely divided fibers of cellulose, the principal structural chemical in cotton, wood, and most other plants. Cotton is actually a polymer, which like any other plastic is a giant molecule consisting of many small molecules linked together in an enormous chain or treelike structure. The small molecules or "monomers" that make up cellulose are sugar molecules. We can't get any nutritional value out of cellulose because we don't have the enzymes necessary to split the sugars apart. Cows, on the other hand, have microorganisms in their stomachs that produce the necessary enzymes and allow the cows to digest cellulose.
Despite the fact that cellulose isn't as tasty as sugar, it does have one important thing in common with sugar: both chemicals cling tightly to water molecules. The presence of many hydroxyl groups (-OH) on the sugar and cellulose molecules allow them to form relatively strong bonds with water molecules (HOH). This clinginess makes normal sugar very soluble in water and makes water very soluble in cellulose fibers. When you dip your paper towel in water, the water molecules rush into the towel to bind to the cellulose fibers and the towel absorbs water.
Incidentally, this wonderful solubility of water in cellulose is also what causes shrinkage and wrinkling in cotton clothing when you launder it. The cotton draws in water so effectively that the cotton fibers swell considerably when wet and this swelling reshapes the garment. Hot drying chases the water out of the fibers quickly and the forces between water and cellulose molecules tend to compress the fibers as they dry. The clothes shrink and wrinkle in the process.
Sunlight consists not only of light across the entire visible spectrum, but of invisible infrared and ultraviolet lights as well. The latter is probably what is causing the color-changing effects you mention.
Ultraviolet light is high-energy light, meaning that whenever it is emitted or absorbed, the amount of energy involved in the process is relatively large. Although light travels through space as waves, it is emitted and absorbed as particles known as photons. The energy in a photon of ultraviolet light is larger than in a photon of visible light and that leads to interesting effects.
First, some molecules can't tolerate the energy in an ultraviolet photon. When these molecules absorb such an energetic photon, their electrons rearrange so dramatically that the entire molecule changes its structure forever. Among the organic molecules that are most vulnerable to these ultraviolet-light-induced chemical rearrangements are the molecules that are responsible for colors. The same electronic structural characteristics that make these organic molecules colorful also make them fragile and susceptible to ultraviolet damage. As a result, they tend to bleach white in the sun.
Second, some molecules can tolerate high-energy photons by reemitting part of the photon's energy as new light. Such molecules absorb ultraviolet or other high-energy photons and use that energy to emit blue, green, or even red photons. The leftover energy is converted into thermal energy. These fluorescent molecules are the basis for the "neon" colors that are so popular on swimwear, in colored markers, and on poster boards. When you expose something dyed with fluorescent molecules to sunlight, the dye molecules absorbs the invisible ultraviolet light and then emit brilliant visible light.
Whenever you accelerate, you experience a gravity-like sensation in the direction opposite that acceleration. Thus when you accelerate to the left, you feel as though gravity were pulling you not only downward, but also to the right. The rightward "pull" isn't a true force; it's just the result of your own inertia trying to prevent you from accelerating. The amount of that rightward "pull" depends on how quickly you accelerate to the left. If you accelerate to the left at 9.8 meters/second2, an acceleration equal in amount to what you would experience if you were falling freely in the earth's gravity, the rightward gravity-like sensation you feel is just as strong as the downward gravity sensation you would feel when you are standing still. You are experiencing a rightward "fictitious force" of 1 g. The g-force you experience whenever you accelerate is equal in amount to your acceleration divided by the acceleration due to gravity (9.8 meters/second2) and points in the direction opposite your acceleration. Often the true downward force of gravity is added to this figure, so that you start with 1 g in the downward direction when you're not accelerating and continue from there. If you are on a roller coaster that is accelerating you upward at 19.6 meters/second2, then your total experience is 3 g's in the downward direction (1 g from gravity itself and 2 g's from the upward acceleration). And if you are accelerating downward at 9.8 meters/second2, then your total experience is 0 g's (1 g downward for gravity and 1 g upward from the downward acceleration). In this last case, you feel weightless-the weightlessness of a freely falling object such as an astronaut, skydiver, or high jumper.
Note added: A reader pointed out that I never actually answered the question. He's right! So here is the answer: they use accelerometers. An accelerometer is essentially a test mass on a force sensor. When there is no acceleration, the test mass only needs to be supported against the pull of gravity (i.e., the test mass's weight), so the force sensor reports that it is pushing up on the test mass with a force equal to the test mass's weight. But once the accelerometer begins to accelerate, the test mass needs an additional force in order to accelerate with the accelerometer. The force sensor detects this additional force and reports it. If you carry an accelerometer with you on a roller coaster, it will report the force it exerts on the test mass at each moment during the trip. A recording device can thus follow the "g-forces" throughout the ride.
As far as how accelerometers work, modern ones are generally based on tiny mechanical systems known as MEMS (Micro-Electro-Mechanical Systems). Their test masses are associated with microscopic spring systems and the complete accelerometer sensor resides on a single chip.
Both processes allow dissolved gases to escape from the water so that they can't serve as seed bubbles for boiling. When you heat water and then let it cool, the gases that came out of solution as small bubbles on the walls of the container escape into the air and are not available when you reheat the water. When you let the water sit out overnight, those same dissolved gases have time to escape into the air and this also reduces the number and size of the gas bubbles that form when you finally heat the water. Without those dissolved gases and the bubbles they form during heating it's much harder for the steam bubbles to form when the water reaches boiling. The water can then superheat more easily.
A helium balloon experiences an upward force that is equal to the weight of the air it displaces (the buoyant force on the balloon) minus its own weight. At sea level, air weighs about 0.078 pounds per cubic foot, so the upward buoyant force on a cubic foot of helium is about 0.078 pounds. A cubic foot of helium weighs only about 0.011 pounds. The difference between the upward buoyant force on the cubic foot of helium and the weight of the helium is the amount of extra weight that the helium can lift, which is about 0.067 pounds per cubic foot. To lift a 100 pound person, you'll need about 1500 cubic feet of helium in your balloon.
Don't operate the oven open. You're just asking for trouble. The oven will emit between 500 and 1100 watts of microwaves, depending on its rating, and you don't need to be exposed to such intense microwaves. The chamber effect is important; without the sealed chamber, the microwaves pass through the food only about once before heading off into the kitchen and you. The food won't cook well and you'll be bathed in the glow from a kilowatt source of invisible "light."
Imagine standing in front of a 10-kilowatt light bulb (which emits about 1 kilowatt of visible light and the rest is other forms of heat) and then imagine that you can't see light at all and can only feel it when it is causing potential damage. Would you feel safe? Your video camera won't enjoy the microwave exposure, either.
If you want to videotape your experiments without having to view them through the metal mesh on the door, you can consider drilling a small hole in the side of the cooking chamber. If you keep the hole's diameter to a few millimeters, the microwaves will not leak out. Then put one of the tiny inexpensive video cameras that widely available a centimeter or so away from that hole. You should get a nice unobstructed view of the cooking process without risking life and limb.
The cooking chamber of a microwave oven has mesh-covered holes to permit air to enter and exit. The holes in the metal mesh are small enough that the microwaves themselves cannot pass through and are instead reflected back into the cooking chamber. However, those holes are large enough that air (or light in the case of the viewing window) can pass through easily. Sending air through the cooking chamber keeps the cooking chamber from turning into a conventional hot oven and it carries food smells out into the kitchen.
When you put fans in front of the vents, you are probably causing the air conditioner to pump roughly the same amount of heat out of the room air as it would at 75 °F without the fans. As a result, the fans probably aren't making the air conditioner work less and aren't saving much electricity. In fact, the fans themselves consume electricity and produce heat that the air conditioner must then remove, so in principle the fans are a waste of energy.
However, if the fans are directing the cold air in a way that makes you more comfortable without having to cool all the room air or if the fans are creating fast moving air that cools you via evaporation more effectively, then you may be experiencing a real savings of electricity.
To figure out which is the case, you'd have to log the time the air conditioner cycles on during a certain period while the fans were off and the thermostat set to 75 °F and then repeat that measurement during a similar period with the fans on and the thermostat set to 78 °F. If the fans significantly reduce the units runtime while leaving you just as comfortable, then you're saving power.
The bulb will operate perfectly well, regardless of which way you connected the lamp's two wires. Current will still flow in through one wire, pass through the bulb's filament, and return to the power company through the other wire. The only shortcoming of reversing the connections is that you will end up with the "hot" wire connected to the outside of the socket and bulb, rather than to the central pin of the socket and bulb. That's a slight safety issue: if you touch the hot wire with one hand and a copper pipe with the other, you'll get a shock. That's because a large voltage difference generally exists between the hot wire and the earth itself.
In contrast, there should be very little voltage difference between the other wire (known as "neutral") and the earth. In a properly wired lamp, the large spade on the electric plug (the neutral wire) should connect to the outside of the bulb socket. That way, when you accidentally touch the bulb's base as you screw it in or out, you'll only be connecting your hand to the neutral wire and won't receive a shock. If you miswire the lamp and have the hot wire connected to the outside of the socket, you can get a shock if you accidentally touch the bulb base at any time.
Superheated water doesn't always wait until triggered before undergoing sudden boiling. All that's needed to start an explosion is for something to introduce an initial "seed" bubble into the liquid. Sometimes the container already has everything necessary to form a seed bubble and it's just a matter of getting the water hot enough to start that process. Many seed bubbles begin as trapped air in tiny crevices. As the water gets hotter, the size of any trapped air pocket grows and eventually it may be able to break free as a real seed bubble. When water is sufficiently superheated, just a single seed bubble is enough to start an explosion and empty the container completely. In your case, the coffee flash boiled spontaneously after something inside it nucleated the first bubble.
This sort of accident happens fairly often and we rarely think much about it as we sponge up the spilled liquid inside the microwave oven. But had your friend been unlucky enough to stop heating the coffee a second or two before that POP, she might have been injured while taking the coffee out of the oven. The moral of this story is to avoid overcooking any liquid in the microwave oven. If you must drink your coffee boiling hot, pay attention to it as it heats up so that it doesn't cook too long and then let it sit for a minute after the oven turns off. If you don't like your coffee boiling hot, then don't heat it to boiling at all.
I'm afraid that there's no easy answer to this question. You can use a microwave oven to superheat water in any container that doesn't assist bubble formation. How a particular container behaves is hard for me to say without experimenting. I'd heat a small amount of water (1/2 cup or less) in the container and look at it through the oven's window to see if the water boils nicely, with lots of steam bubbles streaming upward from many different points on the inner surface of the container. The more easily water boils in the container, the less likely it is to superheat when you cook it too long. (If you try this experiment, leave the potentially superheated water in the closed microwave oven to cool!)
Glass containers are clearly the most likely to superheat water because their surfaces are essentially perfect. Glasses have the characteristics of frozen liquids and a glass surface is as smooth as... well, glass. When you overheat water in a clean glass measuring cup, your chances of superheating it at least mildly are surprisingly high. The spontaneous bubbling that occurs when you add sugar, coffee powder, or a teabag to microwave-heated water is the result of such mild superheating. Fortunately, severe superheating is much less common because defects, dirt, or other impurities usually help the water boil before it becomes truly dangerous. That's why most of us avoid serious injuries.
However, even non-transparent microwaveable containers often have glass surfaces. Ceramics are "glazed," which means that they are coated with glass for both sealing and decoration. Many heavy mixing bowls are glass or glass-ceramics. As you can see, it's hard to get away from trouble. I simply don't know how plastic microwaveable containers behave when heating water; they may be safe or they may be dangerous.
If you're looking for a way out of this hazard, here are my suggestions. First, learn to know how long a given amount of liquid must be heated in your microwave in order to reach boiling and don't cook it that long. If you really need to boil water, be very careful with it after microwaving or boil it on a stovetop instead. My microwave oven has a "beverage" setting that senses how hot the water is getting. If the water isn't hot enough when that setting finishes, I add another 30 seconds and then test again. I never cook the water longer than I need to. Cooking water too long on a stovetop means that some of it boils away, but doing the same in a microwave oven may mean that it becomes dangerously superheated. Your children can still "cook" soup in the microwave if they use the right amount of time. Children don't like boiling hot soup anyway, so if you figure out how long it takes to heat their soup to eating temperature and have them cook their soup only that long, they'll never encounter superheating. As for dad's coffee water, same advice. If dad wants his coffee boiling hot, then he should probably make it himself. Boiling water is a hazard for children even without superheating.
Second, handle liquids that have been heated in a microwave oven with respect. Don't remove a liquid the instant the oven stops and then hover over it with your face exposed. If the water was bubbling spasmodically or not at all despite heavy heating, it may be superheated and deserves particular respect. But even if you see no indications of superheating, it takes no real effort to be careful. If you cooked the water long enough for it to reach boiling temperature, let it rest for a minute per cup before removing it from the microwave. Never put your face or body over the container and keep the container at a safe distance when you add things to it for the first time: powdered coffee, sugar, a teabag, or a spoon.
Finally, it would be great if some entrepreneurs came up with ways to avoid superheating altogether. The makers of glass containers don't seem to recognize the dangers of superheating in microwave ovens, despite the mounting evidence for the problem. Absent any efforts on their parts to make the containers intrinsically safer, it would be nice to have some items to help the water boil: reusable or disposable inserts that you could leave in the water as it cooked or an edible powder that you could add to the water before cooking. Chemists have used boiling chips to prevent superheating for decades and making sanitary, nontoxic boiling sticks for microwaves shouldn't be difficult. Similarly, it should be easy to find edible particles that would help the water boil. Activated carbon is one possibility.
Last night's report wasn't meant to scare you away from using your microwave oven or keep you from heating water in it. It was intended to show you that there is a potential hazard that you can avoid if you're informed about it. Microwave ovens are wonderful devices and they prepare food safely and efficiently as long as you use them properly. "Using them properly" means not heating liquids too long in smooth-walled containers.
Water doesn't always boil when it is heated above its normal boiling temperature (100 °C or 212 °F). The only thing that is certain is that above that temperature, a steam bubble that forms inside the body of the liquid will be able to withstand the crushing effects of atmospheric pressure. If no bubbles form, then boiling will simply remain a possibility, not a reality. Something has to trigger the formation of steam bubbles, a process known as "nucleation." If there is no nucleation of steam bubbles, there will be no boiling and therefore no effective limit to how hot the water can become.
Nucleation usually occurs at hot spots during stovetop cooking or at defects in the surfaces of cooking vessels. Glass containers have few or no such defects. When you cook water in a smooth glass container, using a microwave oven, it is quite possible that there will be no nucleation on the walls of the container and the water will superheat. This situation becomes even worse if the top surface of the water is "sealed" by a thin layer of oil or fat so that evaporation can't occur, either. Superheated water is extremely dangerous and people have been severely injured by such water. All it takes is some trigger to create the first bubble-a fork or spoon opening up the inner surface of the water or striking the bottom of the container-and an explosion follows. I recently filmed such explosions in my own microwave (low-quality movie (749KB), medium-quality movie (5.5MB)), or high-quality movie (16.2MB)). As you'll hear in my flustered remarks after "Experiment 13," I was a bit shaken up by the ferocity of the explosion I had triggered, despite every expectation that it would occur. After that surprise, you'll notice that I became much more concerned about yanking my hand out of the oven before the fork reached the water. I recommend against trying this dangerous experiment, but if you must, be extremely careful and don't superheat more than a few ounces of water. You can easily get burned or worse. For a reader's story about a burn he received from superheated water in a microwave, touch here.
Here is a sequence of images from the movie of my experiment, taken 1/30th of a second apart:
The spoon will have essentially no effect at all on the food. Metal left in the microwave oven during cooking will only cause trouble if (a) it is very thin or (b) it has sharp edges or points. The microwaves push electric charges back and forth in metal, so if the metal is too thin, it will heat up like the filament of a light bulb and may cause a fire. And if the metal has sharp edges or points, charges may accumulate on those sharp spots and then leap into space as a spark. But because your spoon was thick and had rounded edges, the charges that flowed through it during cooking didn't have any bad effects on the spoon: no heating and no sparks.
As far as the food is concerned, the presence of the spoon redirected the microwaves somewhat, but probably without causing any noticeable changes in how the food cooked. There is certainly no residual radiation of any sort and the food is no more likely to cause cancer after being cooked with metal around than had there been no spoon with it. In general, leaving a spoon in a cup of coffee or bowl of oatmeal isn't going to cause any trouble at all. I do it all the time. In fact, having a metal spoon in the liquid may reduce the likelihood of superheating the liquid, a dangerous phenomenon that occurs frequently in microwave cooking. Superheated liquids boil violently when you disturb them and can cause serious injuries as a result.
No, you are right. In the long run, the number of CO2 molecules left in the bottle when you close it is all that matters. Those molecules will drift in and out of the liquid and gas phases until they reach equilibrium. At the equilibrium point, there will be enough molecules in the gas phase to pressurize the bottle and enough in the liquid phase to give the beverage a reasonable amount of bite.
By giving the sealed bottle a shake, your mother-in-law is simply speeding up the approach to equilibrium. She is helping the CO2 molecules leave the beverage and enter the gas phase. The bottle then pressurizes faster, but at the expense of dissolved molecules in the beverage itself. If there is any chance that you'll drink more before equilibrium has been reached, you do best not to shake the bottle. That way, the equilibration process will be delayed as much as possible and you may still be able to drink a few more of those CO2 molecules rather than breathing them.
Incidentally, shaking a new bottle of soda just before you open it also speeds up the equilibration process. For an open bottle, equilibrium is reached when essentially all the CO2 molecules have left and are in the gas phase (since the gas phase extends over the whole atmosphere). That's not what you want at all. Instead, you try not to shake the beverage so that it stays away from equilibrium (and flatness) as long as possible. For most opened beverages, equilibrium is not a tasty situation.
The simple answer to your question is yes, you can do it. But you'll encounter two significant problems with trying to turn your ordinary TV into a projection system. First, the lens you'll need to do the projection will be extremely large and expensive. Second, the image you'll see will be flipped horizontally and vertically. You'll have to hang upside-down from your porch railing, which will make drinking a beer rather difficult.
About the lens: in principle, all you need is one convex lens. A giant magnifying glass will do. But it has a couple of constraints. Because your television screen is pretty large, the lens diameter must also be pretty large. If it is significantly smaller than the TV screen, it won't project enough light onto your wall. And to control the size of the image it projects on the wall, you'll need to pick just the right focal length (curvature) of the lens. You'll be projecting a real image on the wall, a pattern of light that exactly matches the pattern of light appearing on the TV screen. The size and location of that real image depends on the lens's focal length and on its distance from the TV screen. You'll have to get these right or you'll see only a blur. Unfortunately, single lenses tend to have color problems and edge distortions. Projection lenses need to be multi-element carefully designed systems. Getting a good quality, large lens with the right focal length is going to cost you.
The other big problem is more humorous. Real images are flipped horizontally and vertically relative to the light source from which they originate. Unless you turn your TV set upside-down, your wall image will be inverted. And, without a mirror, you can't solve the left-right reversal problem. All the writing will appear backward. Projection television systems flip their screen image to start with so that the projected image has the right orientation. Unless you want to rewire your TV set, that's not going to happen for you. Good luck.
A submerged object's buoyancy (the upward force exerted on it by a fluid) is exactly equal to the weight of the fluid it displaces. In this case, the upward buoyant force on the bathysphere is equal in amount to the weight of the water it displaces. Since the bathysphere is essentially incompressible, it always displaces the same volume of water. And since water is essentially incompressible, that fixed volume of water always weighs the same amount. That's why the bathysphere experiences a constant upward force on it due to the surrounding water. To sink the bathysphere, they weight it down with heavy metal particles. And to allow the bathysphere to float back up, they release those particles and reduce the bathysphere's total weight.
The microwaves would flow out of the oven's cooking chamber like light streaming out of a brightly illuminated mirrored box. If you were nearby, some of those microwaves would pass through you and your body would absorb some of them during their passage. This absorption would heat your tissue so that you would feel the warmth. In parts of your body that have rapid blood circulation, that heat would be distributed quickly to the rest of your body and you probably wouldn't suffer any rapid injuries. But in parts of your body that don't have good blood flow, such as the corneas of your eyes, tissue could heat quickly enough to be permanently damaged. In any case, you'd probably feel the warmth and realize that something was wrong before you suffered any substantial permanent injuries.
When you lift the sack, you are pushing it upward (to support its weight) and it is moving upward. Since the force you exert on the sack and the distance it is traveling are in the same direction, you are doing work on the sack. As a result, the sack's energy is increasing, as evidenced by the fact that it is becoming more and more dangerous to a dog sitting beneath it.
But when you carry the sack horizontally at a steady pace, the upward force you exert on the sack and the horizontal distance it travels are at right angles to one another. You don't do any work on the sack in that case. The evidence here is that the sack doesn't become any more dangerous; its speed doesn't increase and neither does its altitude. It just shifts from one place to an equivalent one to its side.
I'm afraid that you're facing a difficult problem. Magnetic levitation involving permanent magnets is inherently and unavoidably unstable for fundamental reasons. One permanent magnet suspended above another permanent magnet will always crash. That's why all practical maglev trains use either electromagnets with feedback circuitry (magnets that can be changed electronically to correct for their tendencies to crash) or magnetoelectrodynamic levitation (induced magnetism in a conducting track, created by a very fast moving (>100 mph) magnetized train). There are no simple fixes if what you have built so far is based on permanent magnets alone. Unfortunately, you have chosen a very challenging science fair project.
The more pressure a basketball has inside it, the less its surface dents during a bounce and the more of its original energy it stores in the compressed air. Air stores and returns energy relatively efficiently during a rapid bounce, so the pressurized ball bounces high. But an underinflated ball dents deeply and its skin flexes inefficiently. Much of the ball's original energy is wasted in heating the bending skin and it doesn't bounce very high. In general, the higher the internal pressure in the ball, the better it will bounce.
However, the ball doesn't bounce all by itself when you drop it on a flexible surface. In that case, the surface also dents and is responsible for part of the ball's rebound. If that surface handles energy inefficiently, it may weaken the ball's bounce. For example, if you drop the ball on carpeting, the carpeting will do much of the denting, will receive much of the ball's original energy, and will waste its share as heat. The ball won't rebound well. My guess is that you dropped the ball on a reasonably hard surface, but one that began to dent significantly when the ball's pressure reached 12psi. At that point, the ball was extremely bouncy, but it was also so hard that it dented the surface and let the surface participate strongly in the bouncing. The surface probably wasn't as bouncy as the ball, so it threw the ball relatively weakly into the air.
I'd suggest repeating your experiment on the hardest, most massive surface you can find. A smooth cement or thick metal surface would be best. The ball will then do virtually all of the denting and will be responsible for virtually all of the rebounding. In that case, I'll bet that the 12psi ball will bounce highest.
Fluorescent paints and many laundry detergents contain fluorescent chemicals-chemicals that absorb ultraviolet light and use its energy to produce visible light. Fluorescent paints are designed to do exactly that, so they certainly contain enough "phosphor" for that purpose. Detergents have fluorescent dyes or "brighteners" added because it helps to make fabrics appear whiter. Aging fabric appears yellowish because it absorbs some blue light. To replace the missing blue light, the brighteners absorb invisible ultraviolet and use its energy to emit blue light.
If you can't alter the air's humidity, warm air will definitely heat up your window faster and defrost it faster than cold air. The only problem with using hot air is that rapid heating can cause stresses on the window and its frame because the temperature will rise somewhat unevenly and lead to uneven thermal expansion. Such thermal stress can actually break the window, as a reader informed me recently: "On one of the coldest days of this Boston winter, I turned up the heat full blast to defrost the windshield. The outside of the window was still covered with ice, which I figured would melt from the heat. After about 10 minutes of heating, the windshield "popped" and a fracture about 8 inches long developed. The windshield replacement company said I would have to wait a day for service, since this happened to so many people over the cold evening that they were completely booked." If you're nervous about breaking the windshield, use cooler air.
About the humidity caveat: if you can blow dry air across your windshield, that will defrost it faster than just about anything else, even if that air is cold. The water molecules on your windshield are constantly shifting back and forth between the solid phase (ice) and the gaseous phase (steam or water vapor). Heating the ice will help more water molecules leave the ice for the water vapor, but dropping the density of the water vapor will reduce the number of water molecules leaving the water vapor for the ice. Either way, the ice decreases and the water vapor increases. Since you car's air condition begins drying the air much soon after you start the car than its heater begins warming the air, many modern cars concentrate first on drying the air rather than on heating it.
Batteries are "pumps" for electric charge. A battery takes an electric current (moving charge) entering its negative terminal and pumps that current to its positive terminal. In the process, the battery adds energy to the current and raises its voltage (voltage is the measure of energy per unit of electric charge). A typical battery adds 1.5 volts to the current passing through it. As it pumps current, the battery consumes its store of chemical potential energy so that it eventually runs out and "dies."
If you send a current backward through a battery, the battery extracts energy from the current and lowers its voltage. As it takes energy from the current, the battery adds to its store of chemical potential energy so that it recharges. Battery charges do exactly that: they push current backward through the batteries to recharge them. This recharging only works well on batteries that are designed to be recharged since many common batteries undergo structural damage as their energy is consumed and this damage can't be undone during recharging.
When you use a chain of batteries to power an electric device, you must arrange them so that each one pumps charge the same direction. Otherwise, one will pump and add energy to the current while the other extracts energy from the current. If all the batteries are aligned positive terminal to negative terminal, then they all pump the same direction and the current experiences a 1.5 volt (typically) voltage rise in passing through each battery. After passing through 2 batteries, its voltage is up by 3 volts, after passing through 3 batteries, its voltage is up by 4.5 volts, and so on.
A parabolic dish microphone is essentially a mirror telescope for sound. A parabolic surface has the interesting property that all sound waves that propagate parallel its central axis travel the same distance to get to its focus. That means that when you aim the dish at a distant sound source, all of the sound from that object bounces off the dish and converges toward the focus in phase—with its pressure peaks and troughs synchronized so that they work together to make the loudest possible sound vibrations. The sound is thus enhanced at the focus, but only if it originated from the source you're aiming at. Sound from other sources misses the focus. If you put a sensitive microphone in the parabolic dish's focus, you'll hear the sound from the distant object loud and clear.
Not significantly. Air doesn't absorb them well, which is why the air in a microwave oven doesn't get hot and why satellite and cellular communication systems work so well. The molecules in air are poor antennas for this long-wavelength electromagnetic radiation. They mostly just ignore it.
Devices that sense your presence are either bouncing some wave off you or they are passively detecting waves that you emit or reflect. The wave-bouncing detectors emit high frequency (ultrasonic) sound waves or radio waves and then look for reflections. If they detect changes in the intensity or frequency pattern of the reflected waves, they know that something has moved nearby and open the door. The passive detectors look for changes in the infrared or visible light patterns reaching a detector and open the door when they detect such changes.
What a neat observation! Digital cameras based on CCD imaging chips are sensitive to infrared light. Even though you can't see the infrared light streaming out of the remote control when you push its buttons, the camera's chip can. This behavior is typical of semiconductor light sensors such as photodiodes and phototransistors: they often detect near infrared light even better than visible light. In fact, a semiconductor infrared sensor is exactly what your television set uses to collect instructions from the remote control.
The color filters that the camera employs to obtain color information misbehave when they're dealing with infrared light and so the camera is fooled into thinking that it's viewing white light. That's why your camera shows a white spot where the remote's infrared source is located.
I just tried taking some pictures through infrared filters, glass plates that block visible light completely, and my digital camera worked just fine. The images were as sharp and clear as usual, although the colors were odd. I had to use incandescent illumination because fluorescent light doesn't contain enough infrared. It would be easy to take pictures in complete darkness if you just illuminated a scene with bright infrared sources. No doubt there are "spy" cameras that do exactly that.
No, there is no sound in space. That's because sound has to travel as a vibration in some material such as air or water or even stone. Since space is essentially empty, it cannot carry sound, at least not the sorts of sound that we are used to.
Ice will melt fastest in whatever delivers heat to it fastest. In general that will be water because water conducts heat and carries heat better than air. But extremely hot air, such as that from a torch, will beat out very cold water, such as ice water, in melting the ice.
The laser you're using is a neodymium-YAG laser. It uses a crystal of YAG (yttrium aluminum garnet), a synthetic gem that was once sold as an imitation diamond, that has been treated with neodymium atoms to give it a purple color. When placed in a laser cavity and exposed to intense visible light, this crystal gives off the infrared light you describe. You can't see this light but, at up to 600 watts, it is actually incredibly bright. You don't want to look at it or even at its reflection from a surface that you're machining. That's because the lens of your eye focuses it onto your retina and even though your retina won't see any light, it will experience the heat. It's possible to injure your eyes by looking at this light, particularly if you catch a direct reflection of the laser beam in your eye.
In all likelihood, the manufacturer of this unit has shielded all the light so that none of it reaches your eyes. If that's not the case, you should wear laser safety glasses that block 1064 nm light. But it's also possible that the irritation you're experiencing is coming from the burned material that you are machining. Better ventilation should help. High voltage power supplies, which may be present in the laser, could also produce ozone. Ozone has a spicy fresh smell, like the smell after a lightning storm, and it is quite irritating to eyes and nose.
The answer is gravity. Gravity smashes the planets into spheres. To understand this, imagine trying to build a huge mountain on the earth's surface. As you begin to heap up the material for your mountain, the weight of the material at the top begins to crush the material at the bottom. Eventually the weight and pressure become so great that the material at the bottom squeezes out and you can't build any taller. Every time you put new stuff on top, the stuff below simply sinks downward and spreads out. You can't build bumps bigger than a few dozen miles high on earth because there aren't any materials that can tolerate the pressure. In fact, the earth's liquid core won't support mountains much higher than the Himalayas—taller mountains would just sink into the liquid. So even if a planet starts out non-spherical, the weight of its bumps will smash them downward until the planet is essentially spherical.
The flattened poles are the result of rotation—as the planet spins, the need for centripetal (centrally directed) acceleration at its equator causes its equatorial surface to shift outward slightly, away from the planet's axis of rotation. The planet is therefore wider at its equator than it is at its poles.
Yes, this sort of accident can and does happen. The water superheated and then boiled violently when disturbed. Here's how it works:
Water can always evaporate into dry air, but it normally only does so at its surface. When water molecules leave the surface faster than they return, the quantity of liquid water gradually diminishes. That's ordinary evaporation. However, when water is heated to its boiling temperature, it can begin to evaporate not only from its surface, but also from within. If a steam bubble forms inside the hot water, water molecules can evaporate into that steam bubble and make it grow larger and larger. The high temperature is necessary because the pressure inside the bubble depends on the temperature. At low temperature, the bubble pressure is too low and the surrounding atmospheric pressure smashes it. That's why boiling only occurs at or above water's boiling temperature. Since pressure is involved, boiling temperature depends on air pressure. At high altitude, boiling occurs at lower temperature than at sea level.
But pay attention to the phrase "If a steam bubble forms" in the previous paragraph. That's easier said than done. Forming the initial steam bubble into which water molecules can evaporate is a process known as "nucleation." It requires a good number of water molecules to spontaneously and simultaneously break apart from one another to form a gas. That's an extraordinarily rare event. Even in a cup of water many degrees above the boiling temperature, it might never happen. In reality, nucleation usually occurs at a defect in the cup or an impurity in the water—anything that can help those first few water molecules form the seed bubble. When you heat water on the stove, the hot spots at the bottom of the pot or defects in the pot bottom usually assist nucleation so that boiling occurs soon after the boiling temperature is reached. But when you heat pure water in a smooth cup using a microwave oven, there may be nothing present to help nucleation occur. The water can heat right past its boiling temperature without boiling. The water then superheats—its temperature rising above its boiling temperature. When you shake the cup or sprinkle something like sugar or salt into it, you initiate nucleation and the water then boils violently.
Fortunately, serious microwave superheating accidents are fairly unusual. However, they occur regularly and some of the worst victims require hospital treatment. I have heard of extreme cases in which people received serious eye injuries and third degree burns that required skin grafts and plastic surgery.
You can minimize the chance of this sort of problem by not overcooking water or any other liquid in the microwave oven, by waiting about 1 minute per cup for that liquid to cool before removing it from the microwave if there is any possibility that you have superheated it, and by being cautious when you first introduce utensils, powders, teabags, or otherwise disturb very hot liquid that has been cooked in a microwave oven. Keep the water away from your face and body until you're sure it's safe and don't ever hover over the top of the container. Finally, it's better to have the liquid boil violently while it's inside the microwave oven than when it's outside on your counter and can splatter all over you. Once you're pretty certain that the water is no longer superheated, you can ensure that it's safe by deliberately nucleating boiling before removing the cup from the microwave. Inserting a metal spoon or almost any food into the water should trigger boiling in superheated water. A pinch of sugar will do the trick, something I've often noticed when I heat tea in the microwave. However, don't mess around with large quantities of superheated water. If you have more than 1 cup of potentially superheated water, don't try to nucleate boiling until you've waited quite a while for it to cool down. I've been scalded by the stuff several times even when I was prepared for an explosion. It's really dangerous.
The relative stabilities of liquid and gaseous water depend on both temperature and pressure. To understand this, consider what is going on at the surface of a glass of water. Water molecules in the liquid water are leaving the water's surface to become gas above it and water molecules in the gas are landing and joining the liquid water below. It's like a busy airport, with lots of take-offs and landings. If the glass of water is sitting in an enclosed space, the arrangement will eventually reach equilibrium—the point at which there is no net transfer of molecules between the liquid in the glass and the gas above it. In that case, there will be enough water molecules in the gas to ensure that they land as often as they leave.
The leaving rate (the rate at which molecules break free from the liquid water) depends on the temperature. The hotter the water is, the more frequently water molecules will be able to break away from their buddies and float off into the gas. The landing rate (the rate at which molecules land on the water's surface and stick) depends on the density of molecules in the gas. The more dense the water vapor, the more frequently water molecules will bump into the liquid's surface and land.
As you raise the temperature of the water in your glass, the leaving rate increases and the equilibrium shifts toward higher vapor density and less liquid water. By the time you reach 100° Celsius, the equilibrium vapor pressure is atmospheric pressure, which is why water tends to boil at this temperature (it can form and sustain steam bubbles). Above this temperature the equilibrium vapor pressure exceeds atmospheric pressure. The liquid water and the gas above it can reach equilibrium, but only if you allow the pressure in your enclosed system to exceed atmospheric pressure. However, if you open up your enclosed system, the water vapor will spread out into the atmosphere as a whole and there will be a never-ending stream of gaseous water molecules leaving the glass. Above 100° C, liquid water can't exist in equilibrium with atmospheric pressure gas, even if that gas is pure water vapor.
So how can you superheat water? Don't wait for equilibrium! The road to equilibrium may be slow; it may take minutes or hours for the liquid water to evaporate away to nothing. In the meantime, the system will be out of equilibrium, but that's ok. It happens all the time: a snowman can't exist in equilibrium on a hot summer day, but that doesn't mean that you can't have a snowman at the beach... for a while. Superheated water isn't in equilibrium and, if you're patient, something will change. But in the short run, you can have strange arrangements like this without any problem.
While helium itself doesn't actually defy gravity, it is lighter than air and floats upward as descending air pushes it out of the way. Like a bubble in water, the helium goes up to make room for the air going down. The buoyant force that acts on the helium is equal to the weight of air that the helium displaces.
A cubic foot of air weighs about 0.078 pounds so the upward buoyant force on a cubic foot of helium is about 0.078 pounds. A cubic foot of helium weighs only about 0.011 pounds. The difference between the upward buoyant force on the cubic foot of helium and the weight of the helium is the amount of extra weight that the helium can lift; about 0.067 pounds. Since you weigh 85 pounds, it would take about 1300 cubic feet of helium to lift you and a thin balloon up into the air. That's a balloon about 13.5 feet in diameter.
Illumination matters because your skin only reflects light to which it's exposed. When you step into a room illuminated only by red light your skin appears red, not because it's truly red but because there is only red light to reflect.
Ordinary incandescent bulbs produce a thermal spectrum of light with a "color temperature" of about 2800° C. A thermal light spectrum is a broad, featureless mixture of colors that peaks at a particular wavelength that's determined only by the temperature of the object emitting it. Since the bulb's color temperature is much cooler than that of the sun's (5800° C), the bulb appears much redder than the sun and emits relatively little blue light. A fluorescent lamp, however, synthesizes its light spectrum from the emissions of various fluorescent phosphors. Its light spectrum is broad but structured and depends on the lamp's phosphor mixture. The four most important phosphor mixtures are cool white, deluxe cool white, warm white, and deluxe warm white. These mixtures all produce more blue than an incandescent bulb, but the warm white and particularly the deluxe warm white tone down the blue emission to give a richer, warmer glow at the expense of a little energy efficiency. Cool white fluorescents are closer to natural sunlight than either warm white fluorescents or incandescent bulbs.
To answer your question about shaves: without blue light in the illumination, it's not that easy to distinguish beard from skin. Since incandescent illumination is lacking in blue light, a shave looks good even when it isn't. But in bright fluorescent lighting, beard and skin appear sharply different and it's easy to see spots shaving has missed. As for makeup illumination, it's important to apply makeup in the light in which it will be worn. Blue-poor incandescent lighting downplays blue colors so it's easy to overapply them. When the lighting then shifts to blue-rich fluorescents, the blue makeup will look heavy handed. Some makeup mirrors provide both kinds of illumination so that these kinds of mistakes can be avoided.
After falling for a long time, an object will descend at a steady speed known as its "terminal velocity." This terminal velocity exists because an object moving through air experiences drag forces (air resistance). These drag forces become stronger with speed so that as a falling object picks up speed, the upward air resistance it experiences gradually becomes stronger. Eventually the object reaches a speed at which the upward drag forces exactly balance its downward weight and the object stops accelerating. It is then at "terminal velocity" and descends at a steady pace.
The terminal velocity of an object depends on the object's size, shape, and density. A fluffy object (a feather, a parachute, or a sheet of paper) has a small terminal velocity while a compact, large, heavy object (a cannonball, a rock, or a bowling ball) has a large terminal velocity. An aerodynamic object such as an arrow also has a very large terminal velocity. A person has a terminal velocity of about 200 mph when balled up and about 125 mph with arms and feet fully extended to catch the wind.
Popular in movies as a source of long glowing sparks, a Tesla coil is basically a high-frequency, very high-voltage transformer. Like most transformers, the Tesla coil has two circuits: a primary circuit and a secondary circuit. The primary circuit consists of a capacitor and an inductor, fashioned together to form a system known as a "tank circuit". A capacitor stores energy in its electric field while an inductor stores energy in its magnetic field. When the two are wired together in parallel, their combined energy sloshes back and forth from capacitor to inductor to capacitor at a rate that's determined by various characteristics of the two devices. Powering the primary of the Tesla coil is a charge delivery system that keeps energy sloshing back and forth in the tank circuit. This delivery system has both a source of moderately high voltage electric current and a pulsed transfer system to periodically move charge and energy to the tank. The delivery system may consist of a high voltage transformer and a spark gap, or it may use vacuum tubes or transistors.
The secondary circuit consists of little more than a huge coil of wire and some electrodes. This coil of wire is located around the same region of space occupied by the inductor of the primary circuit. As the magnetic field inside that inductor fluctuates up and down in strength, it induces current in the secondary coil. That's because a changing magnetic field produces an electric field and the electric field surrounding the inductor pushes charges around and around the secondary coil. By the time the charges in the secondary coil emerge from the coil, they have enormous amounts of energy; making them very high voltage charges. They accumulate in vast numbers on the electrodes of the secondary circuit and push one another off into the air as sparks.
While most circuits must form complete loops, the Tesla coil's secondary circuit doesn't. Its end electrodes just spit charges off into space and let those charges fend for themselves. Many of them eventually work their ways from one electrode to the other by flowing through the air or through objects. But even when they don't, there is little net build up of charge anywhere. That's because the direction of current flow through the secondary coil reverses frequently and the sign of the charge on each electrode reverses, too. The Tesla coil is a high-frequency device and its top electrode goes from positively charged to negatively charge to positively charged millions of times a second. This rapid reversal of charge, together with reversing electric and magnetic fields means that a Tesla coil radiates strong electromagnetic waves. It therefore interferes with nearby radio reception.
Finally, it has been pointed out to me by readers that a properly built Tesla coil is resonant—that the high-voltage coil has a natural resonance at the same frequency that it is being excited by the lower voltage circuit. The high-voltage coil's resonance is determined by its wire length, shape, and natural capacitance.
Yes. The paint is simply decoration on the metal walls. The cooking chamber of the microwave has metal walls so that the microwaves will reflect around inside the chamber. Thick metal surfaces are mirrors for microwaves and they work perfectly well with or without thin, non-conducting coatings of paint.
Just before burning their fuels, both engines compress air inside a sealed cylinder. This compression process adds energy to the air and causes its temperature to skyrocket. In a spark ignition engine, the air that's being compressed already contains fuel so this rising temperature is a potential problem. If the fuel and air ignite spontaneously, the engine will "knock" and won't operate at maximum efficiency. The fuel and air mixture is expected to wait until it's ignited at the proper instant by the spark plug. That's why gasoline is formulated to resist ignition below a certain temperature. The higher the "octane" of the gasoline, the higher its certified ignition temperature. Virtually all modern cars operate properly with regular gasoline. Nonetheless, people frequently put high-octane (high-test or premium) gasoline in their cars under the mistaken impression that their cars will be better for it. If your car doesn't knock significantly with regular gasoline, use regular gasoline.
A diesel engine doesn't have spark ignition. Instead, it uses the high temperature caused by extreme compression to ignite its fuel. It compresses pure air to high temperature and pressure, and then injects fuel into this air. Timed to arrive at the proper instant, the fuel bursts into flames and burns quickly in the superheated compressed air. In contrast to gasoline, diesel fuel is formulated to ignite easily as soon as it enters hot air.
An audio speaker generates sound by moving a surface back and forth through the air. Each time the surface moves toward you, it compresses the air in front of it and each time the surface moves away from you, it rarefies that air. By doing this repetitively, the speaker forms patterns of compressions and rarefactions in the air that propagate forward as sound.
The magnet is part of the system that makes the surface move. Attached to the surface itself is a cylindrical coil of wire and this coil fits into a cylindrical channel cut into the speaker's permanent magnet. That magnet is carefully designed so that its magnetic field lines radiate outward from the inside of the channel to the outside of the channel and thus pass through the cylindrical coil the way bicycle spokes pass through the rim of the wheel.
When an electric current is present in the wire, the moving electric charges circulate around this cylinder and cut across the magnetic field lines. But whenever a charge moves across a magnetic field line, it experiences a force known as the Lorenz force. In this case, the charges are pushed either into or out of the channel slot, depending on which way they are circulating around the coil. The charges drag the coil and surface with them, so that as current flows back and forth through the coil, the coil and surface pop in and out of the magnet channel. This motion produces sound.
It's a common misconception that the microwaves in a microwave oven excite a natural resonance in water. The frequency of a microwave oven is well below any natural resonance in an isolated water molecule, and in liquid water those resonances are so smeared out that they're barely noticeable anyway. It's kind of like playing a violin under water—the strings won't emit well-defined tones in water because the water impedes their vibrations. Similarly, water molecules don't emit (or absorb) well-defined tones in liquid water because their clinging neighbors impede their vibrations.
Instead of trying to interact through a natural resonance in water, a microwave oven just exposes the water molecules to the intense electromagnetic fields in strong, non-resonant microwaves. The frequency used in microwave ovens (2,450,000,000 cycles per second or 2.45 GHz) is a sensible but not unique choice. Waves of that frequency penetrate well into foods of reasonable size so that the heating is relatively uniform throughout the foods. Since leakage from these ovens makes the radio spectrum near 2.45 GHz unusable for communications, the frequency was chosen in part because it would not interfere with existing communication systems.
As for there being a laser in a microwave oven, there isn't. Lasers are not the answer to all problems and so the source for microwaves in a microwave oven is a magnetron. This high-powered vacuum tube emits a beam of coherent microwaves while a laser emits a beam of coherent light waves. While microwaves and light waves are both electromagnetic waves, they have quite different frequencies. A laser produces much higher frequency waves than the magnetron. And the techniques these devices use to create their electromagnetic waves are entirely different. Both are wonderful inventions, but they work in very different ways.
The fact that this misleading information appears in a science book, presumably used in schools, is a bit discouraging. It just goes to show you that you shouldn't believe everything read in books or on the web (even this web site, because I make mistakes, too).
Your son has magnetized the shadow mask that's located just inside the screen of your color television. It's a common problem and one that can easily be fixed by "degaussing" the mask (It'll take years or longer to fade on its own, so you're going to have to actively demagnetize the mask). You can have it done professionally or you can buy a degaussing coil yourself and give it a try (Try a local electronics store or contact MCM Electronics, (800) 543-4330, 6" coil is item #72-785 for $19.95 and 12" coil is item #72-790 for $32.95).
Color sets create the impression of full color by mixing the three primary colors of light—blue, green, and red—right there on the inside surface of the picture tube. A set does the mixing by turning on and off three separate electron beams to control the relative brightnesses of the three primary colors at each location on the screen. The shadow mask is a metal grillwork that allows the three electrons beams to hit only specific phosphor dots on the inside of the tube's front surface. That way, electrons in the "blue" electron beam can only hit blue-glowing phosphors, while those in the "green" beam hit green-glowing phosphors and those in the "red" beam hit red-glowing phosphors. The three beams originate at slightly different locations in the back of the picture tube and reach the screen at slightly different angles. After passing through the holes in the shadow mask, these three beams can only hit the phosphors of their color.
Since the shadow mask's grillwork and the phosphor dots must stay perfectly aligned relative to one another, the shadow mask must be made of a metal that has the same thermal expansion characteristics as glass. The only reasonable choice for the shadow mask is Invar metal, an alloy that unfortunately is easily magnetized. Your son has magnetized the mask inside your set and because moving charged particles are deflected by magnetic fields, the electron beams in your television are being steered by the magnetized shadow mask so that they hit the wrong phosphors. That's why the colors are all washed out and rearranged.
To demagnetize the shadow mask, you should expose it to a rapidly fluctuating magnetic field that gradually decreases in strength until it vanishes altogether. The degaussing coils I mentioned above plug directly into the AC power line and act as large, alternating-field electromagnets. As you wave one of these coils around in front of the screen, you flip the magnetization of the Invar shadow mask back and forth rapidly. By slowly moving this coil farther and farther away from the screen, you gradually scramble the magnetizations of the mask's microscopic magnetic domains. The mask still has magnetic structures at the microscopic level (this is unavoidable and a basic characteristic of all ferromagnetic metals such as steel and Invar). But those domains will all point randomly and ultimately cancel each other out once you have demagnetized the mask. By the time you have the coil a couple of feet away from the television, the mask will have no significant magnetization left at the macroscopic scale and the colors of the set will be back to normal.
Incidentally, I did exactly this trick to my family's brand new color television set in 1965. I had enjoyed watching baseball games and deflecting the pitches wildly on our old black-and-white set. With only one electron beam, a black-and-white set needs no shadow mask and has nothing inside the screen to magnetize. My giant super alnico magnet left no lingering effect on it. But when the new set arrived, I promptly magnetized its shadow mask and when my parent watched the "African Queen" that night, the colors were not what you'd call "natural." The service person came out to degauss the picture tube the next day and I remember denying any knowledge of what might have caused such an intense magnetization. He and I agreed that someone must have started a vacuum cleaner very close to the set and thus magnetized its surface. I was only 8, so what did I know anyway.
Finally, as many readers have pointed out, many modern televisions and computer monitors have built-in degaussing coils. Each time you turn on one of these units, the degaussing circuitry exposes the shadow mask to a fluctuating magnetic field in order to demagnetize it. If your television set or monitor has such a system, then turning it on and off a couple of times should clear up most or all of the magnetization problems. However, you may have to wait about 15 minutes between power on/off cycles because the built-in degaussing units have thermal protection that makes sure they cool down properly between uses.
Flies travel at modest speeds relative to the air that surrounds them. Since the outside air is nearly motionless relative to the ground (usually), a fly outside the van is also nearly motionless. When the fast-moving van collides with the nearly motionless fly, the fly's inertia holds it in place while the van squashes it.
But when the fly is inside the van, the fly travels about in air that is moving with the van. If the van is moving at 70 mph, then so is the air inside it and so is the fly. In fact, everything inside the van moves more or less together and from the perspective of the van and its contents, the whole world outside is what is doing the moving—the van itself can be considered stationary and the van's contents are then also stationary.
As long as the fly and the air it is in are protected inside the van, the movement of the outside world doesn't matter. The fly buzzes around in its little protected world. But if the van's window is open and the fly ventures outside just as a signpost passes the car, the fly may get creamed by a collision with the "moving" sign. Everything is relative and if you consider the van as stationary, then it is undesirable for the van's contents to get hit by the moving items in the world outside (passing trees, bridge abutments, or oncoming vehicles.
In the classical view of the world, the view before the advent of quantum theory, nature seemed entirely deterministic and mechanical. If you knew exactly where every molecule and atom was and how fast it was moving, you could perfectly predict where it would be later on. In principle, this classical world would allow you to throw a 6 every time. Of course, you'd have to know everything about the air's motion, the thermal energy in the die, and even the pattern of light in the room. But the need for enormous amounts of information just means that controlling the dice will be incredibly hard, not that it will be impossible. For simple throws, you could probably get by without knowing all that much about the initial conditions. As the throws became more complicated and more sensitive to initial conditions, you'd have to know more and more.
However, quantum mechanics makes controlling the die truly impossible. The problem stems from the fact that position and velocity information are not fully defined at the same time in our quantum mechanical universe. In short, you can't know exactly where a die is and how fast it is moving at the same time. And that doesn't mean that you can't perform these measurements well. It means that the precise values don't exist together; they are limited by Heisenberg uncertainty. So quantum physics imposes a fundamental limit on how well you can know the initial conditions before your throw and it thus limits your ability to control the outcome of that throw. How much quantum physics affects your ability to throw a 6 depends on the complexity of the throw. If you just drop a die a few inches onto a table, you can probably get a 6 most of the time, despite quantum mechanics and without even knowing much classical information. But as you begin throwing the die farther, you'll begin to lose control of it because of quantum mechanics and uncertainty. In reality, you'll find classical physics so limiting that you'll probably never observe the quantum physics problem. Knowing everything about a system is already unrealistic, even in a classical universe. The problems arising from quantum mechanics are really just icing on the cake for this situation.
What a great find! This site is filled with pseudo-science at its best. I don't know the history or training of these people, but it's pure garbage. They use the words of science but without any meaningful content. Just as putting on a crown doesn't make you a king, using phrases like "action and reaction" and "Newton's third law" doesn't mean that you are discussing real science.
I watched the video on the "Counter Rotation Device" and found the discussion of "Newton's Fourth Law of Motion" quite amusing. The speaker claims that this fourth law was discovered about 30 years ago by a person now at their research lab. It is based on Newton's third law, which the speaker simplifies to "for every action there is an equal and opposite reaction." In a nutshell, his fourth law claims that you can take the reaction caused by a particular action and apply it to the action in the same direction—action causes reaction which causes more action which causes more reaction and so on. Pretty soon you have so much action and reaction that anything becomes possible. The video goes on to show devices that yield more power than they consume and that can easily become net sources of energy—by using part of the output energy from one of these energy multiplying devices to power that device, you can create endless energy from nothing at all.
Sadly enough, it's all just nonsense. Newton's third law is not as flexible as the speaker supposes and this endless feedback process in which reaction is used as action to produce more reaction is ridiculous. A more accurate version of Newton's third law is: "Whenever one object pushes on a second object, the second object pushes back on the first object equally hard but in the opposite direction". Thus when you push on the handle of a water pump, that handle pushes back on you with an equal but oppositely directed force. The speaker's claim is that there is a way to use the handle's push on you as part of your push on the handle so that, with your help, the handle essentially pushes itself through action and reaction. You can then pump water almost without effort. Sorry, this is just nonsense. It's mostly just playing with the words action and reaction in their common language form: if you scare me, I react by jumping. That action and reaction has nothing to do with physics.
The speaker uses at least three clever techniques to make his claims more compelling and palatable. First, he refers frequently to a power-company conspiracy that is out to destroy his company and its products. Conspiracy theories are so popular these days that having a conspiracy against you makes you more believable. Second, he describes the fellow who discovered the fourth law of motion as a basement inventor who has taken on the rigid scientific establishment. Ordinary people love to see pompous, highly educated academics brought low by other ordinary people; it's kind of a team spirit issue. And third, he makes casual use of technical looking equipment and jargon, as though he is completely at ease in the world of advanced technology. Movies have made it easier to trust characters like Doc Brown from "Back to the Future" than to trust real scientists.
In fact, there is no power-company conspiracy because there is no free electricity. The proof is in the pudding: if these guys really could make energy from nothing, they'd be doing it every day and making a fortune. They would be the power companies. If they were interested in public welfare rather than money, they'd have given their techniques away already. If they were interested in proving the scientific establishment wrong, they'd have accepted challenges by scientific organization and demonstrated their devices in controlled situations (where they can't cheat). The fact is, they're just frauds and of no more interest to the power companies than snake oil salespeople are to doctors. No decent people want to see others defrauded of money, property, or health, but the free electricity people present no real threat to the power companies.
The popular notion that an ordinary person is likely to upset established science is an unfortunate product of the anti-intellectual climate of our present world. Becoming a competent scientist is generally hard work and requires dedication, time, and an enormous amount of serious thinking. Physics is hard, even for most physicists. The laws governing the universe are slowly being exposed but it has taken very smart, very hardworking people almost half a millennium to get to the current state of understanding. Each new step requires enormous effort and a detailed understanding of a good part of the physics that is already known. Still, there is a common myth that some clever and lucky individual with essentially no training or knowledge of what has been discovered before will make some monumental breakthrough. The movies are filled with such events. Unfortunately, it won't happen. In new or immature fields or subfields, it is possible for an essentially untrained or self-trained genius to jump in and discover something important. Galileo and Newton probably fit this category in physics and Galois and Ramanujan probably fit it in mathematics. But most of physics is now so mature that broad new discoveries are rare, and accessible only to those with extremely good understandings of what is already known. A basement tinkerer hasn't got a prayer.
Finally, real scientists don't always walk around in white lab coats looking serious, ridiculing the less educated, and trying to figure out how to trick the government into funding yet another silly, fraudulent, or unethical research project. In fact, most scientists wear practical clothes, have considerable humor, enjoy speaking with ordinary folk about their science, and conduct that science because they love and believe in it rather than as a means to some diabolic end. These scientists use the words of science in their conversations because it is the appropriate language for their work and there is meaning in each word and each sentence. The gibberish spoken by "scientists" in movies is often offensive to scientists in the same way that immigrant groups find it offensive when people mock their native languages.
I don't know about any patent history for the free electricity organization but everyone should be aware that not all patented items actually do what they're supposed to. In principle, the U.S. Patent Office only awards a patent when it determines that a concept has not been patented previously, is not already known, is not obvious, and is useful. The utility requirement should eliminate items that don't actually work. One of my readers, a patent attorney, reports that he regularly invokes the utility regulation while escorting the "inventors" of impossible devices such as "free electricity" to the door. They consider him part of the conspiracy against them, but he is doing us all a service by keeping foolishness out of the patent system. However, proving that something doesn't work often takes time and money, so sometimes nonfunctional items get patented. Thus a patent isn't always a guarantee of efficacy. Patented nonsense is exactly that: nonsense.
Finally, how do I know that Free Electricity is really not possible? Couldn't I have missed something somewhere in the details? No. The impossibility of this scheme is rooted in the very groundwork of physics; at the deepest level where there is no possibility of mistake. For the counter rotation device to generate 15 kilowatts of electricity out of nothing, it would have to be a net source of energy—the device would be creating energy from nothing. That process would violate the conservation of energy, whereby energy cannot be created or destroyed but can only be transferred from one object to another or converted from one form to another. Recognizing that our universe is relativistic (it obeys the laws of special relativity), the actual conserved quantity is mass/energy, but the concept is the same: you can't make mass/energy from nothing.
The origin of this conservation law lies in a mathematical theorem noted first by C. G. J. Jacobi and fully developed by Emmy Noether, that each symmetry in the laws of physics gives rise to a conserved quantity. The fact that a translation in space—shifting yourself from one place to another—does not change the laws of physics gives rise to a conserved quantity: momentum. The fact that a rotation—changing the direction in which you are facing—does not change the laws of physics gives rise to another conserved quantity: angular momentum. And the fact that waiting a few minutes—changing the time at which you are—does not change the laws of physics gives rise to a third conserved quantity: energy. The conservation of energy is thus intimately connected with the fact that the laws of physics are the same today as they were yesterday and as they will be tomorrow.
Scientists have been looking for over a century for any changes in the laws of physics with translations and rotations in space and with movement through time, and have never found any evidence for such changes. Thus momentum, angular momentum, and energy are strictly conserved in our universe. For the counter rotation device to create energy from nothing, all of physics would have to be thrown in the trashcan. The upset would be almost as severe as discovering that 1+1 = 3. Furthermore, a universe in which physics was time-dependent and energy was not conserved would be a dangerous place. Free electricity devices would become the weapons of the future—bombs and missiles that released energy from nothing. Moreover, as the free electricity devices produced energy from nothing, the mass/energy of the earth would increase and thus its gravitational field would also increase. Eventually, the gravity would become strong enough to cause gravitational collapse and the earth would become a black hole. Fortunately, this is all just science fiction because free electricity isn't real.
Generators and motors are very closely related and many motors that contain permanent magnets can also act as generators. If you move a permanent magnet past a coil of wire that is part of an electric circuit, you will cause current to flow through that coil and circuit. That's because a changing magnetic field, such as that near a moving magnet, is always accompanied in nature by an electric field. While magnetic fields push on magnetic poles, electric fields push on electric charges. With a coil of wire near the moving magnet, the moving magnet's electric field pushes charges through the coil and eventually through the entire circuit.
A convenient arrangement for generating electricity endlessly is to mount a permanent magnet on a spindle and to place a coil of wire nearby. Then as the magnet spins, it will turn past the coil of wire and propel currents through that coil. With a little more engineering, you'll have a system that looks remarkably like the guts of a typical permanent magnet based motor. In fact, if you take a common DC motor out of a toy and connect its two electrical terminals to a 1.5 V light bulb or a light emitting diode (try both directions with an LED because it can only carry current in one direction), you'll probably be able to light that bulb or LED by spinning the motor's shaft rapidly. A DC motor has a special switching system that converts the AC produced in the motor's coils into DC for delivery to the motor's terminals, but it's still a generator. So the easiest answer to your question is: "find a nice DC motor and turn its shaft".
Iron and most steels are intrinsically magnetic. By that, I mean that they contain intensely magnetic microscopic domains that are randomly oriented in the unmagnetized metal but that can be aligned by exposure to an external magnetic field. In pure iron, this alignment vanishes quickly after the external field is removed, but in the medium carbon steel of a typical screwdriver, the alignment persists days, weeks, years, or even centuries after the external field is gone.
To magnetize a screwdriver permanently, you should expose it briefly to a very strong magnetic field. Touching the screwdriver's tip to one pole of a strong magnet will cause some permanent magnetization. Rubbing or tapping the screwdriver also helps to free up its domains so that they can align with this external field. But the better approach is to put the screwdriver in a coil of wire that carries a very large DC electric current.
The current only needs to flow for a fraction of a second—just long enough for the domains to align. A car battery is a possibility, but it has safety problems: it can deliver an incredible current (400 amperes or more) for a long time (minutes) and can overheat or even explode your coil of wire. Moreover, it may leak hydrogen gas, which can be ignited by the sparks that will inevitably occur while you are magnetizing your screwdriver.
A safer choice for the current source is a charged electrolytic capacitor—a device that stores large quantities of separated electric charge. A charged capacitor can deliver an even larger current than a battery can, but only for a fraction of a second—only until the capacitor's store of separated charge is exhausted. Looking at one of my hobbyist electronics catalogs, Marlin P. Jones, 800-652-6733, I'd pick a filter capacitor with a capacity of 10,000 microfarads and a maximum voltage of 35 volts (Item 12104-CR, cost: $1.50). Charging this device with three little 9V batteries clipped together in a series (27 volts overall) will leave it with about 0.25 coulombs of separated charge and just over 3.5 joules (3.5 watt-seconds or 3.5 newton-meters) of energy.
Make sure that you get the polarity right—electrolytic filter capacitors store separated electric charge nicely but you have to put the positive charges and negative charges on the proper sides. [To be safe, work with rubber gloves and, as a general rule, never touch anything electrical with more than one hand at a time. Remember that a shock across your heart is much more dangerous than a shock across you hand. And while 27 volts is not a lot and is unlikely to give you a shock under any reasonable circumstances, I can't accept responsibility for any injuries. If you're not willing to accept responsibility yourself, don't try any of this.]
If you wrap about 100 turns of reasonably thick insulated wire (at least 18 gauge, but 12 gauge solid-copper home wiring would be better) around the screwdriver and then connect one end of the coil to the positively charged side of the capacitor and the other end of the coil to the negatively charged side, you'll get a small spark (wear gloves and safety glasses) and a huge current will flow through the coil. The screwdriver should become magnetized. If the magnetization isn't enough, repeat the charging-discharging procedure a couple of times, always with the same connections so that the magnetization is in the same direction.
It turns out that the electrons in copper travel quite slowly even though "electricity" travels at almost the speed of light. That's because there are so many mobile electrons in copper (and other conductors) that even if those electrons move only an inch per second, they comprise a large electric current. Picture the electrons as water flowing through a pipe or river and now consider the Mississippi River. Even if the Mississippi is flowing only inches per second, it sure carries lots of water past St. Louis each second.
The fact that electricity itself travels at almost the speed of light just means that when you start the electrons moving at one end of a long wire, the electrons at the other end of the wire also begin moving almost immediately. But that doesn't mean that an electron from your end of the wire actually reaches the far end any time soon. Instead, the electrons behave somewhat like water in a long hose. When you start the water moving at one end, it pushes on water in front of it, which pushes on water in front of it, and so on so that water at the far end of the hose begins to leave the hose almost immediately. In the case of water, the motion proceeds forward at the speed of sound. In a wire, the motion proceeds forward at the speed of light in the wire (actually the speed at which electromagnetic waves propagate along the wire), which is only slightly less than the speed of light in vacuum.
Note for the experts: as one of my readers (KT) points out, the water-in-a-hose analogy for current-in-a-wire is far from perfect. Current in a wire flows throughout the wire, including at its surface, and the wire's resistance to steady current flow scales as the cross-sectional area of the wire. In contrast, water in a hose only flows through the open channel inside the hose and the hose's resistance to flow scales approximately as the fourth power of that channel's diameter.
Actually, faster moving fluids don't necessarily have lower pressure. For example, a bottle of compressed air in the back of a pickup truck is still high-pressure air, even though it's moving fast. The real issue here is that when fluid speeds up in passing through stationary obstacles, its pressure drops. For example, when air rushes into the open but stationary mouth of a vacuum cleaner, that air experiences not only a rise in speed, it also experiences a drop in pressure. Similarly, when water rushes out of the nozzle of a hose, its speed increases and its pressure drops. This is simply conservation of energy: as the fluid gains kinetic energy, it must lose pressure energy. However, if there are sources of energy around—fans, pumps, or moving surfaces—then these exchanges of pressure for speed may no longer be present. That's why I put in the qualifier of there being only stationary obstacles.
Just as most good camera lenses have more than one optical element inside them, so your eye has more than one optical element inside it. The outside surface of your eye is curved and actually acts as a lens itself. Without this surface lens, your eye can't bring the light passing through it to a focus on your retina. The component in your eye that is called "the lens" is actually the fine adjustment rather than the whole optical system.
When you put your eye in water, the eye's curved outer surface stops acting as a lens. That's because light travels at roughly the same speed in water as it does in your eye and that light no longer bends as it enters your eye. Everything looks blurry because the light doesn't focus on your retina anymore. But by inserting an air space between your eye and a flat plate of glass or plastic, you recover the bending at your eye's surface and everything appears sharp again.
The only source of common light source that presents any real danger to a child with a magnifying glass is the sun. If you let sunlight pass through an ordinary magnifying glass, the convex lens of the magnifier will cause the rays of sunlight to converge and they will form a real image of the sun a short distance after the magnifying glass. This focused image will appear as a small, circular light spot of enormous brilliance when you let it fall onto a sheet of white paper. It's truly an image—it's round because the sun is round and it has all the spatial features that the sun does. If the image weren't so bright and the sun had visible marks on its surface, you'd see those marks nicely in the real image.
The problem with this real image of the sun is simply that it's dazzlingly bright and that it delivers lots of thermal power in a small area. The real image is there in space, whether or not you put any object into that space. If you put paper or some other flammable substance in this focused region, it may catch on fire. Putting your skin in the focus would also be a bad idea. And if you put your eye there, you're in serious trouble.
So my suggestion with first graders is to stay in the shade when you're working with magnifying glasses. As soon as you go out in direct sunlight, that brilliant real image will begin hovering in space just beyond the magnifying glass, waiting for someone to put something into it. And many first graders just can't resist the opportunity to do just that.
Converting units is always a matter of multiplying by 1. But you must use very fancy versions of 1, such as 60 seconds/1 minute and 1 gallon/3.7854 liters. Since 60 seconds and 1 minute are the same amount of time, 60 seconds/1 minute is 1. Similarly, since 1 gallon (U.S. liquid) and 3.7854 liters are the same amount of volume, 1 gallon/3.7854 liters is 1. So suppose that you have measured the flow of water through a pipe as 283 liters/second. You can convert to gallons/minute by multiplying 283 liters/second by 1 twice: (283 liters/second)(60 seconds/1 minute)(1 gallon/3.7854 liters). When you complete this multiplication, the liter units cancel, the second units cancel, and you're left with 4,486 gallons/minute.
As a number of readers have informed me, the watches you're referring to generate electricity that then powers a conventional electronic watch. These electromechanical watches use mechanical work done by wrist motions on small weights inside the watches to generate electricity. Seiko's watch spins a tiny generator—a coil of wire moves relative to a magnetic field and electric charges are pushed through the coil as a result. I have been told that other watches exist that use piezoelectricity—the electricity that flows when certain mechanical objects are deformed or strained—to generate their electricity. In any case, your wrist motion is providing the energy that becomes electric power.
These electromechanical watches are the modern descendants of the automatic mechanical watches. An automatic watch had a main spring that was wound by the motion of the wearer's hand. A small mass inside the watch swung back and forth on the end of a lever. Because of its inertia, this mass resisted changes in velocity and it moved relative to the watch body whenever the watch accelerated. If you like, you can picture the mass as a ball that rolls about inside a wagon as you roll the wagon around an obstacle course. When the lever turned back and forth relative to the watch body, the watch was able to extract energy from it. Gears attached to the lever allowed the watch to use the mass's energy to wind its mainspring. The energy extracted from the mass with each swing was very small, but it was enough to keep the mainspring fully wound. Ultimately, this energy came from your hand—you did work on the watch in shaking it about and some of this energy eventually wound up in the mainspring.
These same sorts of motions are what power the electromechanical watches of today. Instead of winding a spring, your wrist motions swing weights about inside the watches and these moving weights spin generators to produce electric power.
Actually, the system of cloud and ground that produces lightning is itself a giant capacitor and the lightning is a failure of that capacitor. Like all capacitors, the system consists of two charged surfaces separated by an insulating material. In this case, the charged surfaces are the cloud bottom and the ground, and the insulating material is the air. During charging, vast amounts of separated electric charge accumulate on the two surfaces—the cloud bottom usually becomes negatively charged and the ground below it becomes positively charge. These opposite charges produce an intense electric field in the region between the cloud and the ground, and eventually the rising field causes charge to begin flowing through the air: a stroke of lightning.
In principle, you could tap into a cloud and the ground beneath and extract the capacitor's charge directly with wires. But this would be a heroic engineering project and unlikely to be worth the trouble. And catching a lightning strike in order to charge a second capacitor is not likely to be very efficient: most of the energy released during the strike would have to dissipate in the air and relatively little of it could be allowed to enter the capacitor. That's because no realistic capacitor can handle the voltage in lightning.
Here's the detailed analysis. The power released during the strike is equal to the strike's voltage times its current: the voltage between clouds and ground and the current flowing between the two during the strike. Voltage is the measure of how much energy each unit of electric charge has and current is the measure of how many units of electric charge are flowing each second. Their product is energy per second, which is power. Added up over time, this power gives you the total energy in the strike. If you want to capture all this energy in your equipment, it must handle all the current and all the voltage. If it can only handle 1% of the voltage, it can only capture 1% of the strike's total energy.
While the current flowing in a lightning strike is pretty large, the voltage involved is astonishing: millions and millions of volts. Devices that can handle the currents associated with lightning are common in the electric power industry but there's nothing reasonable that can handle lightning's voltage. Your equipment would have to let the air handle most of that voltage. The air would extract power from the flowing current in the lightning bolt and turning it into light, heat, and sound. Your equipment would then extract only a token fraction of the stroke's total energy. Finally, your equipment would have to prepare the energy properly for delivery on the AC power grid—its voltage would have to be lowered dramatically and a switching system would have to convert the static charge on the capacitors to an alternating flow of current in the power lines.
When he established his temperature scale, Daniel Gabriel Fahrenheit defined 32 degrees "Fahrenheit" (32 F) as the melting temperature of ice—the temperature at which ice and water can coexist. When you assemble a mixture of ice and water and allow them to reach equilibrium (by waiting, say, 3 minutes) in a reasonably insulated container (something that does not allow much heat to flow either into or out of the ice bath), the mixture will reach and maintain a temperature of 32 F. At that temperature and at atmospheric pressure, ice and water are both stable and can coexist indefinitely.
To see why this arrangement is stable, consider what would happen if something tried to upset it. For example, what would happen if this mixture were to begin losing heat to its surroundings? Its temperature would begin to drop but then the water would begin to freeze and release thermal energy: when water molecules stick together, they release chemical potential energy as thermal energy. This thermal energy release would raise the temperature back to 32 F. The bath thus resists attempts at lowering its temperature.
Similarly, what would happen if the mixture were to begin gaining heat from its surroundings? Its temperature would begin to rise but then the ice would begin to melt and absorb thermal energy: separating water molecules increases their chemical potential energy and requires an input of thermal energy. This lost thermal energy would lower the temperature back to 32 F. The bath thus resists attempts at raising its temperature.
So an ice/water bath self-regulates its temperature at 32 F. The only other quantities affecting this temperature are the air pressure (the bath temperature could shift upward by about 0.003 degrees F during the low pressure of a hurricane) and dissolved chemicals (half an ounce of table salt per liter of bath water will shift the bath temperature downward by about 1 degree F).
It's true that the force of gravity decreases with depth, so that if you were to find yourself in a cave at the center of the earth, you would be completely weightless. However, pressure depends on more than local gravity: it depends on the weight of everything being supported overhead. So while you might be weightless, you would still be under enormous pressure. Your body would be pushing outward on everything around you, trying to prevent those things from squeezing inward and filling the space you occupy. In fact, your body would not succeed in keeping those things away and you would be crushed by their inward pressure.
More manageable pressures surround us everyday. Our bodies do their part in supporting the weight of the atmosphere overhead when we're on land or the weight of the atmosphere and a small part of the ocean when we're swimming at sea. The deeper you go in the ocean, the more weight there is overhead and the harder your body must push upward. Thus the pressure you exert on the water above you and the pressure that that water exerts back on you increases with depth. Even though gravity is decreasing as you go deeper and deeper, the pressure continues to increase. However, it increases a little less rapidly as a result of the decrease in local gravity.
The foam consists of tiny air bubbles surrounded by very thin films of soap and water. When light enters the foam, it experiences partial reflections from every film surface it enters or exits. That is because light undergoes a partial reflection whenever it changes speed (hence the reflections from windows) and the speed of light in soapy water is about 30% less than the speed of light in air. Although only about 4% of the light reflects at each entry or exit surface, the foam contains so many films that very little light makes it through unscathed. Instead, virtually all of the light reflects from film surfaces and often does so repeatedly. Since the surfaces are curved, there is no one special direction for the reflections and the reflected light is scattered everywhere. And while an individual soap film may exhibit colors because of interference between reflections from its two surfaces, these interference effects average away to nothing in the dense foam. Overall, the foam appears white—it scatters light evenly, without any preference for a particular color or direction. White reflections appear whenever light encounters a dense collection of unoriented transparent particles (e.g. sugar, salt, clouds, sand, and the white pigment particles in paint).
As for the fact that even colored soaps create only white foam, that's related to the amount of dye in the soaps. It doesn't take much dye to give bulk soap its color. Since light often travels deep into a solid or liquid soap before reflecting back to our eyes, even a modest amount of dye will selectively absorb enough light to color the reflection. But the foam reflects light so effectively with so little soap that the light doesn't encounter much dye before leaving the lather. The reflection remains white. To produce a colored foam, you would have to add so much dye to the soap that you'd probably end up with colored hands as well.
Fortunately, you don't have to wait that long. From astronomical observations, we are fairly certain that the laws of physics as we know them apply throughout the visible universe. It wouldn't take large changes in the physical laws to radically change the structures of atoms, molecules, stars, and galaxies. So the fact that the light and other particles we see coming from distant places is so similar to what we see coming from nearby sources is pretty strong evidence that the laws of physics don't change with distance. Also, the fact that the light we see from distant sources has been traveling for a long time means that the laws of physics don't seem to have changed much (if at all) with time, either. While there are theories that predict subtle but orderly changes in the laws of physics with time and location, effectively making those laws more complicated, no one seriously thinks that the laws of physics change radically and randomly from place to place in the Universe.
Nearly all metals are crystalline, meaning that their atoms are arranged in neat and orderly stacks, like the piles of oranges or soup cans at the grocery store or the cannonballs at the courthouse square. When you bend a metal, its crystals can deform either by changing the spacings between atoms or by letting those atoms slide past one another as great moving sheets of atoms. When the atoms keep their relative orientations but change their relative spacings, the deformation is called elastic. When the atom sheets slide about and move, the deformation is called plastic.
Metals that bend permanently are experiencing plastic deformation. Their atoms change their relative orientations during the bend and they lose track of where they were. Once plastic deformation has occurred, the metal can't remember how to get back to its original shape and stays bent.
Metals that bend only temporarily and return to their original shape when freed from stress are experiencing elastic deformation. Their sheets of atoms aren't sliding about and they can easily spring back to normal when the stresses go away. Naturally, springs are made from materials that experience only elastic deformation in normal circumstances. Hardened metals such as spring steel are designed and heat-treated so that the atomic sliding processes, known technically as "slip," are inhibited. When you bend them and let go, they bounce back to their original shapes. But if you bend them too far, they either experience plastic deformation or they break.
Non-crystalline materials such as glass also make good springs. But since these amorphous materials have no orderly rows of atoms, they can't experience plastic deformation at all. They behave as wonderful springs right up until you bend them too far. Then, instead of experience plastic deformation and bending permanently, they simply crack in two.
One last detail: there are a few exotic materials that undergo complicated deformations that are neither temporary nor permanent. With changes in temperature, these shape memory materials can recover from plastic deformation and spring back to their original shapes.
A superconductor is a material that carries electric current without any loss of energy. Currents lose energy as they flow through normal wires. This energy loss appears as a voltage drop across the material—the voltage of the current as it enters the material is higher than the voltage of the current when it leaves the material. But in a superconductor, the current doesn't lose any voltage at all. As a result, currents can even flow around loops without stopping. Currents are magnetic and superconducting magnets are based on the fact that once you get a current flowing around a loop of superconductor, it keeps going forever and so does its magnetism.
At low speeds, mass and energy appear to be separate quantities. Mass is the measure of inertia and can be determined by shaking an object. Energy is the measure of how much work an object can do and can be determined by letting it do that work. Conveniently enough, the object's weight—the force gravity exerts on it—is exactly proportional to its mass, which is why people carelessly interchange the words "mass" and "weight," even though they mean different things.
But when something is moving at speeds approaching the speed of light, mass and kinetic energy no longer separate so easily. In fact, the relativistic equations of motion are more complicated than those describing slow objects and the way in which gravity affects fast objects is more complicated than simply giving them "weight."
Overall, you can view the bending of light by gravity in one of two ways. First, you can view it approximately as gravity affecting not on mass, but also energy so that light falls because its energy gives it something equivalent to a "weight." Second, you can view it more accurately as the bending of light as caused by a change in the shape of space and time around a gravitating object. Space is curved, so that light doesn't travel straight as it moves past gravitating objects—it follows the curves of space itself. The second or Einsteinian view, which correctly predicts twice as much bending of light as the first or Newtonian view, is a little disconcerting. That's why it took some time for the theory of general relativity to be widely accepted. (Thanks to DP for pointing out the factor of two.)
The helium balloon is the least dense thing in the car and is responding to forces exerted on it by the air in the car. To understand this, consider what happens to you, the air, and finally the helium balloon as the car first starts to accelerate forward.
When the car starts forward, inertia tries to keep all of the objects in the car from moving forward. An object at rest tends to remain at rest. So the car must push you forward in order to accelerate you forward and keep you moving with the car. As the car seat pushes forward on you, you push back on the car seat (Newton's third law) and dent its surface. Your perception is that you are moving backward, but you're not really. You're actually moving forward; just not quite as quickly as the car itself.
The air in the car undergoes the same forward acceleration process. Its inertia tends to keep it in place, so the car must push forward on it to make it accelerate forward. Air near the front of the car has nothing to push it forward except the air near the back of the car, so the air in the front of the car tends to "dent" the air in the back of the car. In effect, the air shifts slightly toward the rear of the car. Again, you might think that this air is going backward, but it's not. It's actually moving forward; just not quite as quickly as the car itself.
Now we're ready for the helium balloon. Since helium is so light, the helium balloon is almost a hollow, weightless shell that displaces the surrounding air. As the car accelerates forward, the air in the car tends to pile up near the rear of the car because of its inertia. If the air can push something out of its way to get more room near the rear of the car, it will. The helium balloon is that something. As inertia causes the air to drift toward the rear of the accelerating car, the nearly massless and inertialess helium balloon is squirted toward the front of the car to make more room for the air. There is actually a horizontal pressure gradient in the car's air during forward acceleration, with a higher pressure at the rear of the car than at the front of the car. This pressure gradient is ultimately what accelerates the air forward with the car and it's also what propels the helium balloon to the front of the car.
Finally, when the car is up to speed and stops accelerating forward, the pressure gradient vanishes and the air returns to its normal distribution. The helium balloon is no longer squeezed toward the front of the car and it floats once again directly above the gear shift.
One last note: OGT from Lystrup, Denmark points out that when you accelerate a glass of beer, the rising bubbles behave in the same manner. They move toward the front of the glass as you accelerate it forward and toward the back of the glass as you bring it to rest.
Most objects make no light of their own and are visible only because they reflect some of the light that strikes them. Without sunlight (or any other light source), these passive objects would appear black. Black is what we "see" when there is no light reaching our eyes from a particular direction. The only objects we would see would be those that made their own light and sent it toward our eyes.
The fact that we see mostly reflected light makes for some interesting experiments. A red object selectively reflects only red light; a blue object reflects only blue light; a green object reflects only green light. But what happens if you illuminate a red object with only blue light? The answer is that the object appears black! Since it is only able to reflect red light, the blue light that illuminates it is absorbed and nothing comes out for us to see. That's why lighting is so important to art. As you change the illumination in an art gallery, you change the variety of lighting colors that are available for reflection. Even the change from incandescent lighting to fluorescent lighting can dramatically change the look of a painting or a person's face. That's why some makeup mirrors have dual illumination: incandescent and fluorescent.
The one exception to this rule that objects only reflect the light that strikes them is fluorescent objects. These objects absorb the light that strikes them and then emit new light at new colors. For example, most fluorescent cards or pens will absorb blue light and then emit green, orange, or red light. Try exposing a mixture of artwork and fluorescent objects to blue light. The artwork will appear blue and black: blue wherever the art is blue and black wherever the art is either red, green, or black. But the fluorescent objects will display a richer variety of colors because those objects can synthesize their own light colors.
If we neglect the mass of the rope, the two teams always exert equal forces on one another. That's simply an example of Newton's third law—for every force team A exerts on team B, there is an equal but oppositely directed force exerted by team B on team A. While it might seem that these two forces on the two teams should always balance in some way so that the teams never move, that isn't the case. Each team remains still or accelerates in response to the total forces on that team alone, and not on the teams as a pair. When you consider the acceleration of team A, you must ignore all the forces on team B, even though one of those forces on team B is caused by team A. There are two important forces on team A: (1) the pull from team B and (2) a force of friction from the ground. That force of friction approximately cancels the pull from the team B because the two forces are in opposite horizontal directions. As long as the two forces truly cancel, team A won't accelerate. But if team A doesn't obtain enough friction from the ground, it will begin to accelerate toward team B. The winning team is the one that obtains more friction from the ground than it needs and accelerates away from the other team. The losing team is the one that obtains too little friction from the ground and accelerates toward the other team.
An ordinary wire will carry electric current in either direction, while a diode will only carry current in one direction. That's because the electric charges in a wire are free to drift in either direction in response to electric forces but the charges in a diode pass through a one-way structure known as a p-n junction. Charges can only approach the junction from one side and leave from the other. If they try to approach from the wrong side, they discover that there are no easily accessible quantum mechanical pathways or "states" in which they can travel. Sending the charges toward the p-n junction from the wrong side can only occur if something provides the extra energy needed to reach a class of less accessible quantum mechanical states. Light can provide that extra energy, which is why many diodes are light sensitive—they will conduct current in the wrong direction when exposed to light. That is the basis for many light sensitive electronic devices and for most photoelectric or "solar" cells.
The amount of hot water that's cooling doesn't necessarily determine which bowl of water will cool fastest. That depends on how quickly each gram of the hot water loses heat, a rate that depends both on how much hotter the water is than its surroundings and on how that water is exposed to those surroundings. In general, hot water loses heat through its surface so the more surface that's exposed, the faster it will lose heat. But surface that's exposed to air will lose heat via evaporation and will be particularly important in cooling the water.
In answer to your question, my guess is that the larger bowl of water also exposes much more of that water to the air. Although the larger bowl had more water in it, it allowed that water to exchange heat faster with its environment. If the larger bowl contained twice as much water but let that water lose heat twice as fast, the two bowls would maintain equal temperatures. If you want to see the effect of thermal mass in slowing the loss of temperature, you'll need to control heat loss. Try letting equal amounts of hot water cool in two identical containers—one wrapped in insulation and covered with clear plastic wrap (to prevent evaporation) and one open to the air. You'll see a dramatic change in cooling rate. And if you want to compare unequal amounts of water, use two indentical containers that are only exposed to the cooler environment through a controlled amount of surface area. For example, try two identical insulated cups, one full of water and one only half full. If both lose heat only through their open tops, the full cup should cool more slowly than the half full cup.
I'd suggest finding a hollow rubber ball with a relatively thin, flexible skin and putting different things inside it. You can just cut a small hole and tape it over after you put in "the stuff." Compare the ball's bounciness when it contains air, water, shaving cream, beans, rice, and so on. Just drop it from a consistent height and see how high it rebounds. The ratio of its rebound height to its drop height is a good measure of how well the ball stores energy when it hits the ground and how well it uses that energy to rebound. A ball that bounces to full height is perfect at storing energy while a ball that doesn't bounce at all is completely terrible at storing energy. You'll get something in between for most of your attempts—indicating that "the stuff" is OK but not perfect at storing energy during the bounce. The missing energy isn't destroyed, it's just turned into thermal energy. The ball gets a tiny bit hotter with every bounce.
You won't get any important quantitative results from this sort of experiment, but it'll be fun anyway. I wonder what fillings will make the ball bounce best or worst?
It is science. The needle is able to enter latex without tearing it because the latex molecules are stretching out of the way of the needle without breaking. Like all polymers (plastics), latex consists of very large molecules. In latex, these molecules are basically long chains of atoms that are permanently linked to one another at various points along their lengths. You can picture a huge pile of spaghetti with each pasta strand representing one latex molecule. Now picture little links connecting pairs of these strands at random, so that when you try to pick up one strand, all the other strands come with it. That's the way latex looks microscopically. You can't pull the strands of latex apart because they are all linked together. But you can push a spoon between the strands.
That is what happens when you carefully weave a needle into a latex balloon—the needle separates the polymer strands locally, but doesn't actually pull them apart or break them. Since breaking the latex molecules will probably cause the balloon to tear and burst, you have to be very patient and use a very sharp needle. I usually oil the needle before I do this and I don't try to insert the needle in the most highly stressed parts of the balloon. The regions near the tip of the balloon and near where it is filled are the least stressed and thus the easiest to pierce successfully with a needle. A reader has informed me that coating the needle with Vasoline is particularly helpful.
One final note: a reader pointed out that it is also possible to put a needle through a balloon with the help of a small piece of adhesive tape. If you put the tape on a patch of the inflated balloon, it will prevent the balloon from ripping when you pierce the balloon right through the tape. This "cheaters" approach is more reliable than trying to thread the needle between the latex molecules, but it's less satisfying as well. But it does point out the fact that a balloon bursts because of tearing and that if you prevent the balloon from tearing, you can pierce it as much as you like.
A dehumidifier makes use of the fact that water tends to be individual gas molecules in the air at higher temperatures but condensed liquid molecules on surfaces at lower temperatures. At its heart, a dehumidifier is basically a heat pump, one that transfers heat from one surface to another. Its components are almost identical to those in an air conditioner or refrigerator: a compressor, a condenser, and an evaporator. The evaporator acts as the cold surface, the source of heat, and the condenser acts as the hot surface, the destination for that heat.
When the unit is operating and pumping heat, the evaporator becomes cold and the condenser becomes hot. A fan blows warm, moist air from the room through the evaporator coils and that air's temperature drops. This temperature drop changes the behavior of water molecules in the air. When the air and its surroundings were warm, any water molecule that accidentally bumped into a surface could easily return to the air. Thus while water molecules were always landing on surfaces or taking off, the balance was in favor of being in the air. But once the air and its surroundings become cold, any water molecules that bump into a surface tend to stay there. Water molecules are still landing on surfaces and taking off, but the balance is in favor of staying on the surface as either liquid water or solid ice. That's why dew or frost form when warm moist air encounters cold ground. In the dehumidifier, much of the air's water ends up dripping down the coils of the evaporator into a collection basin.
All that remains is for the dehumidifier to rewarm the air. It does this by passing the air through the condenser coils. The thermal energy that was removed from the air by the evaporator is returned to it by the condenser. In fact, the air emerges slightly hotter than before, in part because it now contains all of the energy used to operate the dehumidifier and in part because condensing moisture into water releases energy. So the dehumidifier is using temperature changes to separate water and air.
To make good ice cream, you want to freeze the cream in such a way that the water in the cream forms only very tiny ice crystals. That way the ice cream will taste smooth and creamy. The simplest way to achieve this goal is to stir the cream hard while lowering its temperature far enough to freeze the water in it and to make the fat solidify as well. That's where the ice and salt figure in.
By itself, melting ice has a temperature of 0° C (32° F). When heat flows into ice at that temperature, the ice doesn't get hotter, it just transforms into water at that same temperature. Separating the water molecules in ice to form liquid water takes energy and so heat must flow into the ice to make it melt.
But if you add salt to the ice, you encourage the melting process so much that the ice begins to use its own internal thermal energy to transform into water. The temperature of the ice drops well below 0° C (32° F) and yet it keeps melting. Eventually, the drop in temperature stops and the ice and salt water reach an equilibrium, but the mixture is then quite cold—perhaps -10° C (14° F) or so. To melt more ice, heat must flow into the mixture. When you place liquid cream nearby, heat begins to flow out of the cream and into the ice and salt water. More ice melts and the liquid cream get colder. Eventually, ice cream starts to form. Stirring keeps the ice crystals small and also ensures that the whole creamy liquid freezes uniformly.
During a bounce from a rigid surface, the ball's surface dents. Denting a surface takes energy and virtually all of the ball's energy of motion (kinetic energy) goes into denting its own surface. For a moment the ball is motionless and then it begins to rebound. As the ball undents, it releases energy and this energy becomes the ball's new energy of motion.
The issue is in how well the ball's surface stores and then releases this energy. The ideal ball experiences only elastic deformation—the molecules within the ball do not reorganize at all, but only change their relative spacings during the dent. If the molecules reorganize—sliding across one another or pulling apart in places—then some of the denting energy will be lost due to internal friction-like effects. Even if the molecules slide back to their original positions, they won't recover all the energy and the ball won't bounce to its original height.
In general, harder rubber bounces more efficiently than softer rubber. That's because the molecules in hard rubber are too constrained to be able to slide much. A superball is very hard and bounces well. But there are also sophisticated thermal effects that occur in some seemingly hard rubbers that cause them to lose their stored energy.
Ozone is an unstable molecule that consists of three oxygen atoms rather than then usual two. Because of its added complexity, an ozone molecule can interact with a broader range of light wavelengths and has the wonderful ability to absorb harmful ultraviolet light. The presence of ozone molecules in our upper atmosphere makes life on earth possible.
However, because ozone molecules are chemically unstable, they can be depleted by contaminants in the air. Ozone molecules react with many other molecules or molecular fragments, making ozone useful as a bleach and a disinfectant. Molecules containing chlorine atoms are particularly destructive of ozone because a single chlorine atom can facilitate the destruction of many ozone molecules through a chlorine recycling process.
In contrast, nitrogen molecules are extremely stable. They are so stable that there are only a few biological systems that are capable of separating the two nitrogen atoms in a nitrogen molecule in order to create organic nitrogen compounds. Without these nitrogen-fixing organisms, life wouldn't exist here. Because nitrogen molecules are nearly unbreakable, they survive virtually any amount or type of chemical contamination.
Yes, fluorescents are more energy efficient overall. To begin with, fluorescent lights have a much longer life than incandescent lights—the fluorescent tube lasts many thousands of hours and its fixture lasts tens of thousands of hours. So the small amount of energy spent building an incandescent bulb is deceptive—you have to build a lot of those bulbs to equal the value of one fluorescent system.
Second, although there is considerable energy consumed in manufacturing the complicated components of a fluorescent lamp, it's unlikely to more than a few kilowatt-hours—the equivalent of the extra energy a 100 watt incandescent light uses up in a week or so of typical operation. So it may take a week or two to recover the energy cost of building the fluorescent light, but after that the energy savings continue to accrue for years and years.
First, your bus can't be going at the speed of light because massive objects are strictly forbidden from traveling at that speed. Even to being traveling near the speed of light would require a fantastic expenditure of energy.
But suppose that the bus were traveling at 99.999999% of the speed of light and you were to run toward its front at 0.000002% of the speed of light (about 13 mph or just under a 5 minute mile). Now what would happen?
First, the bus speed I quoted is in reference to some outside observer because the seated passengers on the bus can't determine its speed. After all, if the shades are pulled down on the bus and it's moving at a steady velocity, no one can tell that it's moving at all. So let's assume that the bus speed I gave is according to a stationary friend who is watching the bus zoom by from outside.
While you are running toward the front of the bus at 0.000002% of the speed of light, your speed is in reference to the other passengers in the bus, who see you moving forward. The big question is what does you stationary friend see? Actually, your friend sees you running toward the front of the bus, but determines that your personal speed is only barely over 99.999999%. The two speeds haven't added the way you'd expect. Even though you and the bus passengers determine that you are moving quickly toward the front of the bus, your stationary friend determines that you are moving just the tiniest bit faster than the bus. How can that be?
The answer lies in the details of special relativity, but here is a simple, albeit bizarre picture. Your stationary friend sees a deformed bus pass by. Ignoring some peculiar optical effects due to the fact that it takes time for light to travel from the bus to your friend's eyes so that your friend can see the bus, your friend sees a foreshortened bus—a bus that is smashed almost into a pancake as it travels by. While you are in that pancake, running toward the front of the bus, the front is so close to the rear that your speed within the bus is miniscule. Why the bus becomes so short is another issue of special relativity.
Heat pipes use evaporation and condensation to move heat quickly from one place to another. A typical heat pipe is a sealed tube containing a liquid and a wick. The wick extends from one end of the tube to the other and is made of a material that attracts the liquid—the liquid "wets" the wick. The liquid is called the "working fluid" and is chosen so that it tends to be a liquid the temperature of the colder end of the pipe and tends to be a gas at the temperature of the hotter end of the pipe. Air is removed from the pipe so the only gas it contains is the gaseous form of the working fluid.
The pipe functions by evaporating the liquid working fluid into gas at its hotter end and allowing that gaseous working fluid to condense back into a liquid at its colder end. Since it takes thermal energy to convert a liquid to a gas, heat is absorbed at the hotter end. And because a gas gives up thermal energy when it converts from a gas to a liquid, heat is released at the colder end.
After a brief start-up period, the heat pipe functions smoothly as a rapid conveyor of heat. The working fluid cycles around the pipe, evaporating from the wick at the hot end of the pipe, traveling as a gas to the cold end of the pipe, condensing on the wick, and then traveling as a liquid to the hot end of the pipe.
Near room temperature, heat pipes use working fluids such as HFCs (hydrofluorocarbons, the replacements for Freons), ammonia, or even water. At elevated temperatures, heat pipes often use liquid metals such as sodium.
Sound consists of small fluctuations in air pressure. We hear sound because these changes in air pressure produce fluctuating forces on various structures in our ears. Similarly, microphones respond to the changing forces on their components and produce electric currents that are effectively proportional to those forces.
Two of the most common types of microphones are capacitance microphones and electromagnetic microphones. In a capacitance microphone, opposite electric charges are placed on two closely spaced surfaces. One of those surfaces is extremely thin and moves easily in response to changes in air pressure. The other surface is rigid and fixed. As a sound enters the microphone, the thin surface vibrates with the pressure fluctuations. The electric charges on the two surfaces pull on one another with forces that depend on the spacing of the surfaces. Thus as the thin surface vibrates, the charges experience fluctuating forces that cause them to move. Since both surfaces are connected by wires to audio equipment, charges move back and forth between the surfaces and the audio equipment. The sound has caused electric currents to flow and the audio equipment uses these currents to record or process the sound information.
In an electromagnetic microphone, the fluctuating air pressure causes a coil of wire to move back and forth near a magnet. Since changing or moving magnetic fields produce electric fields, electric charges in the coil of wire begin to move as a current. This coil is connected to audio equipment and again uses these currents to represent sound.
When air flows past an airplane wing, it breaks into two airstreams. The one that goes under the wing encounters the wing's surface, which acts as a ramp and pushes the air downward and forward. The air slows somewhat and its pressure increases. Forces between this lower airstream and the wing's undersurface provide some of the lift that supports the wing.
But the airstream that goes over the wing has a complicated trip. First it encounters the leading edge of the wing and is pushed upward and forward. This air slows somewhat and its pressure increases. So far, this upper airstream isn't helpful to the plane because it pushes the plane backward. But the airstream then follows the curving upper surface of the wing because of a phenomenon known as the Coanda effect. The Coanda effect is a common behavior in fluids—viscosity and friction keep them flowing along surfaces as long as they don't have to turn too quickly. (The next time your coffee dribbles down the side of the pitcher when you poured too slowly, blame it on the Coanda effect.)
Because of the Coanda effect, the upper airstream now has to bend inward to follow the wing's upper surface. This inward bending involves an inward acceleration that requires an inward force. That force appears as the result of a pressure imbalance between the ambient pressure far above the wing and a reduced pressure at the top surface of the wing. The Coanda effect is the result (i.e. air follows the wing's top surface) but air pressure is the means to achieve that result (i.e. a low pressure region must form above the wing in order for the airstream to arc inward and follow the plane's top surface).
The low pressure region above the wing helps to support the plane because it allows air pressure below the wing to be more effective at lifting the wing. But this low pressure also causes the upper airstream to accelerate. With more pressure behind it than in front of it, the airstream accelerates—it's pushed forward by the pressure imbalance. Of course, the low pressure region doesn't last forever and the upper airstream has to decelerate as it approaches the wing's trailing edge—a complicated process that produces a small amount of turbulence on even the most carefully designed wing.
In short, the curvature of the upper airstream gives rise to a drop in air pressure above the wing and the drop in air pressure above the wing causes a temporary increase in the speed of the upper airstream as it passes over much of the wing.
Dissolving solids in water always lowers the water's freezing temperature by an amount that's proportional to the density of dissolved particles. If you double the density of particles in water, you double the amount by which the freezing temperature is lowered.
While salt and sugar both dissolve in water and thus both lower its freezing temperature, salt is much more effective than sugar. That's because salt produces far more dissolved particles per pound or per cup than sugar. First, table salt (sodium chloride) is almost 40% more dense than cane sugar (sucrose), so that a cup of salt weighs much more than a cup of cane sugar. Second, a salt molecule (NaCl) weighs only about 8.5% as much as a sucrose molecule (C12H22O11), so there are far more salt molecules in a pound of salt than sugar molecules in a pound of sugar. Finally, when salt dissolves in water, it decomposes into ions: Na+ and Cl-. That decomposition doubles the density of dissolved particles produced when salt dissolves. Sugar molecules remain intact when they dissolve, so there is no doubling effect. Thus salt produces a much higher density of dissolved particles than sugar, whether you compare them cup for cup or pound for pound, and thus lowers water's freezing temperature more effectively. That's why the salt water is so slow to freeze.
They measure the volume of liquid they deliver and shut off when they have dispensed enough soda to fill the cup. Accurate volumetric flowmeters, such as those used in the dispensers, typically have a sophisticated paddlewheel assembly inside that turns as the liquid goes through a channel. When the paddlewheel has gone around the right number of times, an electronic valve closes to stop the flow of liquid.
Yes, there would be a simple relationship between the periods of the three pendulums. That's because the period of a pendulum depends only on its length and on the strength of gravity. Since a pendulum's period is proportional to the square root of its length, you would have to make your model four times as long to double the time it takes to complete a swing. A typical grandfather's clock has a 0.996-meter pendulum that takes 2 seconds to swing, while a common wall clock has a 0.248-meter pendulum that takes 1 second to swing. Note that the effective length of the pendulum is from its pivot to its center of mass or center of gravity. A precision pendulum has special temperature compensating components that make sure that this effective length doesn't change when the room's temperature changes.
There certainly is such a mechanism. The air at a jetliner's cruising altitude is much too thin to support life so it must be compressed before introducing it into the airplane's passenger cabin. The compressed air is actually extracted from an intermediate segment of the airplane's jet engines. In the course of their normal operations, these engines collect air entering their intake ducts, compress that air with rotary fans, inject fuel into the compressed air, burn the mixture, and allow the hot, burned gases to stream out the exhaust duct through a series of rotary turbines. The turbines provide the power to operate the compressor fans. Producing the stream of exhaust gas is what pushes the airplane forward.
But before fuel is injected into the engine's compressed air, there is a side duct that allows some of that compressed air to flow toward the passenger cabin. So the engine is providing the air you breathe during a flight.
There is one last interesting point about this compressed air: It is initially too hot to breathe. Even though air at 30,000 feet is extremely cold, the act of compressing it causes its temperature to rise substantially. This happens because compressing air takes energy and that energy must go somewhere in the end. It goes into the thermal energy of the air and raises the air's temperature. Thus the compressed air from the engines must be cooled by air conditioners before it goes into the passenger cabin.
You are right that adding salt to water raises the water's boiling temperature. Contrary to one's intuition, adding salt to water doesn't make it easier for the water to boil, it makes it harder. As a result, the water must reach a higher temperature before it begins to boil. Any foods you place in this boiling salt water (e.g. eggs or pasta) find themselves in contact with somewhat hotter water and should cook faster as a result. That's because most cooking is limited by the boiling temperature of water in or around food and anything that lowers this boiling temperature, such as high altitude, slows most cooking while anything that raises the boiling temperature of water, such as salt or the use of a pressure cooker, speeds most cooking. However, it takes so much salt to raise the boiling temperature of water enough to affect cooking times that this can't be the main motivation for cooking in salted water. By the time you've salted the water enough to raise its boiling temperature more than a few degrees, you've made the water too salty for cooking. It's pretty clear that salting your cooking water is basically a matter of taste, not temperature.
If you were directly between the two planets, their gravitational forces on you would oppose one another and at least partially cancel. Which planet would exert the stronger force on you would depend on their relative masses and on your distances from each of them. If one planet pulled on you more strongly than the other, you would find yourself falling toward that planet even though the other planet's gravity would oppose your descent and prolong the fall. However, there would also be a special location between the planets at which their gravitational forces would exactly cancel. If you were to begin motionless at that point in space, you wouldn't begin to fall at all. While the planets themselves would move and take the special location with them, there would be a brief moment when you would be able to hover in one place.
But there is something I've neglected: you aren't really at one location in space. Because your body has a finite size, the forces of gravity on different parts of your body would vary subtly according to their exact locations in space. Such variations in the strength of gravity are normally insignificant but would become important if you were extremely big (e.g. the size of the moon) or if the two planets you had in mind were extremely small but extraordinarily massive (e.g. black holes or neutron stars). In those cases, spatial variations in gravity would tend to pull unevenly on your body parts and might cause trouble. Such uneven forces are known as tidal forces and are indeed responsible for the earth's tides. While the tidal forces on a spaceship traveling between the earth and the moon would be difficult to detect, they would be easy to find if the spaceship were traveling between two small and nearby black holes. In that case, the tidal forces could become so severe that they could rip apart not only the spaceship and its occupants, but also their constituent molecules, atoms, and even subatomic particles.
These purported gravitational anomalies are just illusions. Because gravity is a relatively weak force, enormous concentrations of mass are required to create significant gravitational fields. Since it takes the entire earth to give you your normal weight, the mass concentration needed to cancel or oppose the earth's gravitation field in only one location would have to be extraordinary. While objects capable of causing such bizarre effects do exist elsewhere in our universe (e.g. black holes and neutron stars), there fortunately aren't any around here. As a result, the strength of the gravitational field at the earth's surface varies less than 1% over the earth's surface and always points almost exactly toward the center of the earth. Any tourist attraction that claims to have gravity pointing in some other direction with some other strength is claiming the impossible.
This is an interesting question because it brings up the tricky issue of what is the temperature in a microwave oven. In fact, there is no specific temperature in the oven because the microwaves that do the cooking are not thermal. Rather than emerging from a hot object with a well-defined temperature, these microwaves are produced in a coherent fashion by a vacuum tube. Like the light emerging from a laser, these microwaves can heat objects they encounter as hot as you like, or at least until heat begins to escape from those objects as fast as it's being added.
So instead of measuring the "temperature of the microwave oven," people normally put thermometers in the food to measure the food's temperature. This works well as long as the thermometers don't interact with the microwaves in ways that make them either hotter or inaccurate. Electronic thermometers are common in high-end microwaves. There is nothing special about these electronic thermometers except that they are carefully shielded so that the microwaves don't heat them or affect their readings. By "shielded," I mean that each of these thermometers has a continuous metallic sheath that reflects the microwaves. This sheath extends from the wall of the oven's cooking chamber all the way to the thermometer probe's tip so that the microwaves themselves can't enter the measurement electronics. Since the sheath reflects microwaves, the thermometer isn't heated by the microwaves and only measures the temperature of the food it contacts.
On the other hand, putting a mercury thermometer in a microwave oven isn't a good idea. While mercury is a metal and will reflect most of the microwaves that strike it, the microwaves will push a great many electric charges up and down the narrow column of mercury. This current flow will cause heating of the mercury because the column is too thin to tolerate the substantial current without becoming warm. The mercury can easily overheat, turn to gas, and explode the thermometer. (A reader of this web site reported having blown up a mercury thermometer just this way as a child.) Moreover, as charges slosh up and down the mercury column, they will periodically accumulate at the upper end. Since there is only a thin vapor of mercury gas above this upper surface, the accumulated charges will probably ionize this vapor and create a luminous mercury discharge. The thermometer would then turn into a mercury lamp, emitting ultraviolet light. I used microwave-powered mercury lamps similar to this in my thesis research fifteen years ago and they work very nicely.
When you view something in a flat mirror, you are looking at a virtual image of the object and this virtual image isn't located on the surface of the mirror. Instead, it's located on the far side of the mirror at a distance exactly equal to the distance from the mirror to the actual object. In effect, you are looking through a window into a "looking glass world" and seeing a distant object on the other side of that window. The reflected light reaching your eyes has all the optical characteristics of having come the full distance from that virtual image, through the mirror, to your eyes. The total distance between what you are seeing and your eyes is the sum of the distance from your eyes to the mirror plus the distance from the mirror to the object. That's why you must use your distance glasses to see most reflected objects clearly. Even when you observe your own face, you are seeing it as though it were located twice as far from you as the distance from your face to the mirror.
While your book's claim is well intended, it's actually incorrect. The author is trying to point out that atoms aren't created or destroyed during the reaction and that all the reactant atoms are still present in the products. But equating the conservation of atoms with the conservation of mass overlooks any mass loss associated with changes in the chemical bonds between atoms. While bond masses are extremely small compared to the masses of atoms, they do change as the results of chemical reactions. However even the most energy-releasing or "exothermic" reactions only produce overall mass losses of about one part in a billion and no one has yet succeeded in weighing matter precisely enough to detect such tiny changes.
Heater-based refrigerators make use of an absorption cycle in which a refrigerant is driven out of solution as a gas in a boiler, condenses into a liquid in a condenser, evaporates back into a gas in an evaporator, and finally goes back into solution in an absorption unit. The cooling effect comes during the evaporation in the evaporator because converting a liquid to a gas requires energy and thus extracts heat from everything around the evaporating liquid.
The most effective modern absorption cycle refrigerators use a solution of lithium bromide (LiBr) in water. What enters the boiler is a relatively dilute solution of LiBr (57.5%) and what leaves is dense, pure water vapor and a relatively concentrated solution of LiBr (64%). The pure water vapor enters a condenser, where it gives up heat to its surroundings and turns into liquid water. To convert this liquid water back into gas, all that has to happen is for its pressure to drop. That pressure drop occurs when the water enters a low-pressure evaporator through a narrow orifice. As the water evaporates, it draws heat from its surroundings and refrigerates them.
Finally, something must collect this low pressure water vapor and carry it back to the boiler. That "something" is the concentrated LiBr solution. When the low-pressure water vapor encounters the concentrated LiBr solution in the absorption unit, it quickly goes back into solution. The solution becomes less concentrated as it draws water vapor out of the gas above it. This diluted solution then returns to the boiler to begin the process all over again.
Overall, the pure water follows one path and the LiBr solution follows another. The pure water first appears as a high-pressure gas in the boiler (out of the boiling LiBr solution), converts to a liquid in the condenser, evaporates back into a low-pressure gas in the evaporator, and finally disappears in the absorption unit (into the cool LiBr solution). Meanwhile, the LiBr solution shuttles back and forth between the boiler (where it gives up water vapor) and the absorption unit (where it picks up water vapor). The remarkable thing about this whole cycle is that its only moving parts are in the pump that moves LiBr solution from the absorption unit to the boiler. Its only significant power source is the heater that operates the boiler. That heater can use propane, kerosene, electricity, waste heat from a conventional power plant, and so on.
Since the discovery of relativity, people have recognized that there is energy associated with rest mass and that the amount of that energy is given by Einstein's famous equation: E=mc2. However, the energy associated with rest mass is hard to release and only tiny fractions of it can be obtained through conventional means. Chemical reactions free only parts per billion of a material's rest mass as energy and even nuclear fission and fusion can release only about 1% of it. But when equal quantities of matter and antimatter collide, it's possible for 100% of their combined rest mass to become energy. Since two metric tons is 2000 kilograms and the speed of light is 300,000,000 meters/second, the energy in Einstein's formula is 1.8x1020 kilogram-meters2/second2 or 1.8x1020 joules. To give you an idea of how much energy that is, it could keep a 100-watt light bulb lit for 57 billion years.
While it's true that microwaves twist water molecules back and forth, this twisting alone doesn't make the water molecules hot. To understand why, consider the water molecules in gaseous steam: microwaves twist those water molecules back and forth but they don't get hot. That's because the water molecules beginning twisting back and forth as the microwaves arrive and then stop twisting back and forth as the microwaves leave. In effect, the microwaves are only absorbed temporarily and are reemitted without doing anything permanent to the water molecules. Only by having the water molecules rub against something while they're twisting, as occurs in liquid water, can they be prevented from remitting the microwaves. That way the microwaves are absorbed and never remitted—the microwave energy becomes thermal energy and remains behind in the water.
Visualize a boat riding on a passing wave—the boat begins bobbing up and down as the wave arrives but it stops bobbing as the wave departs. Overall, the boat doesn't absorb any energy from the wave. However, if the boat rubs against a dock as it bobs up and down, it will converts some of the wave's energy into thermal energy and the wave will have permanently transferred some of its energy to the boat and dock.
Yes, VCR's work on the same principle as an audio tape player: as a magnetized tape moves past the playback head, that tape's changing magnetic field produces a fluctuating electric field. This electric field pushes current back and forth through a coil of wire and this current is used to generate audio signals (in a tape player) or video and audio signals (in a VCR).
However, there is one big difference between an audio player and a VCR. In an audio player, the tape moves past a stationary playback head. In a VCR, the tape moves past a spinning playback head. When you pause an audio tape player, the tape stops moving and there is no audio signal. But when you pause a VCR, the playback head continues to spin. As the playback head (actually 2 or even 4 heads that trade off from one another) sweeps across a few inches of the tape, it experiences the changing magnetic fields and fluctuating electric fields needed to produce the video and audio signals. That's why you can still see the image from a paused VCR. To prevent the spinning playback heads from wearing away the tape, most VCRs limit the pause time to about 5 minutes.
A transformer transfers power between two or more electrical circuits when each of those circuits is carrying an alternating electric current. Transfers of this sort are important because many electric power systems have incompatible circuits—one circuit may use large currents of low voltage electricity while another circuit may use small currents of high voltage electricity. A transformer can move power from one circuit of the electric power system to another without any direct connections between those circuits.
Now for the technical details: a transformer is able to make such transfers of power because (1) electric currents are magnetic, (2) the magnetic fields from an alternating electric current changes with time, (3) a time-varying magnetic field creates an electric field, and (4) an electric fields pushes on electric charges and electric currents. Overall, one of the alternating currents flowing through a transformer creates a time-varying magnetic field and thus an electric field in the transformer. This electric field does work on (transfers power to) another alternating current flowing through the transformer. At the same time, this electric field does negative work on (saps power from) the original alternating current. When all is said and done, the first current has lost some of its power and the second current has gained that missing power.
Yes. For very fundamental reasons, light can't change its speed in vacuum; it always travels at the so-called "speed of light." So light that is traveling straight downward toward a celestial object doesn't speed up; only its frequency and energy increase. But light that is traveling horizontally past a celestial object will bend in flight, just as a satellite will bend in flight as it passes the celestial object. This trajectory bending is a consequence of free fall. While the falling of light as it passes through a gravitational field is a little more complicated than for a normal satellite—the light's trajectory must be studied with fully relativistic equations of motion—both objects fall nonetheless.
Diodes are one-way devices for electric current and are thus capable of separating positive charges from negative charges and keeping them apart. Those charges can separate by moving away from one another in the diode's allowed direction and then can't get back together because doing so would require them to move through the diode in the forbidden direction. Given a diode's ability to keep separated charges apart, all that's needed to start collecting separated charges is a source of energy. This energy is required to drive the positive and negative charges apart in the first place. One such energy source is a particle of light—a photon. When a photon with the right amount of energy is absorbed near the one-way junction of the diode, it can produce an electron-hole pair (a hole is a positively charged quasiparticle that is actually nothing more than a missing electron). The junction will allow only one of these charged particles to cross it and, having crossed, that particle cannot return. Thus when the diode is exposed to light, separated charge begins to accumulate on its two ends and a voltage difference appears between those ends.
While most of the "science" in that movie is actually nonsense, the use of lightning as a source of power has some basis in reality. The current in a lightning bolt is enormous, peaking at many thousands of amperes, and the voltages available are fantastically high. With so much current and voltage available, the flow of current during a lightning strike can be very complicated. Even though Doc Brown provided one path through which the lightning current could flow into the ground, he only conducted a fraction of the overall current. The remaining current flowed through the wire and into the "flux capacitor." This branching of the current is common during a lightning strike and makes lightning particularly dangerous. You don't have to be struck directly by lightning or to be in contact with the main conducting pathway between the strike and the earth for you to be injured. Current from the strike can branch out in complicated ways and follow a variety of unexpected paths to ground. You don't want to be on any one of them. Doc Brown wasn't seriously hurt because it was only a movie. In real life, people don't recover so quickly.
Your lights are dimming because something is reducing the voltage of the electricity in your house. The lights expect the electric current passing through them to experience a specific voltage drop—that is, they expect each electric charge to leave behind a certain amount of energy as the result of its passage through the lights. If the voltage of electricity in your house is less than the expected amount, the lights won't receive enough energy and will glow dimly.
The most probable cause for this problem is some power-hungry device in or near your house that cycles on every 5 or 10 minutes. In all likelihood, this device contains a large motor—motors have a tendency to draw enormous currents while they are first starting to turn, particularly if they are old and in need of maintenance. The wiring and power transformer systems that deliver electricity to your neighborhood and house have limited capacities and cannot transfer infinite amounts of power without wasting some of it. In general, wires waste power in proportion to the square of the current they are carrying. While the amount of power wasted in your home's wiring is insignificant in normal situations, it can become sizeable when the circuits are overloaded. This wasted power in the wiring appears as a loss of voltage—a loss of energy per charge—at your lights and appliances. When the heavy equipment turns on and begins to consume huge amounts of power, the wiring and other electric supply systems begin to waste much more power than normal and the voltage reaching your lights is significantly reduced. Your lights dim until the machinery stops using so much power.
To find what device that's making your lights dim, listen carefully the next time your lights fade. You'll probably hear an air conditioner, a fan, or even an elevator starting up somewhere, either in your house or in your neighborhood. There may be nothing you can do to fix the problem, but it's possible that replacing a motor or its bearings will reduce the problem. Another possible culprit is an electric heating system—a hot water heater, a radiant heater, an oven, a toaster, or even a hair-dryer. These devices also consume large amounts of power and, in an older house with limited electric services, may dim the lights.
To keep soda carbonated, you should minimize the rate at which carbon dioxide molecules leave the soda and maximize the rate at which those molecules return to it. That way, the net flow of molecules out of the soda will be small. To reduce the leaving rate, you should cool the soda—as long as ice crystals don't begin to form, cooling the soda will make it more difficult for carbon dioxide molecules to obtain the energy they need to leave the soda and will slow the rate at which they're lost. To increase the return rate, you should increase the density of gaseous carbon dioxide molecules above the soda—sealing the soda container or pressurizing it with extra carbon dioxide will speed the return of carbon dioxide molecules to the soda. Also, minimizing the volume of empty bottle above the soda will make it easier for the soda to pressurize that volume itself. The soda will lose some of its carbon dioxide while filling that volume, but the loss will quickly cease.
One final issue to consider is surface area: the more surface area there is between the liquid soda and the gas above it, the faster molecules are exchanged between the two phases. Even if you don't keep carbon dioxide gas trapped above soda, you can slow the loss of carbonation by keeping the soda in a narrow-necked bottle with little surface between liquid and gas. But you must also be careful not to introduce liquid-gas surface area inside the liquid. That's what happens when you shake soda or pour it into a glass—you create tiny bubbles inside the soda and these bubbles grow rapidly as carbon dioxide molecules move from the liquid into the bubbles. Cool temperatures, minimal surface area, and plenty of carbon dioxide in the gas phases will keep soda from going flat.
As for pouring the soda over ice causing it to bubble particularly hard, that is partly the result of air stirred into the soda as it tumbles over the ice cubes and partly the result of adding impurities to the soda as the soda washes over the rough and impure surfaces of the ice. The air and impurities both nucleate carbon dioxide bubbles—providing the initial impetus for those bubbles to form and grow. Washing the ice to smooth its surfaces and remove impurities apparently reduces the bubbling when you then pour soda of it.
Terminal velocity is the result of a delicate balance between two forces—an object's downward weight and the upward drag force that object experiences as it moves downward through the air. Terminal velocity is reached when those two forces exactly balance one another and the object experiences a net force of zero, stops accelerating, and simply coasts downward at a constant velocity. Since the upward drag force increases with downward speed, there is generally a velocity at which this balance occurs—the terminal velocity.
But while a parachutist can't change her weight, she can change the relationship between her downward speed and the upward drag force she experiences. If she rolls herself into a compact ball, she weakens the drag force and ultimately increases her terminal velocity. On the other hand, if she spreads her arms and legs wide so as to catch more air, she strengthens the drag force and decreases her terminal velocity. Popping open her parachute strengthens the drag force so much that her terminal velocity diminishes almost to zero and she coasts slowly downward to a comfortable landing. So to answer your question—two twin parachutists will descend at very different terminal velocities if they adopt different profiles or if only one opens a parachute.
Your comparison between the limitless counting numbers and the limited speeds in the universe is an interesting one because it points out a fundamental difference between the older Galilean/Newtonian understanding of the universe and the newer Einsteinian understanding. The older understanding claims that velocities can be added in the same way that counting numbers can be added and that there is thus no limit to the speeds that can exist in our universe. For example, if you are jogging eastward at 5 mph and a second runner passes you traveling eastward 5 mph faster, then a person watching the two of you from a stationary vantage point sees the second runner traveling eastward at 10 mph. The velocities add, so that 5 mph + 5 mph = 10 mph. If the second runner is now passed by a third runner, who is traveling eastward 5 mph faster than the second runner, then the stationary observer sees that third runner traveling eastward at 15 mph. And so it goes. As long as velocities add in this manner, objects can reach any speed they like.
At this point, you might assert that velocities do add and that objects should be able to reach any speed. But that's not the case. The modern, relativistic understanding of the universe says that even at these small speeds, velocities don't quite add. To the stationary observer, the second runner travels at only 9.9999999999999994 mph and the third runner at only 14.9999999999999988 mph. As you can see, when two or more velocities are combined, the final velocity isn't quite as large as the simple sum. What that means is that the velocity you observe in another object is inextricably related to your own motion. This interrelatedness is part of the theory of relativity—that observers who are moving relative to one another will see space and time somewhat differently.
For objects traveling close to the speed of light, the failure of velocity addition becomes quite severe. For example, if one spaceship travels past the earth at half the speed of light and the people in that spaceship watch a second spaceship pass them at half the speed of light in the same direction, then a person on earth will see the second spaceship traveling only four-fifths of the speed of light. As you can see, relativity is making it difficult to reach the speed of light. In fact, it's impossible to reach the speed of light! No matter how you combine velocities, no observer will ever see a massive object reach or exceed the speed of light. The only objects that can reach the speed of light are objects without mass and they can only travel at the speed of light.
So while the counting numbers obey simple addition and go on forever, velocities do not obey simple addition and have a firm limit—the speed of light. The additive counting numbers are an example of a mathematical group that extends infinitely in both directions, but there are many examples of groups that do not extend to infinity. The group that describes relativistic, real-world velocities is one such group. You can visualize another simple limited group—the one associated with walking around the surface of the earth. No matter how much you try, you can't walk more than a certain distance northward. While it seems as though steps northward add, so that 5 steps north plus 5 steps north equals 10 steps north, things aren't quite that simple. Eventually you reach the north pole and start walking south!
While I'm not an expert on geysers and would need to visit the library to verify my ideas, I believe that they operate the same way a coffee percolator does. Both objects involve a narrow water-filled channel that's heated from below. As the temperature at the bottom of the water column increases, the water's stability as a liquid decreases and its tendency to become gaseous steam increases. What prevents this heated water from converting into gas is the weight of the water and air above it, or more accurately the pressure caused by that weight. But when the water's temperature reaches a certain elevated level, it begins to turn into steam despite the pressure. Since steam is less dense than liquid water, the hot water expands as it turns into steam and it lifts the column of water above it. Water begins to spray out of the top of the channel, decreasing the weight of water in the channel and the pressure at the bottom of the channel. With less pressure keeping the water liquid, the steam forming process accelerates and the column of water rushes up the channel and into the air. Once the steam itself reaches the top of the channel, it escapes freely into the air and the pressure in the channel plummets. Water begins to reenter the channel and the whole process repeats.
What a great idea! Mylar is DuPont's brand of PET film, where "PET" is Poly(ethylene terephthalate)—the same plastic used in most plastic beverage containers (look for "PET" or "PETE" in the recycling triangle on the bottom). PET isn't a particularly inert plastic and you shouldn't have any trouble gluing to it. To form a rigid structure, you need either a glassy plastic backing (one that is stiff and brittle at room temperature) or a stiff composite backing. I'd go with fiberglass—mount the Mylar in a large quilting or needlepoint frame, coat the back of the Mylar with the glass and epoxy mixture, invert it, weight it with water, and let it harden. Mylar doesn't stretch easily, so you'll get a very shallow curve and a very long focal length mirror. While the mirror will probably have some imperfections and a non-parabolic shape, it should still do a decent job of concentrating sunlight.
I'm afraid that you confuse the hypothetical with the actual. While people have hypothesized about superluminal particles called tachyons, they have never been observed and probably don't exist. This speculation is based on an interesting but apparently non-physical class of solutions to the relativistic equations of motion. Although tachyons make for fun science fiction stories, they don't seem to have a place in the real world.
If a whistle's tube is relatively narrow, its pitch is determined primarily by its length and by how many of its ends are open to the air. That's because as you blow the whistle, a "standing" sound wave forms inside it—the same sound wave that you hear as it "leaks" out of the whistle. If the whistle is open at both ends, almost half a wavelength of this standing sound wave will fit inside the tube. Since a sound's wavelength times its frequency must equal the speed of sound (331 meters per second or 1086 feet per second), a double-open whistle's pitch is approximately the speed of sound divided by twice its length. For example, a whistle that's 0.85 centimeters long can hold one wavelength of a sound with a frequency near 19,500 cycles per second—at the upper threshold of hearing for a young person. If the whistle is closed at one end, the air inside it vibrates somewhat different; only a quarter of a wavelength of the standing sound wave will fit inside the tube. In that case, its pitch is approximately the speed of sound divided by four times its length. However, if you blow a whistle hard enough, you can cause more wavelengths of a standing sound wave to fit inside it. A strongly blown double-open whistle can house any half-integer number of wavelengths (1/2, 1, 3/2, or more), emitting higher pitched tones as it does so. A strongly blown single-open whistle can house any odd quarter-integer number of wavelengths (1/4, 3/4, 5/4, or more).
To understand the two bulges, imagine three objects: the earth, a ball of water on the side of the earth nearest the moon, and a ball of water on the side of the earth farthest from the moon. Now picture those three objects orbiting the moon. In orbit, those three objects are falling freely toward the moon but are perpetually missing it because of their enormous sideways speeds. But the ball of water nearest the moon experiences a somewhat stronger moon-gravity than the other objects and it falls faster toward the moon. As a result, this ball of water pulls away from the earth—it bulges outward. Similarly, the ball of water farthest from the moon experiences a somewhat weaker moon-gravity than the other objects and it falls more slowly toward the moon. As a result, the earth and the other ball of water pull away from this outer ball so that this ball bulges outward, away from the earth.
It's interesting to note that the earth itself bulges slightly in response to these tidal forces. However, because the earth is more rigid than the water, its bulges are rather small compared to those of the water.
Your solution should work nicely—the pulley and weight system should protect your cable from breaking because the weights should maintain a constant tension in the line. As the tree swings back and forth, the weights should rise and fall while the tension in the cord remains almost steady. Obviously, if the rising weights reach the pulley the cord will pull taut and break, so you must leave enough hanging slack.
However, if the tree's motion is too violent, even this weight and pulley system may not save the cable. As long as everything moves slowly, the tension in the cord should be equal to the weight of the weights. But if the tree moves away from the house very suddenly, then the tension in the cord will increase suddenly because the cord must not only support the weights, it must accelerate them upward as well. Part of the cord's tension acts to overcome the weights' inertia. Just as a sudden yank on a paper towel will rip it free from the roll, so a sudden yank on your cable will rip it free from the weights. If sudden yanks of this type cause trouble for you, you can fix the problem by coupling the cord to the weights via a strong spring. On long timescales, the spring will have no effect on the tension in the cord—it will still be equal to the weight of the weights. But the spring will stretch or contract during sudden yanks on the cord and will prevent the tension in the cord from changing abruptly either up or down. The spring shouldn't be too stiff—the less stiff and the more it stretches while supporting the weights, the more effectively it will smooth out changes in tension.
As far as the weight of the weights, that depends on how much curvature you want in the cable supporting the feeders. The more weight you use, the less the cable will sag but the more stress it will experience. You can determine how much weight you need by pulling on the far end of the cable with your hands and judging how hard you must pull to get a satisfactory amount of sag.
You can produce colored flames by adding various metal salts to the burning materials. That's what's done in fireworks. These metal salts decompose when heated so that individual metal atoms are present in the hot flame. Thermal energy in the flame then excites those atoms so that their electrons shift among the allowed orbits or "orbitals" and this shifting can lead to the emission of particles of light or "photons". Since the orbitals themselves vary according to which chemical element is involved, the emitted photons have specific wavelengths and colors that are characteristic of that element.
To obtain a wide variety of colors, you'll need a wide variety of metal salts. Sodium salts, including common table salt, will give you yellow light—the same light that's produced by sodium vapor lamps. Potassium salts yield purple, copper and barium salts yield green, strontium salts yield red, and so on. The classic way to produce a colored flame is to dip a platinum wire into a metal salt solution and to hold the wire in the flame. Since platinum is expensive, you can do the same trick with a piece of steel wire. The only problem is that the steel wire will burn eventually.
Because the electrons in an atom move about as waves, they can follow only certain allowed orbits that we call orbitals. This limitation is equivalent to the case of a violin string—it can only vibrate at certain frequencies. If you try to make a violin string vibrate at the wrong frequency, it won't do it. That's because the string vibrates in a wave-like manner and only certain waves fit properly along the strong. Similarly, the electron in an atom "vibrates" in a wave-like manner and only certain waves fit properly around the nucleus.
Most of the collisions between an electron and a neon atom are completely elastic—the electron bounces perfectly from the neon atom and retains essentially all of its kinetic energy. But occasionally the electron induces a structural change in the neon atom and transfers some of its energy to the neon atom. In such a case, the electron rebounds weakly and retains only a fraction of its original kinetic energy. The missing energy is left in the neon atom, which usually releases that energy as light.
Some experiments are so sensitive to electromagnetic waves that they must be performed inside "Faraday cages". A Faraday cage is a metal or metal screen box. Its walls conduct electricity and act as mirrors for electromagnetic waves. As long as a wave has a wavelength significantly longer than the largest hole in the walls, that wave will be reflected and will not enter the box. This reflection occurs because the wave's electric field pushes charges inside the metal walls and causes those charges to accelerate. These accelerating charges redirect (absorb and reemit) the wave in a new direction—a mirror reflection. Just as a box made of metal mirrors will keep light out, a box made with metal walls will keep electromagnetic waves out.
A properly built and maintained microwave oven leaks so little microwave power that you needn't worry about it. There are also inexpensive leakage testers available that you can use at home for a basic check, or for a more reliable and accurate check—as recommended by both the International Microwave Power Institute (IMPI) and the FDA—you can take your microwave oven to a service shop and have it checked with an FDA certified meter. It's only if you have dropped the oven or injured its door in some way that you might have cause to worry about standing near it. If it were to leak microwaves, their main effect would be to heat your tissue, so you would feel the leakage.
CB or citizens band radio refers to some parts of the electromagnetic spectrum that have been set aside for public use. You can operate a CB radio without training and without serious legal constraints, although the power of your transmitted wave is strictly limited. The principal band for CB radio is around 27 MHz and I think that the transmissions use the AM audio encoding scheme. As you talk, the power of your transmission increases and decreases to represent the pressure fluctuations in your voice. The receiving CB radio detects the power fluctuations in the radio wave and moves its speaker accordingly.
When you first turn on a typical computer, it must run an initial program that sets up the operating system. This initial program has to run even before the computer is able to interact with its hard drive, so the program must be available at the very instant the computer's power becomes available. Read-only memory is used for this initial bootup operation. Unlike normal random access memory, which is usually "volatile" and loses its stored information when power is removed, read-only memory retains its information without power. When you turn on the computer, this read-only memory provides the instructions the computer uses to begin loading the operating system from the hard drive.
Actually, you are asking about a current of electrons, which carry a negative charge. It's true that electrons can't be sent across the p-n junction from the p-type side to the n-type side. There are several things that prevent this reverse flow of electrons. First, there is an accumulation of negative charge on the p-type side of the p-n junction and this negative charge repels any electrons that approach the junction from the p-type end. Second, any electron you add to the p-type material will enter an empty valence level. As it approaches the p-n junction, it will find itself with no empty valence levels in which to travel the last distance to the junction. It will end up widening the depletion region—the region of effectively pure semiconductor around the p-n junction; a region that doesn't conduct electricity.
A microwave oven that's built properly and not damaged emits so little electromagnetic radiation that the speaker should never notice. The speaker might have some magnetic field leakage outside its cabinet, and that might have some effect on a microwave oven. However, most microwaves have steel cases and the steel will shield the inner workings of the microwave oven from any magnetic fields leaking from the speaker. The two devices should be independent.
A phonograph record represents the air pressure fluctuations associated with sound as surface fluctuations in long, spiral groove. This groove is V-shaped, with two walls cut at right angles to one another—hence the "V". Silence, the absence of pressure fluctuations in the air, is represented by a smooth portion of the V groove, while moments of sound are represented by a V-groove with ripples on its two walls. The depths and spacings of the ripples determine the volume and pitch of the sounds and the two walls represent the two stereo channels on which sound is recorded and reproduced.
To sense the ripples in the V-groove, a phonograph places a hard stylus in the groove and spins the record. As the stylus rides along the walls of the moving groove, it vibrates back and forth with each ripple in a wall. Two transducers attached to this stylus sense its motions and produce electric currents that are related to those motions. The two most common transduction techniques are electromagnetic (a coil of wire and a magnet move relative to one another as the stylus moves and this causes current to flow through the coil) and piezoelectric (an asymmetric crystal is squeezed or unsqueezed as the stylus moves and this causes charge to be transferred between its surfaces). The transducer current is amplified and used to reproduce the recorded sound.
Exactly. When you switch your tape recorder to the record mode, it has a special erase head that becomes active. This erase head deliberately scrambles the magnetic orientations of the tape's magnetic particles. The erase head does this by flipping the magnetizations back and forth very rapidly as the particles pass by the head, so that they are left in unpredictable orientations. There are, however, some inexpensive recorders that use permanent magnets to erase the tapes. This process magnetizes all the magnetic particles in one direction, effectively erasing a tape. Because it leaves the tape highly magnetized, this second technique isn't as good as the first one. It tends to leave some noise on the recorded tape.
The basis for Einstein's theory of relativity is the idea that everyone sees light moving at the same speed. In fact, the speed of light is so special that it doesn't really depend on light at all. Even if light didn't exist, the speed of light would still be a universal standard—the fastest possible speed for anything in our universe.
Once we recognize that the speed of light is special and that everyone sees light traveling at that speed, our views of space and time have to change. One of the classic "thought experiments" necessitating that change is the flashbulb in the boxcar experiment. Suppose that you are in a railroad boxcar with a flashbulb in its exact center. The flashbulb goes off and its light spreads outward rapidly in all directions. Since the bulb is in the center of the boxcar, its light naturally hits the front and back walls of the boxcar at the same instant and everything seems simple.
But your boxcar is actually hurtling forward on a track at an enormous speed and your friend is sitting in a station as the train rushes by. She looks into the boxcar through its window and sees the flashbulb go off. She watches light from the flashbulb spread out in all directions but it doesn't hit the front and back walls of the boxcar simultaneously. Because the boxcar is moving forward, the front wall of the boxcar is moving away from the approaching light while the back wall of the boxcar is moving toward that light. Remarkably, light from the flashbulb strikes the back wall of the boxcar first, as seen by your stationary friend.
Something is odd here: you see the light strike both walls simultaneously while your stationary friend sees light strike the back wall first. Who is right? The answer, strangely enough, is that you're both right. However, because you are moving at different velocities, the two of you perceive time and space somewhat differently. Because of these differences, you and your friend will not always agree about the distances between points in space or the intervals between moments in time. Most importantly, the two of you will not always agree about the distance or time separating two specific events and, in certain cases, may not even agree about which event happened first!
The remainder of the special theory of relativity builds on this groundwork, always treating the speed of light as a fundamental constant of nature. Einstein's famous formula, E=mc2, is an unavoidable consequence of this line of reasoning.
Some metals are composed of microscopic permanent magnets, all lumped together. Such metals include iron, nickel, and cobalt. This magnetism is often masked by the fact that the tiny magnets in these metals are randomly oriented and cancel one another on a large scale. But the magnetism is revealed whenever you put one of these magnetic metals in an external magnetic field. The tiny magnets inside these metals then line up with the external field and the metal develops large scale magnetism.
However, most metals don't have any internal magnetic order at all and there is nothing to line up with an external field. Metals such as copper and aluminum have no magnetic order in them—they don't have any tiny magnets present. The only way to make aluminum or copper magnetic is to run a current through it.
An electric current is itself magnetic—it creates a structure in the space around it that exerts forces on any magnetic poles in that space. The magnetic field around a single straight wire forms loops around the wire—the current's magnetic field would push a magnetic pole near it around in a circle about the wire. But if you wrap the wire up into a coil, the magnetic field takes on a more familiar shape. The current-carrying coil effectively develops a north pole at one end of the coil and a south pole at the other. Which end is north depends on the direction of current flow around the loop. If current flows around the loop in the direction of the fingers of your right hand, then your thumb points to the north pole that develops at one end of the coil.
While the full answer to this question is complicated, the most important issues are the strengths and locations of the magnetic poles in each magnet. Since each magnet has north poles and south poles of equal strengths, there are always attractive and repulsive forces at work between a pair of magnets—their opposite poles always attract and their like poles always repel. You can make two magnets attract one another by turning them so that their opposite poles are closer together than their like poles (e.g. by turning a north pole toward a south pole).
To maximize the attraction between the magnets, opposite magnetic poles should be as near together as possible while like magnetic poles are as far apart as possible. With long bar magnets, you align the magnets head to toe so that you have the north pole of one magnet opposite the south pole of the other magnet and vice versa. But long magnets also tend to have weaker poles than short stubby magnets because it takes energy to separate a magnet's north pole from its south pole. With short stubby magnets, the best you can do is to bring the north pole of one magnet close to the south pole of the other magnet while leaving their other poles pointing away from one another. Horseshoe magnets combine some of the best of both magnets—they can have the strong poles of short stubby magnets with more distance separating those poles.
Returning to the paper question, size is less important than pole strength and separation. The stronger the magnets and the farther apart their poles, the more paper you can hold between them.
The sound you hear may be related to the vortices that swirl behind a plane's wingtips as it moves through the air. These vortices form as a consequence of the wing's lift-generating processes. Because the air pressure above a wing is lower than the air pressure below the wing, air is sucked around the wingtip and creates a swirling vortex. The two vortices, one at each wingtip, trail behind the plane for miles and gradually descend. You may be hearing them reach the ground after the airplane has passed low over your home. If someone reading this has another explanation, please let me know.
Those dispensers measure the volume of liquid they dispense and shut off when they've delivered enough liquid to fill the cup. They don't monitor where that liquid is going, so if you put the wrong sized cup below them or press the button twice, you're in trouble.
The number of "basic forces" has changed over the years, increasing as new forces are discovered and decreasing as seemingly separate forces are joined together under a more sophisticated umbrella. A good example of this evolution of understanding is electromagnetism—electric and magnetic forces were once thought separate but gradually became unified, particularly as our understanding of time and space improved. More recently, weak interactions have joined electromagnetic interactions to become electroweak interactions. In all likelihood, strong and gravitational interactions will eventually join electroweak to give us one grand system of interactions between objects in our universe.
But regardless of counting scheme, I can still answer your question about how the four basic forces differ. Gravitational forces are attractive interactions between concentrations of mass/energy. Everything with mass/energy attracts everything else with mass/energy. Because this gravitational attraction is exceedingly weak, we only notice it when there are huge objects around to enhance its effects.
Electromagnetic forces are strong interactions between objects carrying electric charge or magnetic pole. While most of these interactions can be characterized as attractive or repulsive, that's something of an oversimplification whenever motion is involved.
Weak interactions are too complicated to call "forces" because they almost always do more than simply pull two objects together or push them apart. Weak interactions often change the very natures of the particles that experience them. But the weak interactions are rare because they involve the exchange of exotic particles that are difficult to form and live for exceedingly short times. Weak interactions are responsible for much of natural radioactivity.
Strong forces are also very complicated, primarily because the particles that convey the strong force themselves experience the strong force. Strong forces are what hold quarks together to form familiar particles like protons and neutrons.
The effects you are referring to are extremely subtle, so no one will ever notice them in an astronaut. But with ultraprecise clocks, it's not hard to see strange effects altering the passage of time in space. There are actually two competing effects that alter the passage of time on a spaceship—one that slows the passage of time as a consequence of special relativity and the other that speeds the passage of time as a consequence of general relativity.
The time slowing effect is acceleration—a person or clock that takes a fast trip around the earth and then returns to the starting point will experience slightly less time than a person or clock that remained at the starting point. This effect is a consequence of acceleration and the changing relationships between space and time that come with different velocities.
The time speeding effect is gravitational redshift—a person or clock that is farther from the earth's center experiences slightly more time than a person or clock that remains at the earth's surface. This effect is a consequence of the decreased potential energy that comes with being deeper in the earth's gravitational potential well.
When an astronaut is orbiting the earth, he isn't really weightless. The earth's gravity is still pulling him toward the center of the earth and his weight is almost as large as it would be on the earth's surface. What makes him feel weightless is the fact that he is in free fall all the time! He is falling just as he would be if he had jumped off a diving board or a cliff. If it weren't for the astronaut's enormous sideways velocity, he would plunge toward the earth faster and faster and soon crash into the earth's surface. But his sideways velocity carries him past the horizon so fast that he keeps missing the earth as he falls. Instead of crashing into the earth, he orbits it.
During his orbit, the astronaut feels weightless because all of his "pieces" are falling together. Those pieces don't need to push on one another to keep their relative positions as they fall, so he feels none of the internal forces that he interprets as weight when he stands on the ground. A falling astronaut can't feel his weight.
To prepare for this weightless feeling, the astronaut needs to fall. Jumping off a diving board or riding a roller coaster will help, but the classic training technique is a ride on the "Vomit Comet"—an airplane that follows a parabolic arc through the air that allows everything inside it to fall freely. The airplane's arc is just that of a freely falling object and everything inside it floats around in free fall, too—including the astronaut trainee. The plane starts the arc heading upward. It slows its rise until it reaches a peak height and then continues arcing downward faster and faster. The whole trip lasts at most 20 seconds, during which everyone inside the plane feels weightless.
Europe uses alternating current, just as we do, however some of the characteristics of that current are slightly different. First, Europe uses 50 cycle-per-second current, meaning that current there reverses directions 100 times per second. That's somewhat slower than in the U.S., where current reverses 120 times per second (60 full cycles of reversal each second or 60 Hz). Second, their standard voltage is 230 volts, rather than the 120 volts used in the U.S.
While some of our appliances won't work in Europe because of the change in cycles-per-second, the biggest problem is with the increase in voltage. The charges entering a U.S. appliance in Europe carry about twice the energy per change (i.e. twice the voltage) and this increased "pressure" causes about twice the number of charges per second (i.e. twice the current) to flow through the appliance. With twice the current flowing through the appliance and twice as much voltage being lost by this current as it flows through the appliance, the appliance is receiving about four times its intended power. It will probably burn up.
They contain highly purified and refined chemicals and are actually marvels of engineering. It's more surprising to me that they are so cheap, given how complicated they are to make.
It's useful to describe moving electric charges as a current and for that current to flow in the direction that the charges are moving. Suppose that we define current as flowing in the direction that electrons take and look at the result of letting this current of electrons flow into a charge storage device. We would find that as this current flowed into the storage device, the amount of charge (i.e. positive) charge in that device would decrease! How awkward! You're "pouring" something into a container and the contents of that container are decreasing! So we define current as pointing in the direction of positive charge movement or in the direction opposite negative charge movement. That way, as current flows into a storage device, the charge in that device increases!
The bulb in a battery doesn't care which way current flows through it. The metal has no asymmetry that would treat left-moving charges differently from right-moving charges. That's not true of the transistors in a walkman or gameboy. They contain specialized pieces of semiconductor that will only allow positive charges to move in one direction, not the other. When you put the batteries in backward and try to propel current backward through its parts, the current won't flow and nothing happens.
Your body is similar to salt water and is thus a reasonably good conductor of electricity. Once current penetrates your skin (which is insulating), it flows easily through you. At high currents, this electricity can deposit enough energy in you to cause heating and thermal damage. But at lower currents, it can interfere with normal electrochemical and neural process so that your muscles and nerves don't work right. It takes about 0.030 amperes of current to cause serious problems for your heart, so that currents of that size can be fatal.
The battery stops separating charges once enough have accumulated on its terminals. If the flashlight is off, so that charges build up, then the battery soon stops separating charge and the light bulb doesn't light.
You can recharge any battery by pushing charge through it backward (pushing positive charge from its positive terminal to its negative terminal). However, some batteries don't take this charge well or heat up. The ones that recharge most effectively are those that can rebuild their chemical structures most effectively as they operate backward.
If you are asking why doesn't the earth itself get pulled up toward a large magnet or electromagnet that I'm holding in my hand, the answer is that the magnetic forces just aren't strong enough to pull the magnet and earth together. I'm holding the two apart with other forces and preventing them from pulling together. The forces between poles diminish with distance. Those forces are proportional to the inverse square of the distance between poles, so they fall off very quickly as the poles move apart. Moreover, each north pole is connected to a south pole on the same magnet, so the attraction between opposite poles on two separate magnets is mitigated by the repulsions of the other poles on those same magnets. As a result, the forces between two bar magnets fall over even faster than the simple inverse square law predicts. It would take an incredible magnet, something like a spinning neutron star, to exert magnet forces strong enough to damage the earth. But then a neutron star would exert gravitational forces that would damage the earth, too, so you'd hardly notice the magnetic effects.
The earth is a huge magnet and it is made out of metal. The earth's core is mostly iron and nickel, both of which can be magnetic metals. However, the earth's magnetism doesn't appear to come from the metal itself. Current theories attribute the earth's magnetism to movements in and around the core. There are either electric currents associated with this movement or some effects that orient the local magnetization of the metal. I don't think that there is any general consensus on the matter.
If the ball was pitched straight and true, the same way every pitch, good batters could hit every one. There is enough time in the wind-up and pitch for the batter to determine where and when to swing and to hit the ball just right. But the pitches vary and the balls curve. That limits the batter's ability to predict where the ball is going. There aren't any physical laws that limit a batter's ability to hit every ball well, but there are physiological and mental limits that lower everyone's batting average.
Actually, if you drive fast over a real speed bump, it's not good for your wheels and suspension. The springs in your car do protect the car from some of the effects of the bump, but not all of them. However, imagine driving over a speed bump on a traditional bicycle—one that has no spring suspension. The faster you drive over that bump, the more it will throw you into the air.
First, magnets don't involve charges, they involve poles. So the question should probably be "are all metals magnetically poled?" The answer to this question is that they are never poled—they never have a net pole. They always have an even balance of north and south pole. However, there are some metals that have their north and south poles separated from one another. A magnetized piece of steel is that way. Only a few metals can support such separated poles and we will study those metals in a few weeks.
No. Blue light causes the photoconductor to conduct. When you use white light in a xerographic copier, it's the blue and green portions of the light that usually do the copying. The red is wasted.
There don't appear to be any isolated poles in our universe, or at least none have been found. That's just the way it is. As a result of this situation, the only way to create magnetism is through its relationship with electricity. When you use electricity to create magnetic fields, you effectively create equal pairs of poles—as much north pole as south pole.
Yes. The light sensitive particles in black-and-white photographic paper don't respond to red light because the energy in a photon of red light doesn't have enough energy to cause the required chemical change. In effect, electrons are being asked to shift between levels when the light hits them and red light can't make that happen in the photographic paper. However, most modern black-and-white films are sensitive to red light because that makes roses and other red objects appear less dark and more realistic in the photographs.
They assemble 4 colors, yellow, cyan, magenta, and black together to form the final image. The photoconductor creates charge images using blue, red, green, and white illumination successively and uses those images to form patterns of yellow, cyan, magenta, and black toner particles. These particles are then superimposed to form the final image, which appears full color. Naturally, the photoconductor used in such a complicated machine must be sensitive to the whole visible spectrum of light.
As one of my readers (Tom O.) points out, most modern color copiers are essentially scanners plus color printers. They use infrared lasers to write the images optically onto four light-sensitive drums, one drum for each of the four colors (some systems reuse the same drum four times).
Yes. Particles of light, photons, cause chemical changes in the film. You can work with some black-and-white films in red light because red light photons don't have enough energy to cause changes in those films. However, color film and most modern black-and-white films require complete darkness during processing. If you expose them to any visible light, you'll cause chemistry to occur.
They are generally more conducive. Black light is actually ultraviolet light and its photons carry more energy than any visible photon. They can cause chemical changes in many materials, including skin.
I don't know. That question has puzzled me for years. The mixture should find its molecules clinging together. They must contain something that keeps the oppositely charged systems separate from one another so that they don't aggregate.
In a metal, electrons can easily shift from one level to another empty level because the levels are close together in energy. In a full insulator, it's very difficult for the electrons to shift from one level to an empty level because all of the empty levels are far above the filled levels in energy. In a photoconductor, the empty levels are modestly above the filled levels in energy, so a modest amount of energy is all that's needed to shift an electron. This energy can be supplied by a particle or "photon" of light. An illuminated photoconductor conducts electricity.
The simplest way to make these fields is with electric charges (for an electric field) or with magnets (for a magnetic field). Charges are naturally surrounded by electric fields and magnets are naturally surrounded by magnetic fields. But fields themselves can create other fields by changing with time. That's how the fields in a light wave work—the electric field in the light wave changes with time and creates the magnetic field and the magnetic field changes with time and creates the electric field. This team of fields can travel through space without any charge or magnets nearby.
If you put a conditioner on your hair, it will attract enough moisture to allow static charge to dissipate.
They leave a layer of conditioning soap on the clothes and this soap attracts moisture. The moisture conducts electricity just enough to allow static charge to dissipate.
No, an MRI uses a very different technique for imaging your body. A copier uses light to examine the original document while an MRI machine uses the magnetic responses of hydrogen atoms to map your body.
While charges can move freely through a metal, allowing the metal to carry electric current, it's much harder for charges to travel outside of a conductor. Charges can move through the air or through plastic or glass, but not very easily. It takes energy to pull the charges out of a metal and allow them to move through a non-metal. Most of the time, this energy requirement prevents charges from moving through insulators such as plastic, glass, air, and even empty space.
It is possible to simply pull up your legs. When you do that, you reduce the downward force your feet exert on the ground and the ground responds by pushing upward on your feet less strongly. With less upward force to support you, you begin to fall.
When you complete a circuit by plugging an appliance into an electrical outlet, current flows out one wire to the appliance and returns to the electric company through the other wire. With alternating current, the roles of the two wires reverse rapidly, so that at one moment current flows out the black wire to the appliance and moments later current flows out the white wire to the appliance. But the power company drives this current through the wires by treating the black wire specially—it alternately raises and lowers the electrostatic potential or voltage of the black wire while leaving the voltage of the white wire unchanged with respect to ground. When the voltage of the black wire is high, current is pushed through the black wire toward the appliance and returns through the white wire. When the voltage of the black wire is low, current is pulled through the black wire from the appliance and is replaced by current flowing out through the white wire.
The white wire is rather passive in this process because its voltage is always essentially zero. It never has a net charge on it. But the black wire is alternately positively charged and then negatively charged. That's what makes its voltage rise and fall. Since the black wire is capable of pushing or pulling charge from the ground instead of from the white wire, you don't want to touch the black wire while you're grounded. You'll get a shock.
Heat is thermal energy that is flowing from one object to another. While several centuries ago, people thought heat was a fluid, which they named "caloric," we now know that it is simply energy that is being transferred. Heat moves via several mechanisms, including conduction, convection, and radiation. Conduction is the easiest to visualize—the more rapidly jittering atoms and molecules in a hotter object will transfer some of their energy to the more slowly jittering atoms in molecules in a colder object when you touch the two objects together. Even though no atoms or molecules are exchanged, their energy is. In convection, moving fluid carries thermal energy along with it from one object to another. In this case, there is material exchanged although usually only temporarily. In radiation, the atoms and molecules exchange energy by sending thermal radiation back and forth. Thermal radiation is electromagnetic waves and includes infrared light. A hotter object sends more infrared light toward a colder object than vice versa, so the hotter object gives up thermal energy to the colder object.
Yes, but only if some of the poles are weaker than other so that when you sum up the total north pole strength and the total south pole strength, those two sums are equal. For example, you can make a magnet that has two north poles and one south pole if the north poles are each half as strong as the south pole. All magnets that we know of have exactly equal amounts of north and south pole. That's because we have never observed a pure north or a pure south pole in nature and you'd need such a pure north or south pole to unbalance the poles of a magnet. A
The absence of such "monopoles" is an interesting puzzle and scientists haven't given up hope of finding them. Some theories predict that they should exist, but be very difficult to form artificially. There may be magnetic monopoles left over from the big bang, but we haven't found any yet.
Not exactly. Sliding friction refers to the situation in which two surfaces slide across one another while touching. In hydroplaning, the two surfaces are sliding across one another, but they aren't touching. Instead, they're separated by a thin layer of trapped water. While hydroplaning still converts mechanical energy into thermal energy, just as sliding friction does, the lubricating effect of the water dramatically reduces the energy conversion. That's why you can hydroplane for such a long distance on the highway; there is almost no slowing force at all.
Dan Barker, one of my readers, informed me of a NASA study showing that there is a minimum speed at which a tire will begin to hydroplane and that that speed depends on the square root of the tire pressure. Higher tire pressure tends to expel the water layer and prevent hydroplaning, while lower tire pressure allows the water layer to remain in place when the vehicle is traveling fast enough. As Dan notes, a large truck tire is typically inflated to 100 PSI and resists hydroplaning at speed of up to about 100 mph. But a passanger car tire has a much lower pressure of about 32 PSI and can hydroplane at speeds somewhat under 60 mph. That's why you have to be careful driving on waterlogged pavement at highway speeds and why highway builders carefully slope their surfaces to shed rain water quickly.
Ideally, it doesn't matter how many steps you take with each step—the work you do in lifting yourself up a staircase depends only on your starting height and your ending height (assuming that you don't accelerate or decelerate in the overall process and thus change your kinetic energy, too). But there are inefficiencies in your walking process that lead you to waste energy as heat in your own body. So the energy you convert from food energy to gravitational potential energy in climbing the stairs is fixed, but the energy you use in carrying out this procedure depends on how you do it. The extra energy you use mostly ends up as thermal energy, but some may end up as sound or chemical changes in the staircase, etc.
Actually, some bearings are dry (no grease or oil) and still last a very long time. The problem is that the idea touch-and-release behavior is hard to achieve in a bearing. The balls or rollers actually slip a tiny bit as they rotate and they may rub against the sides or retainers in the bearing. This rubbing produces wear as well as wasting energy. To reduce this wear and sliding friction, most bearings are lubricated.
If you brake your car too rapidly, the force of static friction between the wheels and the ground will become so large that it will exceed its limit and the wheels will begin to skid across the ground. Once skidding occurs, the stopping force becomes sliding friction instead of static friction. The sliding friction force is generally weaker than the maximum static friction force, so the stopping rate drops. But more importantly, you lose steering when the wheels skid. An anti-lock braking system senses when the wheels suddenly stop turning during braking and briefly release the brakes. The wheel can then turn again and static friction can reappear between the wheel and the ground.
When a ball bounces, some of its molecules slide across one another rather than simply stretching or bending. This sliding leads to a form of internal sliding friction and sliding friction converts useful energy into thermal energy. The more sliding friction that occurs within the ball, the less the ball stores energy for the rebound and the worse the ball's bounce. The missing energy becomes thermal energy in the ball and the ball's temperature increases.
Actually, both a mouse ball and a bowling ball will bounce somewhat if you drop them on a suitably hard surface. It does have to do with elasticity. During the impact, the ball's surface dents and the force that dents the ball does work on the ball—the force on the ball's surface is inward and the ball's surface moves inward. Energy is thus being invested in the ball's surface. What the ball does with this energy depends on the ball. If the ball is an egg, the denting shatters the egg and the energy is wasted in the process of scrambling the egg's innards. But in virtually any normal ball, some or most of the work done on the ball's surface is stored in the elastic forces within the ball—this elastic potential energy, like all potential energies, is stored in forces. This stored energy allows the surface to undent and do work on other things in the process. During the rebound, the ball's surface undents. Although it's a little tricky to follow the exact flow of energy during the rebound, the elastic potential energy in the dented ball becomes kinetic energy in the rebounding ball. But even the best balls waste some of the energy involved in denting their surfaces. That's why balls never bounce perfectly and never return to their original heights when dropped on a hard, stationary surface. Some balls are better than others at storing and returning this energy, so they bounce better than others.
Yes, when a falling object hits a table, the table pushes up on the falling object. What happens from then on depends on the object's characteristics. The egg shatters as the table pushes on it and the ball bounces back upward.
Each time the ball bounces, it rises to a height that is a certain fraction of its height before that bounce. The ratio of these two heights is the fraction of the ball's energy that is stored and returned during the bounce. A very elastic ball will return about 90% of its energy after a bounce, returning to 90% of its original height after a bounce. A relatively non-elastic ball may only return about 20% of its energy and bounce to only 20% of its original height. It is this energy efficiency that determines how many times a ball bounces. The missing energy is usually converted into thermal energy within the ball's internal structure.
While we ordinarily associate energy with an object's overall movement or position or shape, the individual atoms and molecules within the object can also have their own separate portions of energy. Thermal energy is the energy associated with the motions and positions of the individual atoms within the object. While an object may be sitting still, its atoms and molecules are always jittering about, so they have kinetic energies. When they push against one another during a bounce, they also have potential energies. These internal energies, while hard to see, are thermal energy.
You are merging two equations out of context. The force you exert on an object can be non-zero without causing that object to accelerate. For example, if someone else is pushing back on the object, the object may not accelerate. If the object moves away from you as you push on it, then you'll be doing work on the object even though it's not accelerating. The only context in which you can merge those two equations (Force=mass x acceleration and Work=Force x distance) is when you are exerting the only force on the object. In that case, your force is the one that determines the object's acceleration and your force is the one involved in doing work. In that special case, if the object doesn't accelerate, then you do no work because you exert no force on the object! If someone else is pushing the object, then the force causing it to accelerate is the net force and not just your force on the object. As you can see, there are many forces around and you have to be careful tacking formulae together without thinking carefully about the context in which they exist.
Different forces acting on a single object are not official pairs; not the pairs associated with Newton's third law of action-reaction. While it is possible for an object to experience two different forces that happen to be exactly equal in magnitude (amount) but opposite in direction, that doesn't have to be the case. When an egg falls and hits a table, the egg's downward weight and the table's upward support force on the egg are equal in magnitude only for a fleeting instant during the collision. That's because the table's support force starts at zero while the egg is falling and then increases rapidly as the egg begins to push against the table's surface. For just an instant the table pushes upward on the egg with a force equal in magnitude to the egg's weight. But the upward support force continues to increase in strength and eventually pushes a hole in the egg's bottom.
The enormous upward force on the egg when it hits the table does cause the egg to accelerate upward briefly. The egg loses all of its downward velocity during this upward acceleration. But the egg breaks before it has a chance to acquire any upward velocity and, having broken, it wastes all of its energy ripping itself apart into a mess. If the egg had survived the impact and stored its energy, it probably would have bounced, at least a little. But the upward force from the table diminished abruptly when the egg broke and the egg never began to head upward for a real bounce.
When an egg is sitting on a table, each object is exerting a support force on the other object. Those two support forces are equal in magnitude (amount) but opposite in direction. To be specific, the table is pushing upward on the egg with a support force and the egg is pushing downward on the table with a support force. Both forces have the same magnitude—both are equal in magnitude to the egg's weight. The fact that the egg is pushing downward on the table with a "support" force shows that not all support forces actually "support" the object they are exert on. The egg isn't supporting the table at all. But a name is a name and on many occasions, support forces do support the objects they're exerted on.
I'm afraid that spoon bending is simply a hoax. While there are electrochemical processes going on in the mind that exert detectable forces on special probes located outside the head, these forces are so small that they are incapable of doing anything as demanding as bending a spoon. Spoon bending and all other forms of telekinesis are simply tricks played on gullible audiences.
The fact that more massive objects also weigh more is just an observation of how the universe works. However, any other behavior would lead to some weird consequences. Suppose, for example, that an object's weight didn't depend on its mass, that all objects had the same weight. Then two separate balls would each weigh this standard amount. But now suppose that you glued the two balls together. If you think of them as two separate balls that are now attached, they should weigh twice the standard amount. But if you think of them as one oddly shaped object, they should weigh just the standard amount. Something wouldn't be right. So the fact that weight is proportional to mass is a sensible situation and also the way the universe actually works.
A ball bounces because its surface is elastic and it stores energy during the brief period of collision when the ball and floor are pushing very hard against one another. Much of this stored energy is released in a rebound that tosses the ball back upward for another bounce. But people don't store energy well during a collision and they don't rebound much. The energy that we should store is instead converted into thermal energy—we get hot rather than bouncing back upward.
The force that gravity exerts on an object is that object's weight. An object that has more gravity pulling on it weighs more and vice versa.
While you are throwing the ball upward, you are pushing it upward and there is an upward force on the ball. But as soon as the ball leaves your hand, that upward force vanishes and the ball travels upward due to its inertia alone. In the discussion of that upward flight, I always said "after the ball leaves your hand," to exclude the time when you are pushing upward on the ball. Starting and stopping demonstrations are often tricky and I meant you to pay attention only to the period when the ball was in free fall.
The fact that both balls fall together is the result of a remarkable balancing effect. Although the larger ball is more massive than the smaller ball, making the larger ball harder to start or stop, the larger ball is also heavier than the smaller ball, meaning that gravity pulls downward more on the larger ball. The larger ball's greater weight exactly compensates for its greater mass, so that it is able to keep up with the smaller ball as the two objects fall to the ground. In the absence of air resistance, the two balls will move exactly together-the larger ball with its greater mass and greater weight will keep up with the smaller ball.
It's very important to distinguish velocity from acceleration. Acceleration is caused only by forces, so while a ball is falling freely it is accelerating according to gravity alone. In that case it accelerates downward at 9.8 m/s2 throughout its fall (neglecting air resistance). But while the ball's acceleration is constant, its velocity isn't. Instead, the ball's velocity gradually increases in the downward direction, which is to say that the ball accelerates in the downward direction. Velocity doesn't "act"—only forces "act." Instead, a ball's velocity shifts more and more toward the downward direction as it falls.
About terminal velocity: when an object descends very rapidly through the air, it experiences a large upward force of air resistance. This new upward force becomes stronger as the downward speed of the object becomes greater. Eventually this upward air resistance force balances the object's downward weight and the object stops accelerating downward. It then descends at a constant velocity—obeying its inertia alone. This special downward speed is known as "terminal velocity." An object's terminal velocity depends on the strength of gravity, the shape and other characteristics of the object, and the density and other characteristics of the air.
Inertia is everywhere. Left to itself, an object will obey inertia and travel at constant velocity. In deep space, far from any planet or star that exerts significant gravity, an object will exhibit this inertial motion. But on earth, the earth's gravity introduces complications that make it harder to observe inertial motion. A ball that's thrown up in the air still exhibits inertial effects, but its downward weight prevents the ball from following its inertia alone. Instead, the ball gradually loses its upward speed and eventually begins to descend instead. So inertia is the basic underlying principle of motion while gravity is a complicating factor.
When you stand on the floor, the floor exerts two different kinds of forces on you—an upward support force that balances your downward weight and horizontal frictional forces that prevent you from sliding across the floor. Ultimately, both forces involve electromagnetic forces between the charged particles in the floor and the charged particles in your feet. The support force develops as the atoms in the floor act to prevent the atoms in your feet from overlapping with them. The frictional forces have a similar origin, although they involve microscopic structure in the surfaces.
Since light carries energy with it, a cloth that absorbs light also absorbs energy. In most cases, this absorbed energy becomes thermal energy in the cloth. Because of this extra thermal energy, the cloth's temperature rises and it begins to transfer the thermal energy to its surroundings as heat. Its temperature stops rising when the thermal energy it receives from the light is exactly equal to the thermal energy it transfers to its surroundings as heat. This final temperature depends on how much light it absorbs—if it absorbs lots of light, then it will reach a high temperature before the balance of energy flow sets in.
A cloth's color is determined by how it absorbs and emits light. Black cloth absorbs essentially all light that hits it, which is why its temperature rises so much. White cloth absorbs virtually no light, which is why it remains cool. Colored cloths fall somewhere in between black and white. Blue cloth absorbs light in the green and red portions of the spectrum while reflecting the blue portion. Red cloth absorbs light in the blue and green portions of the spectrum while reflecting the red portion. Since most light sources put more energy in the red portion of the spectrum than in the blue portion of the spectrum, the blue cloth absorbs more energy than the red cloth. So the sequence of temperatures you observed is the one you should expect to observe.
One final note: most light sources also emit invisible infrared light, which also carries energy. Most of the light from an incandescent lamp is infrared. You can't tell by looking at a piece of cloth how much infrared light it absorbs and how much it reflects. Nonetheless, infrared light affects the cloth's temperature. A piece of white cloth that absorbs infrared light may become surprisingly hot and a piece of black cloth that reflects infrared light may not become as hot as you would expect.
A roller coaster is a gravity-powered train. Since it has no engine or other means of propulsion, it relies on energy stored in the force of gravity to make it move. This energy, known as "gravitational potential energy," exists because separating the roller coaster from the earth requires work—they have to be pulled apart to separate them. Since energy is a conserved quantity, meaning that it can't be created or destroyed, energy invested in the roller coaster by pulling it away from the earth doesn't disappear. It becomes stored energy: gravitational potential energy. The higher the roller coaster is above the earth's surface, the more gravitational potential energy it has.
Since the top of the first hill is the highest point on the track, it's also the point at which the roller coaster's gravitational potential energy is greatest. Moreover, as the roller coaster passes over the top of the first hill, its total energy is greatest. Most of that total energy is gravitational potential energy but a small amount is kinetic energy, the energy of motion.
From that point on, the roller coaster does two things with its energy. First, it begins to transform that energy from one form to another—from gravitational potential energy to kinetic energy and from kinetic energy to gravitational potential energy, back and forth. Second, it begins to transfer some of its energy to its environment, mostly in the form of heat and sound. Each time the roller coaster goes downhill, its gravitational potential energy decreases and its kinetic energy increases. Each time the roller coaster goes uphill, its kinetic energy decreases and its gravitational potential energy increases. But each transfer of energy isn't complete because some of the energy is lost to heat and sound. Because of this lost energy, the roller coaster can't return to its original height after coasting down hill. That's why each successive hill must be lower than the previous hill. Eventually the roller coaster has lost so much of its original total energy that the ride must end. With so little total energy left, the roller coaster can't have much gravitational potential energy and must be much lower than the top of the first hill.
It's then time for the riders to get off, new riders to board, and for a motor-driven chain to drag the roller coaster back to the top of the hill to start the process again. The chain does work on the roller coaster, investing energy into it so that it can carry its riders along the track at break-neck speed again. Overall, energy enters the roller coaster by way of the chain and leaves the roller coaster as heat and sound. In the interim, it goes back and forth between gravitational potential energy and kinetic energy as the roller coaster goes up and down the hills.
Bouncing is related to elasticity. Any object that stores energy when deformed will rebound when it collides with a rigid surface. As long as the object is elastic, it doesn't matter whether it's hard or soft. It will still rebound from a rigid surface. Thus both a rubber ball and a steel marble will rebound strongly when you drop them on a steel anvil.
But hardness does have an important effect on bouncing from a non-rigid surface. When a hard object collides with a non-rigid surface, the surface does some or all of the deforming so that the surface becomes involved in the energy storage and bounce. If the surface is elastic, storing energy well when it deforms, then it will make the object rebound strongly. That's what happens when a steel marble collides with a rubber block. However, if the surface isn't very elastic, then the object will not rebound much. That's what happens when a steel marble collides with a thick woolen carpet.
A dead ball, a ball that doesn't bounce, is one with enormous internal friction. A bouncy ball stores energy when it collides with a surface and then returns this energy when it rebounds. But no ball is perfectly elastic, so some of the collision energy extracted from the ball and surface when they collide is ultimately converted into heat rather than being returned during the rebound. The deader the ball is, the less of the collision energy is returned as rebound energy. A truly dead ball converts all of the collision energy into heat so that it doesn't rebound at all.
Most of the missing collision energy is lost because of sliding friction within the ball. Molecules move across one another as the ball's surface dents inward and these molecules rub. This rubbing produces heat and diminishes the elastic potential energy stored in the ball. When the ball subsequently undents, there just isn't as much stored energy available for a strong rebound. The classic dead "ball" is a beanbag. When you throw a beanbag at a wall, it doesn't rebound because all of its energy is lost through sliding friction between the beans as the beanbag dents.
To track someone in a forest, he must be emitting or reflecting something toward you and doing it in a way that is different from his surroundings. For example, if he is talking in a quiet forest, you can track him by his sound emissions. Or if he is exposed to sunlight in green surroundings, you can track him by his reflections of light.
But while both of these techniques work fine at short distances, they aren't so good at large distances in a dense forest. A better scheme is to look for his thermal radiation. All objects emit thermal radiation to some extent and the spectral character of this thermal radiation depends principally on the temperatures of the objects. If the person is hotter than his surroundings, as is almost always the case, he will emit a different spectrum of thermal radiation than his surrounds. Light sensors that operate in the deep infrared can detect a person's thermal radiation and distinguish it from that of his cooler surroundings. Still, viewing that thermal radiation requires a direct line-of-sight from the person to the infrared sensor, so if the forest is too dense, the person is untrackable.
The large, rounded head of a badminton birdie serves at least two purposes: it makes sure that the birdie bounces predictably off the racket's string mesh and it protects the strings and birdie from damage. If the birdie's head were smaller, it would strike at most a small area on one of the racket strings. If it hit that string squarely, the birdie might bounce predictably. But if it hit at a glancing angle, the birdie would bounce off at a sharp angle. By spreading out the contact between the birdie and the string mesh, the large head makes the birdie bounce as though it had hit a solid surface rather than one with holes.
Spreading out the contact also prevents damage to the racket and birdie. If they collided over only a tiny area, the forces they exerted on one another would be concentrated over that area and produce enormous local pressures. These pressures could cut the birdie or break a string. But with the birdie's large head, the pressures involved are mild and nothing breaks.
Any time you hit an object with a racket or bat, there's a question about how heavy the racket or bat should be for maximum distance. Actually, it isn't weight that's most important in a racket or bat, it's mass—the measure of the racket or bat's inertia. The more massive a racket or bat is, the more inertia it has and the less it slows down when it collides with something else. A more massive racket will slow less when it hits a birdie. From that observation, you might think that larger mass is always better. But a more massive racket or bat is also harder to swing because of its increased inertia.
So there are trade offs in racket or bat mass. For badminton, the birdie has so little mass that it barely slows the racket when the two collide. Increasing the racket's mass would allow it to hit the birdie slightly farther, but only if you continued to swing the racket as fast as before. Since increasing the racket mass will make it harder to swing, it's probably not worthwhile. In all likelihood, people have experimented with racket masses and have determined that the standard mass is just about optimal for the game.
An event horizon is the surface around a black hole from which not even light can escape. But to make it clearer what that statement means, consider first what happens to the light from a flashlight that's resting on the surface of a large planet. Light is affected by gravity—it falls just like everything else. The reason you never notice this fact is that light travels so fast that it doesn't have time to fall very far. But suppose that the gravity on the planet is extremely strong. If the flashlight is aimed horizontally, the light will fall and arc downward just enough that it will hit the surface of the planet before escaping into space. To get the light to leave the planet, the flashlight must be tipped a little above horizontal.
If the planet's gravity is even stronger, the flashlight will have to be tipped even more above horizontal. In fact, if the gravity is sufficiently strong, light can only avoid hitting the planet if the flashlight is aimed almost straight up. And beyond a certain strength of gravity, even pointing the flashlight straight up won't keep the light from hitting the planet's surface.
When that situation occurs, an event horizon forms around the planet and forever separates the planet from the universe around it. Actually, the planet ceases to exist as a complex object and is reduced to its most basic characteristics: mass, electric charge, and angular momentum. The planet becomes a black hole. and light emitted at or within this black hole's event horizon falls inward so strongly that it doesn't escape. Since nothing can move faster than light, nothing else can escape from the black hole's event horizon either.
The nature of space and time at the event horizon are quite complicated and counter-intuitive. For example, an object dropped into a black hole will appear to spread out on the event horizon without ever entering it. That's because, to an outside observer, time slows down in the vicinity of the event horizon. By that, I mean that it takes an infinite amount of our time for an object to fall through that event horizon. But the object itself doesn't experience a change in the flow of time. For it, time passes normally and it zips right through the event horizon.
Finally, event horizons and the black holes that have them aren't truly black—quantum mechanical fluctuations at the event horizon allow black holes to emit particles and radiation. This "Hawking radiation," discovered by Stephen Hawking about 25 years ago, means that black holes aren't truly black. Nonetheless, objects that fall into an event horizon never leave intact.
While tracking a radio transmitter is easy—you only need to follow the radio waves back to their source—you might think that tracking a radio receiver is impossible. After all, a radio receiver appears to be a passive device that collects radio waves rather than emitting them. But that's not entirely true. Sophisticated radio receivers often use heterodyne techniques in which the signal from a local radio-frequency oscillator is mixed with the signal coming from the antenna. The mixing process subtracts one frequency from the other so that antenna signals from a particular radio station are shifted downward in frequency into the range the radio uses to create sound. This mixing process allows the radio receiver to be very selective about which station it receives. The receiver can easily distinguish the station that's nearest in frequency to its local oscillator from all the other stations, just as its easy to tell which note on a piano is closest in pitch to a particular tuning fork.
But heterodyne techniques have a side effect: they cause the radio receiver to emit radio waves. These waves originate with the local radio-frequency oscillator, and with other internal mixing frequencies such as the intermediate frequency oscillator present in many sophisticated receivers. Because these oscillators don't use very much power, the waves they emit aren't very strong. Nonetheless, they can be detected, particularly at short range. For example, it's possible for police to detect a radar detector that contains its own local microwave oscillator. Similarly, people who have tried to pirate microwave transmissions have been caught because of the microwaves emitted from their receivers. In WWII, the Japanese were apparently very successful at locating US forces by detecting the 455 kHz intermediate frequency oscillators in their radios—a problem that quickly led to a redesign of the radios to prevent that 455 kHz signal from leaking onto the antennas (thanks to Tom Skinner for pointing this out to me). As you can see, it is possible to track someone who is listening to the right type of radio receiver. However, the radio waves from that receiver are going to be very weak and you won't be able to follow them from a great distance.
While the moon's gravity is the major cause of tides (the sun plays a secondary role), the moon's gravity isn't directly responsible for any true currents. Basically, water on the earth's surface swells up into two bulges: one on the side of the earth nearest the moon and one on the side farthest from the moon. As the earth turns, these bulges move across its surface and this movement is responsible for the tides.
If there were more than one moon, the tidal bulges would become misshapen. That is essentially what happens because of the sun. As the moon and sun adopt different arrangements around the earth, the strengths of the tides vary. The strongest tides (spring tides) occur when the moon and sun are on the same or opposite sides of the earth. The weakest tides (neap tides) occur when the moon and sun are at 90° from one another. Extra moons would probably just complicate this situation so that the strengths of the tides would vary erratically as the moons shifted their positions around the earth. Since the timing of the tides is still basically determined by the earth's rotation, there would still be approximately 2 highs and 2 lows a day.
This comment, which responds to a previous posting on this site, points out one of the most important differences between physical science and pseudo-science: the fact that pseudo-science isn't troubled by its lack of self-consistency.
Physical science, particularly physics itself, is completely self-consistent. By that I mean that the same set of physical rules applies to every possible situation in the universe and that this set of rules never leads to paradoxical results. Despite its complicated behavior, the universe is orderly and predictable. It's precisely this order and predictability that is the basis for the whole field of physics.
In contrast, pseudo-science is eclectic—it draws from physics and magic as it sees fit. It uses the laws of physics when it finds those laws useful and it ignores the laws of physics when they conflict with its interests. But the laws of physics only make sense if they apply universally—if there were even one situation in which a law of physics didn't apply, physics would lose its self-consistency and predictive power. That's just what happens with pseudo-science when it begins to ignore the laws of physics on occasion. Moreover, the new rules that pseudo-science introduces to replace the ones it ignores make the trouble even worse. Overall, pseudo-science is inconsistent and can't be counted on to predict anything.Pseudo-science might argue that the laws of physics are correct as far as they go, but that they're incomplete. No doubt the laws of physics are incomplete; physicists have frequently discovered improvements to the laws of physics that have allowed them to make even more accurate predictions of the universe's behavior. But in the years since the discoveries of relativity and quantum physics, the pace of such discoveries has slowed and what remains to be understood is at a very deep and subtle level. It's extraordinarily unlikely that the laws of physics as they're currently understood are wrong at a level that would allow a person to bend a spoon with their thoughts alone or predict the order of a deck of cards without assistance. Just because I haven't dropped a particular book doesn't prevent me from predicting that it will fall when I let go of it. I understand the laws that govern its motion and I know that having it fly upward would violate those laws. Similarly, I don't have to watch someone try to bend a spoon with their thoughts to know that it can't be done legitimately. Again, I understand the laws that govern the spoon's condition and I know that having it bend without an identifiable force acting on it would violate those laws. I also don't have to watch someone try to predict cards to know that it, too, can't be done legitimately. Without a clear physical mechanism for transporting information from the cards to the person, a mechanism that must involve forces or exchanges of particles, there is no way for the person to predict the cards.
The pole vault is all about energy and energy storage. Lifting a person upward takes energy because there is an energy associated with altitude—gravitational potential energy. Lifting a person 5 or 6 meters upward takes a considerable amount of energy and that energy has to come from somewhere. In the case of a pole-vaulter, most of the lifting energy comes from the pole. But the pole also had to get the energy from somewhere and that somewhere is the vaulter himself. Here is the story as it unfolds:
When the pole-vaulter stands ready to begin his jump, he is motionless on the ground and he has no kinetic energy (energy of motion), minimal gravitational potential energy (energy of height), and no elastic energy in his pole. All he has is chemical potential energy in his body, energy that he got by eating food. Now he begins to run down the path toward the jump. As he does so, he converts chemical potential energy into kinetic energy. By the time he plants his pole at the jump, his kinetic energy is quite large.
But once he plants the pole, the pole begins to bend. As it does, he slows down and his kinetic energy is partially transferred to the pole, where it becomes elastic potential energy. The pole then begins to lift the vaulter upward, returning its stored energy to him as gravitational potential energy. By the time the vaulter clears the bar, 5 or 6 meters above the ground, almost all of the energy in the situation is in the form of gravitational potential energy. The vaulter has only just enough kinetic energy to carry him past the bar before he falls. On his way down, his gravitational potential energy becomes kinetic energy and he hits the pit at high speed. The pit's padding extracts his kinetic energy from him gently and converts that energy into thermal energy. This thermal energy then floats off into the air as heat.
One interesting point about jumping technique involves body shape. The vaulter bends his body as he passes over the bar so that his average height (his center of gravity) never actually gets above the bar. Since his gravitational potential energy depends on his average height, rather than the height of his highest part, this technique allows him to use less overall energy to clear the bar.
A mirror doesn't really flip your image horizontally or vertically. After all, the image of your head is still on top and the image of your left hand is still on the left. What the mirror does flip is which way your image is facing. For example, if you were facing north, then your image is facing south. This front-back reversal makes your image fundamentally different from you in the same way a left shoe is fundamentally different from a right shoe. No matter how you arrange those two shoes, they'll always be reversed in one direction. Similarly, no matter how you arrange yourself and your image, they'll always be reversed in one direction.
While you're looking at your image, the reversed direction is the forward-backward direction. But it's natural to imagine yourself in the place of your image. To do this you imagine turning around to face in the direction that your image is facing. When you turn in this manner, you mentally eliminate the forward-backward reversal but introduce a new reversal in its place: a left-right reversal. If you were to imagine standing on your head instead, you would still eliminate the forward-backward reversal but would now introduce an up-down reversal. Since it's hard to imagine standing on your head in order to face in the direction your image is facing, you tend to think only about turning around. It's this imagined turning around that leads you to say that your image is reversed horizontally.
The atoms in a molecule are usually held together by the sharing or exchange of some of their electrons. When two atoms share a pair of electrons, they form a covalent bond that lowers the overall energy of the atoms and sticks the atoms together. About half of this energy reduction comes from an increase in the negatively charged electron density between the atoms' positively charged nuclei and about half comes from a quantum mechanical effect—giving the two electrons more room to move gives them longer wavelengths and lowers their kinetic energies.
When two atoms exchange an electron, they form an ionic bond that again lowers the overall energy of the atoms and sticks them together. Although moving the electron from one atom to the other requires some energy, the two atomic ions that are formed by the transfer have opposite charges and attract one another strongly. The reduction in energy that accompanies their attraction can easily exceed the energy needed to transfer the electron so that the two atoms become permanently stuck to one another.
It's true that the earth's surface is moving eastward rapidly relative to the earth's center of mass. However, that motion is very difficult to detect. When you are standing on the ground, you move with it and so does everything around you, including the air. While you are actually traveling around in a huge circle once a day, for all practical purposes we can imagine that you are traveling eastward in a straight line at a constant speed of 950 mph relative to the earth's center of mass. Ignoring the slight curvature of your motion, you are in what is known as an inertial frame of reference, meaning a viewpoint that is not accelerating but is simply coasting steadily through space.
You'll notice that I keep saying "relative to the earth's center of mass" when I discuss motion. I do that because there is no special "absolute" frame of reference. Any inertial frame is as good as any other frame and your current inertial frame is just as good as anyone else's. In fact, you are quite justified in declaring that your frame of reference is stationary and that everyone else's frames of reference are moving. After all, you don't detect any motion around you so why not declare that your frame is officially stationary. Since the air is also stationary in that frame of reference, flying about in the air doesn't make things any more complicated. You are flying through stationary air in your old stationary frame of reference. The only way in which the 950 mph speed appears now is in comparing your frame of reference to the rest of the earth: in your frame of reference, the earth's center of mass is moving westward at 950 mph.
While it is sometimes noted that old cathedral glass is now thicker at the bottom than at the top, such cases appear to be the result of how the glass was made, not of flow. Medieval glass was made by blowing a giant glass bubble on the end of a blowpipe or "punty" and this bubble was cut open at the end and spun into a huge disk. When the disk cooled, it was cut off the punty and diced into windowpanes. These panes naturally varied in thickness because of the stretching that occurred while spinning the bubble into a disk. Evidently, the panes were usually put in thick end down.
Modern studies of glass show that below the glass transition temperature, which is well above room temperature, molecular rearrangement effectively vanishes altogether. The glass stops behaving like a viscous liquid and becomes a solid. Its heat capacity and other characteristics are consistent with its being a solid as well.
When a light wave passes through matter, the charged particles in that matter do respond—the light wave contains an electric field that pushes on electrically charged particles. But how a particular charged particle responds to the light wave depends on the frequency of the light wave and on the quantum states available to the charged particle. While the charged particle will begin to vibrate back and forth at the light wave's frequency and will begin to take energy from the light wave, the charged particle can only retain this energy permanently if doing so will promote it to another permanent quantum state. Since light energy comes in discrete quanta known as photons and the energy of a photon depends on the light's frequency, it's quite possible that the charged particle will be unable to absorb the light permanently. In that case, the charged particle will soon reemit the light.
In effect, the charged particle "plays" with the photon of light, trying to see if it can absorb that photon. As it plays, the charged particle begins to shift into a new quantum state—a "virtual" state. This virtual state may or may not be permanently allowed. If it is, it's called a real state and the charged particle may remain in it indefinitely. In that case, the charged particle can truly absorb the photon and may never reemit it at all. But if the virtual state turns out not to be a permanently allowed quantum state, the charged particle can't remain in it long and must quickly return to its original state. In doing so, this charged particle reemits the photon it was playing with. The closer the photon is to one that it can absorb permanently, meaning the closer the virtual quantum state is to one of the real quantum states, the longer the charged particle can play with the photon before recognizing that it must give the photon up.
A colored material is one in which the charged particles can permanently absorb certain photons of visible light. Because this material only absorbs certain photons of light, it separates the components of white light and gives that material a colored appearance.
A transparent material is one in which the charged particles can't permanently absorb any photons of visible light. While these charged particles all try to absorb the visible light photons, they find that there are no permanent quantum states available to them when they do. Instead, they play with the photons briefly and then let them continue on their way. This playing process slows the light down. In general blue light slows down more than red light in a transparent material because blue light photons contain more energy than red light photons. The charged particles in the transparent material do have real permanent states available to them, but to reach those states, the charged particles would have to absorb high-energy photons of ultraviolet light. While blue photons don't have as much energy as ultraviolet photons, they have more energy than red photons do. As a result, the charged particles in a transparent material can play with a blue photon longer than they can play with a red photon—the virtual state produced by a blue photon is closer to the real states than is the virtual state produced by a red photon. Because of this effect, the speed at which blue light passes through a transparent material is significantly less than the speed at which red light passes through that material.
Finally, about quantum states: you can think of the real states of one of these charged particles the way you think about the possible pitches of a guitar string. While you can jiggle the guitar string back and forth at any frequency you like with your fingers, it will only vibrate naturally at certain specific frequencies. You can hear these frequencies by plucking the string. If you whistle at the string and choose one of these specific frequencies for your pitch, you can set the string vibrating. In effect, the string is absorbing the sound wave from your whistle. But if you whistle at some other frequency, the string will only play briefly with your sound wave and then send it on its way. The string playing with your sound waves is just like a charged particle in a transparent material playing with a light wave. The physics of these two situations is remarkably similar.
There are two forces present when the cars collide: each car pushes on the other car so each car experiences a separate force. As for the strength of these two forces, all I can say is that they are exactly equal in amount but opposite in direction. That relationship between the forces is Newton's third law of motion, the law dealing with action and reaction. In accordance with this law of motion, no matter how big or small the cars are, they will always exert equal but oppositely directed forces on one another.
The amount of each force is determined by how fast the cars approach one another before they hit and by how stiff their surfaces and frames are. If the cars are approaching rapidly and are extremely stiff and rigid, they will exert enormous forces on one another when they collide and will do so for a very short period of time. During that time, the cars will accelerate violently and their velocities will change radically. If you happened to be in one of the cars, you would also accelerate violently in response to severe forces and would find the experience highly unpleasant.
If, on the other hand, the cars are soft and squishy, they will exert much weaker forces on another and they will accelerate much more gently for a long period of time. That will be true even if they were approaching one another rapidly before impact. When the collision period is over, the cars will again have changed velocities significantly but the weaker forces will have made those changes much more gradual. If you have to be in a collision, chose the soft squishy cars over the stiff ones—the accelerations and forces are much weaker and less injurious. That's why cars have crumple zones and airbags: they are trying to act squishy so that you don't get hurt as much.
You're right about the glass expanding along with the liquid inside it. But liquids normally expand more than solids as their temperatures increase. That's because the atoms and molecules in a liquid have more freedom to move around than those in a solid and they respond to increasing temperatures by forming less and less tightly packed arrangements. Since the liquid in a thermometer expands more than the glass container around it, the liquid level rises as the thermometer's temperature increases.
A halogen bulb uses a chemical trick to prolong the life of its filament. In a regular bulb, the filament slowly thins as tungsten atoms evaporate from the white-hot surface. These lost atoms are carried upward by the inert gases inside the bulb and gradually darken the bulb's upper surface. In a halogen bulb, the gases surrounding the filament are chemically active and don't just deposit the lost atoms at the top of the bulb. Instead, they react with those tungsten atoms to form volatile compounds. These compounds float around inside the bulb until they collide with the filament again. The extreme heat of the filament then breaks the compounds apart and the tungsten atoms stick to the filament.
This tungsten recycling process dramatically slows the filament's decay. Although the filament gradually develops thin spots that eventually cause it to fail, the filament can operate at a higher temperature and still last two or three times as long as the filament of a regular bulb. The hotter filament of a halogen bulb emits relatively more blue light and relatively less infrared light than a regular bulb, giving it a whiter appearance and making it more energy efficient.
In real life, only explosive sounds will break normal glass. That's because normal glass vibrates poorly and has no strong natural frequencies. You can see this by tapping a glass window or cup—all you hear is a dull "thunk" sound.
For an object to vibrate strongly in response to a tone, that object must exhibit a strong natural resonance and the tone's pitch must be perfectly matched to the frequency of that resonance. A crystal wineglass vibrates well and emits a clear tone when you tap it. If you listen to the pitch of that tone and then sing it loudly, you can make the wineglass vibrate. A crystal windowpane would also have natural resonances and would vibrate in response to the right tones. But it would take very loud sound at exactly the right pitch to break this windowpane. A few extraordinary voices have been able to break crystal wineglasses unassisted (i.e., without amplification) and it would take such a voice to break the crystal windowpane.
The answer to that question is complicated—glass is neither a normal liquid nor a normal solid. While the atoms in glass are essentially fixed in place like those in a normal solid, they are arranged in the disorderly fashion of a liquid. For that reason, glass is often described as a frozen liquid—a liquid that has cooled and thickened to the point where it has become rigid. But calling glass a liquid, even a frozen one, implies that glass can flow. Liquids always respond to stresses by flowing. Since unheated glass can't flow in response to stress, it isn't a liquid at all. It's really an amorphous or "glassy" solid—a solid that lacks crystalline order.
Yes, but not as quickly as without the glass. While glass absorbs short wavelength ultraviolet light, it does pass 350 to 400 nanometer ultraviolet. While this longer wavelength ultraviolet is less harmful than the shorter wavelength variety, you can still tan or burn if you get enough exposure. Glass is like sunscreen—it protects you pretty well but it isn't perfect.
A center punch is a common tool used to dent a surface prior to drilling. The drill bit follows the pointed dent and the hole ends up passing right through it. But in the situation you describe, the center punch is being used to damage the surface of a car window. When you push the handle of the center punch inward, you are compressing a spring and storing energy. A mechanism inside the center punch eventually releases that spring and allows it to push a small metal cylinder toward the tip of the punch. This cylinder strikes the tip of the punch and pushes it violently into the glass. The glass chips.
In normal glass, this chipping would be barely noticeable. But the side and rear windows of a car are made of tempered glass—glass that has been heat processed in such a way that its surfaces are under compression and its body is under tension. Tempering strengthens the glass by making it more resistant to tearing. But once an injury gets through the compressed surface of the tempered glass and enters the tense body, the glass rips itself apart. The spider web pattern of tearing you observe is a feature of the tempered glass, not the center punch. Any deep cut or chip in the tempered glass will cause this "dicing fracture" to occur.
Whenever you wipe a CD to clean it, there is a chance that you will scratch its surface. If that scratch is wide enough, it may prevent the player's optical system from reading the data recorded beneath it and this loss of data may make the CD unplayable. It turns out that tangential scratches are much more serious than radial scratches. When the scratch is radial (extending outward from the center of the disc to its edge), the player should still be able to reproduce the sound without a problem. That's because sound information is recorded in a spiral around the disc and there is error-correcting information included in each arc shaped region of this spiral. Since a radial scratch only destroys a small part of each arc it intersects, the player can use the error correcting information to reproduce the sound perfectly.
But when the scratch is tangential (extending around the disc and along the spiral), it may prevent the player from reading a large portion of an arc. If the player is unable to read enough of the arc to perform its error correcting work, it can't reproduce the sound. That's why a tangential scratch can ruin a CD much more easily than a radial scratch can. That's why you should never wipe a CD tangentially. Always clean them by wiping from the center out.
A CD player reads ahead of the sound it is playing so that it always has sound information from at least one full turn of the disc in its memory. It has to read ahead as part of the error correcting process—the sound information associated with one moment in time is actually distributed around the spiral rather than squeezed into one tiny patch. This reading ahead is particularly important for a portable CD player, which usually saves several seconds of sound information in its memory so that it will have time to recover if its optical system is shaken out of alignment. When you pause the CD player, it reads ahead until its memory is full and then lets its optical system hover while the disc continues to turn. When you unpause the player, it uses the sound information it has saved in its memory to continue where it left off and its optical system resumes the reading ahead process.
Yes. Heavy water ice is about 1% more dense than liquid water at its melting temperature of 3.82° C. I wouldn't recommend drinking large amounts of heavy water, but you could make sinking ice cubes out of it.
When you heat water on the stove, heat flows into the water from below and the water at the bottom of the pot becomes a little hotter than the water above it. As a result, the water at the bottom of the pot boils first and its steam bubbles begin to rise up through the cooler water above. As they rise, these steam bubbles cool and collapse—they are crushed back into liquid water by the ambient air pressure. These collapsing steam bubbles are noisy. When the water finally boils throughout, the steam bubbles no longer collapse as they rise and simply pop softly at the surface of the liquid.
I can't think of any situation in which what you say would be true. Hot water should always defrost things faster than cold water. That's because the rate of heat flow between two objects always increases as the temperature difference between them increases. When you put frozen food in hot water, heat flows into that food faster than it would from cold water because the temperature difference is larger.
Let's start with three simpler problems: the coexistences of ice and water, of water and steam, and of ice and steam. Each pair of phases can coexist whenever the water molecules leaving one phase are replaced at an equal rate by water molecules leaving the second phase. This isn't as hard as it sounds. In ice water, the water molecules leaving the ice cubes for the liquid are replaced at an equal rate by water molecules leaving the liquid for the ice cubes. In a sealed bottle of mineral water, the water molecules leaving the liquid for the water vapor above it are replaced at an equal rate by water molecules leaving the water vapor for the liquid. And in an old-fashioned non-frostfree freezer with a tray of ice cubes, the water molecules leaving the ice cubes for the water vapor around them are replaced at an equal rate by water molecules leaving the water vapor for the ice cubes.
In each case, there is some flexibility in temperature—these coexistence conditions can be reached over at least a small range of temperature by varying the pressure on the system. In fact, at 0.03° C and a pressure of 6.11 torr; pure water, pure ice, and pure steam can coexist as a threesome. At this triple point, water molecules will be moving back and forth between all three phases but without producing any net change in the amount of ice, water, or steam.
The microwave oven is superheating the water to a temperature slightly above its boiling temperature. It can do this because it doesn't help water boil the way a normal coffee maker does. For water to boil, two things must occur. First, the water must reach or exceed its boiling temperature—the temperature at which a bubble of pure steam inside the water becomes sturdy enough to avoid being crushed by atmospheric pressure. Second, bubbles of pure steam must begin to nucleate inside the water. It's the latter requirement that's not being met in the water you're heating with the microwave. Steam bubbles rarely form of their own accord unless the water is far above its boiling temperature. That's because a pure nucleation event requires several water molecules to break free of their neighbors simultaneously to form a tiny steam bubble and that's very unlikely at water's boiling temperature. Instead, most steam bubbles form either at hot spots, or at impurities or imperfections—scratches in a metal pot, the edge of a sugar crystal, a piece of floating debris. When you heat clean water in a glass container using a microwave oven, there are no hot spots and almost no impurities or imperfections that would assist boiling. As a result, the water has trouble boiling. But as soon as you add a powder to the superheated water, you trigger the formation of steam bubbles and the liquid boils madly.
Not without using something other than pure, normal water for the ice. The density of ice is always less than that of water at the same pressure. While squeezing the ice will increase its density, it will also increase the density of the water so the ice will always float. Of course, you could add dense materials to the ice to weight it down to neutral buoyancy, but then it wouldn't be pure ice any more.
The simple answer is entropy—the ever-increasing disorder of the universe. Salt water is far more disordered than the salt and water from which it's formed, so separating those components doesn't happen easily. The second law of thermodynamics observes that the entropy of an isolated system cannot decrease—you can't reduce the disorder of the salty water without paying for it elsewhere. In effect, you have to export the salty water's disorder somewhere else as you separate it into pure water and pure salt.
In most cases, this exported disorder winds up in the energy used to desalinating sea water. You start with nicely ordered energy—perhaps electricity or gasoline—and you end up with junk energy such as waste heat. While some desalination techniques such as reverse osmosis can operate near the efficiency limits imposed by thermodynamics, they can't avoid those limits. If you want to desalinate water, you must consume ordered resources and those resources usually cost money (an exception is sunlight). The desalinating equipment is also expensive. Until water becomes scarce enough or energy cheap enough, desalinated water will remain uncommon in the United States.
When you simply heat the cold air, you lower its relative humidity—the heated air is holding a smaller fraction of its maximum water molecule capacity and is effectively dry. Dry air always feels colder than humid air at the same temperature. That's because water molecules are always evaporating from your skin. If the air is dry, these evaporating molecules aren't replaced and they carry away significant amounts of heat. On a hot day, this evaporation provides pleasant cooling but on a cold day it's much less welcome. If the air near your skin is humid, water molecules will return to your skin almost as frequently as they leave and will bring back most of the heat that you would have lost to evaporation. Thus humid air spoils evaporative cooling, making humid weather unpleasant in the summer but quite nice in the winter.
A hot water heater is built so that hot water is drawn out of its top and cold water enters it at its bottom. Since hot water is less dense than cold water, the hot water floats on the cold water and they don't mix significantly. As you take your shower, you slowly deplete the hot water at the top of the tank and the level of cold water rises upward. But the shower doesn't turn cold until almost all the hot water has left the tank and the cold water level has risen to its top.
You're right. The greater the temperature difference between two objects, the faster heat flows between them. This effect is useful whenever you forget to chill drinks for a party. Just don't leave a glass bottle in the freezer too long; if the water inside freezes, it may expand enough to break the bottle.
While the cannonball is in your boat, its great weight pushes the boat deeper into the water. To support the cannonball, the boat must displace the cannonball's weight in water—a result known as Archimedes principle. Since the cannonball is very dense, the boat must displace perhaps 8 cannonball volumes of water in order to obtain the buoyancy needed to support the cannonball. This displaced water appears on the surface of the lake so that the lake's level rises.
Now suppose that you throw the cannonball overboard. The cannonball quickly sinks to the bottom. The boat now floats higher than before because it no longer needs to displaces the extra 8 cannonball volumes of water. Although the cannonball itself is displacing 1 cannonball volume of water, there are still 7 cannonball volumes less water being displaced by objects in the water. As a result, the water level of the lake drops slightly when you throw the cannonball overboard.
A nuclear reactor operates just below critical mass so that each radioactive decay in its fuel rods induces a large but finite number of subsequent fissions. Since each chain reaction gradually weakens away to nothing, there is no danger that the fuel will explode. But operating just below critical mass is a tricky business and it involves careful control of the environment around the nuclear fuel rods. The operators use neutron absorbing control rods to dampen the chain reactions and keep the fuel just below critical mass.
Fortunately, there are several effects that make controlled operation of a reactor relatively easy. Most importantly, some of the neutrons involved in the chain reactions are delayed because they come from radioactive decay processes. These delayed neutrons slow the reactor's response to changes—the chain reactions take time to grow stronger and they take time to grow weaker. As a result, it's possible for a reactor to exceed critical mass briefly without experiencing the exponentially growing chain reactions that we associate with nuclear explosions. In fact, the only nuclear reactor that ever experienced these exponentially growing chain reactions was Chernobyl. That flawed and mishandled reactor went so far into the super-critical regime that even the neutron delaying effects couldn't prevent exponential chain reactions from occurring. The reactor superheated and ripped itself apart.
Critical, sub-critical, and super-critical mass all refer to the chain reactions that occur in fissionable material—a material in which nuclei can shatter or "fission" when struck by a passing neutron. When this nuclear fuel is at critical mass, each nucleus that fissions directly induces an average of one subsequent fission. This situation leads to a steady chain reaction in the fuel: the first fission causes a second fission, which causes a third fission, and so on. Steady chain reactions of this sort are used in nuclear reactors.
When the fuel is below critical mass, there aren't quite enough nuclei around to keep the chain reactions proceeding steadily and each chain gradually dies away. While such a sub-critical mass of fuel continues to experience chain reactions, they aren't self-sustaining and depend on natural radioactive decay to restart them.
When the fuel is above critical mass, there are more than enough nuclei around to sustain the chain reactions. In fact, each chain reaction grows exponentially in size with the passage of time. Since each fission directly induces more than one subsequent fission, it takes only a few generations of fissions before there are astronomical numbers of nuclei fissioning in the fuel. Explosive chain reactions of this sort occur in nuclear weapons.
Almost the instant the nuclear fuel reaches critical mass, it begins to release heat and explode. If this fuel overheats and rips itself apart before most its nuclei have undergone fission, only a small fraction of the fuel's nuclear energy will have been released in the explosion. There are at least two possible causes for such a "fizzle": slow assembly of the super-critical mass needed for explosive chain reactions and poor containment of the exploding fuel. A well designed fission bomb assembles its super-critical mass astonishingly quickly and it shrouds that mass in an envelope that prevents it from exploding until most of the nuclei have had time to shatter.
Critical mass is something of a misnomer because in addition to mass, it also depends on shape, density, and even the objects surrounding the nuclear fuel. Anything that makes the nuclear fuel more efficient at using its neutrons to induce fissions helps that fuel approach critical mass. The characteristics of the materials also play a role. For example, fissioning plutonium 239 nuclei release more neutrons on average than fissioning uranium 235 nuclei. As a result, plutonium 239 is better at sustaining a chain reaction than uranium 235 and critical masses of plutonium 239 are typically smaller than for uranium 235.
Apart from obtaining fissionable material, this is the biggest technical problem with building a nuclear weapon. Although a fission bomb's nuclear fuel begins to heat up and explode almost from the instant it reaches critical mass, just reaching critical mass isn't good enough. To use its fuel efficiently—to shatter most of its nuclei before the fuel rips itself apart—the bomb must achieve a significantly super-critical mass. It needs the explosive chain reactions that occur when each fission induces an average of far more than one subsequent fission.
There are two classic techniques for reaching super-critical mass. The technique used in the uranium bomb dropped over Hiroshima in WWII involved a collision between two objects. A small cannon fired a piece of uranium 235 into a nearly complete sphere of uranium 235. The uranium projectile entered the incomplete sphere at enormous speed and made the overall structure a super-critical mass. But despite the rapid mechanical assembly, the bomb still wasn't able to use its nuclei very efficiently. It wasn't sufficiently super-critical for an efficient explosion.
The technique used in the two plutonium bombs, the Gadget tested in New Mexico and the Fat Man dropped over Nagasaki, involved implosions. In each bomb, high explosives crushed a solid sphere of plutonium 239 so that its density roughly doubled. With its nuclei packed more tightly together, this fuel surged through critical mass and went well into the super-critical regime. It consumed a much larger fraction of its nuclei than the uranium bomb and was thus a more efficient device. However, its design was so complicated and technically demanding that its builders weren't sure it would work. That's why they tested it once on the sands of New Mexico. The builders of the uranium bomb were confident enough of its design and too worried about wasting precious uranium to test it.
Once the bomb has assembled a super-critical mass of fissionable material, each chain reaction that occurs will grow exponentially with time and lead to a catastrophic release of energy. But you're right in wondering just what starts those chain reactions. The answer is natural radioactivity from a trigger material. While the nuclear fuel's own radioactivity could provide those first few neutrons, it's generally not reliable enough. To make sure that the chain reactions get started properly, most nuclear weapons introduce a highly radioactive neutron-emitting trigger material into the nuclear fuel assembly.
Your hot water heater is powered by 240 volt electric power through the two black wires. Each black wire is hot, meaning that its voltage fluctuates up and down significantly with respect to ground. In fact, each black wire is effectively 120 volts away from ground on average, so that if you connected a normal light bulb between either black wire and ground, it would light up normally. However, the two wires fluctuate in opposite directions around ground potential and are said to be "180° out of phase" with one another. Thus when one wire is at +100 volts, the other wire is at -100 volts. As a result of their out of phase relationship, they are always twice as far apart from one another as they are from ground. That's why the two wires are effectively 240 volts apart on average.
Most homes in the United States receive 240 volt power in the form of two hot wires that are 180° out of phase, in addition to a neutral wire. 120-volt lights and appliances are powered by one of the hot wires and the neutral wire, with half the home depending on each of the two hot wires. 240-volt appliances use both hot wires.
An airplane supports itself in flight by deflecting the passing airstream downward. The plane's wings push this airstream downward and the airstream reacts by pushing the wings upward. This action/reaction effect is an example of Newton's third law of motion, which observes that forces always come in equal but oppositely directed pairs: if one object pushes on another, then the second object must push back on the first object with a force of equal strength pointing in the opposite direction. Even air obeys this law so that when the plane's wings push air downward, the air must push the wings upward in response. In level flight, the deflected air pushes upward so hard that it supports the entire weight of the plane. Just how the airplane's wings deflect the airstream downward to obtain this upward lift force is a marvel of fluid dynamics. We can view it from at least two perspectives: a Newtonian perspective which concentrates on the accelerations of the passing airstream and a Bernoullian perspective which concentrates on speeds and pressures in that airstream.
The Newtonian perspective is the most intuitive and where we will start. The airstream arriving at the forward or "leading" edge of the airplane wing splits into two separate flows that travel over and under the wing, respectively. The wing is shaped and tilted so that these two flows experience very different accelerations as they travel around the wing. The flow that goes under the wing encounters a downward sloping surface that pushes it downward and it accelerates downward. In response to this downward push, the air pushes upward on the bottom of the wing and provides part of the force that supports the plane.
The air that flows over the wing follows a more complicated route. At first, this flow encounters an upward sloping surface that pushes it upward and it accelerates upward. In response to this upward force, the air pushes downward on the leading portion of the wing's top surface. But the wing's top surface is curved so that it soon begins to slope downward rather than upward. When this happens, the airflow must accelerate downward to stay in contact with it. A suction effect appears, in which the rear or "trailing" portion of the wing's top surface sucks downward on the air and the air sucks upward on it in response. This upward suction force more than balances the downward force at the leading edge of the wing so that the air flowing over the wing provides an overall upward force on the wing.
Since both of these air flows produce upward forces on the wing, they act together to support the airplane's weight. The air passing both under and over the wings is deflected downward and the plane remains suspended.
In the Bernoullian view, air flowing around a wing's sloping surfaces experiences changes in speed and pressure that lead to an overall upward force on the wing. The fact that each speed change is accompanied by a pressure change is the result of a conservation of energy in air passing a stationary surface—when the air's speed and motional energy increase, the air's pressure and pressure energy must decrease to compensate. In short, when air flowing around the wing speeds up, its pressure drops and when it slows down, its pressure rises.
When air going under the wing encounters the downward sloping bottom surface, it slows down. As a result, the air's pressure rises and it exerts a strong upward force on the wing. But when air going over the wing encounters the up and down sloping top surface, it slows down and then speeds up. As a result, the air's pressure first rises and then drops dramatically, and it exerts a very weak overall downward force on the wing. Because the upward force on the bottom of the wing is much stronger than the downward force on the top of the wing, there is an upward overall pressure force on the wing. This upward force can be strong enough to support the weight of the airplane.
But despite the apparent differences between these two descriptions of airplane flight, they are completely equivalent. The upward pressure force of the Bernoullian perspective is exactly the same as the upward reaction force of the Newtonian perspective. They are simply two ways of looking at the force produced by deflecting an airstream, a force known as lift.
An object doesn't have to be on the ground to be a target for lightning. In fact, most lightning strikes don't reach the ground at all—they occur between different clouds. All that's needed for a lightning strike between two objects is for them to have very different voltages, because that difference in voltages means that energy will be released when electricity flows between the objects.
If an airplane's voltage begins to differ significantly from that of its surroundings, it's going to have trouble. Sooner or later, it will encounter something that will exchange electric charge with it and the results may be disastrous. To avoid a lightning strike, the airplane must keep its voltage near that of its surroundings. That's why it has static dissipaters on the tips of its wings. These sharp metal spikes use a phenomenon known as a corona discharge to spray unwanted electric charges into the air behind the plane. Any stray charges that the plane picks up by rubbing against the air or by passing through electrically charged clouds are quickly released to the air so that the plane's voltage never differs significantly from that of its surroundings and it never sticks out as a target for lightning. While an unlucky plane may still get caught in an exchange of lightning between two other objects, the use of static dissipaters significantly reduces its chances of being hit directly.
In effect, you would be a skydiver without a parachute and would survive up until the moment of impact with the ground. Like any skydiver who has just left a forward-moving airplane, you would initially accelerate downward (due to gravity) and backward (due to air resistance). In those first few seconds, you would lose your forward velocity and would begin traveling downward rapidly. But soon you would be traveling downward so rapidly through the air that air resistance would keep you from picking up any more speed. You would then coast downward at a constant speed and would feel your normal weight. If you closed your eyes at this point, you would feel as though you were suspended on a strong upward stream of air. Unfortunately, this situation wouldn't last forever—you would eventually reach the ground. At that point, the ground would exert a tremendous upward force on you in order to stop you from penetrating into its surface. This upward force would cause you to decelerate very rapidly and it would also do you in.
When two objects collide with one another, they usually bounce. What distinguishes an elastic collision from an inelastic collision is the extent to which that bounce retains the objects' total kinetic energy—the sum of their energies of motion. In an elastic collision, all of the kinetic energy that the two objects had before the collision is returned to them after the bounce, although it may be distributed differently between them. In an inelastic collision, at least some of their overall kinetic energy is transformed into another form during the bounce and the two objects have less total kinetic energy after the bounce than they had before it.
Just where the missing energy goes during an inelastic collision depends on the objects. When large objects collide, most of this missing energy usually becomes heat and sound. In fact, the only objects that ever experience perfectly elastic collisions are atoms and molecules—the air molecules in front of you collide countless times each second and often do so in perfectly elastic collisions. When the collisions aren't elastic, the missing energy often becomes rotational energy or occasionally vibrational energy in the molecules. Actually, some of the collisions between air molecules are superelastic, meaning that the air molecules leave the collision with more total kinetic energy than they had before it. This extra energy came from stored energy in the molecules—typically from their rotational or vibrational energies. Such superelastic collisions can also occur in large objects, such as when a pin collides with a toy balloon.
Returning to inelastic collisions, one of the best examples is a head-on automobile accident. In that case, the collision is often highly inelastic—most of the two cars' total kinetic energy is transformed into another form and they barely bounce at all. Much of this missing kinetic energy goes into deforming and heating the metal in the front of the car. That's why well-designed cars have so called "crumple zones" that are meant to absorb energy during a collision. The last place you want this energy to go is into the occupants of the car. In fact, the occupants will do best if they transfer most of their kinetic energies into their airbags.
While I don't know the details of the jump, there are some basic physics issues that must be present. At a fundamental level, the skater approaches the jump in a non-spinning state, leaps into the air while acquiring a spin, spins three times in the air, lands on the ice while giving up the spin, and then leaves the jump in a non-spinning state. Most of the physics is in spin, so that's what I'll discuss.
To start herself spinning, something must exert a twist on the skater and that something is the ice. She uses her skates to twist the ice in one direction and, as a result, the ice twists her in the opposite direction. This effect is an example of the action/reaction principle known as Newton's third law of motion. Because of the ice's twist on her, she acquires angular momentum during her takeoff. Angular momentum is a form of momentum that's associated with rotation and, like normal momentum, angular momentum is important for one special reason: it's a conserved physical quantity, meaning that it cannot be created or destroyed; it can only be transferred between objects. The ice transfers angular momentum to the skater during her takeoff and she retains that angular momentum throughout her flight. She only gives up the angular momentum when she lands and the ice can twist her again.
During her flight, her angular momentum causes her to spin but the rate at which she spins depends on her shape. The narrower she is, the faster she spins. This effect is familiar to anyone who has watched a skater spin on the tip of one skate. If she starts spinning with her arms spread widely and then pulls them in so that she becomes very narrow, her rate of rotation increases dramatically. That's because while she is on the tip of one skate, the ice can't twist her and she spins with a fixed amount of angular momentum. By changing her shape to become as narrow as possible, she allows this angular momentum to make her spin very quickly. And this same rapid rotation occurs in the triple axle jump. The jumper starts the jump with arms and legs widely spread and then pulls into a narrow shape so that she spins rapidly in the air.
Finally, in landing the skater must stop herself from spinning and she does this by twisting the ice in reverse. The ice again reacts by twisting her in reverse, slowing her spin and removing her angular momentum. She skates away smoothly without much spin.
In the form used for water desalination, reverse osmosis involves a special membrane that allows water molecules to pass through it while blocking the movement of salt ions. When water molecules are free to move between two volumes of water, they move in whichever direction reduces their chemical potential energy. The concept of a chemical potential is part of statistical physics—the area of physics that deals with vast collections of particles—and it depends partly on energy and partly on probability. Factors that contribute to a water molecule's chemical potential are the purity of the water and the water's pressure. Increasing the salt content of the water lowers a water molecule's chemical potential while increasing the water's pressure raises its chemical potential.
Because salty water has a lower chemical potential for water molecules than pure water, water molecules tend to move from purer water to saltier water. This type of flow is known as osmosis. To slow or stop osmosis, you must raise the chemical potential on the saltier side by applying pressure. The more you squeeze the saltier side, the higher the chemical potential there gets and the slower water molecules move from the purer side to the saltier side. If you squeeze hard enough, you can actually make the water molecules move backwards—toward the purer side! This flow of water molecules from the saltier water toward the purer water with the application of extreme pressure is known as reverse osmosis.
In commercial desalination, high-pressure seawater is pushed into jellyroll structures containing the semi-permeable membranes. The pressure of the salty water is so high that the water molecules flow through the membrane from the salty water side to the pure water side. This pure water is collected for drinking.
While it may seem that you are somehow attracting the water to your mouth when you suck, you are really just making it possible for air pressure to push the water up toward you. By removing much of the air from within the hose, you are lowering the air pressure in the hose. There is then a pressure imbalance at the bottom end of the hose: the pressure outside the hose is higher than the pressure inside it. It's this pressure imbalance that pushes water into the hose and upward toward your mouth.
But air pressure can't push the water upward forever. As the column of water in the hose rises, its weight increases. Atmospheric pressure can only lift the column of water so high before the upward force on the water is balanced by the water's downward weight. Even if you remove all of the air inside the hose, atmospheric pressure can only support a column of water about 30 feet tall inside the hose. If you're higher than that on your balcony, the water won't reach you no matter how hard you try. The only way to send the water higher is to put a pump at the bottom end of the hose. This pump can push upward harder than atmospheric pressure can and it can support a taller column of water. That's why deep home wells have submersible pumps at their bottoms—they must pump the water upward because it's impossible to suck it upward more than 30 feet from above.
Yes, the speed of light. The gravitational interaction between two objects can be viewed as the exchange of particles called "gravitons," just as the electromagnetic interaction between two objects can be viewed as the exchange of particles called "photons." Gravitons and photons are both massless particles and therefore travel at a special speed: the "speed of light." Since light is easier to work with than gravity, people discovered this special speed in the context of light first. If gravity had been easier to work with, they might have named it "the speed of gravity" instead. Sometime in the not too distant future, gravity-wave detectors such as the LIGO project will begin to observe gravity waves traveling through space from nearby cosmic events, particularly star collapses. These gravity waves will reach us at essentially the same time as light waves from those events since the gravity and light travel at the same speed.
Like any tape recorder, a cassette recorder uses the magnetization of the tape's surface to represent sound. The tape is actually a thin plastic film that's coated with microscopic cigar-shaped permanent magnets. These particles are aligned with the tape's length and can be magnetized in either of two directions—they can have their north magnetic poles pointing in the direction of tape motion or away from that direction. In a blank tape, the particles are magnetized randomly so that there are as many of them magnetized in one direction as the other. In this balanced arrangement, the tape is effectively non-magnetic. But in a recorded tape, the balance is upset and the tape has patches of strong magnetization. These magnetized patches represent sound.
When you are recording sound on the tape, the microphone measures the air pressure changes associated with the sound and produces a fluctuating electric current that represents those changes. This current is amplified and used to operate an electromagnet in the recording head. The electromagnet magnetizes the tape—it flips the magnetization of some of those tiny magnetic particles so that the tape becomes effectively magnetized in one direction or the other. The larger the pressure change at the microphone, the more current flows through the electromagnet and the deeper the magnetization penetrates into the tape's surface. After recording, the tape is covered with tiny patches of magnetization, of various depths and directions. These magnetized patches retain the sound information indefinitely.
During playback, the tape moves past the playback head. As the magnetic fields from magnetized regions of the tape sweep past the playback head, they cause a fluctuating electric current to flow in that head. The process involved is called electromagnetic induction; a moving or changing magnetic field produces an electric field, which in turn pushes an electric current through a wire. The current from the playback head is amplified and used to operate speakers, which reproduce the original sound.
The rest of the cassette recorder is just transport mechanism—wheels and motors that move the tape smoothly and steadily past the recording or playback heads (which are often the same object). There is also an erase head that demagnetizes the tape prior to recording. It's an electromagnet that flips its magnetic field back and forth very rapidly so that it leaves the tiny magnetic particles that pass near it with randomly oriented magnetizations.
Although electricity involves the movement of electrically charged particles through conducting materials, it can also be viewed in terms of electromagnetic waves. For example, programs that reach your home through a cable TV line are actually being carried by electromagnetic waves that travel in the cylindrical space between coaxial cable's central wire and the tubular metal shield around it. These waves would travel at the speed of light, except that whenever charged particles in the wires interact with the passing waves, they introduce delays. The charged particles in the wires don't respond as quickly as empty space does to changes in electric or magnetic fields, so they delay these changes and therefore slow down the waves. The materials that insulate the wires also influence the speed of the electricity by responding slowly to the changing fields. The fastest wires are ones with carefully chosen shapes and almost empty space for insulation. In general, the less the charges in the wire respond to the passing electromagnetic waves, the faster those waves can move.
While the designers of low speed planes focus primarily on lift and drag, designers of high speed planes must also consider shock waves—pressure disturbances that fan out in cones from regions where the plane's surface encounters supersonic airflow. The faster a plane goes, the easier it is for the plane's wings to generate enough lift to support it, but the more likelihood there is that some portions of the airflow around the plane will exceed the speed of sound and produce shock waves. Since a transonic or supersonic plane needs only relatively small wings to support itself, the designers concentrate on shock wave control. Sweeping the wings back allows them to avoid some of their own shock waves, increasing their energy efficiencies and avoiding shock wave-induced surface damage to the wings. Slower planes can't use swept wings easily because they don't generate enough lift at low speeds.
It seems that quarks are forever trapped inside the particles they comprise—no one has ever seen an isolated quark. But inside one of those particles, the quarks move at tremendous speeds. Their high speeds are a consequence of quantum mechanics and the uncertainty principle—whenever a particle (such as a quark) is confined to a small region of space (i.e. its location is relatively well defined), then its momentum must be extremely uncertain and its speed can be enormous. In fact, a substantial portion of the mass/energy of quark-based particles such as protons and neutrons comes from the kinetic energy of the fast-moving quarks inside them.
But despite these high speeds, the quarks never exceed the speed of light. As a massive particle such as a quark approaches the speed of light, its momentum and kinetic energy grow without bounds. For that reason, even if you gave all the energy in the world to a single quark, its speed would still remain just a hair less than the speed of light.
Thermal energy is actually bad for permanent magnets, reducing or even destroying their magnetizations. That's because thermal energy is related to randomness and permanent magnetization is related to order. Not surprisingly, cooling a permanent magnet improves its ordering and makes its magnetization stronger (or at least less likely to become weaker with time). At absolute zero, a permanent magnet's magnetic field will be in great shape—assuming that the magnet itself doesn't suffer any mechanical damage during the cooling process.
All three of these objects contain solids, liquids, and gases, so I'll begin by describing how pressure affects those three states of matter. Solids and liquids are essentially incompressible, meaning that as the pressure on a solid or a liquid increases, its volume doesn't change very much. Without extraordinary tools, you simply can't squeeze a liter of water or liter-sized block of copper into a half-liter container. Gases, on the other hand, are relatively compressible. With increasing pressure on it, a certain quantity of gas (as measured by weight) will occupy less and less volume. For example, you can squeeze a closet full of air into a scuba tank.
Applying these observations to the three objects, it's clear that the solid and liquid portions of these objects aren't affected very much by the pressure, but the gaseous portions are. In a fish or diver, the gas-filled parts (the swim bladder in a fish and the lungs in a diver) become smaller as the fish or diver go deeper in the water and are exposed to more pressure. In a submarine, the hull of the submarine must support the pressure outside so that the pressure of the air inside the submarine doesn't increase. If the pressure did reach the air inside the submarine, that air would occupy less and less volume and the submarine would crush. That's why the hull of a submarine must be so strong—it must hide the tremendous water pressure outside the hull from the air inside the hull.
Apart from these mechanical effects on the three objects, there is one other interesting effect to consider. Increasing pressure makes gases more soluble in liquids. Thus at greater depths and pressures, the fish and diver can have more gases dissolved in their blood and tissues. Decompression illness, commonly called "the bends", occurs when the pressure on a diver is suddenly reduced by a rapid ascent from great depth. Gases that were soluble in that diver's tissue at the initial high pressure suddenly become less soluble in that diver's tissue at the final low pressure. If the gas comes out of solution inside the diver's tissue, it causes damage and pain.
For very fundamental reasons, the speed of light in vacuum cannot be exceeded. Calling it the "speed of light" is something of a misnomer—it is the fundamental speed at which all massless particles travel. Since light was the first massless particle to be studied in detail, it was the first particle seen to travel at this special speed.
While nothing can travel faster than this special speed, it's easy to go slower. In fact, light itself travels more slowly than this when it passes through a material. Whenever light encounters matter, its interactions with the charged particles in that matter delay its movement. For example, light travels only about 2/3 of its vacuum speed while traveling in glass. Because of this slowing of light, it is possible for massive objects to exceed the speed at which light travels through a material. For example, if you send very, very energetic charged particles (such as those from a research accelerator) into matter, those particles may move faster than light can move in that matter. When this happens, the charged particles emit electromagnetic shock waves known as Cherenkov radiation—there is light emitted from each particle as it moves.
I suppose that the brochure could have been talking about this light/matter interaction. But since that effect has been observed for decades, there is nothing special about 1995. More likely, the brochure is talking about nonsense.
A bipolar transistor is a sandwich consisting of three layers of doped semiconductor. A pure semiconductor such as silicon or germanium has no mobile electric charges and is effectively an insulator (at least at low temperatures). Dope semiconductor has impurities in it that give the semiconductor some mobile electric charges, either positive or negative. Because it contains mobile charges, doped semiconductor conducts electricity. Doped semiconductor containing mobile negative charges is called "n-type" and that with mobile positive charges is called "p-type." In a bipolar transistor, the two outer layers of the sandwich are of the same type and the middle layer is of the opposite type. Thus a typical bipolar transistor is an npn sandwich—the two end layers are n-type and the middle layer is p-type.
When an npn sandwich is constructed, the two junctions between layers experience a natural charge migration—mobile negative charges spill out of the n-type material on either end and into the p-type material in the middle. This flow of charge creates special "depletion regions" around the physical p-n junctions. In this depletion regions, there are no mobile electric charges any more—the mobile negative and positive charges have cancelled one another out!
Because of the two depletion regions, current cannot flow from one end of the sandwich to the other. But if you wire up the npn sandwich—actually an npn bipolar transistor—so that negative charges are injected into one end layer (the "emitter") and positive charges are injected into the middle layer (the "base"), the depletion region between those two layers shrinks and effectively goes away. Current begins to flow through that end of the sandwich, from the base to the emitter. But because the middle layer of the sandwich is very thin, the depletion region between the base and the second end of the sandwich (the "collector") also shrinks. If you wire the collector so that positive charges are injected into it, current will begin to flow through the entire sandwich, from the collector to the emitter. The amount of current flowing from the collector to the emitter is proportional to the amount of current flowing from the base to the emitter. Since a small amount of current flowing from the base to the emitter controls a much larger current flowing from the collector to the emitter, the transistor allows a small current to control a large current. This effect is the basis of electronic amplification—the synthesis of a larger copy of an electrical signal.
A transformer only works with ac current because it relies on changes in a magnetic field. It is the changing magnetic field around the transformer's primary coil of wire that produces the electric field that actually propels current through the transformer's secondary coil of wire.
When dc current passes through the primary coil of wire, the coil does have a magnetic field around it, but it doesn't have an electric field around it. The electric field is what pushes electric charges through the secondary coil to transfer power from the primary coil to the secondary coil. In contrast, when ac current passes through that primary coil of wire, the magnetic field around the coil flips back and forth in direction and this changing magnetic field gives rise to an electric field around the coil. It is this electric field that pushes on electrically charged particles—typically electrons—in the secondary coil of wire. These electrons pick up speed and energy as they move around the secondary coil's turns. The more turns these charged particles go through, the more energy they pick up. That's why doubling the turns in a transformer's secondary coil doubles the voltage of the current leaving the secondary coil.
A slot machine is a classic demonstration of rotational inertia. When you pull on the lever, you are exerting a torque (a twist) on the three disks contained inside the machine. These disks undergo angular acceleration—they begin turning toward you faster and faster as you complete the pull. When you stop pulling on the lever, the lever decouples itself from the disks and they continue to spin because of their rotational inertia alone—they are coasting. However, their bearings aren't very good and they experience frictional torques that gradually slow them down. They eventually stop turning altogether and then an electromechanical system determines whether you have won. Each disk is actually part of a complicated rotary switch and the positions of the three disks determine whether current can flow to various places on an electromechanical counter. That counter controls the release of coins—coins that are dropped one by one into a tray if you win. Sadly, computerized gambling machines are slowly replacing the beautifully engineered electromechanical ones. These new machines are just video games that handle money—they have little of the elegant mechanical and electromechanical physics that makes the real slot machines so interesting.
You can tell how far away a lightning flash is by counting the time separating the flash from the thunderclap. Every five seconds is about a mile. The reason that this technique works is that light and sound travel at very different speeds. The light and sound are created simultaneously, but the light travels much faster than the sound. You see the flash almost immediately after it actually occurs, but the thunderclap takes time to reach your ears. You can determine how long it takes sound to travel from the lightning bolt to your ears by counting the seconds between the flash and the thunderclap. Since it takes sound about 5 seconds to travel a mile, you can determine the distance to the lightning bolt in miles by dividing the seconds of sound delay by 5.
The atmosphere maintains a natural temperature gradient of about 10° C (which is equivalent to 18° F) per kilometer in dry air and about 6 or 7° C (which is equivalent to about 12° F) per kilometer in moist air. The higher you look in the lower atmosphere, the colder the air is. Because of this gradient, it may be 20° C (68° F) in the valley and 0° C (32° F) at the top of a 2,000 meter high mountain.
This temperature gradient has its origin in the physics of gases—when a gas expands and does work on its surroundings, its temperature decreases. To see why this effect is important, imagine that you have a plastic bag that's partially filled with valley air. If you carry this bag up the side of the mountain, you will find that the bag's volume will gradually increase. That's because there will be less and less air overhead as you climb and the pressure that this air exerts on the bag will diminish. With less pressure keeping it small, the air in the bag will expand and the bag will fill up more and more. But for the bag's size to increase, it must push the air around it out of the way. Pushing this air away takes work and energy, and this energy comes from the valley air inside the bag. Since the valley air has only one form of energy it can give up—thermal energy—its temperature decreases as it expands. By the time you reach the top of the mountain, your bag of valley air will have cooled dramatically. If it started at 20° C, its temperature may have dropped to 0° C, cold enough for snow.
If you now turn around and walk back down the mountain, the increasing air pressure will gradually squeeze your bag of valley air back down to its original size. In doing do, the surrounding air will do work on your valley air, giving it energy, and will increase that air's thermal energy—the valley air will warm up! When you reach the valley, the air in your bag will have returned to its original temperature.
Air often rises and falls in the atmosphere and, as it does, it experiences these same changes in temperature. Air cools as it blows up into the mountains (often causing rain to form) and warms as it flows down out of the mountains (producing dry mountain winds). These effects maintain a temperature gradient in the atmosphere that allows snow to remain on mountaintops even when it's relatively warm in the valleys.
The red blood cells in your blood contain large amounts of a complicated and brightly colored molecule known as hemoglobin. This molecule's ability to bind and later release oxygen molecules is what allows blood to carry oxygen efficiently throughout your body.
Each hemoglobin molecule contains four heme groups, the iron-containing structures that actually form the reversible bond with oxygen molecules and that also give the hemoglobin its color. However, this color depends on the oxidization state of the heme group—red when the heme group is binding oxygen and blue-purple when the heme group is alone. That color difference explains why someone who is holding their breath may "turn blue"—their hemoglobin is lacking in oxygen. The clip you wore was analyzing the color of your blood to determine the extent of oxygenation in its hemoglobin. It measured your pulse rate by looking for periodic fluctuations in the opacity of your finger, brought on by changes in your finger's blood content with each heartbeat.
Once lightning strikes you, whether or not you are wearing rubber-soled shoes will make little difference. The voltages involved in lightning are so enormous (hundreds of millions of volts) that the insulating character of rubber soles will be completely overwhelmed. If the electric current can't pass through your rubber soles, it will simply form an electric arc around them or through them.
However, I would guess that rubber-soled shoes provide some slight protection against being hit by lightning in the first place. Lightning tends to strike objects that have acquired an electric charge that is opposite that of the cloud overhead. This opposite charge naturally appears on grounded conducting objects because the cloud's charge pulls opposite charges up from the ground and onto the objects. Once this charging has taken place, the object is a prime target for a lightning strike.
If you are standing alone and barefoot on the top of a mountain during a thunderstorm, the cloud will draw opposite charge up from the ground through your feet and you will become very highly charged. There are even photographs of people on mountaintops with their hair standing up because of this charging effect. Unfortunately, some of these people were struck by lightning shortly after experiencing this effect. If you ever experience it, run for your life down the mountain! It's possible that wearing rubber soles shoes will prevent or delay this charging effect, and it might keep you from being struck by lightning. But I sure wouldn't count on it.
When the bottle is sealed, its contents are in equilibrium. In this context, equilibrium means that while carbon dioxide gas molecules are continuously shifting from solution in the water to independence in the gas underneath the cap, there is no net movement of gas molecules between the two places. Since the company that bottled the water put a great many gas molecules in the bottle, the concentration of dissolved molecules in the water is high and so is the density of molecules in the gas under the cap. This high density of gaseous carbon dioxide molecules under the cap makes the pressure inside the bottle quite high, which is why the bottle's surface is taut and hard.
While you can't see it in this unopened bottle, there is activity both at the surface of the water and within the water. At the water's surface, carbon dioxide molecules are constantly leaving the water for the gas under the cap and returning from the gas under the cap to the water. The rates of departure and return are equal, so that nothing happens overall. Within the water, tiny bubbles are also forming occasionally. But these tiny bubbles, which nucleate through random fluctuations within the liquid or more often at defects in the bottle's walls, can't grow. Even though these bubbles contain gaseous carbon dioxide molecules, the molecules aren't dense enough to keep the bubbles from being crushed by the pressurized water. So these tiny bubbles form and collapse without ever becoming noticeable.
However, once you remove the top from the bottle, everything changes. The bottle's contents are no longer in equilibrium. To begin with, carbon dioxide molecules that leave the surface of the water are no longer replaced by molecules returning to the liquid. That's one reason why an opened bottle of carbonated water begins to lose its dissolved carbon dioxide and become "flat." Secondly, without its trapped portion of dense carbon dioxide gas, the bottle is no longer pressurized and it stops being taut and hard (assuming that it's made of plastic rather than gas). Thirdly, with the loss of pressure, the water in the bottle stops crushing the tiny gas bubbles that form within it. In fact, once one of those bubbles forms, carbon dioxide molecules can enter it from the liquid just as they enter the gas at the top of the bottle. As a result, each bubble that forms grows larger and larger. Since the gas in a bubble is less dense than water, the bubble begins to float upward until it reaches the top of the bottle. Because the bottle is taller than a typical water glass, a bubble has more time to grow before reaching the top in the bottle than it would have in the glass. That's one reason why the bubbles in a bottle are taller than in a glass. Another reason is that the concentration of dissolved carbon dioxide molecules is higher while the water is in the bottle than it is by the time the water reaches the glass, so that bubbles grow faster in the bottle than in the glass.
An acetylene miner's lamp produces acetylene gas through the reaction of solid calcium carbide with water. An ingenious system allows the production of gas to self-regulate—the gas pressure normally keeps the water away from the calcium carbide so that gas is only generated when the lamp runs short on gas. In contrast, a propane lamp obtains its gas from pressurized liquid propane. Whenever the propane lamp runs short on gas, the falling gas pressure allows more liquid propane to evaporate.
Only the propane lamp needs a mantle to produce bright light. That's because the hot gas molecules that are produced by propane combustion aren't very good at radiating their thermal energy as visible light. The mantle extracts thermal energy from the passing gas molecules and becomes incandescent—it converts much of its thermal energy into thermal radiation, including visible light. Mantles are actually delicate ceramic structures consisting of metal oxides, including thorium oxide. Thorium is a naturally occurring radioactive element, similar to uranium, and lamp mantles are one of the few unregulated uses of thorium.
The light emitted by these oxide mantles is shorter in average wavelength than can be explained simply by the temperature of the burning gases, so it isn't just thermal radiation at the ambient temperature. The mantle's unexpected light emission is called candoluminescence and is thought to involve non-thermal light emitted as the result of chemical reactions and radiative transitions involving the burning gases and the mantle oxides.
In contrast, the acetylene miner's lamp works pretty well without a mantle. I think that's because the flame contains lots of tiny carbon particles that act as the mantle and emit an adequate spectrum of yellow thermal radiation. Many of these particles then go on to become soot. A candle flame emits yellow light in the same manner.
One last feature of a properly constructed miner's lamp, a safety lamp, is that it can't ignite gases around it even if those gases are present in explosive concentrations. That's because the lamp's flame is surrounded by a fine metal mesh. This mesh draws heat out of any gas within its holes and thus prevents the flame inside the mesh from igniting any gas outside the mesh.
No. If you are above the clouds, then the sky above you is free from droplets of condensed moisture. While that doesn't mean that there is no water overhead, that water must be entirely in the form of gaseous water molecules. Since rain forms when droplets of condensed moisture grow large enough to descend rapidly through the air, the absence of any condensed droplets makes it impossible for full raindrops to form. In short, no clouds overhead, no rain.
An automatic transmission contains two major components: a fluid coupling that controls the transfer of torque from the engine to the rest of the transmission and a gearbox that controls the mechanical advantage between the engine and the wheels. The fluid coupling resembles two fans with a liquid circulating between them. The engine turns one fan, technically known as an "impeller," and this impeller pushes transmission fluid toward the second impeller. As the liquid flows through the second impeller, it exerts a twist (a "torque") on the impeller. If the car is moving or is allowed to move, this torque will cause the impeller to turn and, with it, the wheels of the car. If, however, the car is stopped and the brake is on, the transmission fluid will flow through the second impeller without effect. Overall, the fluid coupling allows the efficient transfer of power from the engine to the wheels without any direct mechanical linkage that would cause trouble when the car comes to a stop.
Between the second impeller and the wheels is a gearbox. The second impeller of the fluid coupling causes several of the gears in this box to turn and they, in turn, cause other gears to turn. Eventually, this system of gears causes the wheels of the car to turn. Along with these gears are several friction plates that can be brought into contact with one another by the transmission to change the relative rotation rates between the second impeller and the car's wheels. These changes in relative rotation rate give the car the variable mechanical advantage it needs to be able to both climb steep hills and drive fast on flat roadways.
Finally, some cars combine parts of the gear box with the fluid coupling in what is called a "torque converter." Here the two impellers in the fluid coupling have different shapes so that they naturally turn at different rates. This asymmetric arrangement eliminates the need for some gears in the gearbox itself.
Unfortunately, the answer is no. The atmosphere is too complicated to be described by a simple formula or equation, although you can always fit a formulaic curve to measured pressure values if you make that formula flexible enough. The complications arise largely because of thermodynamic issues: air expands as it moves upward in the atmosphere and this expansion causes the air to cool. As a result of this cooling, the air in the atmosphere doesn't have a uniform temperature and, without a uniform temperature, the air's pressure is difficult to predict. Radiative heating of the greenhouse gases and phase changes in the air moisture content further complicate the atmosphere's temperature profile and consequently its pressure profile. If you want to know the air pressure at specific altitude, you do best to look it up in a table.
Both of your observations are correct: short wavelength light, such as violet, carries more energy per particle (per "photon") than long wavelength light, such as red, and red light does appear "warmer" than blue light. But the latter observation is one of feelings and psychology, rather than of physics. It is ironic that colors we associate with cold and low thermal energies are actually associated with higher energy light particles than are colors we associate with heat and high thermal energies.
First, an electromagnetic wave consists of an electric and a magnetic field. These two fields create one another as they change with time and they travel together through empty space. An electromagnetic wave of this sort carries energy with it because electric and magnetic fields both contain energy. That much was well understood by the end of the 19th century, but something new was discovered at the beginning of the 20th century: an electromagnetic wave cannot carry an arbitrary amount of energy. Instead, it can carry one or more units of energy, units that are commonly called "quanta." An electromagnetic wave that carries only one quanta of energy is called a "photon."
The amount of energy that a photon carries depends on the frequency of that photon—the higher the frequency, the more energy. Photons of visible light carry enough energy to induce various changes in atoms and molecules, which is why they provide our eyes with such useful information about the objects around us—we see how this visible light is interacting with the world around us.
Radio waves are a class of electromagnetic waves, specifically the lowest frequency, longest wavelength electromagnetic waves. Actually, the electromagnetic waves used in cellular & PCS transmissions are technically known as microwaves because they have wavelengths of less than 1 meter, but there are no important differences between radio waves and microwaves.
Like all electromagnetic waves, radio waves and microwaves consist of coupled electric and magnetic fields that sustain one another in stable structures that move rapidly through empty space. Because an electromagnetic wave's electric field changes with time, it is able to create the wave's magnetic field and, because its magnetic field changes with time, that magnetic field is able to create the wave's electric field. Since they consist only of electric and magnetic fields, these waves cannot stay still—they must move (although you can trap them between mirrors so that they appear to stand in one place as they bounce back and forth). While they contain no true mass, they do contain energy and an electromagnetic wave carries energy from one place to another.
Electromagnetic waves are created whenever electrically charged particles change speed or direction; whenever they accelerate. Since there are accelerating electric charges everywhere—thermal energy keeps them moving about—there are also electromagnetic waves everywhere. But the radio waves used in communications systems are generated deliberately by moving electric charges back and forth. When charges are sent up and down a radio antenna, these charges are accelerating and they form complicated electric and magnetic fields that include electromagnetic waves. Once launched, those electromagnetic waves propagate through space at approximately the speed of light.
To send information with radio waves, a transmitter makes modifications in one or more the wave's characteristics. In an amplitude modulation scheme (AM), the transmitter changes the strength or "amplitude" of the wave to convey information—like sending radio smoke signals. In the frequency modulation scheme (FM), the transmitter changes the frequency of the wave to convey information—like whistling a tune with a complicated melody.
The VCR Plus codes contain just enough information to tell the VCR what time and day a program starts, what channel that program is on, and how long it will last. What is remarkable about these codes is not that they exist, but that many of them are so short. A long number that contained the complete date, the entire channel number, and the length of the program in minutes would obvious fulfill the requirements, but the actually numbers are never that long. While I don't know the precise encoding scheme, the date is clearly compressed—a daily or weekly program is represented by a very small code—and so is the record time for programs with a common duration. The VCR Plus codes get significantly longer when they must represent one-time only shows and shows with complicated durations. Even then, the date is truncated so that there are no current codes to represent a show five years in the future.
The rice cooker turns off when there is no longer enough liquid water on its heating element to keep that element's temperature at the boiling temperature of water (212° F or 100° C). As long as the element is covered with liquid water, it is hard for that element's temperature to rise above water's boiling temperature. That's because as the water boils, all of the thermal energy produced in the heating element is converted very efficiently into chemical potential energy in the resulting steam. In short, boiling water remains at 212° F even as you add lots of thermal energy into it.
But as soon as the liquid water is gone (and, fortuitously, the rice is fully cooked), there is nothing left to keep the heating element's temperature from rising. As more electric energy enters the element and becomes thermal energy, the element gets hotter and hotter. A thermostat, probably a bimetallic strip like that used in most toasters, senses the sudden temperature rise. It releases a switch that turns off the electric power to the rice cooker.
One of the principal observations of thermodynamics (and statistical mechanics, a related field) is that vast, complicated systems naturally evolve from relatively unlikely arrangements to relatively likely arrangements. This trend is driven by the laws of probability and the fact that improbable things don't happen often. Here's an example: consider your sock drawer, which contains 100 each of red and blue socks (it's a large drawer and you really like socks). Suppose you arrange the drawer so that all the red socks are on one side and all the blue socks are on the other. This arrangement is highly improbable—it didn't happen by chance; you caused it to be ordered. If you now turn out the light and randomly exchange socks within the drawer, you're awfully likely to destroy this orderly situation. When you turn the light back on, you will almost certainly have a mixture of red and blue socks on each side of the drawer. You could turn the light back out and try to use chance to return the socks to their original state, but your chances of succeeding are very small. Even though the system you are playing with has only 200 objects in it, the laws of probability are already making it nearly impossible to order it by chance alone. By the time you deal with bulk matter, which contains vast numbers of individual atoms or electrons or bits of energy, chance and the laws of probability dominate everything. Even when you try to impose order on a system, the laws of probability limit your success: there are no perfect crystals, perfectly clean rooms, flawless structures. These objects aren't forbidden by the laws of motion, they are simply too unlikely to ever occur.
A fan and a propeller are actually the same thing. Both are rotating wings that push the air in one direction and experience a reaction force in the opposite direction as a result. Each experiences a "lift" force, typically called "thrust," in the direction opposite the airflow. If you put a strong fan on a low-friction cart or a good skateboard, it will accelerate forward as it pushes the air backward. Similarly, if you prevent a propeller plane from moving, its spinning blades will act as powerful fans.
Most CD's are made from polycarbonate plastic (though other plastics with the same index of refraction are occasionally used). Polycarbonate is a pretty tough material, so it should survive most common stain or gum removing solvents. Try your favorite solvent on an unimportant CD first; such as one of the free discs that come occasionally in the mail. However, if the stain molecules have diffused into the plastic and have become trapped within the tangle of plastic molecules, you're probably out of luck. Removing such a stain will require wearing away some of the plastic. Since the disc's surface finish must remain smooth and the thickness of the disc shouldn't change much, serious resurfacing is likely to make the disc unplayable. Also, stay away from the printed side of the disc—it has only a thin layer of varnish protecting the delicate aluminum layer from injury. Solvents can wreck this side of the disc. Finally, if the stain is a white mark (or a scratch), you may be able to render the disc clear again by filling the tiny air gaps that make it white with another plastic. I'll bet that a clear furniture polish or liquid wax will soak into the white spot, replace the air, and render the disc clear and playable.
Apparently there are conditions in which green light from the sun is bent by the atmosphere so that it is visible first as the sun begins to rise above the horizon. Instead of seeing the yellow edge of the sun peaking up from behind the water or land, you see a green edge that lasts a second or two before being replaced by the usual yellow. This green flash is the result of refraction (bending of light) and dispersion (color-dependent light-speed) in air and is discussed in considerable detail at http://www.isc.tamu.edu/~astro/research/sandiego.html. According to the author of that site, Andrew Young, given a low enough horizon, which is the primary consideration, and clear air, which is also important, and a little optical aid, which helps a lot, one can certainly see green flashes at most sunsets.
When light passes into a material, it interacts primarily with the negatively charged electrons in that material. Since light consists in part of electric fields and electric fields push on charged particles, light pushes on electrons. If the electrons in a material can't move long distances and can't shift from one quantum state to another as the result of the light forces, then all that will happen to the light as it passes through the material is that it will be delayed and possibly redirected. But if the electrons in the material can move long distance or shift between states, then there is the chance that the light will be absorbed by the material and that the light energy will become some other type of energy inside the material.
Which of these possibilities occurs in a particular organic material depends on the precise structure of that material. Carbon atoms can be part of transparent organic materials, such as sugar, or of opaque organic materials, such as asphalt. The carbon atoms and their neighbors determine the behaviors of their electrons and these electrons in turn determine the optical properties of the materials.
While most microwave ovens operate at 2.45 GHz, that frequency is not a resonant frequency for the water molecule. In fact, using a frequency that water molecules responded to strongly (as in a resonance) would be a serious mistake—the microwaves would all be absorbed by water molecules at the surface of the food and the center of the food would remain raw. Instead, the 2.45 GHz frequency was chosen because it is absorbed weakly enough in liquid water (not free water molecules) that the waves maintain good strength even deep inside a typical piece of food. Higher frequencies would penetrate less well and cook less evenly. Lower frequencies would penetrate better, but would be absorbed so weakly that they wouldn't cook well. The 2.45 GHz frequency is a reasonable compromise between the two extremes.
In three-phase power, the voltages of the three power wires fluctuate up and down cyclically so that they are "120 degrees" apart. By "120 degrees" apart, I mean that each wire reaches its peak voltage at a separate time—first the X wire, then the Y wire, and then the Z wire—with the Y wire reaching its peak 1/3 of the 360 degree cycle (or 120 degrees) after the X wire and the Z wire reaching its peak 1/3 of the 360 degree cycle (or 120 degrees) after the Y wire.
The specific voltages and their relationships with ground or a possible fourth "neutral" wire depend on the exact type of transformer arrangement that supplies your home or business. In the standard "Delta" arrangement (which you can find discussed at sites dealing with power distribution), the voltage differences between any pair of the three phases is typically 240 VAC. In the standard "Wye" arrangement, the typical voltage difference between any pair of phases is 208 VAC and the voltage difference between any single phase and ground is 120 VAC. And in the "Center-Tapped Grounded Delta" arrangement, the voltage difference between any pair of phases is 240 VAC and the voltage difference between a single phase and neutral is 120, 120, and 208 VAC respectively (yes, the three phases behave differently in this third arrangement).
If you run a single-phase 220 VAC motor from two wires of a Delta arrangement power outlet, that motor will receive a little more voltage (240 VAC) than it was designed for and if you run it from two wires of a Wye arrangement outlet, it will receive a little less voltage (208 VAC) than appropriate. Still, the motor will probably run adequately and it's unlikely that you'll ever notice the difference.
The magnetic interaction between the stator and the rotor is repulsive—the rotor is pushed around in a circle by the stator's magnetic field; it is not pulled. To see why this is so, imagine unwrapping the curved motor so that instead of having a magnetic field that circles around a circular metal rotor you have a magnet (or magnetic field) that moves along a flat metal plate. As you move this magnet across the plate, it will induce electric currents in that plate and the plate will develop magnetic poles that are reversed from those of the moving magnet-the two will repel one another. That choice of pole orientation is the only one consistent with energy conservation and is recognized formally in "Lenz's Law". For reasons having to do with resistive energy loss and heating, the repulsive forces in front of and behind the moving magnet don't cancel perfectly, leading to a magnetic drag force between the moving magnet and the stationary plate. This drag force tends to push the plate along with the moving magnet. In the induction motor, that same magnetic drag force tends to push the rotor around with the rotating magnetic field of the stator. In all of these cases, the forces involved are repulsive-pushes not pulls.
If any current reaching the equipment through the three-phase power cord returns through that same power cord, then the net current in the cord is always exactly zero. Despite the complicated voltage and current relationships between the three power wires, one simple fact remains: the equipment can't store electric charge. As a result, any current that flows toward the equipment must be balanced by a current flowing away from the equipment, and if both flows are in the same power cord, they'll cancel perfectly. Since there is no net current flowing through the power cord, it develops no magnetic field and exhibits no inductive reactance or voltage drop.
When a moving magnet generates electricity, it does transfer energy to the electric current. However, that energy comes from either the magnet's kinetic energy (its energy of motion) or from whatever is pushing the magnet forward. The magnet's magnetism is basically unchanged by this process.
Nonetheless, a large permanent magnet isn't really permanent. The random fluctuations of thermal energy and the influences of passing magnetic fields gradually demagnetize large permanent magnets. However, good permanent magnets demagnetize so slowly that the changes are completely undetectable. You might have to wait a billion years to detect any significant weakening in the magnetic field around such a magnet.
The best conventional conductors are silver, copper, gold, and aluminum. What makes them good conductors is that electrons move through them for relatively long distances without colliding with anything that wastes their energy. These materials become better conductors as their purities increase and as their temperatures decrease. A cold, near-perfect crystal is ideal, because all of the atoms are then neatly arranged and nearly motionless, and the electrons can move through them with minimal disruption. However, there is a class of even better conductors: the so-called "superconductors." These materials allow electric current to travel through them will absolutely no loss of energy. The carriers of electric current are no longer simply independent electrons; they are typically pairs of electrons. Still, superconductivity appears because the moving charged particles can no longer suffer collisions that waste their energy-they move with perfect ease. We would be using superconductors everywhere in place of copper or aluminum wires if it weren't for the fact that superconductors only behave that way at low temperatures.
As for the best insulators, I'd vote for good crystals of salts like lithium fluoride and sodium chloride (table salt), and covalently-bound substances like aluminum oxide (sapphire) or diamond. All of these materials are pretty nearly perfect insulators.
While metal detectors can easily distinguish between ferromagnetic metals such as steel and non-ferromagnetic metals such as aluminum, gold, silver, and copper, it is difficult for them to distinguish between the particular members of those two classes. Ferromagnetic metals are ones that have intrinsic magnetic structure and respond very strongly to outside magnetic fields. The non-ferromagnetic metals have no intrinsic magnetic structure but can be made magnetic when electric currents are driven through them.
Good metal detectors produce electromagnetic fields that cause currents to flow through nearby metal objects and then detect the magnetism that results. Unfortunately, identifying what type of non-ferromagnetic metal is responding to a metal detector is hard. Mark Rowan, Chief Engineer at White's Electronics of Sweet Home, Oregon, a manufacturer of consumer metal detecting equipment, notes that their detectors are able to classify non-ferromagnetic metal objects based on the ratio of an object's inductance to its resistivity. They can reliably distinguish between all denominations of U.S. coins—for example, nickels are relatively more resistive than copper and clad coins, and quarters are more inductive than smaller dimes. The primary mechanism they use in these measurements is to look at the phase shift between transmitted and received signals (signals typically at, or slightly above, audio frequencies). However, they are unable to identify objects like gold nuggets where the size, shape, and alloy composition are unknown.
No, I don't think that anti-gravity is possible. The interpretation of gravity found in Einstein's General Theory of Relativity is as a curvature of space-time around a concentration of mass/energy. That curvature has a specific sign, leading to what can be viewed as an attractive force. There is no mechanism for reversing the sign of the curvature and creating a repulsive force—anti-gravity. I know of only one case, involving a collision between two rapidly spinning black holes, in which two objects repel one another through gravitational effects. But that bizarre case is hardly the anti-gravity that people would hope to find.
When carbon dioxide gas (CO2) dissolves in water (H2O), its molecules often cling to water molecules in such a way that they form carbonic acid molecules (H2CO3). Carbonic acid is a weak acid, an acid in which most molecules are completely intact at any given moment. But some of those molecules are dissociated and exist as two dissolved fragments: a negatively charged HCO3- ion and a positively charged H+ ion. The H+ ions are responsible for acidity—the higher their concentration in a solution, the more acidic that solution is. The presence of carbonic acid in carbonated water makes that water acidic—the more carbonated, the more acidic. What you're feeling when you drink a carbonated beverage is the moderate acidity of that beverage "irritating" your throat.
A battery uses electrochemical processes to provide power to a current passing it. This statement means that if you send an electric charge through the battery in the normal direction, that charge will emerge from the battery with more energy than it had when it entered the battery. But while it might seem that the number of electric charges passing through the battery each second doesn't matter—that each charge will pick up the usual amount of extra energy during its passage—that's not always the case. To understand this fact, let's look at how charges "pass through" the battery and how they pick up energy.
What's really happening is that electrochemical processes are spontaneously separating charges from one another inside the battery and placing those separated charges on the battery's terminals—the battery's negative terminal becomes negatively charged and its positive terminal becomes positively charged. This charge separating process proceeds in a random, statistical manner until enough charges accumulate on the terminals to prevent any further charge separation. Because like charges repel one another, sufficiently large accumulations of positive charges on the positive terminal and negative charges on the negative terminal stop further arrivals of those charges.
But when you send a positive charge through a wire and onto the battery's negative terminal, you reduce the amount of negative charge there and weaken the repulsive forces. As a result, the chemicals in the battery separate another pair of charges. The battery's negative terminal returns to normal, but now there is an extra positive charge on the battery's positive terminal. This extra charge flows away through a wire. Overall, it appears that your positive charge "passed through" the battery—entering the battery's negative terminal and emerging from the positive terminal with more energy than it had when it arrived at the negative terminal. But what really happened was that the battery's chemicals separated another pair of charges.
In a warm environment, the battery's chemicals can separate charges rapidly and can keep up with reasonably large currents of arriving charges. But in a cold battery, the electrochemical processes slow down and it becomes hard for the battery to keep up. If you try to send too much current through the battery while it's cold, it is unable to replace the charges on its terminals quickly enough and it voltage sags—it doesn't have enough separated charges on its terminals to give the charges "passing through" it their full increase in energy. If you use a battery while it's very cold, you should be careful not to send too much current through it because it will become inefficient and will provide less than its usual voltage.
You have every reason to be skeptical about this sort of activity. Despite its length, I have included your entire question here because it gives me an opportunity to point out some of the differences between science and pseudo-science. You have written a wonderful survey of some of the quackery that exists in our society and have illustrated beautifully the widespread view that science is fundamentally nothing more than gibberish. I cringe as I read your review of "healing science" because in that description I see science, a field that has been developed with care by people I respect and admire, tossed cavalierly into the gutter by self-important know-nothings who aren't worth a moments notice. That these miserable individuals draw such attention, often at the expense of far more deserving real scientists—or worse, by "standing on the shoulders" of those real scientists—is a tragedy of modern society. It's just dreadful.
Let me begin to pick up the pieces by pointing out that terms like "human energy field", "vibrational medicine", and "energy imbalance" are simply meaningless and that the use of "Einstein's Theory" to justify healing-at-a-distance is typical of people who don't have a clue about what science actually is. The meaningless misuse of scientific terms and the uninformed and careless misapplication of scientific techniques is an activity called pseudo-science. Pseudo-science may sound and look like science, but the two have almost nothing else in common. Among the benefits of a good college education is learning how vast is the world of human knowledge, recognizing how little you know of that world, discovering how much others have already thought about everything you can imagine, and finding out how dangerous it is to venture unprepared into any area you do not know well. Most of these pseudo-scientific quacks are either oblivious of their own ignorance or so arrogant that they dismiss the work of others as not worthy of their attention. Either way, they make terrible students and, consequently, useless teachers. You'll do best to leave their books on the shelves.
Because real science is not buzzwords, simply stringing together the words of science does not make one a scientist. Science is an intense, self-reflective, skeptical, objective investigative process in which we try to form conceptual models for the universe and its contents, and try to test those models against the universe itself. We do this modeling and testing over and over again, improving and perfecting the models and discarding or modifying models that do not appear consistent with actual observations. Accurate models are valuable because they have predictive power—you can tell in advance how something will behave if you have modeled it correctly.
In the course of these scientific investigations, concepts arise which deserve names and so we assign names to them. In that manner, words such as "energy" and "vibration" have entered our language. Each such