How come planets are spherical, albeit with somewhat flattened poles?

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How come planets are spherical, albeit with somewhat flattened poles? — DB

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.

I always thought that pure water cannot exceed 100° Celsius at atmospheric p…

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I always thought that pure water cannot exceed 100° Celsius at atmospheric pressure without first turning into its gaseous state. How is it that the water heated in the microwave oven can superheat and exceed 100° Celsius? — AC

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.

I am twelve years old and weigh 85 pounds. How much helium would it take to lift…

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I am twelve years old and weigh 85 pounds. How much helium would it take to lift me off the ground?

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.

Why does a shave that looks great under incandescent light look terrible under f…

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Why does a shave that looks great under incandescent light look terrible under fluorescent light? And, for a woman, what light is best for putting on makeup? — JE

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.

What is terminal velocity?

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What is terminal velocity? — EW, Fisher, Australia

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.

How does a Tesla coil work?

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How does a Tesla coil work? — EK

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.

If a microwave oven with painted inside walls has some of the paint removed due …

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If a microwave oven with painted inside walls has some of the paint removed due to a very small fire caused by arcing, is it still safe to use?

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.

What is the difference between spark ignition engines and diesel engines?

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What is the difference between spark ignition engines and diesel engines? — JC

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.

What is the function of a magnet in an audio speaker?

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What is the function of a magnet in an audio speaker? — EB

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.

My science book said that a microwave oven uses a laser resonating at the natura…

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My science book said that a microwave oven uses a laser resonating at the natural frequency of water. Does such a laser exist or was that a major typo?

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).