Month: January 1999

What properties of rubber change in order to make one ball bounce better than an…

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What properties of rubber change in order to make one ball bounce better than another? — JM

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.

We know that ozone can be depleted in the atmosphere as a result of various man-…

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We know that ozone can be depleted in the atmosphere as a result of various man-made factors. What would happen if nitrogen were depleted? What man-made influences, if any, would deplete nitrogen? — BS, Los Angeles

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.

Is the total energy savings still significant for long tube fluorescent lights, …

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Is the total energy savings still significant for long tube fluorescent lights, as compared to incandescent lights, when you consider the energy involved in manufacturing all the components of the lights? — AB, San Antonio, TX

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.

If you were at the back of a bus going the speed of light, and you were to run t…

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If you were at the back of a bus going the speed of light, and you were to run toward the front, would you be moving faster than the speed of light or turn into energy? — TM, Ft. Bragg, NC

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.

How does a heat pipe work?

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How does a heat pipe work? — SG, Sugar Land TX

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.

How is sound picked up on a microphone?

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How is sound picked up on a microphone? — PB, Marion, MA

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.

Why does air speed up as it flows over an airplane wing?

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Why does air speed up as it flows over an airplane wing? — MS

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.

I tried freezing two cups of water, one with salt added and one with sugar added…

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I tried freezing two cups of water, one with salt added and one with sugar added, to see which would freeze first. I conducted my experiment three times and each time the sugar water froze first. Why? — AM

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.

How do the automatic soda dispensers at fast food joints know when the cup is fu…

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How do the automatic soda dispensers at fast food joints know when the cup is full? — MB

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.

Is there any mathematical relevance to the period of motion of a pendulum? For e…

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Is there any mathematical relevance to the period of motion of a pendulum? For example, if I made a scale model of a pendulum and then squared it or cubed it, would there be any mathematical correlation between the results?

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.