## How can a basketball weigh 7.5 to 8.5 pounds when blown up but much less when deflated?

### How can a basketball weigh 7.5 to 8.5 pounds when blown up but much less when deflated? What is it filled with when deflated?

So what is the 7.5 to 8.5 pounds that a basketball is supposed to contain? Or the 13 pounds that a football is supposed to contain? Those aren’t weights at all. In fact, they are careless abbreviations for a different physical quantity: pressure. They should actually be written “7.5 to 8.5 pounds-per-square-inch” and “13-pounds-per-square inch” respectively.

Fluids such as air have pressures — the forces they exert on each unit of surface area they contact. For example, air that is listed as having a pressure of 7.5 pounds per square inch exerts a force of 7.5 pounds on each square inch of surface it touches. That means that the air in a properly inflated basketball pushes outward with a force of 7.5 to 8.5 pounds on each square inch of the inner surface of that ball. That outward push stretches the ball tight and gives it its feel and bounciness. Similarly, a properly inflated football has a pressure of 13 pounds per square inch and thus the air inside it exerts an outwardÂ  force of 13 pounds on each square inch of surface inside the ball. Again, this outward push stretches the ball taut and gives it its bounciness and feel.

An underinflated basketball or football weighs just slightly less than a properly inflated ball because its skin hasn’t changed and the weight of the air it contains is so insignificant. But the decrease in outward forces on the skin of the ball significantly changes its feel and bounciness.

## Why does a diving bounce up and down after the diver jumps off its surface?

### Why does a diving bounce up and down after the diver jumps off its surface?

When left alone, the diving board settles down to its equilibrium shape and position — arrangement at which all of its parts are experiencing zero net force and are therefore not accelerating. If the board is disturbed from that arrangement and released, it will vibrate back and forth about that equilibrium arrangement until it settles down again.

When the diver leaves the diving board, the board is usually far from its equilibrium arrangement and its parts are usually moving as well. It consequently vibrates back and forth. Whenever it is above the equilibrium arrangement, the springiness of the board, assisted slightly by gravity, causes its parts to experience downward net forces and those parts accelerate downward. If the board was rising, it slows to a stop and then begins to descend toward the equilibrium. Whenever the board is below the equilibrium arrangement, its springiness, opposed slight by gravity, causes its parts to experience upward net forces and those parts accelerate upward. If the board was descending, it slows to a stop and then begins to rise toward equilibrium.

So whenever the board is away from equilibrium, it is accelerating toward that equilibrium and will soon be moving toward equilibrium. When it reaches equilibrium, however, it will be moving and will thus coast through equilibrium and overshoot. That’s why it bounces up and down — it keeps coasting through equilibrium, turning around, heading back toward equilibrium, and coasting through again. But with each bounce, the board wastes some of its energy as thermal energy via internal friction and air resistance. Its bounces get weaker and weaker until it eventually settles at equilibrium and stops moving altogether.

## Why does a basketball bounce poorly when it’s cold?

#### Why does cold temperature affect the bounce of a basketball? Will a basketball freeze if placed in a freezer? — SS, Lebanon, Tennessee

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.

## I am in 4th grade, and working on a science fair project using a basketball and …

#### I am in 4th grade, and working on a science fair project using a basketball and have it pumped with 0 psi, 3 psi, 6 psi, 9 psi and 12 psi of air. Why is it that the 9psi ball bounces the highest when dropped from 6ft? – T

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.

## I was recently riding as a passenger in a van and there was a housefly buzzing a…

#### I was recently riding as a passenger in a van and there was a housefly buzzing around in the van. While trying to squash the fly, I was wondering why was the fly traveling the same speed as the van at 70 mph as it was hovering in mid air. Shouldn’t it have smashed into the rear window of the van just like so many bugs would have been, on the grill of the vehicle?? — DS

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.

## My 5 year old wants to do his kindergarten science project on “why do balls bou…

#### My 5 year old wants to do his kindergarten science project on “why do balls bounce?” His hypothesis is that “balls bounce because of the stuff inside.” Can you advise how best to test this hypothesis and explain this concept on a level that a bright, but still only 5 year old, can truly understand? — MS, Bayside, New York

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?

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

#### 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.

## How does a dead ball work?

#### How does a dead ball work? — DIY, Lyon, France

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.

## Is bouncing related to elasticity or hardness? Can a hard body rebound?

#### Is bouncing related to elasticity or hardness? Can a hard body rebound? — DIY, Lyon, France

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.

## The earth’s surface is moving at something like 950 mph as it rotates. Why don’t…

#### The earth’s surface is moving at something like 950 mph as it rotates. Why don’t we notice this when we are in an airplane? — DT, Nicosia, Cyprus

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.