Re: Does a hollow rubber ball bounce higher than an air-filled rubber ball

Hello Leow,

This is a very good question. However, I have a question to you: How would you make a hollow ball that does not contain any air? If you take an ordinary ball, leave out the air, you'll have an empty ball - not very bouncy at all!

Your question seems to revolve around the weight of the ball. You want to get rid of the air so one ball is lighter than the other. However, what if we replace the gas with a much lighter gas, such as hydrogen. Hydrogen has a molecular weight of 2, while the average molecular weight of air is about 29 [1]. This means the ball has the pressure of an air-filled ball, but loses about 93% of its weight. This should come pretty close to an empty ball, right?

In a very simple model that ignores air friction and the energy loss in the rubber and the gas from bouncing, the ball should bounce equally high as the height from which it was dropped. The amount of energy that is in the heavier ball is larger, but it takes more energy to accelerate as it is heavier. These effects precisely cancel. However, if we consider friction, the ball will bounce back less high.

Let's start with the air friction. Air friction depends on the shape of the ball (the same in both cases), the size of the ball (also the same) and the speed. If the speed were the same, the air friction would be the same. However, because the heavier ball has more energy, it loses less of it (relatively) and hence will bounce better. This is essentially the same reason why a cannonball falls faster than a feather.

The second aspect is how much heat gets produced in the ball. Now, you are right that the heavier ball will produce more friction, as the rubber needs to stretch more. However, the heavier ball also has more energy, so the fact that more is lost does not necessarily mean that it will bounce less high. What matters is whether the energy lost in friction is more or less than proportional to the extra stretching the ball has. It is not easy to answer that question without knowing exactly what sort of rubber the ball is made of.

I've been digging into this a bit deeper. It turns out that an emeritus professor, Rod Cross, has been studying this in great detail (which is a good thing, as I am getting a sneaking suspicion we understand the inside of a star dozens of lightyears away significantly better than we understand bouncing balls). According to him [2], the bounciness of a ball does not depend on its mass. This means that the amount of energy lost is proportional to the stretch, which seems very plausible.

The combination of bounciness and friction means that if anything, a ball filled with a lighter gas will bounce (slightly) less.

As for the temperature, increasing the temperature increases the pressure of the gas in it. If anything, this will make the ball slightly more bouncy (as the rubber indents less). The rubber will also (probably) become softer; this has an opposite, but probably smaller effect.

I hope this answers your question.

Regards,

Bart Broks

[1] http://www.engineeringtoolbox.com/molecular-mass-air-d_679.html

[2] R.C. Cross, The bounce of a ball, Am. J. Phys. 67, 222-227 (1999).