# Does a ball's volume change when it bounces?

Consider a bouncy ball, like a basketball or golf ball what-have-you. When the ball bounces, it will compress vertically. The mass of air inside the ball remains constant, but we expect the pressure to change throughout the volume i.e. the pressure distribution is no longer uniform, and the shear strain on the surface of the ball is expected to become higher at the edges than on the the top of the ball. We model the "bounce" as an isothermal process at first.

My question is, will the ball's volume change when it bounces? Will the volume of the ball increase momentarily, or will the increased strain at the edges counteract the decreased strain on top? Perhaps I've made some incorrect assumptions as well - how might one model the process of a ball bouncing using say, thermodynamics, and stress and strain within the ball?

The process is quite transient of course, so the behavior might not be outright simple. But surely there is a way to model the bounce.

Sam

--EDIT--

I've found that the subject of dynamic deforming solids is contact mechanics which distinguishes between adhesive and non-adhesive contact. This question assumes the non-adhesive case. This is a "sphere in contact with a plane" problem it would appear.

• If you're assuming the gas inside undergoes an isothermal process, and if you assume the air inside is an ideal gas, then the ideal gas law says that increasing pressure decreases volume; $V = NkT/P$. Of course, these assumptions only hold to some degree of accuracy that needs to be evaluated in more detail, but that's a simple first order analysis. – joshphysics Jul 19 '17 at 18:55

• Solids are much less compressible than gases. Hence, if the ball bounces, the gas will be compressed significantly compared to the solid. As you wrote in your comment, the formula which describes this process is given by the ideal gas law. However, I would expect an adiabatic process, $\delta Q \approx 0$, because the duration of a single bounce is "short" so that heat can't be exchanged. But the formula just obscures the simple picture: ... – Semoi Jul 20 '17 at 10:45
• I have to admit, I never saw an empty basketball. However, I reckon they are similar to soccer balls. Soccer balls without (!) air are "scrambled": Their shape is not spherical. Hence, if we agree that the surface area in this state does not differ significantly from the final state (as you pointed out yourself, elasticity $> 0$), I'm sure we do not disagree. – Semoi Jul 22 '17 at 4:43