# Bouncing Squash Balls

Q:
Why do squash balls bounce higher when released from ever increasing heights. Do squash balls bounce higher when they are heated...is the answer to this the same as that of the answer to ’will the temperature of a basketball affect it’s height’
- Lily
New Zealand
A:
Hi Lily,

Squash balls (and almost all balls) will bounce back higher if they are dropped from a greater height. The kinetic energy of a squash ball just before it hits the ground is directly proportional to the height from which it is dropped. For a superball, with little energy loss in the bounce, the ball rebounds with the same speed upwards after the bounce that it had going downwards before the bounce. Balls that aren’t quite so bouncy lose a fraction of their kinetic energy when they collide with the ground, and this fraction doesn’t change much with the height from which they are dropped. Even a superball loses a little bit of energy each time it hits the ground. So each bounce will be a little lower than the previous one. If the height from which the ball is dropped is h, then the bounce height will be f*h, where f is the fraction of kinetic energy the ball keeps after bouncing, and 0 < f < 1, with f=0 meaning not bouncy at all, and f=1 meaning very very bouncy. The next bounce will go up to f*f*h, and the third f*f*f*h, and so on. For example. If the ball started at 1m height and first bounce went to 0.9 m, the next would go to 0.81 m, then 0.729 m, etc

As you probably have noticed, squash balls aren’t very bouncy at all. They deform when they hit a wall or the floor, and a lot of the energy gets converted to heat during the collision. Squash balls heat up over the course of a game. Either the air in them gets pressurized, or the rubber just gets more flexible, but a squash ball will get more bouncy (larger f) as it heats up.

People who are good at squash have to adjust their playing as a game progresses and the ball heats up! I suspect a basketball will also bounce better if it is hot, but I haven’t done the experiment.

Tom

(published on 10/22/2007)

## Follow-Up #1: bouncing polyvinyl balls

Q:
I am doing a science project in my Chemisty Lab class about how to use polyvinyl acetate (glue), polyvinyl alcohol, and sodium borate (borax) to create a bouncing ball. I noticed that my research on heating and cooling the ball were different than what you explained. When I cooled the ball, it bounced higher than with heat. Does this have to do with the chemicals used and how do they differ from a normal bouncing ball? Does the fact that it is solid change the bouncing results?
- Ashley (age 19)
Tampa, FL, USA
A:

I guessed as to which question you were following-up.

Solid balls definitely behave differently from air-filled balls. There's no air in there to get to higher pressure when they're heated. As to whether the balls bounce better when they're heated, there's no general rule. It depends on the details of your particular material. In some materials, heating them makes it easier for molecules to slide past each other, losing energy to internal friction when the ball squashes during the bounce. That would mean that the hotter ball wouldn't bounce as high.

Mike W.

(published on 09/17/2013)

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