# Gravity's affect on the rebounce height of a tennis ball

1. Feb 23, 2007

### cluelessmum

I'm sorry - I don't know if I'm posting in the correct area, but I desperately need help.

1. The problem statement, all variables and given/known data

My son is doing a science project - his theory is as follows:

When a tennis ball is dropped from a low height, it usually bounces back at a rate approximately 2/3 the height of the initial drop. As the height of the initial drop increases, the bounce-back height ratio of the ball begins to decrease.

I believe that the force of gravity will continue to decrease the tennis balls rebound height to the point where the ball will eventually reach a maximum elevation of recoil.

I'm not looking for anyone to support or deny his hypothesis, just some help on where we can look for research information to help him with his project. We've no idea what "label" to put on this hypothesis - what theories are used to prove or disprove, etc. Can anyone help, please?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 23, 2007

### arunbg

What you need to look for is the varation of the coefficeient of restitution with the height from which the ball is dropped.
Here's a wikipedia article http://en.wikipedia.org/wiki/Coefficient_of_Restitution

Remember that with increasing height, you increase the velocity with which the ball hits the ground. The variation of the coefficient will depend on a lot of factors and would be complex to analyse, but I would say that it is propportional to some negative power of drop height. So what you suggest is correct, there really could be a "saturation" value for rebound of the ball, since the height ratios keep dropping, but that height could be really large, and so impractical to find by experiment.

3. Feb 23, 2007

### eaboujaoudeh

Here goes what i think: the higher the initial height, more friction then more losses due to heat before and on impact. More air resistance is encountered the higher u go, because ur lenghthening the time air resistance is beating on the ball then more losses are encountered. the deformation encountered by the ball may also contribute to the energy losses because this deformation absorbs energy.