ball diameter vs. bounce height

[ranigarner]

Dear Science Buddies,

How is the size of a ball related to its bounce height?

Sincerely,
Daniel Crowe

[deleted-2131]

Daniel,

Many factors affect the height a ball bounces. In order to determine hoe the size of a ball is related to how high it bounces, you need to do a controlled experiment. This means that you have a bunch (let's say 10) balls of different diameters (1 cm, 2 cm, 3 cm, 4 cm, 5 cm, etc.). The balls are all exactly the same in every way except for their size (e.g. made of same material, inflated to same pressure, made the same way, etc.).

I would suggest then dropping the balls from a specified height (e.g. 1 m) and then measuring how high each ball bounces on the first bounce, second bounce, third bounce, etc. Record this information in a table. I would suggest you repeat this experiment 10 times and average the height each ball bounces per bounce.

You can then graph the height that the ball bounces on a given bounce against the ball's diameter. You would have a separate graph for each bounce. For example. let's assume the 10 cm ball bounces 75 cm on the first bounce , 50 cm on the second bounce and 25 cm on the third bounce.
You'll have one graph that plots the height of the first bounces, another graph that plots the height of the second bounces, and a third graph that shows the height of the third bounce. So, on the first graph you would have an ordered pair at (10, 75) on the second graph a point at (10, 50) and on the third graph a point at (10, 25).

If you wanted to get really involved, you could plot the data for each of your tests and then run a linear regression analysis of the data to generate a mathematical model describing the relationship between diameter and bounce height. You could then test the prediction made by the linear regression with a ball of a diameter that you didn't use to generate your model. You can then calculate percent error to get an idea of how accurate your model is.

If you want to pusue this higher level analysis, let me know and I will give you more details.

Good Luck!

[deleted-2574]

Hi ranigarner (Daniel)!

There is apparently no correlation between ball size and bounce height. Please consult the following two URLs:

http://www.iit.edu/~smile/mp1498.htm
Note “.. bounce to a similar height, independently of their size.�

http://answers.yahoo.com/question/index ... 351AADAnRr
Note none of the equations have size in determining bounce height.

[ranigarner]

Thanks very much for your help!

Daniel