Infinitely Bouncing Balls

A golf ball or a super ball bounces rather nicely; the height of each bounce is a fraction of the height of the previous bounce (see here for the relation of bounce height and speed to conservation of energy and momentum, see here for a middle school science fair project on how balls actually bounce).  For instance, suppose we drop a golf ball from a height of 64 centimeters.  Say it recovers three-quarters of its height on the next bounce.  Then the next bounce will be (3/4)*64 =  48 cm high.   The next bounce will be  (3/4)*48 = 36 cm high, and the next (3/4)*36 = 27 cm high, etc.    You can try other elasticity coefficients on this page

Surprisingly, if each bounce height is a fraction of the previous bounce height, then the time it takes for one bounce is a different fraction of the time taken by the previous bounce.  We will investigate this relationship on the next page.

Next: Bounce Height and Time

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         copyright: Besson and Styer, Villanova University   12/22/2007  

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