Mr. Coe
Project Title
Bouncing Ball
Author
Problem and solution by AP Physics class'99
Updated 06/3/99
Formatting by Mindy Wu'99
Problem: 
When two balls are dropped to the floor with the balls touching each other (as seen in the accompanying drawing below) some fascinating things happen when the balls hit the floor. Many students have seen this demonstrated in classes--use a basketball for the bottom ball and a baseball or softball for the top ball for an interesting result if you would like to try it on your own (be careful as rebound speeds can be high).

Here’s the problem–it’s clear that the rebound speed of the top ball will depend upon the masses of the two balls, but how?

In other words,

Given the respective masses of the two balls (M1 and m2) and the impact velocity (v0), determine the height to which the top ball rebounds and the fraction of the kinetic energy of the system that is transferred to the top ball, both as a function of M1, m2, and v0.

Try the solution yourself before viewing our data. Good luck!
Solution:

For two colliding blocks A and B,
conservation of momentum requires:

Conservation of Energy (Kinetic) gives:

Rearranging terms:

Factoring both sides:

Using the momentum conservation equation above, and cancelling equal terms yields:

     This was a general result for the velocities of two colliding blocks in an elastic collision. Now, let's solve this particular problem with large ball of mass M and small ball of mass m.

Conservation of momentum after the large ball hits the floor requires the following equation (since the balls have equal and opposite velocities, v0).

The velocity relationship derived above gives:

Rearranging and substituting



Defining the mass ratio by M/m =x, dividing through by m and substituting yields:

    Four sequential pictures of a baseball (Mass =145 grams) dropped with a women's basketball (Mass = 509 grams). Note how high the baseball rebounds in the fourth photo.

Resources Window
Interactive Physics is a powerful simulation program that is available from MSC Working Knowledge. IP documents are playable with Interactive Physics v1.2 or later. Earlier versions may be compatable.
Text versions of the equation work are made with Microsoft Equation Editor and are embedded in Microsoft Word documents.
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