Defective Balls

Most people are familiar with the standard "collision balls" apparatus. Six identical steel balls are suspended in a row; lifting one of the end balls and releasing it causes the one on the opposite side to move away, then fall back, causing the original ball to do the same, etc. This action can be seen in this MPEG video. The motion satisfies all of the requirements of conservation of energy and linear momentum during the various collision processes.

Graphic - Defective Balls Apparatus

Now suppose that we modify this apparatus, as seen in the photograph above, so that one of the balls (the fourth from the left) is made from aluminum rather than steel, and therefore no longer has the same mass.

In this case, how will the collision balls apparaus work? In particular, will it work the same way as the equal mass collision ball apparatus? Will the ensuing motion be one ball moving up on one side, then the other side, back and forth?

Solution

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Solution

The answer is "No": The collision ball apparatus will not work the same if one of the balls has a different mass. What actually happens can be seen in this MPEG video.

When you release the ball at the left end, starting the action, what happens is actually a series of collisions between two balls: the first ball hits the second one, transferring all of its energy and momentum, the second ball hits the third one, etc. The end result is that the ball on the right end gets all of the energy and momentum, and it moves away from the others, rising to the height from which the first ball was released.

When one of the balls is a different mass, the chain is broken, resulting in a collision where the final momentum and energy is divided between the incoming ball and the one being struck. The motion then becomes more complex: the momentum and energy is divided between several of the balls, as can be seen.