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Astroblaster

An equally fun and perhaps safer demonstration is to hold a tennis ball on top a basketball and drop them simultaneously. The tennis ball shoots up. With some practice you can aim it into different parts of the class. The astroblaster magnifies the effect, but the balls are harder to see.


Why does this happen? If you drop a ball to the ground and the collision loses no energy (perfectly elastic), the ball reverses its velocity and returns to the original height. Now suppose the basketball hits the ground, reverses its velocity and then collides with the tennis ball still coming down. It is a much larger collision velocity for the tennis ball and it flies to a greater height.


A calculation, assuming perfectly elastic collisions and a tennis ball much less massive than the basketball, predicts the tennis ball to go up to nine times the drop height!


A Calculation


Just before the basketball hits the ground, both balls have the same downward speed, u. The basketball hits and reverses direction while maintaining speed u. The equations below represent the conservation of energy and momentum in the basketball/ tennis ball collision assumed to be perfectly elastic.


  


Solving these two equations for u1 and u2 gives:



When M >> m the solution becomes:



Since the potential energy goes as the square of the velocity, the tennis ball will go nine times (32) as high as it would just hitting the ground.