Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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1290001     Change in momentum of Earth as a result of bouncing a superball.     1290001
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Question

 

Suppose that you measure the velocity of a 0.015-kg superball just before it hits the floor and find that its velocity is downward with a magnitude of 4.5 m/s. You also measure its velocity just after it hits the floor and find that it is upward with a magnitude of 3.9 m/s. What is the change in momentum of Earth as a result of the collision with the superball?

 



Solution

 

Begin by sketching a picture.


Figure: A superball collides with Earth and rebounds upward.

Define the ball and Earth together to be the system. During the small time interval of the collision, there are no other significant external forces on the ball and Earth. Yes, Earth exerts a force on the ball, and the ball exerts a force on Earth. But these are internal to the system. The net external force on the system is zero. If the net external force on the system is zero, then according to the momentum principle, the change in the momentum of the system is zero.

The change in momentum of the system can be written as the sum of the change in momentum of each object in the system. Thus, the change in momentum of the system in this case is the sum of the change in momentum of Earth and the change in momentum of the ball.

This means that the change in momentum of Earth is equal to the negative of the change in momentum of the ball.

Sketch a picture showing both the change in momentum of the ball and the change in momentum of Earth.


Figure: A superball collides with Earth.

Substitute known quantities:

Check the result. The change in momentum of Earth is downward, exactly as drawn in the picture.

The ball has a change in momentum of 0.126 kg m/s upward. Because momentum is conserved for the system, Earth has a downward change in momentum of -0.126 kg m/s . The result is that the change in momentum of the system is zero.

So why don't we notice the change in momentum of Earth every time someone bounces a ball? Since , Earth's very large mass results in a very small change in velocity. The ball's small mass results in a change in velocity of 8.4 m/s. You can observe the change in velocity of the ball, but Earth's change in velocity has a magnitude which is too small to measure.