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Exploration 8.5: Two and Three Ball Collisions


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If you drop a rubber ball and it hits the ground at 5 m/s, it bounces back at almost the same speed (position is given in meters and time is given in seconds). But what happens if you drop two balls stacked one upon another? A common lecture demonstration has a professor dropping a light ball and a heavy ball at the same time. The light ball is directly above the heavy ball so that the heavy ball hits the ground first, bounces back, and then hits the light ball which is still on its way down. Restart.

This animation uses two balls with a mass ratio of 1:10. We consider motion on a horizontal air track so we can ignore the effect of gravity so as to make the physics as clear as possible. The balls move at constant speed to the left before hitting the wall; assume all collisions are elastic.

  1. Predict the velocities of the balls after the first set of collisions, that is, when both balls are moving to the right.
  2. Predict the velocities if you use three balls with mass ratios of 1:10:100.
  3. Now run the animations. Were you correct? If not, explain why.

Note: The animation will run for 100 seconds.

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