Ping Blaster – An Exercise in Momentum, Elasticity, and Energy

The purpose of this activity is to practice using conservation of momentum and conservation of energy to make a prediction that can be tested with a ping pong ball and a super ball.  The two balls are dropped together as a vertical stack with the ping pong ball on top of the super ball – this causes the ping pong ball to be “blasted” to a relatively great height.  Given an initial drop height predict the height to which the ping pong ball will be launched!

Mass of super ball:  __________________   Mass of ping pong ball:  __________________

Part 1 (Optional):  Determine elasticity of each ball separately.  (You will not be tested on this!)

Elasticity (or “coefficient of restitution”) is equal to the ratio of the speed before to the speed after bouncing when impacting a very large object like the earth.  For example, if a ball hits the floor at speed 10.0 m/s and rebounds upward at speed 7.0 m/s the elasticity is e = 0.7 – a little like saying that it rebounds at 70% of its impact.  You can easily determine the elasticity of each ball by noting how far it rebounds when dropped from a certain height and applying conservation of energy to determine the speeds just before and just after impact.

Elasticity of super ball:  ______________     Elasticity of ping pong ball:  ______________

Part 2:  Analyze the falling stack.

Choose a convenient height between 0.2 m and 0.5 m from which to drop the stacked balls.  Note that it is difficult to get the stack to stay vertical during the fall and this is easier to achieve from a lower drop height.  Take your chosen drop height and use conservation of energy to determine the speed of each ball downward at the instant right before impact.

Drop height:  ________________      Speed of each ball just before impact:  ________________

Part3:  Analyze the first collision.

The super ball hits the ground first and then rebounds upward.  Determine the speed with which the super ball rebounds upward, assuming this is an elastic collision with the floor (or optionally use the elasticity determined in Part 1).  This rebound velocity will be the velocity of the super ball before it hits the ping pong ball.

Rebound velocity of super ball:  ______________   

Part 4:  Analyze the second collision.

The falling ping pong ball hits the super ball which has already rebounded off of the floor at a certain velocity.  The ping pong ball should be falling at the velocity found in Part 2 just before it hits the rising super ball.  Analyze this collision and determine the velocity of each object immediately afterward.  Assume the collision is perfectly elastic (or optionally use the elasticity found in Part 1).

Velocity of super ball before:  ___________   Velocity of ping pong ball before:  ___________

Velocity of super ball after:    ___________    Velocity of ping pong ball after:    ___________

Part 5:  Predict the rebound height.

Use conservation of energy to determine the rebound height of each ball based on the speed of each ball after the second collision.

Predicted values

Rebound height of super ball:  ___________   Rebound height of ping pong balll:  ___________

Test your prediction! 

Measured values

Rebound height of super ball:  ___________   Rebound height of ping pong balll:  ___________

What might cause discrepancies between your predictions and reality?  What simplifying assumptions were made to make the prediction?