# Bouncing the Ball

## Bouncing the Ball

Contributed by Jikai Xu

Introduction

When you drop a ball from the air to the ground, you may naturally suppose the ball will bounce back to a lower height than the releasing position. But, can you imagine a ball to bounce back to an even higher position?

Materials

A small ball that can bounce back from the ground (e.g., a ping-pong ball), a paper/plastic cup

Procedure

1. Release the ball from rest at a random position and see how high it can bounce back to.
2. Fill some water partially in the cup and put the ball in it. Release the cup (together with the ball) at the same position and see how high this time the ball can bounce back to.

Physics Concepts and Questions

An object has a particular amount of “potential energy” due to the position (or more specifically, height) it is located at, and it has another amount of “kinetic energy” directly related to its speed. You may have heard some concept like “conservation of mechanical energy” before. That is saying the sum of potential energy and kinetic energy when there is no other force than gravity exerts on the object in the case of free-fall. The amount of mechanical energy (sum of potential energy and kinetic energy) determines the height which the ball can reach.

The initial mechanical energy of the ball at rest is just the potential energy it has. Because the air friction is small in this case, you may neglect it. There is only gravity exerting on the ball when falling, so the mechanical energy is conserved in this motion. When the ball hits the ground, some energy is lost from the ball during the collision (you may consider it as if some energy is transferred to the Earth which the ball hits). Therefore, the total mechanical energy becomes less for the ball and it bounces back to a lower position than the place where it is released.

However, when you put the ball in a cup with water, not only the ball has mechanical energy, but also the cup with water has an amount of mechanical energy. Thus, this time the total energy is greater. Still some energy loss during the collision, but the remaining energy is greater than that in the previous case because the initial energy is greater. You can observe that the cup and water hardly bounce back so you can assume that they do not “use” the remaining mechanical energy. Almost totally the mechanical energy left contributes to the bounce-back of the ball. Therefore, the ball bounces back higher than the previous case, and even higher than the releasing position as long as you put enough water in the cup.

Conclusions and Further Investigations

You may change the amount of water in the cup and measure the height to which the ball can bounce back. Then you can draw a plot to see a qualitative or roughly quantitative relationship between these two variables. You can think about the variable that determines the mechanical energy from this. (Be sure to release the ball at the same height across trials!)