Warm-up: conservation of energy during an elastic bounce

Imagine dropping a ball from a height y = h above the ground. Define your coordinate system such that y = 0 m is ground-level. Use this information to fill in the chart below assuming that we can ignore air resistance (note this means that the mechanical energy is conserved).

Did you end up needing the mass of the ball?

When the ball impacts the ground, it bounces back up. Let’s assume that the collision with the floor is perfectly elastic, that is, all the mechanical energy is conserved. What does this mean about the speed of the ball just before and just after the ball bounces? (Hint: You don’t need to do any calculations to solve this.)

How high will the ball bounce?  (Hint: You don’t need to do any calculations to solve this.)

To be precise, let’s imagine what happens during the collision of the ball with the floor. Microscopically the floor deforms ever so slightly because it is hard and the ball deforms much more because it is softer, but if the energy is conserved during the bounce then all the energy that goes into deforming the floor and the ball (elastic energy) gets returned to the kinetic energy, K, of the ball. Here we will use the equations you have derived above to help us understand what happens to the energy during successive bounces of a bouncy ball. Of course the above was for a perfect elastic collision with the floor. In practice some energy is lost to other forms. For example friction, sound (after all, you hear the ball impact the ground, that means that energy in the form of sound went to your ear!), etc.