Question

A steel ball with a mass of 0.600 kg is dropped from an initial height of 2.80 m onto a metal plate. The steel ball bounces multiple times and on each bounce it returns to 75% of its previous maximum height.

A)What is the initial mechanical energy of the ball-Earth system, just after the ball is released from its initial height? Use the surface of the steel plate as the y = 0 reference point for the gravitational potential energy.

B)How much mechanical energy does the system lose during its first bounce?

Answer 1

Initially the ball was in rest so it's initial velocity was zero then it was dropped from height 2.80 m. So the initial kinetic energy of the ball was zero . The initial gravitational potential energy of the ball was

Where m is the mass of the ball and H = 2.80 m.

So the total mechanical energy of the ball-Earth system is the sum of kinetic and gravitational potential energy which is given by

This is total mechanical energy of the ball-Earth system just after the ball is released from initial height.

After the first bounce the ball goes up 75% of initial height. So after the first bounce the ball goes up height  

Now after reaching height ball again comes to rest so it's kinetic energy becomes zero again. Now total mechanical energy of the ball-Earth system is the gravitational potential energy of the system as given below

So the loss in the mechanical energy during the first bounce is the difference between above two energies as given below

This is the amount of energy the system lose during first bounce.