Chapter 14, Problem 79A

To determine

To explain: The energy changes in the bouncing of the ball on the spring and check that the total mechanical energy changes or not.

Explanation of Solution

Introduction:

The kinetic energy, gravitational potential energy and elastic potential energy are the different forms of the energy that converts in the bouncing of the ball on the spring.

The gravitational potential energy depends on the position of the ball, elastic potential energy of compression or extension of the spring and kinetic energy depends on the motion of the ball.

The position of the ball at the top is maximum, so the gravitational potential energy of the ball at the top is maximum. The ball is at rest at the top, so the kinetic energy is zero at the top.

The elastic potential energy at the bottom become maximum and gravitational potential energy become minimum. The kinetic energy at the bottom remain as zero.

The kinetic energy become maximum at equilibrium position of the spring and elastic potential energy become zero at equilibrium position.

The sum of the kinetic energy, gravitational potential energy and elastic potential energy remains constant at top, bottom and equilibrium position of the spring. The total mechanical energy remains constant, only energy converts from on form to other form at different positions of the bounce. So, the total mechanical energy of the ball does not change.

Conclusion:

Therefore, the kinetic energy, gravitational potential energy and elastic potential energy converts into each other but the total mechanical energy does not change.