Chapter 9, Problem 55A

Place a small rubber ball on top of a basketball and drop them together. How high does the smaller ball bounce? (Perhaps this is best done in the gym, or outdoors.) Can you reconcile this result with energy conservation?

To determine

The height to which the smaller ball will bounce and whether this reconcile with the conservation of energy.

Explanation of Solution

Introduction:

Momentum of a system of bodies is conserved when no extra forces are applied. The collective mass and velocity product of individual bodies is conserved. For conservation of energy, energy is only transformed from one form of energy to another.

As the momentum of the stacked balls is conserved, when they are dropped, some momentum of the larger ball is transferred to the smaller ball. It depends upon the elasticity of the ball. As the mass of the larger ball is greater it has larger momentum. So the momentum transferred to the smaller ball will make it bounce to a much higher position.

Energy is always conserved in the system, as only gravitational forces are exerted on the balls. Some momentum or energy of the larger ball is transferred to the smaller ball which bounces to a higher position as it has higher momentum or velocity or kinetic energy. This kinetic energy converts into gravitational potential energy as the ball gains height.

Conclusion:

The momentum transferred to the smaller ball will make it bounce to a much higher position. This kinetic energy converts into gravitational potential energy as the ball gains height.