Chapter 8, Problem 47A

Suppose you roll a bowling ball into a pillow and the ball stops. Now suppose you roll it against a spring and it bounces back with an equal and opposite momentum.

a. Which object exerts a greater impulse, the pillow or the spring?

b. If the time it takes the pillow to stop the ball is the same as the time of contact of the ball with the spring, how do the average forces exerted on the ball compare?

To determine

The object which exerts a greater impulse.

Answer to Problem 47A

The spring exerts a greater impulse on the bowling ball as compared to the pillow.

Explanation of Solution

Introduction:

The change in momentum or the product of force and time interval is called impulse.

A pillow cannot exert a sufficient impulse on the ball to stop it. But the spring can exert a sufficient impulse on the ball, due to which bowling ball will be thrown back. This happens because the spring exerts more impulse on the ball as compared to the pillow and turns the momentum of the bowling ball back.

Conclusion:

The spring exerts a greater impulse on the bowling ball as compared to the pillow.

To determine

To Explain: The comparison of the average forces that exerted on the ball.

Answer to Problem 47A

If time was the same then, the average force from the spring was double the force from the pillow.

Explanation of Solution

Introduction:

Impulse is the multiplication of impact force and time. Therefore, the object which exerts more impulse will also exert the greater impulse force, if the time is constant.

The average force from the spring is double the force from the pillow because of which bowling ball bounces back with equal and opposite momentum in case of spring.

Conclusion:

Hence, the average force from the spring is double the force from the pillow.