Chapter 7, Problem 59A

A 7.00-kg bowling ball moving at 8.0 m/s strikes a 1.0-kg bowling pin and slows to 7.0 m/s in 0.040 s.

a. Show that the force of impact on the bowling ball is 175 N.

b. How much force acts on the bowling pin?

To determine

To show: The force of impact on the bowling ball is $175\text{ N}$ .

Explanation of Solution

Given:

Mass of the bowling ball is $m=\text{ 7}\text{.00 kg}$

Initial velocity of the ball is $v_i=8.0\text{ m/s}$

Mass of the bowling pin is $\text{M = 1}\text{.0 kg}$

Final velocity of the ball is $v_f=7.0\text{ m/s}$

Time interval is $\Delta t=0.040\text{ s}$

Formula used:

Initial momentum of the ball is

  $p_i=m{v}_i$

Final momentum of the ball is

  $p_f=m{v}_f$

From the impulse - momentum theorem, the impulse on the ball can be written as

  $F\Delta t=p_f-p_i$

Substituting for $p_f$ and $p_i$ ,

  $F\Delta t=m{v}_f-m{v}_i$

  $\Rightarrow F\Delta t=m\left(v_f-v_i\right)$

  $\Rightarrow F=\frac{m\left(v_f-v_i\right)}{\Delta t}$ $\left(1\right)$

Calculation:

Substituting the numerical values in equation $\left(1\right)$ ,

  $F=\frac{\left(\text{7}\text{.00 kg}\right)\left(7.0\text{ m/s}-8.0\text{ m/s}\right)}{0.040\text{ s}}=-175\text{ N}$

Magnitude of force on the ball is $175\text{ N}$ .

Conclusion:

The force of impact on the bowling ball is $175\text{ N}$ .

To determine

The amount of force acting on the bowling pin.

Answer to Problem 59A

  $175\text{ N}$

Explanation of Solution

Introduction:

Newton’s third law of motion - When there is an interaction among two bodies, both the bodies exerts force on each another whose magnitude are equal but they are acting in reverse direction. This third law is also called by the name law of action and reaction.

In the case of hitting a bowling ball with a bowling pin, both the ball and the pin experiences the force. The magnitude of the force experienced by the bowling ball and the bowling pin are equal and are acting in reverse direction.

Therefore the force acting on the bowling pin is also $175\text{ N}$ .