Chapter 7, Problem 15P

(a)

To determine

The impulse imparted to the golf ball.

Answer to Problem 15P

  $J=2.025\text{kg}\cdot \text{m}/\text{s}$

Explanation of Solution

Given:

Mass of a golf ball $m=0.045\text{kg}$

Final speed of golf ball $v=45\text{m}/\text{s}$

Time of contact is $3.5\times {10}^{-3}\text{sec}$

Formula used:

Impulse is defined as the change in momentum.

  $J=m(v_f-v_i)$   (1)

Where $m$ is mass, $v_f$ is final speed, $v_i$ is initial speed.

Calculation:

Initial speed of golf ball is zero.

By putting the given values in equation (1)

  $\begin{array}{c}J=0.045\left(45-0\right)\\ =0.045\times 45\\ =2.025\text{kg}\cdot \text{m}/\text{s}\end{array}$

Conclusion:

Thus, the impulse imparted to the golf ball is $J=2.025\text{kg}\cdot \text{m}/\text{s}$ .

(b)

To determine

The average force exerted on the ball by the golf ball.

Answer to Problem 15P

  $F_{Avg}=578.57\text{N}$

Explanation of Solution

Given:

Mass of a golf ball $m=0.045\text{kg}$

Speed of golf ball $v=45\text{m}/\text{s}$

Time of contact is $3.5\times {10}^{-3}\text{sec}$

Formula used:

Relation between impulse and force is given as,

  $J=F_{Avg}t$

Where, $F_{Avg}=$ average force, $t=$ contact time

Calculation:

Rearrange the relation.

  $F_{Avg}=\frac{J}{t}$

Substituting the values.

  $\begin{array}{c}{F}_{Avg}=\frac{2.025}{3.5\times {10}^{-3}}\\ =578.57\text{N}\end{array}$

Conclusion:

Thus, the average force exerted on the ball by the golf ball is $578.57\text{N}$ .