Chapter 6, Problem 20P

A baseball (m = 145 g) traveling 32 m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?

To determine

To DetermineAverage force exerted by the ball on the glove.

Answer to Problem 20P

Solution:297 N

Explanation of Solution

Given:Mass of the ball, $m=145\text{g }=0.145\text{ kg}$

Ball moves at speed, $v=32\text{ m/s}$

Distance, $s=25\text{ cm}=0.25\text{m}$

Formula Used:

According to conservation energy theorem, work done by the force equal to change in kinetic energy of the particle

  $\begin{array}{l}W=K.E\\ F\times s=\frac{1}{2}m{v}^2\end{array}$

Where W is the work done, F is a force, m is mass of the ball, v is the speed of the ball

Calculations: Substitute this value in above equation and solve for required force

  $\begin{array}{l}F=\frac{1}{2\times s}m{v}^2\\ F=\frac{1}{2\times 0.25}(0.145\times {32}^2)\\ F\approx 297\text{ N}\end{array}$

Average force exerted by the ball on the glove is 297 N.

Conclusion:297 N forceis exerted by a ball on the glove when 145 g of the ball is moving at $32\text{ m/s}$ .