Chapter 4, Problem 9P

To determine

The average force applied by the ball on the glove.

Answer to Problem 9P

Solution:

The average force exerted by the ball is 780.2N

Explanation of Solution

The concept we must use to solve this problem is average acceleration and force. The average acceleration is the change in velocity with respect to the elapsed time. So, the expression for the average acceleration is given as below:

$a_{\text{avg}}=\frac{v-u}{t}$…… (1)

Here, $v$ is the final velocity, $u$ is the initial velocity and $t$ is the time.

The force on an object is calculated by using the Newton’s second law of motion as given below:

$F_{\text{avg}}=m{a}_{\text{avg}}$…… (2)

Given:

Mass of the baseball $m=0.140\text{ kg}$

Distance $s=11.0\text{ cm}$

Initial speed $u=0\text{ m/s}$

Initial speed $v_i=35.0\text{ m/s}$

Formula used:

$\begin{array}{l}{a}_{\text{avg}}=\frac{v-u}{t}\\ F_{\text{avg}}=m{a}_{\text{avg}}\end{array}$

Calculation:

Initially, we must find a time by using the expression of average speed as given below:

$\begin{array}{c}{v}_{\text{avg}}=\frac{35}{2}\\ =17.5\text{ m/s}\end{array}$

Thus, the time is –

$\begin{array}{c}t=\frac{d}{v_{\text{avg}}}\\ =\frac{0.11}{17.5\text{ m/s}}\\ =6.28\times {10}^{-3}\text{ s}\end{array}$

Now, substitute, $v=35\text{ m/s}$, $u=0\text{ m/s}$ and $t=6.28\times {10}^{-3}\text{ s}$ in the equation (1)so the average acceleration is given as below:

$\begin{array}{c}{a}_{\text{avg}}=\frac{v-u}{t}\\ =\frac{\text{35 m/s-0}}{6.28\times {10}^{-3}\text{ s}}\\ =5573.2{\text{ m/s}}^2\end{array}$

Now we can find the magnitude of force exerted by car by substituting $m=0.140\text{ kg}$ and $a_{\text{avg}}=5573.2{\text{ m/s}}^2$ in equation (2)as given below:

$F_{\text{avg}}=m{a}_{\text{avg}}$

        $\begin{array}{c}=\left(0.140\text{ kg}\right)\left(a_{\text{avg}}=5573.2{\text{ m/s}}^2\right)\\ =780.2\text{ N}\end{array}$