Chapter 9, Problem 50A

a.

To determine

Change n momentum of ball.

Answer to Problem 50A

  $\Delta P=5.075\text{ kg-m/s}$

Explanation of Solution

Given:

Mass of the baseball, $m=0.145\text{ kg}$

Final speed of baseball when player caught it, $v=35\text{ m/s}$

Formula used:

Momentum of any object is given by:

  $P=mv$

Here, P is momentum, m is mass and v is velocity

Calculation:

Initial speed of the baseball, $u=0\text{ m/s}$

Change in momentum is given by:

  $\Delta P=m\left(v-u\right)$

Now, substitute the value of m, v and u and solve.

  $\begin{array}{l}\Delta P=0.145\left(35-0\right)\\ =0.145\times 35\\ =5.075\text{ kg-m/s}\end{array}$

Conclusion:

Therefore, change in momentum is $\Delta P=5.075\text{ kg-m/s}$ .

b.

To determine

Average force exerted on the ball.

Answer to Problem 50A

Average force exerted, $F=101.5\text{ N}$

Explanation of Solution

Given:

Mass of the baseball, $m=0.145\text{ kg}$

Final speed of baseball when player caught it, $v=35\text{ m/s}$

Time interval, $\Delta t=0.050\text{ s}$

Formula used:

Impulse of any body is equal to change in momentum of the body.

  $J=\Delta P$

Here, J is impulse and $\Delta P$ is change in momentum.

Impulse is equal to

  $J=F\Delta t$

Here, F is force and $\Delta t$ time interval

Hence, $F\Delta t=\Delta P$

Calculation:

From part (a), $\Delta P=5.075\text{ kg-m/s}$

Now, substitute the value of $\Delta P$ and $\Delta t$ and solve.

  $\begin{array}{l}F\times 0.050=5.075\\ F=\frac{5.075}{0.050}\\ =101.5\text{ N}\end{array}$

Conclusion:

Therefore, average force exerted is equal to 101.5 N.

c.

To determine

Average force exerted on the ball.

Answer to Problem 50A

Average force exerted, $F=10.15\text{ N}$

Explanation of Solution

Given:

Mass of the baseball, $m=0.145\text{ kg}$

Final speed of baseball when player caught it, $v=35\text{ m/s}$

Time interval, $\Delta t=0.5\text{ s}$

Formula used Impulse of any body is equal to change in momentum of the body.

  $J=\Delta P$

Here, J is impulse and $\Delta P$ is change in momentum.

Impulse is equal to

  $J=F\Delta t$

Here, F is force and $\Delta t$ time interval

Hence, $F\Delta t=\Delta P$

Calculation:

From part (a), $\Delta P=5.075\text{ kg-m/s}$

Now, substitute the value of $\Delta P$ and $\Delta t$ and solve.

  $\begin{array}{l}F\times 0.500=5.075\\ F=\frac{5.075}{0.500}\\ =10.15\text{ N}\end{array}$

Conclusion:

Therefore, average force exerted is equal to 10.15 N.