Chapter 7, Problem 20P

(a)

To determine

The total impulse acting on the ball.

Answer to Problem 20P

The total impulse on the ball is $5.1 \text{N-s}$

Explanation of Solution

Given:

Mass of the tennis ball is 0.060 kg. Force acting on the ball is in +x direction.

The given graph is shown below.

  

Formula used:

The impulse is calculated as the area under the graph of force versus time.

  $\Delta p=F\Delta t=m\Delta v$

Calculation:

Here, the area under the graph of Force versus time can be calculated as total area under the graph. The total number of boxes under the curve is $10.2$ . Each box has a height of $h=50N$ and width $w=0.01\sec$ . Thus,

  $\begin{array}{c}\Delta p=10.2\left(\text{50N}\right)\left(\text{0}\text{.01s}\right)\\ \text{=5}\text{.1}\text{N-sec}\end{array}$

Conclusion:

The total impulse on the ball is $5.1 \text{N-s}$

(b)

To determine

The velocity of the ball after being struck.

Answer to Problem 20P

The velocity of the ball after struck by force is $\text{85 m/s}$

Explanation of Solution

Given:

Mass of the tennis ball is 0.060 kg. Force acting on the ball is in +x direction.

The given graph is shown below.

  

Calculation:

Using the values of impulse from the previous section, we can calculate the final velocity of the ball.

  $\begin{array}{c}\Delta p=m\Delta v=m(v_f-v_i)\\ \Delta p=5.1 N-s\\ 5.1=0.06 \text{kg}(v_f-0)\\ v_f=85 \text{m/s}\end{array}$

Conclusion:

The velocity of the ball after struck by force is $\text{85 m/s}$