Chapter 7, Problem 17P

To determine

The impulse given to the ball.

Answer to Problem 17P

The impulse given to the ball is $-2.12\text{kg}\cdot \text{m}/\text{s}$ .

Explanation of Solution

Given:

The mass of the ball is $m=0.060\text{ kg}$ .

The speed of the ball is $v=25\text{m}/\text{s}$ .

Formula used:

The expression for impulse is,

  $\Delta p=\Delta mv$

Here, m is the mass of the ball and v is the speed of the ball.

Calculation:

Sketch the free body diagram of the ball after and before collision as shown below.

  

The change in momentum is,

  $\begin{array}{c}\Delta p=\Delta mv\\ \Delta p={\left(mv\right)}_{\text{final}}-{\left(mv\right)}_{\text{initial}}\\ \Delta p=\left(-mv\sin 45°\right)-mv\sin 45°\\ \Delta p=-2mv\sin 45°\end{array}$

  $\begin{array}{l}\Delta p=-2\times \left(0.060\text{ kg}\right)\left(25\text{m}/\text{s}\right)\sin 45°\\ \Delta p=-2.12\text{kg}\cdot \text{m}/\text{s}\end{array}$

Conclusion:

Thus, the impulse given to the ball $\Delta p=-2.12\text{kg}\cdot \text{m}/\text{s}$ .