Chapter 7, Problem 62GP

To determine

To Calculate: The average force on the ball during the contact.

Explanation of Solution

Given:

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

Initial horizontal velocity of ball,

The height to which the ball reaches after contact with the bat, $h=\text{55}\text{.6 m}$

Contact time, $\Delta t=\text{1}\text{.4 ms}$

Formula Used:

Average force on the ball during the contact can be obtained using Newton’s second law of motion:

  $F_{avg}=\frac{\Delta p}{\Delta t}=\frac{m\Delta v}{\Delta t}$

Here, $\Delta p$ is the change in momentum, $\Delta t$ is the contact time, $\Delta v$ is the change in the velocity.

Also, velocity of the ball after the contact with the bat can be obtained using the formula:

  $v=\sqrt{2gh}$

Here, g is the acceleration due to gravity and h is the height.

Calculations:

  

Average force:

  

Conclusion: 

Thus, the average force on the ball during contact is $4982\text{N}$ at the angle $43.3°$ .