Chapter 7, Problem 3P

To determine

The average force between the ball and bat during contact

Answer to Problem 3P

  $4.4\times {10}^4\text{N}$ towards the pitcher

Explanation of Solution

Given:

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

Initial velocity of the baseball before collision $=v_i=-39\frac{\text{m}}{\text{s}}$

Final velocity of the baseball after collision $=v_f=52\frac{\text{m}}{\text{s}}$

Time of contact during the collision $=t=3\times {10}^{-3}\text{s}$

Average force acting between ball and bat $=F$

Formula Used:

Momentum of an object is given as

  $\begin{array}{l}p=mv\\ \text{Where }p=\text{momentum}\\ m=\text{mass}\\ v=\text{velocity}\end{array}$

According to Impulse-change in momentum principle,

  $\begin{array}{l}\text{Impulse = Final momentum - initial momentum}\\ Ft=p_f-p_i\\ \text{Where }{p}_f=\text{Final momentum of object after collision}\\ p_i=\text{Initial momentum of object before collision}\end{array}$

Calculation:

Using impulse-change in momentum equation for the collision between ball and bat

  $\begin{array}{l}Ft=p_f-p_i\\ Ft=m{v}_f-m{v}_i\\ Ft=m(v_f-v_i)\end{array}$

Inserting the values

  $\begin{array}{l}F(3\times {10}^{-3})=(0.145)(52-\left(-39\right))\\ F(3\times {10}^{-3})=13.195\\ F=\frac{13.195}{3\times {10}^{-3}}\\ F=4.4\times {10}^4\text{N}\end{array}$

Conclusion:

Therefore, average force is $4.4\times {10}^4\text{N}$ towards the pitcher.