Your forehead can withstand a force of about $6.0kN$before fracturing, while your cheekbone can withstand only about $1.3kN$. Suppose a $140g$baseball traveling at $30m/s$strikes your head and stops in $1.5ms$

a. What is the magnitude of the force that stops the baseball?

b. What force does the baseball exert on your head? Explain.

c. Are you in danger of a fracture if the ball hits you in the forehead? On the cheek?

Forehead withstand force is $6kN$

Cheekbone withstand force is $1.3kN$

localid="1649097490236">v=0u=30m/st=1.5×10-3s

In $1.5ms$the ball will stop; So, we can calculate the acceleration by:

$$\begin{gathered} v=u+at \\ a=\frac{v-u}{t} \\ a=\frac{\left(0-30\right)m/s}{1.5\times {10}^{-3}s} \\ a=-20\times {10}^{3}m/s^2 \end{gathered}$$

Now calculate the magnitude of the force that stops the baseball by

localid="1649099030008" $$\begin{gathered} F=ma \\ F=\left(140\times {10}^{-3}kg\right)\times \left(20\times {10}^{3}m/s^2\right) \\ F=2800N \\ F=2.8kN \end{gathered}$$

Forehead withstand force is$6kN$

Cheekbone withstand force is $1.3kN$

$$\begin{gathered} v=0 \\ u=30m/s^2 \end{gathered}$$

$t=1.5\times {10}^{-3}s$

The magnitude of the force that stops the baseball will be the same as the force exerted on your head by Newton's third law, So the force is $2800N$.

Forehead withstand force is$6kN$

Cheekbone withstand force is $1.3kN$

$$\begin{gathered} v=0 \\ u=30m/s^2 \end{gathered}$$

$t=1.5\times {10}^{-3}s$

The forehead will not fracture because $2800N<6000N$. Forehead can withstand this force but our cheek will fracture because $2800N>1300N$. The cheek cannot withstand this much force and would fracture.