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Your forehead can withstand a force of about 6.0kNbefore fracturing, while your cheekbone can withstand only about 1.3kN. Suppose a 140gbaseball traveling at 30m/sstrikes 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?

Short Answer

Expert verified

(a) The magnitude of the force that stops the baseball is2.8kN

(b) The magnitude of the force that the baseball exerts on your head is2.8kN

(c) Cheek would be fractured if the ball hits you in the forehead.

Step by step solution

01

Given information (part a)

Forehead withstand force is 6kN

Cheekbone withstand force is 1.3kN

localid="1649097490236">v=0u=30m/st=1.510-3s

02

Explanation (part a)

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

v=u+ata=v-uta=0-30m/s1.510-3sa=-20103m/s2

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

localid="1649099030008" F=maF=14010-3kg20103m/s2F=2800NF=2.8kN

03

Given information (part b)

Forehead withstand force is6kN

Cheekbone withstand force is 1.3kN

v=0u=30m/s2

t=1.510-3s

04

Explanation (part b)

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.

05

Given information (part c)

Forehead withstand force is6kN

Cheekbone withstand force is 1.3kN

v=0u=30m/s2

t=1.510-3s

06

Explanation (part c)

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.

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