Question

Your forehead can withstand a force of about 6.0 kn before fracturing, while your cheekbone can withstand only about 1.3 kn. suppose a 140 g baseball traveling at 30 m/s strikes your head and stops in 1.5 ms.
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 fore- head? on the cheek?

Answer 1

The baseball of mass 140g travels at a speed of 30 m/s.
Its momentum is
P₁ = (140 x 10⁻³ kg)*(30 m/s) = 4.2 (kg-m)/s

Part a.
The momentum is dissipated in 1.5 s.
The average force, F, that dissipates the momentum is
(F N)*(1.5 x 10⁻³ s) = 4.2 (kg-m)/s
F = 2800 N = 2.8 kN

Answer: 2.8 kN

Part b.
The average force that the baseball exerts on the head is 2.8 kN, as obtained in part a.
This is true if the time to dissipate the momentum is 1.5 ms.

Answer: 2.8 kN

Part c.
Answer:
(a) The forehead will not fracture because 2.8 kN < 6.0 kN.
(b) Your cheek will fracture because 2.8 kN > 1.3 kN

Answer 2

a.) The 140g (0.14kg) ball decelerates from 30m/s to 0m/s in 0.015s. The acceleration is therefore 30m/s / 0.015s = 2,000m/s^2. Since force, is equal to mass times acceleration, the force is equal to 0.14kg * 2,000m/s^2, which is equal to 280N, or 0.28kN. b.) The baseball exerts 0.28kN of force on your head because the head is the only object applying force required to stop the ball. c.) You are not in danger of fracturing your skull because the force is less than 6.0kN. d.) You are not in danger of fracturing your cheekbone because the force is less than 1.3kN.