Question

Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can only withstand about 1.3 kN .

Part A -
If a
140 baseball strikes your head at 30 m/s and stops in 0.0015s , what is the magnitude of the ball's acceleration?
Part B -
What is the magnitude of the force that stops the baseball?
Part C -
What force does the baseball apply to your head? Explain?
Part D -
Are you in danger of a fracture if the ball hits you in the forehead? Cheek?

Answer 1

Step-by-step explanation:

Maximum force for forehead = 6 kN

maximum force for cheek bone = 1.3 kN

Part A:

mass of base ball, m = 140 g = 0.14 kg

initial velocity of base ball, u = 30 m/s

final velocity of base ball, v = 0

Time, t = 0.0015 s

Acceleration is defined a the rate of change of velocity.

Use first equation of motion

v = u + at

0 = 30 + a x 0.0015

a = - 20000 m/s²

Part B:

Force = mass x acceleration

F = 0.140 x 20000

F = 2800 N

Part C:

Force applied on your head is 2800 N.

Part D:

As the force is 2800 N that means 2.8 kN which is less than 6 kN so you are safe.