Air bag force on head The graph in the figure 1. shows the time variation of the

Question

Air bag force on head The graph in the figure 1. shows the time variation of the force that an automobile's air bag exerts on a person's head during a collision. The mass of the head is 8.0 kg.

Part A

Determine the total impulse of the force exerted by the air bag on the person's head.

Express your answer to two significant figures and include the appropriate units.

Part B

Determine the person's speed just before the collision occurred.

Express your answer to two significant figures and include the appropriate units.

Air bag force on head The graph in the figure 1. shows the time variation of the force that an automobile's air bag exerts on a person's head during a collision. The mass of the head is 8.0 kg. Part A Determine the total impulse of the force exerted by the air bag on the person's head. Express your answer to two significant figures and include the appropriate units. Part B Determine the person's speed just before the collision occurred. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

The figure looks like a sine wave. It is actually

F(t) = -1000cos(2 pi t/0.150 s) + 1000 N

Thus, the area is the impulse. Integrating

p = -1000 (0.150 s / (2 pi)) sin (2 pi t/0.150 s) + 1000t | (0, 0.150 s)

Thus,

J = 150 N*s   [ANSWER]

************************

As

|J| = |pf - pi|

and pf = 0,

|J| = |pi| = 150 N*s

As

pi = mi vi

--> vi = pi / mi

Then

vi = 18.75 m/s   [ANSWER]

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