Question

A government agency estimated that air bags have saved over 14,000 lives as of April 2004 in the United States. (They also stated that air bags have been confirmed as killing 242 people, and they stress that seat belts are estimated to save 11,000 lives a year.) Assume that a car crashes and has come to a stop when the air bag inflates, causing a 75.0 kg person moving forward at 15.0 m/s to stop moving in 0.0250 seconds. (a) What is the magnitude of the person's impulse? (b) What is the magnitude of the average force the airbag exerts on the person?

Answer 1

To solve this problem it is necessary to apply the concepts related to momentum, momentum and Force. Mathematically the Impulse can be described as

$I = F*t$

Where,

F= Force

t= time

At the same time the moment can be described as a function of mass and velocity, that is

$P = m\Delta v \rightarrow P=m(v_1-v_2)$

Where,

m = mass

v = Velocity

From equilibrium the impulse is equal to the momentum, therefore

$I = p$

$Ft = m(v_1-v_2)$

PART A) Since the body ends at rest, we have the final speed is zero, so the momentum would be

$p=m(v_1-v_2)$

$p = 75*0.15$

$p = 1125Kg\cdot m/s$

Therefore the magnitude of the person's impulse is 1125Kg.m/s

PART B) From the equation obtained previously we have that the Force would be:

$Ft = m(v_1-v_2)$

$F(0.025)= 1125$

$F= 45000N$

Therefore the magnitude of the average force the airbag exerts on the person is 45000N