A 85kg person is riding in a car moving at 21m/s (assume this is the positive di

Question

A 85kg person is riding in a car moving at 21m/s (assume this is the positive direction) when the car runs into a bridge abutment. This problem will illustrate why the invention of the airbag drammaticaly improved the safety of automobiles.

a) Calculate the horizontal component of the average force in newtons, on the person, if he is stopped by a padded dashboard that compresses an average of 0.95cm.

b) Calculate the horizontal component of the average force in newtons, on the person, if he is stopped by an air bag that compresses an average of 12.5cm

Explanation / Answer

Ans:-

For both, use Torricelli's equation to find the acceleration:
v² = u² + 2as v = 0
(a) 0 = (21m/s)² + 2*a*9.5*10^-3m
a = -23 210.5 m/s²
F = ma = 85kg * -23210.5m/s² = -167.696 MN (meaning against the direction of motion)

(b) 0 = (21m/s)² + 2 * a * 0.125m
a = -1764 m/s²
F = -150 kN

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