Question

According to safety standard for air bags, the maximum acceleration during a car crash should not exceed 60 g and should last for no more than 36 ms. In such a case, what force does the air bag exert on a 85.0 kg person?

Answer 1

Mass m= 85 Kg

maximum acceleration = 60g = 60 x 9.81 = 588.6 m/sec²

We assume the car is brought to rest in 36 ms.

Hence the velocity of the car = 588.6 x 36 x 10^-3 = 21.1896 m/sec

Momentum = 85 x 21.1896

Average force by the Air bag = 85 x 21.1896 /0.036 = 50031 N

In a simpler way :

Maximum Force exerted by the person = 85 x 60g = 50031 N

Air bag will exert equal and opposite force on the person = 50031 N

Force exerted by the person = mass x acceleration = 85 x 588.6 = 50031 N