Seat belts and air bags save lives by reducing the forces exerted on the driver

Question

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a "crumple zone" in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1 m as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton's first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm.

1. A 59 kg person is in a head-on collision. The car's speed at impact is 20 m/s . Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.

2. Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag.

Explanation / Answer

a) Carspeed impact is 20 m/s

So if the car is travelling at 20m/s.. and the car crumples 1m, that means the accident took 0.1seconds.

So the force would be:
Impulse = change in momentum
F.t = m(change in v)
F = 59kg(0 - 20m/s) / 0.1second
Force = 12800Newtons

b) without restraint and seat belts, the person is still travelling at 20m/s until he/she hits the dash board... so over 5mm the time duration would be 0.005/10 = 0.0005seconds
So using the same eq.
Impulse = change in momentum
F.t = m(change in v)
F = 59kg(0 - 20m/s) / 0.0005second
Force = 2560000N = 2560kN

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