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 . Part APart complete A 60 kg person is in a head-on collision. The car's speed at impact is 15 m/s . Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.

Answer 1

Answer:

The net force is 1350 kN

Solution:

As per the question:

Mass of man, m = 60 kg

Initial speed of the car, v = 15 m/s

Final speed of the car, v' = 0 m/s

Distance covered by the person before coming to rest, d = 5 mm = $5\times 10^{- 3}\ m$

By using the third eqn of motion:

$v'^{2} = v^{2} + 2ad$

$0 = 15^{2} + 2\times a\times 5\times 10^{- 3}$

$a = - 22500\ m/s^{2}$

Thus the force on the person can be given by:

F = ma = $60\times 22500 = 1350\ kN$