Question

Seatbelts provide two main advantages in a car accident (1) they keep you from being thrown from the car and (2) they reduce the force that acts on your during the collision to survivable levels. This second benefit can be illustrated by comparing the net force encountered by a driver in a head-on collision with and without a seat belt.

1)

A driver wearing a seat beat decelerates at roughly the same rate as the car itself. Since many modern cars have a "crumble zone" built into the front of the car, let us assume that the car decelerates of a distance of 1.1 m. What is the net force acting on a 73 kg driver who is driving at 18 m/sec and comes to rest in this distance?

F_{with belt} =

2)

A driver who does not wear a seat belt continues to move at the initial velocity until she or he hits something solid (e.g the steering wheel) and then comes to rest in a very short distance. Find the net force on a driver without seat belts who comes to rest in 1.2 cm.

F_{without belt} =

Answer 1

Using 3rd equation of motion,

V^2 = u^2 + 2as

Acceleration, a = (v^2 - u^2)/2s

Force, F = ma = m(v^2 - u^2)/2s

A)

F = 73 x (0 - 18^2)/2 x 1.1 = 10.75 kN

B)

F = 73 x (0 - 18^2)/2 x 0.012 = 9.86 x 10^5 N

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