Seatbelts provide two main advantages in a car accident: (i) they keep you from

Question

Seatbelts provide two main advantages in a car accident: (i) they keep you from being thrown from the car, and (i) they reduce the force that acts on you during the collision to survivable levels. The second benefit can be illustrated by comparing the net force exerted on the driver of a car in a head-on collision with and without a seatbelt. (a) A driver wearing a seatbelt decelerates at the same rate as the car itself. Since modern cars have a "crumple zone" built into the front of the car, the car will decelerate over a distance of roughly 1.0 m. Find the magnitude of the net force acting on a 64 kg driver who is decelerated from 17 m/s to rest in a distance of 1.0 m. 9.248 kN (b) A driver who does not wear a seatbelt continues to move forward with a speed of 17 m/s (due to inertia) until something solid is encountered. In this case, the driver comes to rest in a much shorter distance - perhaps only a centimeter. Find the net force acting on a 64 kg driver who is decelerated from 17 m/s to rest in 1.0 cm. 1027x kN

Explanation / Answer

a)

F = ma

The deceleration a can be obtained by

v^2 = u^2 - 2as

v = 0

here s = 1 m, u = 17 m/s, m = 64 kg

a = u^2 / 2s

a = 17^2 / (2 x 1)

a = 144.5 m/s^2

substitute in F = ma

F = 64 kg x 144.5 m/s^2

F = 9248 N

F = 9.248 KN

b)

Same as above, put s = 0.01 m

a = u^2 / 2s

a = 17^2 / (2 x 0.01)

a = 14450 m/s^2

substitute in F = ma

F = 64 kg x 14450 m/s^2

F = 924800 N

F = 924.8 KN

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