Seatbelts provide two main advantages in a car accident (1) they keep you from b

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 beat.
1) A driver wearing a seat beat decelerates at roughly the same rate as the car it self. 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 68.0 kg driver who is driving at 16.0 m/sec and comes to rest in this distance?
Fwith 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 0.8 cm.
Fwithout belt =

Explanation / Answer

we will ulitmately use F = m a we know m, and must find a we can find a from vf^2=v0^2 + 2ad vf=final velocity = 0 v0=initial velocity =19m/s a = accel (to be found) d= 1 m in the first case, 0.01 m in the second first case: 0=19^2+2*a*1 => a = 180.5m/s/s and the force on the driver is F = 57kg x 180m/s/s now, we don't even have to do a calculation; from the vf^2=...equation, we can see that if we decrease the stopping distance, d, by a factor of 100, we increase the acceleration by a factor of 100 and therefore the force by a factor of 100 so seat belts, using these numbers, reduce the force by a factor of 100

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