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physics120

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## Homework Statement

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 meter 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.

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

(b) Calculate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag.

(c) How do these two forces compare to the person's weight?

## Homework Equations

F= ma

Vf^2= V0^2 + 2ax

Vf= V0 + at

x= V0*t + .5a(t^2)

## The Attempt at a Solution

Well, for (a), what I thought you do is: Force of seatbelt and airbag = mass * acceleration

Then, using Vf^2= V0^2 + 2ax, make Vf = 0. Solve for ax.

So, ax= -(15^2)/(2*1.005) which equals -111.9 m/s^2

Btw, I got 1.005 because the passenger compartment decelerates over 1 m, and the airbag for 0.05mm, so I assumed adding those two nuumbers together, to give me 1.005 m will give me the distance. I am not sure about this, though.

Then, go back to the Force of seatbelt and airbag = mass * acceleration

F= 60 kg * -111.9 m/s^2

=-6716 N

Please help, Thank-you!

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