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Homework Help: Car Crash numbers not working?

  1. Sep 17, 2008 #1

    1. The problem statement, all variables and given/known data
    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 50 kg person is in a head-on collision. The car's speed at impact is 17 m/s. Calculate the net force on the person if he or she is wearing a seat belt and the air bag deploys correctly.
    7225 N

    (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?

    F(a) / W =
    F(b) / W =

    2. Relevant equations
    F= ma
    Vf^2= V0^2 + 2ax
    Vf= V0 + at
    x= V0*t + .5a(t^2)

    3. The attempt at a solution

    This one I have absolutely why my answers aren't checking. I've done all the force work (answers are in red), and for c) the equations are literally given to us. F(a)/ W and F(b)/ W. Now, correct me if I'm wrong, but F(a) is my answer for a) and F(b) is my answer for b). If my person is 50 kg (and weight is measured in kg) then why in the world are my answers not working? ( 7225 /50 and 1445000 /50).

    Thanks again!
    Last edited: Sep 17, 2008
  2. jcsd
  3. Sep 17, 2008 #2
    I think that the thing that is going wrong is the confusion between the weight and the mass.
    Weight=Mass*Acceleration due to gravity(9.81 m s-2)
  4. Sep 17, 2008 #3

    Ahhh, I see. For weight is a force, and force equals mass*acceleration. Very, very logical. Thank you so much!

  5. Feb 1, 2009 #4

    Can anyone please explain how to get the answers for all three parts?? For example, for the first one, how was 7225 N obtained?
  6. Feb 2, 2009 #5

    In the first part, the deceleration takes place in the space of 1 metre, the speed of the car passes from 17m/sec to zero, and the person has a 50kg mass.

    Use the following equation to find the deceleration then multiply that by the mass to get the force.

    FinalVelocity┬▓ = InitialVelocity┬▓ + 2*Deceleration*Distance

    Note that the deceleration is just a negative acceleration!
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