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Physics120 car collision question

  1. Feb 1, 2009 #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 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?


    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

    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!!
     
    Last edited: Feb 2, 2009
  2. jcsd
  3. Feb 1, 2009 #2

    LowlyPion

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    Homework Helper

    Is the initial speed 17 m/s or 15 m/s?

    As to your 5 mm, ignore it. The idea is that if restrained the person won't strike an unyielding surface.

    Is the weight 50 kg or 60 as in your calculation?
     
  4. Feb 1, 2009 #3

    The initial speed is 15 m/s.

    Also, the mass of the person is 60 kg.

    Do you happen to know how to do this question? PLease help, if you can.
     
  5. Feb 2, 2009 #4

    LowlyPion

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    Homework Helper

    The original statement of the problem says otherwise.
     
  6. Feb 2, 2009 #5

    I apologize, here is the problem with the correct numbers:


    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) Estimate 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?
     
  7. Feb 2, 2009 #6
    NEVERMIND! I completely understand what I was not seeing before. I got the answers for all 3 parts! Thank-you for showing me that I had made an error when I wrote out the numbers in the problem!
     
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