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Kinetic energy and friction force?

  1. Oct 8, 2014 #1
    Please help! I have a test tomorrow.

    1. The problem statement, all variables and given/known data

    A car with a weight of 15,000 N moves horizontally at 30 m/s.
    a) What is the car's KE?
    b) What will be the magnitude friction force to stop the car over a 60m distance?

    2. Relevant equations
    F=ma
    KE=1/2*m*v2

    3. The attempt at a solution
    a) mass of car = 1531 kg
    KE = 1/2(1531)(30)2 = 690,000 J

    b) This is where I hit trouble.
    I found acceleration by (0-30)/2 = -15 m/s2
    Then I used F=ma, so Ff = (1531)(-15) = -22,965 N
    Not the correct answer...
     
    Last edited: Oct 8, 2014
  2. jcsd
  3. Oct 8, 2014 #2

    NascentOxygen

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    Staff: Mentor

    What equation will you use that relates velocity, acceleration, and distance, to allow you to correctly calculate the acceleration (i.e., deceleration)?
     
  4. Oct 8, 2014 #3
    Oh okay! I totally forgot about that equation.
    v2 = vi2 + 2a(delta x)
    That'll give me acceleration, and then I use F=ma, right?
     
  5. Oct 8, 2014 #4

    NascentOxygen

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    Staff: Mentor

    Sounds right. :cool:
     
  6. Oct 8, 2014 #5
    I'm just curious, is there a way to find that without needing that equation??
     
  7. Oct 8, 2014 #6

    gneill

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    Staff: Mentor

    You could use energy conservation. The car starts out with a certain KE (which you calculated), and that energy will be lost to friction acting over the given stopping distance.
     
  8. Oct 8, 2014 #7
    Could someone demonstrate this? Because I'm a little lost.
     
  9. Oct 8, 2014 #8

    gneill

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    What is the work done by a force F acting over a distance d?
     
  10. Oct 9, 2014 #9
    I'm thinking of W = Fdcosθ
     
  11. Oct 9, 2014 #10

    gneill

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    Staff: Mentor

    Sure. Here θ is 180° since the force is acting against the direction of travel. So you can write

    W = -Fd

    So the friction force will be "stealing" energy from the car as it moves.

    Now, the car starts out with a store of KE. This will be lost to friction according to the work done by that friction force. Write an equation that equates the starting KE to the energy lost to friction over distance d.
     
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