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Conservative Forces and Friction

  1. Jul 22, 2009 #1
    1. The problem statement, all variables and given/known data

    A 1.50 kg toy rollercoaster rests on a ramp of height h. When the toy rollercoaster is released, it slides without friction to the bottom of the ramp, and then continues on a flat surface with a rough patch of width 10.0 cm that has a coefficient of kinetic friction µk = 0.770. Find h such that the toy rollercoaster's speed after crossing the rough patch is 3.50 m/s.


    2. Relevant equations

    K = 1/2mv^2
    U = mgh

    3. The attempt at a solution

    Kf = 1/2mv^2 = 1/2(1.5kg)(3.5 m/s)^2
    Kf = 9.188

    fk = ukN = .77(mg) = 11.319 (multiplied by the distance of .1m = 1.132)

    I can't do mgh because I don't know h. I know I probably need to figure out how fast the toy roller coaster was going right before it hit the rough patch, but I can't seem to figure that out without knowing "h" so I am stuck here with no idea where to go.
     
  2. jcsd
  3. Jul 22, 2009 #2

    rl.bhat

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    Homework Helper

    Change in KE is equal to work down against rough surface. So Ki = Kf + fk*d
    And Ki = mgh.
    Find h
     
  4. Jul 22, 2009 #3
    Ahh, brilliant. Thank you so much!
     
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