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Work done by friction (rolling resistance)

  1. Jan 20, 2016 #1
    1. The problem statement, all variables and given/known data
    The carriage and its passengers start at rest at A. At B, the bottom of the ride, the maximum speed of the carriage is 20ms-1. The vertical distance between A and B is 110m. The length of the track between A and B is 510m. The mass of the carriage and the passengers is 4000kg.

    By considering the energy changes from A to B, determine the average frictional force acting on the carriage.

    2. Relevant equations
    3. The attempt at a solution

    GPE at A = mgh = 4000 * 9.81 * 110 = 4316400 J
    KE at B = 0.5 * 4000 * 202 = 800000 J
    4316400 - 800000 = 3516400 J work done.
    W = Fx. 3516400 = F * 510
    F = 6900 N?

     
  2. jcsd
  3. Jan 20, 2016 #2

    haruspex

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    Your arithmetic looks fine, but sadly the question is wrong. You do not have enough information to determine the average force.
    Average force is ##\Delta p/\Delta t##, where p is momentum and t is time. This comes out the same as ##\Delta E/\Delta s## when the force is constant, but in not general.
    See section 3 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/ for a fuller discussion.
     
  4. Jan 20, 2016 #3
    Will be sure to tell my teacher. :P I guess this should suffice though. Thanks.
     
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