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Work negative sign

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data
    See attachment


    2. Relevant equations



    3. The attempt at a solution

    Why is it -umg(50)? Why negative? Also I think this has something to do with conservative force and friction, and I'm very confused on this. Any help would be appreciated thanks.
     

    Attached Files:

  2. jcsd
  3. Feb 5, 2012 #2

    Curious3141

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    Homework Helper

    When the force is constant, Work = Force*Displacement.

    In this case, it's negative because energy is being taken away from the cars by the frictional force, while they're being decelerated to a stop. The energy dissipated by friction is equal to the drop in kinetic energy (as each car comes to rest). This is conservation of energy.

    μ is the coefficient of kinetic friction. mg is the weight (equal to the normal force on the car). 50ft is the distance through which car 1 moves.

    BTW, there's an error in the second part of the solution. The expression for car 2 should be [itex]\sqrt{(2)(20)(0.5)(32.2)}[/itex] (i.e. 20, not 50), since 20ft is the distance car 2 takes to be brought to rest. The final stopping distance was calculated correctly, though.
     
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