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Work and Energy - angular force with friction

  1. Oct 5, 2011 #1
    1. The problem statement, all variables and given/known data

    A cart loaded with bricks has a total mass of 13.8 kg and is pulled at constant speed by a rope. The rope is inclined at 20.8° above the horizontal and the cart moves 30.4 m on a horizontal floor. The coefficient of kinetic friction between ground and cart is 0.7 . The acceleration of gravity is 9.8 m/s[itex]^{2}[/itex] . How much work is done on the cart by the rope?

    2. Relevant equations

    I'm clearly missing something I need because I can't really get close to a solution.

    F[itex]_{friction}[/itex] = [itex]\mu_{k}[/itex] * F[itex]_{normal}[/itex]
    ω = F[itex]_{rope}[/itex] * Δx * COSθ

    3. The attempt at a solution

    I've gotten this far, but there must be something I'm missing because I still can't get any kind of solution out of it.
    F[itex]_{g}[/itex] = 135.2N
    F[itex]_{rope}[/itex]x = F[itex]_{friction}[/itex]
    F[itex]_{n}[/itex] = F[itex]_{g}[/itex] - F[itex]_{rope}[/itex]y
    F[itex]_{rope}[/itex]x = F[itex]_{rope}[/itex] * COSθ
    F[itex]_{rope}[/itex]y = F[itex]_{rope}[/itex] * SINθ

    ω = F[itex]_{rope}[/itex] * 30.4 * COS(20.8)
    F[itex]_{rope}[/itex] = ?

    I've got about 15 more problems just like this to be done tonight so quick responses would be awesome and I REALLY hope its just some small equation or equality that i'm missing.
     
  2. jcsd
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