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Two radii pulley lifting a pack

  1. Mar 3, 2012 #1
    1. The problem statement, all variables and given/known data

    You are pulling on a rope attached to the outer radius of a pulley with a moment of inertia I=676 kgm2 as shown. The tension in the rope that you are pulling is 477.9 N. A pack of mass 30.8 kg is attached to the pulley's inner radius as shown. If the inner radius of the pulley is 0.56 m and the outer radius is 0.8 m, what is the magnitude of the linear acceleration of the pack?

    2. Relevant equations

    Ʃtorque=(I)([itex]\alpha[/itex])
    ƩF=ma

    3. The attempt at a solution

    I found the tension due to the mass of the pack on the pulley.
    Tps=mp(g-at)
    p=pack, at=linear acceleration of pack

    I then summed the torques, and inserted the tension due to the pack on the pulley
    R(Tyr)-r(mp(g-at))=I(at/R)

    solved for at=[R(Tyr)-r(mp*g)]/[(I/R)-(r*mp)]

    my final at=24.233 m/s/s which is not right
     
  2. jcsd
  3. Mar 3, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    You might want to check your expression for Tps. Make sure that the implied forces result in an acceleration in the desired direction for the pack.
     
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