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Rotational and Translational Motion

  1. Apr 4, 2007 #1
    1. The problem statement, all variables and given/known data

    A bucket of water of mass 14.2 kg is suspended by a rope wrapped around a windlass, that is a solid cylinder with diameter 0.350 m with mass 12.1 kg. The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls a distance 11.0 m to the water. You can ignore the weight of the rope.

    Solve for:
    1) tension in the rope
    2) time before the bucket hits the water
    3) speed at which the bucket hits the water
    4) force exerted on the cylinder by the axle during the fall

    2. Relevant equations


    3. The attempt at a solution

    M=12.1 kg (mass of cylinder)
    R=0.175 (radius of cylinder)
    m=14.2 (mass of bucket)

    Torque = 0.175 * Tension = 1/2 * 12.1 * 0.175^2 * alpha

    Torque = 0.175 * Tension = 0.18528125 * alpha

    1.05875 * alpha = Tension

    Weight = 14.2 * 9.8 = 139.16

    ForceNet (on bucket) = Weight - Tension = m*a
    ForceNet = 139.16 - Tension = 14.2 * a
    139.6 - 1.05875*alpha = 14.2 * a

    Tension = (1/2) * M * a

    Tension = 41.57619

    But I've been told that this isn't the correct answer. Can somebody set me straight, please?
  2. jcsd
  3. Apr 4, 2007 #2
    There shouldn't be problems, as long as the rope is assumed to be wrapped on the rim of the cylinder throughout the whole process.
  4. Apr 4, 2007 #3


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    Homework Helper

    It looks pretty good to me. I think you've got it right.

    edit: Worked it out, got the same answer. Can't see why it would be wrong...:confused:
    Last edited: Apr 4, 2007
  5. Apr 4, 2007 #4
    Hahaha, I went through again and it turns out that that really was the right answer after all. I think there are just some wires crossed in my brain.

    Thanks to everyone who looked this over, though.
  6. Oct 20, 2010 #5
    Hey guys, why is the tension 1/2 * M * a ??? Am a bit confused about that..
  7. Oct 20, 2010 #6

    Doc Al

    User Avatar

    Staff: Mentor

    That fact can be deduced by combining these formulas (plus one other):
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