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Homework Help: Double atwood machine

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data


    The double Atwood machine has frictionless, massless pulleys and cords. Determine the acceleration of masses mA,mB,mC, and the tensions in the cords.

    2. Relevant equations


    3. The attempt at a solution

    First I looked down the bottom section. Assuming mB> mA

    mB*g - FTA = mB*a
    FTA - mA*g = mA*a

    I got the following from the equations above, so I think this must be the acceleration for the masses A and B.

    aA,B = g* (mB - mA)/(mB + mA)

    Now Assuming mC*g>FTC

    mC*g - FTC = mC*a

    This is where I choked. What should be the second equation for this pulley? FTC = 2FTA?
    If I were to find FTA in terms of mA, mB, and aA,B, would that be enough for aC's equation?
  2. jcsd
  3. Oct 26, 2014 #2


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    Homework Helper

    A and B hang from the rope around the hanging pulley. Their accelerations are equal with respect to the pulley, but not with respect to the ground.
    I suggest to write the acceleration of C first. It will be the same (with opposite sign) as the acceleration of the hanging pulley. It has no mass, so 2FTA=FTC.
  4. Oct 26, 2014 #3
    What confuses me here is that there are too many possibilities, especially for A and B.

    To write correct equations with respect to ground, I think I should consider the effect of FTC on A and B like you said. But what are their directions?
    I mean if we assume C is going down, no problem. But either A or B could be going down or up in this situation. Should I just assume their directions too?
  5. Oct 26, 2014 #4


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    Assume the directions, and solve.
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