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Double atwood machine

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

    GIANCOLI.ch04.p56.jpg

    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

    F=ma


    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

    ehild

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    Gold Member

    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

    ehild

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    Assume the directions, and solve.
     
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