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Atwood's Machine, massive pulley and upwards force acting upon it.

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data
    The usual configuration of an Atwood's Machine.
    Two masses: m1, m2
    Accelerations (unknown): a1, a2, ap (Pulley)
    Rope Tension: T (Unknown)
    BUT:
    Massive pulley: mp
    Upwards force acting on pulley (i.e the pulley is not in equilibrium): F

    NOTE: Consider that all the pulley's mass in concentrated at the center of the pulley, so as not to consider the moment of inertia. (Is this ok?)

    Question: Find the tension T, and the accelerations a1, a2.

    2. Relevant equations
    Newton's Second Law


    3. The attempt at a solution
    So this is what I tried:
    Analyzing the pulley.
    F - 2T - mp . g = mp . ap............................................(I)

    Analyzing the whole System as a unit:
    F - (mp + m1 + m2) . g = (mp + m1 + m2) . ap.............(II)

    Analyzing m1:
    T - m1 . g = m1 . a1...................................................(III)

    From (II) I derived ap in terms of known constants, then I replaced ap (in terms of the constants) in (I) and I found T in terms of known constants. Finally I replaced the equation for T in (III).


    So this is what I've got. Did I miss anything? Any feedback would be greatly appreciated.

    Thanks-
     
  2. jcsd
  3. Feb 20, 2013 #2

    Simon Bridge

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    That is only OK if the operation of the machine means that the pulley does not rotate.

    The approach you want is to draw three free-body diagrams, one for each mass and another for the pulley. You need to relate the tensions to the torques on the pulley.
     
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