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Pulley system problem

  1. Mar 3, 2014 #1
    1. The problem statement, all variables and given/known data
    No friction, pulleys and also string are weightless, the tension through the string is distributed uniformly. Find the acceleration of the mass 3M (see image attached)


    2. Relevant equations

    II law of Newton

    3. The attempt at a solution
    Well I wrote such equations for all pulleys (counting pulleys from right to left):
    1) M*a1 = T - Mg;
    2) M*a2 = 2T - Mg;
    4) M*a3 = 2T - Mg;
    5) 3M*a = T - 3Mg.

    Now we have 1 more unknowns than equations. Any ideas?
     

    Attached Files:

  2. jcsd
  3. Mar 3, 2014 #2

    BvU

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    Can you make use of the fact that the rope has a fixed length ?
     
  4. Mar 4, 2014 #3
    Do you mean energy conservation?

    Then, I guess, we could write eq.:
    Initial state
    E1 = 3Mgh + Mgh

    Final state (when 3M descends h):
    [itex] E_2 = \frac{3Mv^2}{2} + \frac{Mv^2}{2} + 2*\frac{M\frac{v^2}{4}}{2} + 2Mgh + 2*Mgh/2[/itex]

    Keeping in mind that the first mass M ascends h and has velocity v, second and third ascend h/2 and have velocity v/2 and the last one descends h and has velocity v.

    Then

    E2 = 9/4 Mv^2 + 3Mgh

    Is that true? Then the rest is clear :)
     
  5. Mar 4, 2014 #4
    No, I guess BvU is saying to use string constraints.
    A detailed explanation for proceeding, if you don't know what string contraint is, can be found
    Part A
    Part B
     
  6. Mar 4, 2014 #5
    Thanks, that's extremely helpful!!!
    Had no idea about such thing!
     
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