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Homework Help: Traditional double Atwood's machine

  1. Mar 15, 2007 #1
    Ok, I can understand this problem, I have read it's solution, can see how it is arrived at... but I can't understand WHY it is true.

    It's a traditional double Atwood's machine... have to find the accelerations of the three particles.

    I can understand how they got the equations, for the second pulley, T1 = 2*T2. The force equations for the masses are straightforward too. The "conservation of string" equation is... a1 = -(a2 + a3)/2 which is.... ok, I guess.

    But, I have trouble understanding the solution. For, the acceleration of m1 is
    a1 = g*(4*m2*m3 - m1*(m2+m3))/(4*m2*m3 + m1*(m2+m3)).

    Now, What if I imagine the pulley 2 system as a black box, of mass m2+m3?

    I'll get the equation for a1 as g*(m1 - (m2+m3))/(m1+m2+m3) .
    So, why can't we imagine the second system as a black box?

    There's some obvious reason here, I'm sure, but I just can't get it. :(
     

    Attached Files:

  2. jcsd
  3. Mar 15, 2007 #2

    Doc Al

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    Staff: Mentor

    You cannot replace the 2nd pulley system with a single mass equal to m2 + m3. For one thing, m2 and m3 have different accelerations, while your replacement mass would have only one.
     
  4. Mar 15, 2007 #3
    Ok... thanks... I'm also thinking that maybe it's because T1 is determeined by T2...
     
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