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Homework Help: Friction in a 3 block and pulley system

  1. Jun 21, 2015 #1
    1. The problem statement, all variables and given/known data
    A block of mass m1 is on top of a block of mass m2. Block 2 is connected by an ideal rope passing through a pulley to a block of unknown mass m3 as shown. The pulley is massless and frictionless. There is friction between block 1 and 2 and between the horizontal surface and block 2. Assume that the coefficient of kinetic friction between block 2 and the surface, μ, is equal to the coefficient of static friction between blocks 1 and 2.
    What is the minimum value of m3 for which block 1 will start to move relative to block 2?

    2. Relevant equations
    f= mu*N

    3. The attempt at a solution

    I've taken a couple of approaches. The one I think is most valid is this: The point just before block 2 slips relative to block 1 is where the static friction between m1 and m2 reaches its maximum value. At this point the magnitude of acceleration between all the blocks is the same. I'm then solving for:

    m1*a = mu*m1*g
    m2*a = T-mu*m1*g-mu*(m1+m2)*g

    Which gives me:

    Which is wrong. Am I making a math error or taking the wrong approach entirely?

    Thanks in advance for any help!
  2. jcsd
  3. Jun 21, 2015 #2
    Can you post the diagram or facsimile thereof?
  4. Jun 21, 2015 #3


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  5. Jun 21, 2015 #4


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    You have it almost right, except your sign-convention is inconsistent:
    "a" is supposed to be the same for all three equations, right?
    In the first two equations, "a" takes a positive value, but in the third equation "a" takes a negative value (m3g ≥ T)
  6. Jun 21, 2015 #5

    Got it. Thanks.
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