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Tension in a pulley system

  1. Aug 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Hi. My question is only regarding the early step in this problem that solves for tension. Here is the question:
    "In a pulley system where masses m and M are connected by a rope over a massless and frictionless pulley, find the work done by the tension force in lifting mass m a distance h. Note that M > m and both masses are at the same height above the ground. The system is initially held at rest, and is then released."
    2. Relevant equations
    (T = tension, s = displacement)
    W = F * s, here W = T*h

    3. The attempt at a solution
    So, I have already solved for acceleration of mass M and the v of m after it travels a distance h in another part of the problem, and I thought that I was fine with this one, but: I was summing forces to get the net force on m, which I thought would be T + (-mg) = ma. By following this, I said that T = ma + mg. That made sense to me because 'ma' is the net force, and 'ma' plus the amount of force subtracted by gravity is the total tension of the rope. However, when I finished the problem and checked it, the online review book said that Tension = mg - ma, and I am not sure why that is. Wouldn't that make Tension less than the force of gravity, and so mass m would go down instead of up?
  2. jcsd
  3. Aug 7, 2011 #2


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    The book may have made an error distinguishing between M and m.. You are correct that T = ma + mg.
    It is also correct by looking at the forces acting on M that
    T = Mg - Ma

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  4. Aug 7, 2011 #3
    Thanks. :)
    I was worried that I was missing something important.
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