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Homework Help: Trouble with a classic statics problem

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data
    You are given three weights and 3 pulleys. Each mass hangs below a single pulley, and the pulleys are all connected by strings. The middle weight is 3 kg, the other two are each 2 kg. There are two unknown angles at the central pulley, with respect to the horizontal such that the lines connecting to the other pulleys would form the hypotenuse of a right triangle.

    Essentially it's this: http://forums.xkcd.com/viewtopic.php?f=18&t=45987 only the angles are unknown, and the masses are changed to what I have listed above.

    I have to find the angles if the system is at static equilibrium.

    2. Relevant equations
    None


    3. The attempt at a solution
    I tried breaking it down into force components, but something isn't right.

    I figured the tensions would be 2g, 2g, and 3g all told, and that I'd need the components for the "v" shaped lines. I ended up with 2gcos(theta)-3gcos(theta)+3gcos(theta)-2gcos(theta) for the sum of the x components, and 4gsin(theta)-3gsin(theta) for the y components, but this does not work out correctly. I am now completely lost, and have no idea how to properly set up the force diagram to solve the equation.
     
  2. jcsd
  3. Sep 6, 2010 #2
    I solved the problem. I remembered that tension in the system causes acceleration in a given direction if the force (in this case, just the mass) of the system is greater (or lesser) than the tension. So I found the equilibrium for that.
     
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