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Balancing two rollers on a hill

  1. Feb 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Two rollers, of masses 2kg and 3kg, are connected over a pulley by a massless string. They rest in equilibrium on two inclined slopes, as shown in the diagram to the left. Friction is negligible. What is the distance X?
    upload_2015-2-9_19-28-38.png

    2. Relevant equations
    Fg = mg
    Component of Fg parallel to the slope = mgsin(theta)

    3. The attempt at a solution
    Since they are in equilibrium, the forces on both sides must be equal.
    So I created a separate coordinate system for each side and found the forces acting along the slope.

    On the left side, the force of gravity parallel to the slope is (2kg)(10 m/s^2)(sin(theta)). To find theta, I did arctan(.3/.4) to get 36.87 degrees. So therefore (2kg)(10)(sin(36.87)) = 12 N.

    So the right side force must also be equal to 12 N.
    12 N = (3kg)(10 m/s^2)(sin(theta)).
    So now I found this theta by solving the equation and got 23.58 degrees.

    And finally, to find x, I did sin(23.58) = 0.3/x --> x = 0.75 m.

    But the answer is 0.69 m. What did I do wrong?
     
  2. jcsd
  3. Feb 9, 2015 #2

    TSny

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  4. Feb 9, 2015 #3
    Wow, I don't even know why I thought it was sin for so long.
    Thanks, it should be tan.
     
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