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Statics: Belt friction

  1. Aug 11, 2013 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    where T2 is the larger tension and β is the angle between the tensions.

    3. The attempt at a solution

    Isolating each pipe:
    W1 = 50*9.81 = 490.5N
    For pipe B, β = (2π)/3
    For pipe C, β = π/3

    For pipe B, T2 = 490.5N, so I have:
    490.5/T = e0.25*((2π)/3)
    T = 290.6N

    Now here is where I made the wrong choice. On pipe C, I chose W2 to be T2 because if equilibrium is maintained, it would make sense for W2 to be going down, not up. This got me the wrong answer.

    Then I tried making T2 = T instead:
    290.6/W2 = e0.25*(π/3)
    W2 = 233.7N
    m = 233.7/9.81 = 22.8kg

    22.8kg is the right answer. I am just not understanding why T is the stronger tension on pipe C. It seems to me that it would cause the 50kg weight to start falling.
  2. jcsd
  3. Aug 11, 2013 #2


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    Homework Helper

    You mean as in the 290.6 N outbalancing the 233.7 N?
    The friction force helps the weaker force to hold the balance.
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