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Homework Help: Tension in a string

  1. Mar 11, 2010 #1
    1. The problem statement, all variables and given/known data

    attachment.php?attachmentid=24309&stc=1&d=1268372863.jpg
    A light rigid rod PQ is hinged smoothly to the wall at one end while the other end is connected by an inextensible string to a point R directly above P. A weight W is suspended from a point on the rod. If the rod remains horizontal, which of the following change(s) would increase the tension in the string?

    (1) Shifting the weight towards Q
    (2) Replacing the string with a shorter one and connecting it to the mid-points of PQ and PR
    (3) Replacing the string with a longer one and connecting it to a point higher than R


    2. Relevant equations


    3. The attempt at a solution

    I guess the first one is correct, as the force will be greater when W is farer away from the hinged point, but i have no idea how the length of the string is related to the tension.
    Is it related to the L/g ^1/2?

    Please help:(
    many thanks
     

    Attached Files:

  2. jcsd
  3. Mar 12, 2010 #2

    rl.bhat

    User Avatar
    Homework Helper

    If T is the tension in the string, when the rod is horizontal, the moments on the rod due to T and W are equal and opposite.
    So
    (Tsinθ)*L = W*x.
    T = W*x/L*sinθ . sinθ
    In this expression W and L remain constant.
    Your guess for the first one is correct.
    sinθ = y/sqrt(L^2 + y^2). Hence
    T = W*x*sqrt(L^2 + y^2)/L*y.
    Now try for (2) and (3)
     
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