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Forces in equilibrium. Tension, ring, pulley and lots of string [With Picture!]

  1. Feb 29, 2012 #1
    1. The problem statement, all variables and given/known data
    To make it easier on the people who will try to help me, I've scanned the problem:
    wfydg.jpg

    We are interested in finding the following variables:
    Angles a and c
    The tension between A and B (TAB)


    2. Relevant equations
    The pulley is a "perfect pulley" no friction
    The system is at equilibrium
    We consider on side A that the string is attached to the wall, or a hook, it's fixed.
    All three cords are attached to a ring situated at position B
    There is nothing between A and C, but we know there is 3 meters of distance between the two


    3. The attempt at a solution
    Alright so I decided to make a Free Body Diagram taking the ring as the subject. It goes like that:

    ChGdh.jpg

    Considering the pulley, I guess we can assume that TBC is going to to be the same as FA.

    After that I decided to decompose each of the three forces, and since everything is at equilibrium, I've come with two equations (again in picture, gonna be easier):

    IXZa6.jpg

    At that point I am stuck because I don't see any more equations involving those three unknown variables(a,c, TAB) I can do. So I have 3 unknown variables but only two equations.

    Could someone please help me out?
     
  2. jcsd
  3. Feb 29, 2012 #2

    gneill

    User Avatar

    Staff: Mentor

    Have you considered using some of the trig laws? The law of cosines and the law of sines come to mind.
     
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