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Hookes law

  1. Jun 11, 2012 #1
    1. The problem statement, all variables and given/known data


    Hi
    Can anyone please help with this question?
    A light elastic string AB has natural length l and modulus of elasticity 2mg. Another light elastic string CD has natural length l and modulus of elasticity 4mg. The strings are joined at their ends B and C and the end A is attached to a fixed point. A particle of mass m is hung from the end D and is at rest in equilibrium. Find the length AD.

    this is what I did

    Let Tension AB is T2 and tension CD be T1. since system is at rest
    T2-T1 = mg (Equation 1)
    AD = l +x +y +l (Where x and y are the extensions of AB and CD respectively)
    So, AD = 2l +x+y
    Using Hookes law
    T2 = 2mgx/l

    Similarly, T1 = 4mgy/l

    substituting the above into equation 1
    2x-4y =l
    This is as far as I can go. I wasn't given the distance between the the fixed point and AD. Am I missing something? Kindly comment.
    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 11, 2012 #2

    TSny

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    Homework Helper
    Gold Member

    Draw a free-body diagram for the particle of mass m. What does the diagram tell you about the tension T1?

    Also, what is your justification for claiming T2-T1 = mg ?
     
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