How to find extension of cord using young's modulus

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    How do you find the extension of a cord once given the young's modulus, force, area and UPSTRETCHED cable length? Therefore we are given only extension + original length i.e L + change in L, which does not fit into any of the equations as we have 2 unknowns?
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    (Original post by mayjb)
    How do you find the extension of a cord once given the young's modulus, force, area and UPSTRETCHED cable length? Therefore we are given only extension + original length i.e L + change in L, which does not fit into any of the equations as we have 2 unknowns?
    You'll have to rejig the equations.

    Starting with the definition of Young's modulus:

    \displaystyle E=\frac{F}{A}\frac{L_0}{\delta L}

    Where L_0 is the unstretched length and \delta L the extension.

    If L is the upstretched (sic) length, we can write  \delta L = L - L_0

    Sub into our original equation to get:

    \displaystyle E=\frac{F}{A}\frac{L_0}{(L-L_0)}

    Now make L_0 the subject - left as exercise.

    And hence work out \delta L
 
 
 
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