How to find extension of cord using young's modulus Watch

mayjb
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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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ghostwalker
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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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