A twisted steel clothesline wire of length \(l\) has cross-sectional area \(A\) and modulus of elasticity in tension \(E\). The wire is stretched horizontally between two fixed points \(A\) and \(B\), but without appreciable initial tension. A load \(P\) is then suspended from the mid-point \(C\) of the line. The vertical deflection of the point \(C\) can be expressed as \(\displaystyle\delta\,=\,\frac{l}{m}\sqrt[n]{\frac{P}{AE}}\) where \(m\) and \(n\) are co-prime. Find \(m+n\).

\(\textbf{DETAILS AND ASSUMPTIONS:}\)

\(\bullet\) The deflection is small compared to the length \(l\) of the clothesline.

\(\bullet\) This problem has been taken directly from a book.

\(\bullet\) A clear solution would be greatly appreciated(as I can't solve it).

\(\bullet\) This is my first problem.

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