# Deflection?

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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