Hanging cable

From Wikiversity

A cable is suspended between two towers like a power line between two towers. Assume that the towers are on a level parcel of ground but the heights of the towers maybe different. Using the following notation

$u (x)$ - height of cable center

$L$ - distance between two towers

$u 0$ - height of cable at tower 1

$u L$ - height of cable at tower 2.

$T$ - horizontal component of tension.

$w$ units of weight per unit length of cable.

and the forces acting on the cable, it can be shown that the cable height $u (x)$ is the solution of the differential equation

${d^{2} u(x) \over {dx^{2}}} = {w \over T} \sqrt{1 + ( {du \over {dx}} ) ^ {2} }$

with the end conditions $u (0) = u 0$ and $u (L) = u L$ .

Hanging cable

From Wikiversity

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