# Hanging cable

Classical Mechanics Level 5

A telephone cable hangs between two poles of equal height located $$d=100~\mbox{m}$$ apart. Because of its weight, the cable sags $$h=0.7~\mbox{m}$$ in the middle, that is to say, $$h$$ is the vertical distance between the center of the cable and the points of suspension.

If the mass per unit length of the cable is $$\lambda=0.2~\mbox{kg/m}$$, find the tension of the cable in Newtons at the lowest point (in the middle).

Details and assumptions

Assume $$g=9.8~\mbox{m}/\mbox{s}^2.$$

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