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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