Question

A cable carries a horizontal load of 20kg/m. Neglecting its own weight, find the maximum tension on the cable if the distance between the supports is 100m and the sag is 5m.

I always get 5000 kg but the choices are 5087, 5099, 5079 and 5102.

need solution
Please help. Thank you

Answer 1

Here is my computation:
the length of the cable, is given by the subsequent fromula:
\[\Large L = l\left\{ {1 + \frac{8}{3}{{\left( {\frac{f}{l}} \right)}^2}} \right\} = 100\left\{ {1 + \frac{8}{3}{{\left( {\frac{5}{{100}}} \right)}^2}} \right\} = ...?\]
whereas the maximum tension is:
\[\Large T = \frac{{p \cdot {l^2}}}{{8f}} = \frac{{20 \cdot {{100}^2}}}{{8 \cdot 5}} = ....{\text{Kg}}\]