Question

Question #c0aab

Answer 1

When a cable is hung between two supports only at its ends, it forms a curve or arc under its own weight. The situation is similar to Electrical power lines hung using utility poles.

The curve so formed is called In physics and geometry, a catenary. Catenary applies to a flexible cable that has uniform mass through out its length and is being acted upon by a gravitational force.

It has a U-like shape, superficially similar in appearance to a parabola. However, it is not a parabola. The curve is a scaled and rotated graph of the hyperbolic cosine function.

Figure reproduced above shows Forces acting on a section of hanging cable. Assuming that the lowest point of the catenary curve is located at the origin. Forces acting on the length of cable between origin and point `(x,y)`
Tension `vec T` at point `(x,y)` due to weight of cable between the point and the right pole.
Horizontal Tension `vecH` due to weight of left half of cable fixed at the left pole.

This is stretched string having tension due to its own weight.