Question

A 20kg traffic light hangs midway on a cable between two poles 40meters apart. If the sag in the cable is .4 meters, what is the tension in each side of the cable?

Answer 1

Consider the tension in the sag part as T, then the horizontal component is T*sinTheta, and the vertical component is T cos Theta, where theta is the angle between the vertical and the wire at the center.

Now, because there are two sides, each holding half the weight, then
T cos Theta=10kg*9.8N/kg*cosTheta


but looking at the dimensions, cosTheta is .4/20

So, you can solve for tension T.

Answer 2

4900N