Question

A 20.0-kg traffic light hangs midway on a cable between two poles 30.0 meters apart. If the sag in the cable is 0.40 meters, what is the tension in each side of the cable

Answer 1

Answer:

the tension in each side of the cable is 3677.57 N

Explanation:

given data

traffic light = 20 kg

cable between two poles = 30 m

sag in the cable = 0.40 m

solution

by the free body diagram

tan θ = $\frac{0.4}{15}$    .............1

θ = 1.527 °

and

tension = mg

The net force is along x - axis is express as

T2 cosθ = T1 cosθ     .................2

so T2 - T1     ..............3

and

when we take it along y  axis  that is express as

( T1 + T2) sinθ = mg    ...................4

so by equation 3 we put here

2 × T1 sin(1.527) = 20 × 9.8  

T1 = 3677.57 N