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

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 =    .............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

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