3.

A traffic light is suspended by two cables. What

should be the angle between the cables (0) so that the

tension in each cable will be equal to the weight of the

traffic signal light (W=T, = T) ?

120°

Explanation:

Draw a free body diagram. There are three forces acting on the traffic light. Two tension forces acting along the cables, and weight.

The tension forces have an angle θ between them. That means each tension force forms an angle of θ/2 with respect to the vertical. So the y component of each tension force is:

Ty = T cos (θ/2)

Sum of the forces in the y direction:

∑F = ma

Ty + Ty - W = 0

2 Ty = W

Substituting:

2 T cos (θ/2) = W

If W = T, then:

2 W cos (θ/2) = W

2 cos (θ/2) = 1

cos (θ/2) = 1/2

θ/2 = 60°

θ = 120°