A traffic light of mass is hung at the midpoint of a steel cable stretched between…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A traffic light of mass 15kg is hung at the midpoint of a steel cable stretched between two poles that are at the same height and 9.0m apart. Because of the weight of the light, the cable sags so that the point of suspension is 0.15m lower than the attachments at the poles. Assume the cable is light and inextensible.
(i) By using suitable geometric reasoning, determine the angle θ that each half of the cable makes with the horizontal.
(ii) Draw the free-body diagram for the traffic light, indicating all forces acting on it.
(iii) Hence calculate the tension in each side of the cable and the vertical component of the force exerted by the cable on the light.