Answer to Question #81316 in Physics for Moustafa

Question

An 79 N traffic light is supported at the midpoint of a 45 m length of cable between two poles. Find the tension in each cable if the cable sags a vertical distance of 1 m.

Answer 1

For the equilibrium:
W=2T sin⁡α
The tension in each cable segment is
T=W/(2 sin⁡α )
sin⁡α=h/(l/2)=2h/l
Thus,
T=W/(2 2h/l)=Wl/4h.
T=(79)(45)/4(1) =888.75 N.