An 80 newton traffic light is supported at the midpoint of a 30 meter length of cable between two poles. What is the tension in each cable segment if the cable sags a vertical distance of 1 meter?
I always found these hard. Think about the force at the lowest point of the cable. The traffic light pulls down with a force of 80N The tension in the cable must be pulling up with 80N. That’s 40N per cable. But 40N directed in the upwards direction. Any sideways force in the cables balances. The right triangle made by one half of the cable has a hyptoenuse of 15m And the short side is 1m The force F in this half of the cable is resolved into (1/15)F in the upwards direction, and (sqrt(15^2-1^2)/15)F in the sideways direction. You could also do this by working out the cosine of the larger angle as 1/15, and resolving the force to the upwards direction by multiplying the cosine of this angle turned through.
