Question

A 100 N traffic light is supported at the midpoint of a 20m length of cable between two poles. Find the tension in each cable segment if the cable sags a vertical distance of 0.5m

Answer 1

Answer on Question #72804-Physics-Other

A 100 N traffic light is supported at the midpoint of a 20m length of cable between two poles. Find the tension in each cable segment if the cable sags a vertical distance of 0.5m

Solution

For the equilibrium:

$$W = 2 T \sin \alpha$$

The tension in each cable segment is

$$T = \frac {W}{2 \sin \alpha}$$ $$\sin \alpha = \frac {h}{\frac {l}{2}} = \frac {2 h}{l}$$

Thus,

$$T = \frac {W}{2 \frac {2 h}{l}} = \frac {W l}{4 h}.$$ $$T = \frac {(100)(20)}{4(0.5)} = 1000 \, N.$$

Answer: 1000 N.

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