A 20.0-kg traffic light hangs midway on a cable between two poles 30.0 meters apart.If the sag in the cable is 0.40 meters,what is the tension in each side of the cable?
A)9.8E+1 N
B)9.8E+3 N
C)3.7E+3 N
D)3.8E+2 N
E)2.0E+4 N

Question

Quizplus · Accepted Answer

First, we need to find the total length of the cable. Using Pythagoras' theorem, we have:
distance^2 = sag^2 + (half the distance between the poles)^2
distance^2 = (0.4 m)^2 + (15 m)^2
distance = 15.09 m
Next, we can calculate the weight of the traffic light:
weight = mass x gravity
weight = (20.0 kg) x (9.8 m/s^2)
weight = 196 N
Since the traffic light is in equilibrium, the tension in each side of the cable must be equal. Let T be the tension in each side, then we have:
2T = weight
T = weight/2
T = 196 N / 2
T = 98 N
Therefore, the tension in each side of the cable is 98 N, which is approximately 3.7E+3 N (C).

A 200-Kg Traffic Light Hangs Midway on a Cable Between Two