Final Answer:
The tension in each of the three cables supporting the traffic light is approximately 1.67 × 10^2 N.
Step-by-step explanation:
To find the tension in each cable, we need to consider the equilibrium of forces acting on the traffic light. Let's denote the tensions in the three cables as T1, T2, and T3. The weight of the traffic light acts downward with a force of 2.00 × 10^2 N. In equilibrium, the sum of the vertical forces must be zero. Therefore, the upward forces provided by the tensions in the cables must balance the downward force of the traffic light.
Since the traffic light is in static equilibrium, the tension in each cable is equal. Thus, T1 = T2 = T3. The sum of the upward forces is then 3 times the tension (3T), which must equal the weight of the traffic light. Mathematically, this can be expressed as 3T = 2.00 × 10^2 N. Solving for T, we find that the tension in each cable is approximately 1.67 × 10^2 N. This means that each cable exerts a force of 1.67 × 10^2 N, collectively supporting the traffic light and maintaining its equilibrium.