Final answer:
To calculate the tension in wires supporting a lamp, trigonometric principles are applied. For a 150-degree angle, the tension in each wire is approximately 103.92N, and for a 120-degree angle, it is approximately 100N.
Step-by-step explanation:
The student is trying to determine the tension in the wires supporting a street lamp in two different scenarios, one with an angle of 150 degrees and another with an angle reduced to 120 degrees. We must consider the equilibrium of forces and use principles of physics to solve this problem.
For a 150-degree angle, the horizontal components of tension from the two wires cancel each other out, and the vertical components must add up to the weight of the lamp. Using trigonometric relations, we can determine that each wire supports a vertical force equivalent to half the weight of the lamp. The tension T can be found using the formula T = W / (2 * cos(θ/2)), where W is the weight of the lamp and θ is the angle between the wires. T = 200N / (2 * cos(75)) which calculates to approximately 103.92N in each wire.
When the angle is reduced to 120 degrees, using the same formula, T = 200N / (2 * cos(60)) gives us a tension of approximately 100N in each wire.