Final answer:
The maximum weight that two cables, each with a maximum tension of 850 N and forming a 40-degree angle to the horizontal, can support is 1304 N when accounting for their vertical components.
Step-by-step explanation:
The question asks about the maximum weight that two cables can support when they are each under a maximum tension of 850 N and form a 40-degree angle to the horizontal. Using physics principles, specifically static equilibrium and vector decomposition, we can find the answer.
To determine the maximum weight that the cables can support, we consider the vertical component of the tension because this component will support the weight of the traffic light. The vertical component (Tv) of the tension (T) can be found using the cosine function for each cable: Tv = T * cos(40).
Since there are two cables, the total vertical component that supports the traffic light is 2 * Tv. Substituting the given maximum tension (T = 850 N) into the equation yields 2 * 850 N * cos(40) for the maximum supported weight. Therefore, the maximum weight W that the traffic light can have before the cables reach their tension limit is found using W = 2 * T * cos(40).
Calculating this gives W = 2 * 850 N * cos(40) ≈ 2 * 850 N * 0.766 = 1304 N (rounded to nearest whole number), which is the maximum weight of the traffic light the cables can support.