9. A traffic light weighing 122 N hangs from a cable tied to two other cables fa
ID: 1879940 • Letter: 9
Question
9. A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support as in the figure shown. The upper cables make angles of 37.0° and 53.0° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100 N. Does the traffic light remain hanging in this situation, or will one of the cables break? 9. A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support as in the figure shown. The upper cables make angles of 37.0° and 53.0° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100 N. Does the traffic light remain hanging in this situation, or will one of the cables break? 9. A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support as in the figure shown. The upper cables make angles of 37.0° and 53.0° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100 N. Does the traffic light remain hanging in this situation, or will one of the cables break?Explanation / Answer
The x-components of the tensions are in opposite directions.
So if the x-component of the t2 tension is +t2*cos53.0º, the x-component of the t1 tension must be negative.
(I assume the upper cables form a "V" and the two angles specified are on the left and right of the vertex).
fx = 0 condition is then t2*cos53.0º - t1*cos37.0º = 0
Solve this for t2 to get t2 = t1*cos37.0º/cos53.0º = 1.327
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