Suppose the traffic light is hung so that the tensions T 1 and T 2 are both equa

Question

Suppose the traffic light is hung so that the tensions T1 and T2 are both equal to 84 N. Find the new angles they make with respect to the x-axis. (By symmetry, these angles will be the same.)

T1 = ? N T2 = ? N T3 = ? N x 102 N hangs from a vertical cable tied to two other cables that are fastened to a support, as shown in above. The upper cables make angles of ?1 = 36.0½ and ?2 = 54.0½ with the horizontal. Find the tension in each of the three cables. T1 = ? N T2 = ? N T3 = ? N Suppose the traffic light is hung so that the tensions T1 and T2 are both equal to 84 N. Find the new angles they make with respect to the x-axis. (By symmetry, these angles will be the same.) A traffic light weighing 1.10

Explanation / Answer

Part A)

We can easily start with T3

T3 = 110 N

Part B)

From the sum of forces in the y direction

T1sin(37) + T2(sin 53) = 110

In the x direction

T1cos(37) = T2cos(53)

T1 = .754T2

Sub that into the vertical force equation...

(.754T2)sin(37) + T2(sin 53) = 110

1.252 T2 = 110

T2 = 87.8 N

T1 = .754T2 = .754(87.8)

T1 = 66.2 N

Part B)

In the y direction 2(Tsin angle) = 1078

2(84 sin angle) = 110

angle = 40.9o

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