A traffic light weighing 20 pounds is supported by two cables with the left cabl

Question

A traffic light weighing 20 pounds is supported by two cables with the left cable making an angle of 30 degrees with the horizontal and the right cable making an angle of 32 degrees. Find tension T1 in the right cable and tension T2 in the left cable. Approximate answers to one decimal place. Draw a diagram and label. Resolve the two vectors into their horizontal (i) and vertical (j) components. Add the horizontal and vertical components of the two vectors. Write the augmented matrix to solve the system of equations.

Explanation / Answer

Horizontal forces are equal and opposite:
T1*cos30º = T2*cos32

T1/T2 =0.97924 ---- >1

Vertical forces on the left side must balance:

T1*sin30º +T2*sin32 = mg

given m = 20 pounds = 9.07185 kgs

T1 sin30 + T2 Sin32 = 9.07185*9.8 ---- >2

substituting 1 in 2

0.97924 T2 sin30 + T2 Sin32 = 9.07185*9.8

T2 = 87.2 N

substituting T2 in eq 1

T1 =0.97924 x T2

T1 =0.97924 x 87.2 N

T1 = 85.39 N

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