A traffic light weighing 119 N hangs from a cable tied to two other cables faste

Question

A traffic light weighing 119 N hangs from a cable tied to two other cables fastened to a support as in figure (a). The upper cables make angles of 1 = 38.0° and 2 = 52.0° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 130 N.....

Suppose the traffic light is hung so that the tensions T1 and T2 are both equal to 80.0 N. Find the new angles they make with respect to the x axis. (By symmetry, these angles will be the same.)

=____ °

Explanation / Answer

a) T3 = mg = 119 N

at point , in horizontal

T1cos@1 = T2cos@2

T1 = (cos52 /cos38) T2 = 0.781T2

in vertical,

T1sin38 + T2sin52 = T3 = 119

0.781T2 sin38 + T2sin52 = 119

T2 = 93.77 N ...........Ans

T1 = 73.24 N ........Ans

-------------------------

now in vertial,

Tsin@ +Tsin@ = 119

2 x 80 x sin@ = 119

sin@ = 119 /160

@ = 48.05 deg

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