Use the worked example above to help you solve this problem. A traffic light wei

Question

Use the worked example above to help you solve this problem. A traffic light weighing 1.18 102 N hangs from a vertical cable tied to two other cables that are fastened to a support, as shown in Figure (a). The upper cables make angles of ?1 = 36.5? and ?2 = 53.5? with the horizontal. Find the tension in each of the three cables. T1 = N T2 = N T3 = N Use the values from PRACTICE IT to help you work this exercise. Suppose the traffic light is hung so that the tensions T1 and T2 are both equal to 78 N. Find the new angles they make with respect to the x-axis. (By symmetry, these angles will be the same.) = ?

Explanation / Answer

T1sin?1+T2sin?2=W=T3 ---------1 verical forces T1cos?1=T2cos?2=----------------------2horizontal forces ===>1.34*T1=T2-------------------3 ---------------------- from 1 T1*.6+T2*.79=118 from 3 T1*.6+1.34T1*.79=118 T1=71.14N T2=95.32N part 2 T1cos?1=T2cos?2 becomes cos?1=cos?2 so ?1=?2 T1sin?1+T2sin?2=W=T3 this eq becomes= 2Tsin?=118 sin?=49.14 degres

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