Question

Find the tension in the two wires supporting the 27 kg traffic light shown in the figure below. (Assume that θ1 = 51° and θ2 = 39°.)

Answer 1

Without knowing which is the left hand wire and which is the right hand wire and how the angles are measured I am going to have to make some assumptions. Cable 1 is the right-hand wire and Cable 2 is the left-hand wire. All angles are measure from horizontal. First draw a free-body diagram of the situation to analyze what forces are acting on the stoplight. I clearly cannot draw a free-body diagram in Yahoo! Answers. Second, write expressions for Newton's Laws in both the horizontal and vertical directions. Since the stoplight is motionless, the sum of the forces in each direction is zero. Remember to break up each tension into vector components using your angles. x: T1 cos 51 - T2 cos 39= 0 y: 264.6 N - T1 sin 51 - T2 sin 49 = 0 You now have two simultaneous equations with the variables T1 and T2. I would solve the first (x-direction) for either T1 or T2. T1 = T2 cos 39 / cos 51 Now plug that expression back into second (y-direction) and solve for T2: 264.6 N - T2 cos 39 sin 51 / cos 51 - T2 sin 39= 0 264.6 N = T2 (cos 39 tan 51 + sin 39) T2 = 166.52N Plug T2 back into the first equation (x-direction) to find T1. T1 = T2 cos 39 / cos 51 T1 = 166.52 N cos 39 / cos 51 T1 = 205.635 N I obtain the two tensions as 205.635 N and 166.51 N