The ends of a rope are tied to two hooks on a ceiling. A set of books weighing 36.0 N is tied and hung on the rope so that the segments of the rope make angles of 35 degrees and 50 degrees respectively with the horizontal. Compute for the tension on each segment of the rope.

Answer 1

T1*Cos(180-35) + T2*Cos50 = -36*Cos270.
-0.819T1 + 0.643T2 = 0.
T1 = 0.785T2.

T1*sin(180-35) + T2*sin50 = -36*sin270.
0.574T1 + 0.766T2 = 36.
Replace T1 with 0.785T2:
0.574*0.785T2 + 0.766T2 = 36.
0.451T2 + 0.766T2 = 36.
1.22T2 = 36.
T2 = 29.6 N.

T1 = 0.785T2 = 0.785 * 29.6 = 23.2 N.