Question

a student weighing 160 pounds hangs for dear life from a cable tied to two other cables fastened to a support as shown above. the upper cables make angles of 39 and 55 with the horizontal. these upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 500N
M = 160Lbs * 0.454kg/Lb. = 72.64 kg.

M*g = 72.64 * 9.8 = 711.9 N., Downward = -711.9 N.

T1*Cos(180-39) = -T2*Cos55.
T1 = 0.738T2.

T1*sin(180-39) + T2*sin55 = 711.9.
0.629T1 + 0.819T2 = 711.9,
Replace T1 with 0.738T2:
0.629*0.738T2 + 0.819T2 = 711.9,
1.28T2 = 711.9, T2 = 556 N.

T1 = 0.738T2 = 0.738*556 = 410 N.


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