a 100kg street light is supported equally by two ropes. one rope pulls up and to the right 40 degrees above the horizontal; the other pulls up and to the left 40 degrees . what is the tension of the rope?

Answer 1

M*g = 100kg * 9.8N./kg = 980 N. = Wt. of
st. light.

T1*Cos(180-40) + T2*Cos40 = -980*cos270.
-0.766T1 + 0.766T2 = 0.
0.766T2 = 0.766T1.
T1 = T2.

T1*sin(180-40) + T2*sin40 = -980*sin270.
0.643T1 + 0.643T2 = 980.
Replace T2 with T1:
0.643T1 + 0.643T1 = 980.
1.286T1 = 980.
T1 = 762 N. = T2.

Answer 2

Or T1 = T2.

T1*sin(180-40) + T1*sin40 = -980*sin270.
0.643T1 + 0.643T1 = 980.
1.286T1 = 980.
T1 = 762 N. = T2.