Answer to Question #117732 in Mechanics | Relativity for Wilcox

Question

A 12.2 m crane weighs 18.0 kN and is lifting a 56.9 kN load. The hoisting cable (tension T1) passes
over a pulley at the top of the crane and attaches to an electric winch in the cab. The pendant cable
(tension T2) which supports the crane, is fixed to the top of the crane. Find the tensions in the two cables.

T1 = Blank 1. Calculate the answer by read surrounding text.
kN

T2 = Blank 2. Calculate the answer by read surrounding text.
kN

1

Answer 1

$$T_1=W_2=56.9\ kN$$

$$T_2\cos{35}(L\cos{40} )+ T_1\cos{45}(L\cos{40}) - T_2\sin{35}(L\sin{40} )-\\- T_1\sin{45}(L\sin{40}) - W_2(0.5L\sin{40}) - T_1(L\sin{40})=0$$

$$T_2\cos{35}\cos{40} + T_1\cos{45}\cos{40} - T_2\sin{35}\sin{40} \\- T_1\sin{45}\sin{40} - 0.5W_2\sin{40} - T_1\sin{40}=0$$

$$T_2\cos{35}\cos{40} + 56.9\cos{45}\cos{40} - T_2\sin{35}\sin{40} \\-56.9\sin{45}\sin{40} - 9\sin{40} - 56.9\sin{40}=0$$

$$T_2=144.5\ kN$$