A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. the hoist weighs 430 n. the ropes, fastened at different heights, make angles of 50Â° and 38Â° with the horizontal. find the tension in each rope and the magnitude of each tension. (let t2 and t3, represent the tension vectors corresponding to the ropes of length 2 m and 3 m respectively. round all numerical values to two decimal places.)

Question

Physics

Amara Schmidt

12 January, 03:01

A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. the hoist weighs 430 n. the ropes, fastened at different heights, make angles of 50Â° and 38Â° with the horizontal. find the tension in each rope and the magnitude of each tension. (let t2 and t3, represent the tension vectors corresponding to the ropes of length 2 m and 3 m respectively. round all numerical values to two decimal places.)

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Answers (1)

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Shaun Daniels · Answer 1

Refer to the diagram shown below.

For horizontal equilibrium,

T₃ cos38 = T₂ cos 50

0.788 T₃ = 0.6428 T₂

T₃ = 0.8157 T₂ (1)

For vertical equilibrium,

T₂ sin 50 + T₃ sin 38 = 430

0.766 T₂ + 0.6157 T₃ = 430

1.2441 T₂ + T₃ = 698.392 (2)

Substitute (1) into (2).

(1.2441 + 0.8157) T₂ = 698.392

T₂ = 339.058 N

T₃ = 0.8157 (399.058) = 276.571 N

Answer:

T₂ = 339.06 N

T₃ = 276.57 N