Ablock-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.)

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

T₂ = 339.06 N
T₃ = 276.57 N

The measure of the tension T2 and T3 to two decimal places is 271.22N and 332.52N respectively.

To get the tension and , we will need to resolve the force into the horizontal and vertical components as shown:

For the horizontal component,

For the vertical component:

Since

Hence the measure of the tension T2 and T3 to two decimal places is 271.22N and 332.52N respectively.

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Thanks for the points girly!

Explanation: