calculus 3 vectors help!?

A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. The hoist weighs 380 N. The ropes, fastened at different heights, make angles of 50° and 38° 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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1 Answer

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  • Pope
    Lv 7
    1 month ago

    I cannot read any of the type in the image, but let me suppose T₂ is the tension on the cable having vertical angle 50°, while T₃ is the tension on the cable having vertical angle 38°. The given cable lengths are red herring conditions. They are of no use to you for this particular question.

    The vertical components of the tensions are in opposition, and assuming that the system is in equilibrium, they must be equal in magnitude.

    T₂cos(50°) = T₃cos(38°)

    The pulley has a weight of 380 N. I will assume that includes the load, because otherwise we have nothing to work with. For the same reason, I suppose the cable weights are negligible. The sum of the vertical components must match the given weight.

    T₂sin(50°) + T₃sin(38°) = 380 N

    There you have two linear equations in T₂ and T₃. Solve the system.

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