Math/Physics

A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. The hoist weighs 340 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. (LetT2 and T3, represent the tension vectors corresponding to the ropes of length 2 m and 3 m respectively.

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  1. the horizontal components of the tensions are equal and pull in opposite directions

    the vertical components of the tensions sum to the weight of the hoist

    the longer rope makes the smaller angle with the horizontal

    T2 * cos(50º) = T3 * cos(38º)

    [T2 * sin(50º)] + [T3 * sin(38º)] = 340 N

    solve the system of equations for T2 and T3

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