a block of mass M hangs in equilibrium. the rope which is fastened to the wall is horizontal and has a tension of 38N. the rope which is fas

Question

a block of mass M hangs in equilibrium. the rope which is fastened to the wall is horizontal and has a tension of 38N. the rope which is fastened to the ceiling has a tension of 59N and makes an angle theta with the ceiling. what is the angle

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Doris 6 months 2021-08-18T12:09:28+00:00 1 Answers 0 views 0

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    2021-08-18T12:10:32+00:00

    Answer:

    50°

    Explanation:

    The tension in the rope fastened to the ceiling has horizontal component 59cosθ and its vertical component is 59sinθ. For equilibrium,

    59cosθ = 38 N  (the tension in the rope attached to the wall) (1)and

    59sinθ = Mg (the weight of the block of mass)  (2)

    Dividing (2) by (1)

    59sinθ/59cosθ = Mg/38

    tanθ = Mg/38

    θ = tan⁻¹(Mg/38)

    Also squaring (1) and (2) and adding

    (59cosθ)² = 38² N

    (59sinθ)² = (Mg)²

    (59cosθ)² + (59sinθ)² = 38² + (Mg)²

    59²((cosθ)² + (sinθ)²) = 38² + (Mg)² . Since (cosθ)² + (sinθ)² = 1

    59² = 38² + (Mg)²

    Mg = √(59² – 38²) = √(3481 – 1444) = √2037 = 45.13 N

    θ = tan⁻¹(Mg/38) = tan⁻¹(45.13/38) = tan⁻¹(1.1877) = 49.9° ≅ 50°

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