A 8.91-kg monkey is hanging by one arm from a branch and swinging on a vertical circle. As an approximation, assume a radial distance of 75.

Question

A 8.91-kg monkey is hanging by one arm from a branch and swinging on a vertical circle. As an approximation, assume a radial distance of 75.5 cm is between the branch and the point where the monkey’s mass is located. As the monkey swings through the lowest point on the circle, it has a speed of 2.61 m/s. Find (a) the magnitude of the centripetal force acting on the monkey and (b) the magnitude of the tension in the monkey’s ar

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Mít Mít 4 years 2021-08-26T01:27:24+00:00 1 Answers 12 views 0

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  1. Nho
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    2021-08-26T01:28:35+00:00
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    Answer:

    a) Centripetal force = 80.4 N

    b) Tension in the monkey’s arm = 167.7 N

    Explanation:

    The centripetal force is the force keeping the monkey in circular motion and it is given by

    F = (mv²/r)

    m = mass of the monkey = 8.91 kg

    v = velocity of the monkey = 2.61 m/s

    r = 75.5 cm = 0.755 m

    F = (8.91×2.61²)/0.755

    F = 80.4 N

    b) At the lowest point, there are 3 forces acting on the monkey, the tension in the arm, the monkey’s weight and the centripetal force.

    A quick force balance on the monkey at the lowest point gives

    F = T – mg

    80.4 = T – (8.91×9.8)

    T = 80.4 + 87.32

    T = 167.72 N

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