A steel ball of mass 1.07 kg is attached to a thin (massless) cable and whirled around in a circle in a vertical plane.The circle has a radi

Question

A steel ball of mass 1.07 kg is attached to a thin (massless) cable and whirled around in a circle in a vertical plane.The circle has a radius of 1.38 m. When it is at the bottom of the circle, the ball has a speed of 13.9 m/s. Calculate the magnitude of the tension in the cable when the mass is at the bottom of the circle. (in N)

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Khải Quang 1 day 2021-07-21T05:34:08+00:00 1 Answers 0 views 0

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    2021-07-21T05:36:07+00:00

    Answer:

    160.296 N

    Explanation:

    At the bottom of the circle,

    Applying,

    Tension  = centrifugal force- weight  of the ball

    T = mv²/r-mg…………………….. Equation 1

    Where T = tension in the cable, m = mass of the ball, v = speed of the ball, r = radius of the circle, g = acceleration due to gravity

    Given: m = 1.07 kg, v = 13.9 m/s, r = 1.38 m, g = 9.8 m/s²

    Substitute into equation 1

    T = (1.07(13.9²)/1.38)+[1.07(9.8)]

    T = (1.07(193.21)/1.38)+(10.486)

    T = (206.7347/1.38)+(10.486)

    T = 149.81+10.486

    T =160.296 N

    Hence the tension in the cable when the mass is at the bottom of the circle = 160.296 N

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