Calculate your apparent weight at the top and bottom of a Ferris wheel, given that the radius of the wheel is 7.2 m, it completes one revolu

Question

Calculate your apparent weight at the top and bottom of a Ferris wheel, given that the radius of the wheel is 7.2 m, it completes one revolution every 28 s, and your mass is 55 kg

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King 5 years 2021-09-05T04:51:54+00:00 1 Answers 18 views 0

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  1. thuthuy
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    2021-09-05T04:53:33+00:00
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    Answer:

    559.5 N at the bottom and 519.6 N at the top of the wheel

    Explanation:

    If it completes 1 revolution (or 2π rad) per 28s then its angular speed is

    \omega = 2\pi/28 = 0.224 rad/s

    The centripetal acceleration would be:

    a_c = \omega^2 R = 0.224^2*7.2 = 0.363 m/s^2

    Let gravitational acceleration g = 9.81 m/s2.

    At the bottom of the wheel the net acceleration would be g plus the centripetal acceleration:

    a_b = a_c + g = 9.81 + 0.363 = 10.17 m/s^2

    So the weight at the bottom of the wheel would be

    W_b = a_b*m = 10.17*55 = 559.5 N

    Similarly at the top of the wheel the net acceleration is g subtracted by the centripetal acceleration:

    a_t = g - _a_c = 9.81 - 0363 = 9.45 m/s^2

    And the weight at the top is

    W_t = a_t*m = 9.45*55 = 519.6 N

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