Unlike a roller coaster, the seats in a Ferris wheel swivel so that the rider is always seated upright. An 80-ft-diameter Ferris wheel rotat

Question

Unlike a roller coaster, the seats in a Ferris wheel swivel so that the rider is always seated upright. An 80-ft-diameter Ferris wheel rotates once every 24 s.What is the apparent weight of a 40 kg passenger at the lowest point of the circle?What is the apparent weight of a 40 kg passenger at the highest point of the circle?

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Mít Mít 5 years 2021-08-12T15:19:52+00:00 1 Answers 512 views 1

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  1. Vodka
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    2021-08-12T15:21:16+00:00
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    Answer:

    a

       F_A =425.42 \ N

    b

      F_A_H = 358.58 \ N

    Explanation:

    From the question we are told that

        The diameter of the Ferris wheel is  d = 80 \ ft = \frac{80}{3.281} = 24.383

        The  period of the Ferris wheel is  T = 24 \ s

         The  mass of the passenger is  m_g = 40 \ kg

    The  apparent weight of the passenger at the lowest point is mathematically represented as

               F_A_L = F_c + W

    Where  F_c is the centripetal force on the passenger,  which is mathematically represented as

             F_c =m * r * w^2

    Where w is the angular velocity which is mathematically represented as

             w = \frac{2* \pi }{T}

    substituting values

             w = \frac{2* 3.142 }{24}

             w = 0.2618 \ rad/s

    and  r  is the radius which is evaluated as r = \frac{d}{2}

       substituting values

             r = \frac{24.383}{2}

             r = 12.19 \ ft

    So

              F_c = 40 * 12.19* (0.2618)^2

              F_c = 33.42 \ N

    W is the weight which is mathematically represented as

               W = 40 * 9.8

               W = 392 \ N

    So

             F_A = 33.42 + 392

             F_A =425.42 \ N

    The  apparent weight of the passenger at the highest point is mathematically represented as

              F_A_H = W- F_c

    substituting values

             F_A_H = 392 - 33.42

             F_A_H = 358.58 \ N

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