A roller coaster car is going over the top of a 15-m-radius circular rise. The passenger in the roller coaster has a true weight of 600 N (t

Question

A roller coaster car is going over the top of a 15-m-radius circular rise. The passenger in the roller coaster has a true weight of 600 N (therefore a mass of 61.2 kg). At the top of the hill, the passengers “feel light,” with an apparent weight of only 360 N. How fast is the coaster moving

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Verity 3 years 2021-08-31T18:58:50+00:00 1 Answers 6 views 0

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    2021-08-31T19:00:41+00:00

    Answer:

    v = 7.67 m/s

    Explanation:

    The equation for apparent weight in the situation of weightlessness is given as:

    Apparent Weight = m(g – a)

    where,

    Apparent Weight = 360 N

    m = mass passenger = 61.2 kg

    a = acceleration of roller coaster

    g = acceleration due to gravity = 9.8 m/s²

    Therefore,

    360 N = (61.2 kg)(9.8 m/s² – a)

    9.8 m/s² – a = 360 N/61.2 kg

    a = 9.8 m/s² – 5.88 m/s²

    a = 3.92 m/s²

    Since, this acceleration is due to the change in direction of velocity on a circular path. Therefore, it can b represented by centripetal acceleration and its formula is given as:

    a = v²/r

    where,

    a = centripetal acceleration = 3.92 m/s²

    v = speed of roller coaster = ?

    r = radius of circular rise = 15 m

    Therefore,

    3.92 m/s² = v²/15 m

    v² = (3.92 m.s²)(15 m)

    v = √(58.8 m²/s²)

    v = 7.67 m/s

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