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13 September, 21:24

Determine the required height h of the roller coaster so that when it is essentially at rest at the crest of the hill A it will reach a speed of 100km/h when it comes to the bottom B. Also, what should be the minimum radius of curvature p for the track at B so that the passengers do not experience a normal force greater than 4mg

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  1. 13 September, 21:42
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    a) 39.37 m

    b) 26.25 m

    Explanation:

    Given

    speed of the roller coaster, v = 100 km/h = 100 * (1000/3600) m/s = 27.78 m/s

    Using the law of conservation of energy.

    Potential Energy = Kinetic Energy

    mgh = 1/2mv²

    gh = 1/2v²

    h = v²/2g

    h = 27.78² / 2 * 9.8

    h = 771.7284 / 19.6

    h = 39.37 m

    Also,

    kmg - mg = mv²/p

    kg - g = v²/p

    p = v²/g (k - 1)

    p = 27.78² / 9.8 (4 - 1)

    p = 771.7284 / 29.4

    p = 26.25 m

    Therefore, the height of the roller coaster is 39.37 m and the radius of curvature required is 26.25 m
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