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2 July, 22:40

You are riding a rollercoaster going around a vertical loop, on the inside of the loop. If the loop has a radius of 30 meters, how fast must the cart be moving in order for you to feel three times as heavy at the top of the loop

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  1. 3 July, 01:01
    0
    v = 24.2m/s

    Explanation:

    Given R = 30m

    The two forces acting on you while on the roller coaster ride are the normal force and your weight.

    By Newton's second law

    N - W = mv²/R

    For you to feel 3 time as heavy, the normal force of the seat of the roller coaster on you must be 3 times your weight. That is

    N = 3*W = 3*mg

    W = mg

    3mg - mg = mv²/R

    2mg = mv²/R

    2g = v²/R

    v² = 2gR

    v = √2gR

    v = √ (2*9.8*30)

    v = 24.2m/s
  2. 3 July, 01:02
    0
    Speed of the cart at the top of the loop = 34.3 m/s

    Explanation:

    Gravitational acceleration = g = 9.81 m/s2

    Your mass = m

    You feel three times as heavy at the top of the loop.

    Normal force on you = N = 3mg

    Radius of the loop = R

    Speed of the cart = V

    Centripetal force required for the circular motion = Fc

    F = m

    The centripetal force is provided by the normal force on you which is directed downwards and your own weight which is directed downwards.

    Fc = mg + N

    Fc = mg + 3mg

    Fc = 4mg

    m12 - = 4mg R

    V = 4gR

    V = 4 (9.81) (30)

    V = 34.3 m/s

    Speed of the cart at the top of the loop = 34.3 m/s
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