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Relative g's

  1. May 27, 2009 #1
    1. The problem statement, all variables and given/known data
    A rollercoaster car is going over a hill, with a person sitting with -no- restraints. The velocity of the car and radius of the hill are such that the centripetal acceleration of the cart is 15 m/s^2. What is the relative g environment (for the rider) and how many g's does he feel?

    2. Relevant equations

    g= 10m/s^2

    3. The attempt at a solution

    This is a conceptual problem. I reason that because the car is accelerating down, away from the rider, the rider is accelerating upwards at 15 m/s^2 relative to the car. I understand that there is no force "pushing" the rider up. However, he is also being accelerated downward by the force of gravity at 10 m/s^2. By subtraction I have come to the conclusion that the relative g environment for the rider is 5 m/s^2 upwards, and that he feels 1/2 g (up).

    Is this right? Have I made mistakes? If so, please explain. Also, if the car were to go down into a valley, and centripetally accelerate at 15 m/s^2 , what kind of a g environment would that produce on the passenger?

    All help appreciated,

  2. jcsd
  3. May 27, 2009 #2


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    1/2 g up looks like the right answer.
  4. May 27, 2009 #3
    Hmm ok thanks, do you have any ideas about the second scenario?
  5. May 27, 2009 #4


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    Acceleration is a vector too, so ... they would add to 2.5 g's then wouldn't they?
  6. May 27, 2009 #5

    Ooo I see now. The force of gravity provides the upward acceleration in the first, but the normal force causes the upward acceleration in the second? I believe this is true

    Thanks for the help, and feel free to correct me if I am wrong.

  7. May 27, 2009 #6


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    Not quite. The force of gravity is down in both cases.

    At the top of the hill the centripetal acceleration is on the car. The person is experiencing however a centrifugal outward effect because he is not secured to the car. Upward 1.5 down 1 = .5

    At the bottom the radial accelerations are reversed. There is the downward effect of gravity and the centrifugal effect. 1 + 1.5 = 2.5
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