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?
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,