# Relative g's

## Homework Statement

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?

g= 10m/s^2

## 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,

Oscar

## Answers and Replies

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LowlyPion
Homework Helper
1/2 g up looks like the right answer.

Hmm ok thanks, do you have any ideas about the second scenario?

LowlyPion
Homework Helper
Hmm ok thanks, do you have any ideas about the second scenario?
Acceleration is a vector too, so ... they would add to 2.5 g's then wouldn't they?

Acceleration is a vector too, so ... they would add to 2.5 g's then wouldn't they?

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.

Oscar

LowlyPion
Homework Helper
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.

Oscar
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