G-Forces on a Rollercoaster Ride: Exploring Centripetal Acceleration

[Oscar Wilde]

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?

Homework Equations

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

 

[LowlyPion]

1/2 g up looks like the right answer.

 

[Oscar Wilde]

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

 

[LowlyPion]

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?

 

[Oscar Wilde]

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]

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