# Homework Help: Passengers in roller coaster

1. Jul 20, 2007

### avsj

1. The problem statement, all variables and given/known data

A roller coaster loop has a radius of 12 m. If the passengers are not to fall out at the top of the loop, what is the minium speed the car must have at the top.

2. Relevant equations

Fc = Fg-Fn
Fc= mv^2/r
Fg = mg

3. The attempt at a solution

I figure that for the passengers not to fall, Fn should be equal to Fg, but that gives Fc = 0 which doesnt make sense solving for v. What condition is necessary for the passengers not to fall out?

Thanks,

2. Jul 20, 2007

### cristo

Staff Emeritus
What do you mean by Fn?

3. Jul 20, 2007

### andrevdh

Lets rather consider just one passenger. The forces he/she would experience under such conditions are his/her weight, Fg, and the force normal to the tangential of the tract, Fn (the seat that the passsenger is sitting on pushes him/her).

The normal force points towards the inner side of the curvature of the track. It has to provide the force that makes the passenger go "around the bend" of the track (make him/her change direction towards the inner side of the curvature).

This force needs to be large if the curvature of the track is strong (small radius) and small if the curvature is weak.

The normal force will also be small if the speed of the passenger is small - it need not provide much acceleration towards the inside of the curvature if the speed of the passenger is small.

Last edited: Jul 20, 2007