# Roller Coaster

## Homework Statement

A roller coaster has a mass of 510kg when fully loaded with passengers. The radius at point A is 10.0 m and the radius at point B is 15.0 m.

-If the vehicle has a speed of 19.6 m/s at point A, what is the force exerted by the track on the car at this point? (N)

-What is the maximum speed the vehicle can have at B and still remain on the track? (m/s)

EF=m (v^2 / r)

## The Attempt at a Solution

*For the first problem I thought you would use the equation EF=m (v^2 / r). Which would be EF=510 (19.6^2 / 10.0). Which equals 510*(384.16/10.0). Equals 19592.16. However, this is wrong! Isn't that the right equation?

*For the second problem, I'm not sure where to start. But I'm assuming that I will need the correct force value before I can begin.

Any suggestion as to where I'm going wrong?

## Answers and Replies

Hootenanny
Staff Emeritus
Science Advisor
Gold Member
It all depends on the location of points A and B, perhaps if you could post a diagram or describe the position of the two points we could help you further.

assuming a is on a curve that is convex up, (try it the other way and you'll find its off the track i think), you have two a accelerations to account for, g and the v^2/r which is 19.6^2/10=38.4. Compute the net a, then you have the force pushing on the track.

b must be convex down (or upside down, but then it would be a minimal speed): v^2/15=g as the two accelerations are opposing.