- #1

JessicaHelena

- 188

- 3

## Homework Statement

This isn't really a homework but a project I'm doing that's due soon. In our multivariable calculus class, we're creating a 3D roller coaster, and I need to explain the physics behind the roller coasters.

For a roller coaster loop, if it were perfectly circular, we would have a minimum speed of ##v_{min} = \sqrt{gR}## at the top of the loop where ##g=9.8 m/s^2## and ##R## is the radius of the 'circle'. However, most roller coaster loops are actually not circular but more elliptical. I've been looking for ways to calculate the min. speed at the top for an elliptical loop, but so far I haven't been able to. How could I go about that?

## Homework Equations

F_net = ma_c

## The Attempt at a Solution

I really didn't know how to do this, so I searched google, but as far as I can see, there aren't any explanations for this...

Last edited by a moderator: