# Uniform Circular Motion on a race track

1. Nov 2, 2014

### Physicsnoob90

1. The problem statement, all variables and given/known data
On a banked race track, the smallest circular path on which cars can move has a radius of 116 m, while the largest has a radius of 153 m, as the drawing illustrates. The height of the outer wall is 11.6 m. Find (a) the smallest and (b) the largest speed at which cars can move on this track without relying on friction.

2. Relevant equations

3. The attempt at a solution
I'm stuck on what type of equation to use since i don't know what to do with the given height? What am i supposed to treat it as? Can anyone help me out?

2. Nov 2, 2014

### Simon Bridge

Before looking for equations - try thinking about the physics.

What effect does the height have on the track?
Where, on the track, will the cars be able to travel at the fastest speed (all else remaining equal)?

Start out by drawing a free-body diagram ... what are the forces? Where do they point? Where should the resultant force point?

Once you've done that - some equations should suggest themselves.