Calculating Speed for Banked Racing Track

[superdave]

Homework Statement

Car is driven on a banked circular racing track. Radius R, angle theta.

a) For what speed is the track designed (if there were no friction the car would not slide)
b) If the track is wet, u=0.15, what are the minimum and maximum speeds car must be driven so it stays on the track.

Homework Equations

a=v^2/R (centripetal)
a=sin (theta) * g
a_f=u*g*cos(theta) (for part b, friction)

The Attempt at a Solution

Okay, here's what I don't understand.

Centripetal force pulls the car towards the center. And gravity pulls the car down, again towards the center. So though I know they oppose each other, I can't figure out why they would oppose each other since it seems they don't.

 

[Delphi51]

In my experience these banked road questions are best worked with from the point of view of the car, where you have a centrifugal force rather than a centripetal one. Further to make sense of it, you have to find the components of both forces that are normal to the road and parallel to it. The total normal force determines the friction force. Then you work with the 3 forces parallel to the road to find your answers.