What Is the Minimal Speed for a Car on a Banked Road?

[Skynt]

Basically, we were told that from (mv^2/r)(cos $$\theta$$) = $$\mu$$[(mv^2)/r) sin $$\theta$$ + (mg cos $$\theta$$)] + mg sin$$\theta$$

you could rearrange for the max speed of a car going in a circular path on a banked road at a $$\theta$$ angle. From that equation above, I derived v max, but now I need to get v minimal. I really don't even understand the visual concept of the equation above - I drew a free-body diagram but I still don't understand it.

Could someone help me figure out the minimal speed the car has to go without falling off?

Also in the equation, he substituted a variable N for normal force with the equation in the bracket. So it's basically

(mv^2/r)(cos $$\theta$$) = [$$\mu$$N + (mg cos $$\theta$$)] + mg sin$$\theta$$

 

[Skynt]

Can anyone help me with this?

 

[Skynt]

Well, it's been a few days, so... *BUMP* :)

I can't get credit for the answer, but I am still curious as to what it is.

 

[BlackWyvern]

I think it's the speed of the car, which will provide a centripetal force, which is equal in magnitude to the x component of the normal/support force.

:)

 

[Skynt]

No, I don't think that works. I'm suppose to get the result 8. something
But instead I get 44 with that solution.
The max speed was 16.1 m/s, which means the minimal speed needs to be under that.