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

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The discussion centers on determining the minimal speed required for a car to navigate a banked road without falling off. The initial equation provided relates centripetal force and frictional forces acting on the car. The user has successfully derived the maximum speed but struggles to calculate the minimum speed, expressing confusion over the visual representation of the forces involved. They mention a discrepancy in their calculations, where they expect a result around 8 m/s but are getting 44 m/s instead. Clarification is sought on how to correctly account for the forces to find the minimal speed below the maximum of 16.1 m/s.
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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) = [\muN + (mg cos \theta)] + mg sin\theta
 
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Can anyone help me with this?
 
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.
 
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.

:)
 
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.
 

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