Friction, circular motion (stupid question)

[robs]

Homework Statement

A road bend is circular with a radius $$r$$, the surface is horizontal. The coefficient of friction between car tires and dry asphalt is $$\mu$$.
Determine the maximal speed with which a car can drive through the bend.

The Attempt at a Solution

Actually, I have solved the problem (and checked with the answers given in the textbook), but I don't really understand it.

I simply said that the centripedal force is $$m\cdot v^2/r$$ (m is the mass of the car) which at the maximal speed is equal to the friction force $$mg\mu$$, so I get $$v = \sqrt{rg\mu}$$ which apparently is right.

However, where does the fricition force comes from? I was taught that in fact the friction force $${\bf F_f} = -\mu N {\bf v}/|{\bf v}|$$ (at not too high velocities), so the friction force is oppositely directed to velocity. In the above however, I assumed that the friction force is oppositely directed to the centripedal acceleration (which is perpendicular to velocity), so actually, the friction force shouldn't have any effect on the motion...
Where is my error in reasoning?

 

[Doc Al]

I was taught that in fact the friction force $${\bf F_f} = -\mu N {\bf v}/|{\bf v}|$$ (at not too high velocities), so the friction force is oppositely directed to velocity.

This would describe kinetic friction, but the friction force on the car tires in your problem is static friction.

In the above however, I assumed that the friction force is oppositely directed to the centripedal acceleration (which is perpendicular to velocity), so actually, the friction force shouldn't have any effect on the motion...

The friction is what produces the centripetal acceleration, so it must act toward the center (in the same direction as the centripetal acceleration). No friction and the car couldn't turn.