# Is this a meaningless problem formulation?

1. Oct 10, 2011

### charlesc56

A car is driving along a curved path (with a given radius) that is angled relative to the surface of the earth. The speed is of such magnitude that the friction force between car and road has a component directed downward the incline, however the friction does not have its maximum value. (So obviously the speed can increase a certain amount before the car starts sliding in the radial direction.)

Now the question is as follows:

What's the largest tangential acceleration the car can have?

I suppose the central relation in this situation is the centripetal force: F(radial) = m * v2/R

I don't see how the radial friction force is influenced directly by the tangential acceleration. The radial friction force naturally depends on the speed, since it is a factor in the centripetal force (m * v2/R). But how is the tangential acceleration related to this speed, when there is no mention whatsoever about the distance traveled or the duration of the motion. It suggests the tangential acceleration should be directly connected to the centripetal force, but I don't see the link. Could it be a very bad problem formulation, or what do you guys think? Thank you in advance.

2. Oct 10, 2011

### ehild

The force of friction supplies both the centripetal force and the force needed to tangential acceleration. The acceleration vector has radial (ar) and tangential (at) components and its magnitude is a=sqrt(at^2+ar^2). m*a can not exceed the force of friction.

ehild