# Force of friction in circular motion

1. Dec 15, 2003

### kbrowne29

I'm having trouble with the following problem:
If a curve of radius 80.0 m is perfectly banked for a car moving 70.0 km/hr, what must be the coefficient of friction in order to prevent skidding when the car is moving at 90.0 km/hr.

OK, I know that I need to find the angle of the "perfectly banked" curve first, and I am able to do this. However, what do I do with this angle? It seems that there are too many unknowns.
I know that tan(theta)=v^2/Rg, where r is the radius of the circle. But I'm not sure where to go from here. I would really appreciate any help with this problem. Thanks.

2. Dec 15, 2003

### ShawnD

damn it i misread the question. sorry.

3. Dec 15, 2003

### gnome

I don't know about that formula you mentioned -- it may or may not apply to this problem, & I suspect not.

Anyway, applying a formula is not the way to attack a problem. Think about the geometry of the situation, & then draw a diagram of the forces. You have three: the normal force acting perpendicular to the banked surface, the gravitational force acting vertically down, and friction acting on an angle downward and towards the center of curvature (parallel to the road surface).

You want to resolve the normal force and the friction into their vertical and horizontal components, so the sum of the vertical forces (the gravity plus the vertical components of the normal and frictional forces) is zero, and the sum of the horizontal components of the frictional and normal forces equals the centripetal force needed to keep the car moving along that curve. Knowing "theta" allows you to do that.

Start with the drawing. Then do the trig.