a problem on centripetal forces and friction

[Chiara]

hey this is important, im having this discussion with my father on a Physics problem and i don't think his answer is right. How would you solve this problem?
For a car traveling with speed v around a curve of radiur r, determine a formula for the angle at which the road should be banked so that no friction is required.

[FZ+]

Draw a diagram for the system, and mark on the forces involved. Gravity downwards. Reaction force at right angles to the surface of the curve.

Now, you know the component of the reaction force in the direction towards the centre of the curve (and so at right angles to the ground) as equal to m * V^2/r (from pretty basic circular motion). You also know it's component in the downwards direction (as mg). You can then divide one from the other to get the tan(angle), using geometry to get the angle of the plane.

Much easier to understand with good diagrams.