Help with Banked turns - Physics

[fvalentin]

So I'm having a hard time understanding baked turns involving roads. Mainly I'm confused on how to derive the friction force into the x and y components and why it turns be like so. I also am confused about when i encounter a problem that involves friction in banked turns like in the picture below. Ignore the coefficient of friction; I'm just trying to understand the physics of it.

 

[Simon Bridge]

Welcome to PF;
The key to these problems is to realize that, in order to go around the circle at a constant speed, the net force must point directly towards the center of the circle.
If there is no friction, then there are only twp forces on the car.
Therefore these must sum to a single force pointing horizontally to the right (in the pic).
You can add vectors head-to-tail.

 

[Krishnendu]

when car goes on a banked road, the normal reaction is perpendicular to the road. On breaking up the components, u get the sine component of the normal reaction in the horizontal direction.this is what balances the tendency of the body to slip outwards. Banking makes the bend more safe to traverse at high speed, as NsinA and the friction supply the essential centripetal acceleration for balancing the tendency of slipping which is radially outwards.

"A" is the banked angle.