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What is the difference between banking of road with friction and without friction?

The phenomenon of raising outer edge of the curved road above the inner edge is to provide necessary centripetal force to the vehicles to take a safer turn and the curved road is called Banking of Roads.

If a car is on a level (unbanked) surface, the forces acting on the car are its weight, mg, pulling the car downward, and the normal force, N, due to the road, which pushes the car upward. Both of these forces act in the vertical direction and have no horizontal component. If there is no friction, there is no force that can supply the centripetal force required to make the car move in a circular path - there is no way that the car can turn.

On the other hand, if the car is on a banked turn, the normal force (which is always perpendicular to the road's surface) is no longer vertical. The normal force now has a horizontal component, and this component can act as the centripetal force on the car! The car will have to move with just the right speed so that it needs a centripetal force equal to this available force, but it could be done. Given just the right speed, a car could safely negotiate a banked curve even if the road is covered with perfectly smooth ice!

With friction:

Suppose we consider a particular car going around a particular banked turn. The centripetal force needed to turn the car (mv²/r) depends on the speed of the car (since the mass of the car and the radius of the turn are fixed) - more speed requires more centripetal force, less speed requires less centripetal force. The centripetal force available to turn the car (the horizontal component of the normal force = if you follow the mathematics) is fixed (since the mass of the car and the bank angle are fixed). So, it makes sense that we found one particular speed at which the centripetal force needed to turn the car equals the centripetal force supplied by the road. This is the "ideal" speed, v_ideal, at which the car the car will negotiate the turn - even if it is covered with perfectly-smooth ice. Any other speed, v, will require a friction force between the car's tires and the pavement to keep the car from sliding up or down the embankment: