# Motion of a car on a banked road

1. I read that the maximum possible speed of a car on a banked road is greater than that on a flat road. I know the formula for finding velocity in each case. But I am unable to figure out the reason by comparing the equations.

2. I read about the ideal speed when friction is zero. I cannot understand how can the speed determine the frictional force. Frictional force should only depend on the nature of surfaces in contact. How is it possible that at a certain speed the frictional force is zero.

3. Also I cannot understand that if the velocity is greater than the ideal velocity then what will be the change in the motion of the car.

1. The higher the speed at which a car takes a bend, the greater the centripetal force that is required to keep the car following the curve of the bend. On a flat bend the normal force from the road surface is $$mg$$ and the whole centripetal force is supplied by the friction between the car's tires and the road surface, which is usually assumed to be proportional to the normal force. On a banked bend a component of the normal force acts towards the centre of the curve, and so provides part of the centripetal force.