Banking of roads, How to derive equation from a Banked road. Easy Physics

Banked Roads

When a vehicle goes around a curved road, It requires some centripetal force. If we raise the outer edge, a component of normal reaction of the road will contribute to the centripetal force in addition to the contribution of friction.This phenomenon of raising outer edge of the curved road is called banking of roads.

Deriving equation for banked roads

Since there is no acceleration in the vertical direction. The net force along this direction must be 0, hence

The centripetal force is provided by the horizontal components N and f

But(The law of static friction)

Substituting value of f in equation 1 and 2

From equation 4

Substituting this value in equation 5 gives,

v changes to vmax because we applied law of static friction.

Dividing each term of LHS by cosθ

Equating

We get

When friction is not needed.The equation becomes.

At this speed frictional force is not needed at all to provide the necessary centripetal force.