What happens to the velocity if the angle of banking is reduced to half
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Force of friction is not a reliable source for providing the required centripetal force to the vehicle.
Phenomenon of raising outer edge of the curved road above the inner edge is called banking of roads.
In figure, OX is a horizontal line. OA is the level of banked curved road whose outer edge has been raised. ∠XOA=θ= angle of banking.
Weight (mg) of the vehicle going over the banked road acts vertically downwards. Normal reaction R of the banked road acts upwards in a direction perpendicular to OA. R can be resolved into two rectangular components.
Rcosθ, acting vertically upwards and Rsinθ, acting along the horizontal, towards the centre of the circular track.
If v is velocity of the vehicle over the banked circular road of radius r, then centripetal force required mv2/r.
In equilibrium, Rcosθ balances the weight, ie.,
Rcosθ=mg ....(i)
and Rsinθ provides the necessary centripetal force, ie.,
Rsinθ=rmv2