What is meant by banking of road? What is the need for banking a road ?Obtain
expression for the maximum speed with which a vehicle can safely negotiate a
curved road banked at an angle θ .The coefficient of friction between the wheel and
the road is µ.
Answers
banking of roads : the phenomenon of raising outer edge of the curved road above the inner edge is to take a safer turn is called Banking of Roads. Let a car of mass m moves with speed v m/s in a curved road banked at an angle . and also given that roughness of curved surface is .
Answer:
banking of roads : the phenomenon of raising outer edge of the curved road above the inner edge is to take a safer turn is called Banking of Roads. Let a car of mass m moves with speed v m/s in a curved road banked at an angle .Banking of road means raising the outer edge of the road with respect to inner edge so that the road makes an angle with the horizontal.
When a vehicle moves along a curve, the force of friction provides the necessary centripetal force. But this force has a limit = μmg.When the speed of the vehicle increases beyond this maximum value, the banking of roads is necessary so that the component of normal reaction of the road towards the centre provides the necessary centripetal force.
From the figure, for vertical equilibrium :
Total upwards force = total downwards force
Ncosθ=mg+fsinθmg=Ncosθ−fsinθ...(1)
As the forces Nsinθ,fcosθ provide the necessary centripetal force.
rmv2=Nsinθ+fcosθ...(2)
Thus dividing (2) by (1),
mgrmv2=Ncosθ−fsinθNsinθ+fcosθ
As f=μsN
Thus,
rgv2=cosθ−μssinθsinθ+μscosθ=1−μstanθtanθ+μs=1−tanλtanθtanθ+tanλ=tan(θ+λ)
v=rgtan(θ+λ) where tanλ=
