What is the need for banking of road? Write the expression for the the maxim speed with
which a vehicle can safely negotiate a cured road banked at an angle θ . The coefficient of
friction between the wheels and the road is μ .
which a vehicle can safely negotiate a cured road banked at an angle θ . The coefficient of
friction between the wheels and the road is μ .
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Answer:= 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+fsinθ
mg=Ncosθ−fsinθ...(1)
As the forces Nsinθ,fcosθ provide the necessary centripetal force.
r
mv
2 =Nsinθ+fcosθ...(2)
Thus dividing (2) by (1),