what do you mean by banking of rods?what is it's need?make a diagram and derive the expression of angle of banking when friction is negligible.
Answers
Explanation:
Banking of roads is defined as the phenomenon in which the edges are raised for the curved roads above the inner edge to provide the necessary centripetal force to the vehicles so that they take a safe turn. ... The angle at which the vehicle is inclined is defined as the bank angle
Explanation:
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),
mg
r
mv
2
=
Ncosθ−fsinθ
Nsinθ+fcosθ
As f=μ
s
N
Thus,
rg
v
2
=
cosθ−μ
s
sinθ
sinθ+μ
s
cosθ
=
1−μ
s
tanθ
tanθ+μ
s
=
1−tanλtanθ
tanθ+tanλ
=tan(θ+λ)
v=
rgtan(θ+λ)
where tanλ=μ
