Obtain the expression for max. speed of a vehicle in a circular track on a banked road.
Answers
Answer:
Banking of roads : To avoid risk of skidding as well as to reduce the wear and tear of the car tyres, the road surface at a bend is tilted inwards, i.e., the outer side of road is raised above its inner side. This is called 'banking of roads'.
Consider a car taking a left turn along a road of radius r banked at an angle θ for a designed optimum speed V. Let m be the mass of the car. In general, the forces acting on the car are:
(a) Its weight
mg
, acting vertically down
(b) The normal reaction of the road
N
, perpendicular to the road surface
(c) The frictional force
f
s
along the inclined surface of the road.
Resolve
N
and
f
s
into two perpendicular components Ncosθ vertically up and
f
s
sinθ vertically down, Nsinθ and
f
s
cosθ horizontally towards the centre of the circular path.