Question

obtain an expression for maximum possible speed for a vehicle to move on horizontal unbanked road
​

Answer 1

Explanation:

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 fs along the inclined surface of the road.

Resolve N and fs into two perpendicular components Ncosθ vertically up and fssinθ vertically down, Nsinθ and fscosθ horizontally towards the centre of the circular path.

If vmax is the maximum safe speed without skidding.

rmvmax2=Nsinθ+fscosθ

               =Nsinθ+μsNcosθ

rmvmax2=N(sinθ+μscosθ)....(1)

and 

Ncosθ=mg+fssinθ

               =mg+μsNsinθ

   ∴mg=