Question

Derive an expression for the maximum velocity of a vehicle with which it can
negotiate a banked curved road safely. Draw necessary diagram.​

Answer 1

Answer:

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 fs​

​sinθ vertically down, Nsinθ and fs​

​cosθ horizontally towards the centre of the circular path.

If vmax​ is the maximum safe speed without skidding.

Answer 2

Explanation:

Answer in the figure

Hope this will help you