Draw a diagram showing all components of forces acting on a vehicle moving on a curved banked road. Write the necessary equation for maximum safety, speed and state the significance of each term involved in it.

Explanation

Refer to HSC Paper, July `2017` , Answer `(viii)`.
`:.v_(max)=sqrt((rg(tantheta+mu_(s)))/(1-mu_(s)tantheta))`
This is the expression for the maximum safety speed on a banked road. At the optimum speed, the friction between the car tyres and the road surface is not called into play. Hence, by setting `mu_(s)=0`, the optimum speed on a banked circular road is
`v=sqrt(rgtantheta)`
Significances of the terms involved:
`(a)` The maximum safety speed of a vehicle on a curved road depends upon friction between tyres and roads.
`(b)` It also depends on the angle through which road is banked. It is independent of the mass of the vehicle.