Answer to Question #152735 in Classical Mechanics for GuardianVex

Question

A circular track of radius 300m is kept with outside of track raised to make 5 degree
with the horizontal.
1. Name the process in which outside of the road is raised little above the inner.and
explain why?
2. Obtain an expression for the optimum speed to avoid skidding (considering to
friction)

Answer 1

Answer

(A) this process is known as banking of road.

(B) if $v$ is the maximum speed without skidding then equation can be written as

$Ncos\theta+fsin\theta=\frac{mv^2}{r}\\Ncos\theta+\mu Nsin\theta=\frac{mv^2}{r}.... Eq. 1 \\and \quad 2nd\quad equation\\ Ncos\theta-\mu Nsin\theta=mg...... Eq. 2\\dividing\quad Eq. 1 by \quad Eq. 2\\ \frac{Ncos\theta+\mu Nsin\theta}{Ncos\theta-\mu Nsin\theta}=\frac{\frac{mv^2}{r}}{mg}\\ \frac{v^2}{rg}=\frac{sin\theta +\mu cos\theta}{cos\theta-\mu sin \theta}\\ v=\sqrt{\frac{rg(tan\theta+\mu)}{1-\mu tan\theta}}$

This is the equation of speed without skidding.