Question

A vehicle can travel along a curved road with a speed of $18km{h}^{-1}$. If the total centripetal force is provided by the banking of the road and the radius of the curvature is $10$ m, calculate the banking angle of the road.

• A. ${90}^o$
• B. ${30}^o$
• C. ${14}^o$
• D. ${16}^o$

Answer 1

The correct option is C ${14}^o$

Equation of motion:

$N\cos \theta =mg$

$⟹N=\frac{mg}{\cos \theta }$

and, $N\sin \theta \ge \frac{m{V}^2}{r}$

$⟹mg\frac{\sin \theta }{\cos \theta }\ge \frac{m{V}^2}{r}$

$⟹g\tan \theta \ge \frac{V^2}{r}$

$⟹\tan \theta \ge \frac{V^2}{rg}$

$⟹\tan {\theta }_{max}=\frac{V^2}{rg}$

Velocity, $V=18$ $km/h$

$⟹V=\frac{18\times {10}^3}{3600}$

$⟹V=5$ $m/s$

$r=10$ $m$,

$⟹\tan \theta =\frac{25}{100}$

$⟹\tan \theta =0.25$

$⟹\theta ={\tan }^{-1}0.25$

$⟹\theta ={14}^o$