Question

A circular road of radius 50 m has the angle of banking equal to 30°. At what speed should a vehicle go on this road so that the friction is not used?

Answer 1

Given:
Angle of banking = θ = 30°
Radius = r = 50 m
Assume that the vehicle travels on this road at speed v so that the friction is not used.
We get:
$$\begin{gathered} \tan \theta =\frac{v^2}{rg} \\ \Rightarrow \tan 30°=\frac{v^2}{rg} \\ \Rightarrow \frac{1}{\sqrt{3}}=\frac{v^2}{rg} \\ \Rightarrow v^2=\frac{rg}{\sqrt{3}}=\frac{50\times 10}{\sqrt{3}} \\ \Rightarrow v=\sqrt{\frac{500}{\sqrt{3}}}=17\mathrm{m}/\mathrm{s} \end{gathered}$$