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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?
Solution
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 :
\[\tan\theta = \frac{\text{v}^2}{\text{rg}}\]
\[ \Rightarrow \tan 30^\circ = \frac{\text{v}^2}{\text{rg}}\]
\[ \Rightarrow \frac{1}{\sqrt{3}} =\frac{\text{v}^2}{\text{rg}}\]
\[ \Rightarrow \text{v}^2 = \frac{\text{rg}}{\sqrt{3}} = \frac{50 \times 10}{\sqrt{3}}\]
\[ \Rightarrow v = \sqrt{\frac{500}{\sqrt{3}}} = 17 \ \text{m/s}\]
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