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P 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? - Physics

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ConceptExamples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road)

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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Solution P 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? Concept: Examples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road).
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