A car moves along a circular track of radius R banked at an angle of 30° to the horizontal. The coefficient of static friction between the wheels and the track is μ . The maximum speed with which the

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A car moves along a circular track of radius R banked at an angle of 30° to the horizontal. The coefficient of static friction between the wheels and the track is μ . The maximum speed with which the car can move without skidding out is :-

TestHub · Accepted Answer

When car is moving with maximum speed then friction (f) points inward $N cos 3 0^{\circ} = mg + f sin 3 0^{\circ}$ $N sin 3 0^{\circ} + f cos 3 0^{\circ} = \frac{mv ^{2}}{R}$ At maximum speed friction is also maximum $(f = μ N)$ $N cos 3 0^{\circ} = mg + μ N sin 3 0^{\circ}$ $N sin 3 0^{\circ} + μ N cos 3 0^{\circ} = \frac{mv ^{2}}{R}$ Solving these two equations we get $v = [Rg [\frac{3 μ + 1}{3 - μ}]]^{1/2}$

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