Circular MotionHardBloom L3
Question
For a curved track of radius R, banked at angle θ (Take v0 = $\sqrt{Rg\tan\theta}$ )
Options
A.a vehicle moving with a speed v0 is able to negotiate the curve without calling friction into play at all
B.a vehicle moving with any speed V > V0 is always able to negotiate the curve, with friction called into play
C.a vehicle moving with any speed V < V0 must have the force of friction into play
D.the minimum value of the angle of banking for a vehicle parked on the banked road can stay there without slipping, is given by θ = tan–1 µ0 (µ0 = coefficient of static friction)
Solution
For No friction & safely turn
$\frac{mv_{0}^{2}}{R}\cos\theta = mg\sin\theta$
$\boxed{v_{0} = \sqrt{Rg\tan\theta}}$
Vmin < V0 < Vmax
In Vmin & Vmax must be come into play for safely turn maximum value of angle of banking
$\boxed{\theta = \tan^{- 1}\mu_{0}}$
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