A block of mass m is placed on a vertical fixed circular track and then it is given velocity v along the track at position A on track. The coefficient of friction between the block and the track varie

Question

A block of mass m is placed on a vertical fixed circular track and then it is given velocity v along the track at position A on track. The coefficient of friction between the block and the track varies with the angle θ . If the block moves on track with constant speed then the coefficient of friction is

TestHub · Accepted Answer

Since the block is moving with a constant speed, at any instant its tangential acceleration is zero. Hence,

$f = m g s i n θ$

Also,

$N - m g c o s θ = \frac{m v^{2}}{R}$

$N = \frac{m v^{2}}{R} + m g \cos θ$

$f = μ N = μ \frac{m v^{2}}{R} + μ m g \cos θ$

$m g \sin θ = μ \frac{m v^{2}}{R} + μ m g \cos θ$

$\Rightarrow μ = \frac{s i n θ}{c o s θ + \frac{v^{2}}{R g}}$

Physics - W.E.P. Question with Solution | TestHub

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