Question

Figure shows a man standing stationary with respect to a horizontal conveyor belt. If the coefficient of static friction between the man's shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg).

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Answer 1

Let's assume a is the maximum acceleration that the belt and man can have while moving together.

Friction will provide this acceleration. So for max acceleration we need maximum frictional force or ${\mu }_{s}N$

${\mu }_{s}N=ma$

${\mu }_{s}mg=ma$

$a=0.2\times 10=2m/s^2$

The man can have a maximum acceleration of $2m/s^2$ if the conveyer belt moves with the same acceleration then man is at rest with respect to belt.