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Firstly, let's address the net force acting on the man standing on the conveyor belt. When the belt is accelerating, two forces come into play: the force of friction between the belt and the man's shoes, and the man's weight.
Net Force on the Man: The net force is given by Newton's second law: Fnet=m⋅aFnet=m⋅a, where mm is the mass of the man and aa is the acceleration of the belt. In this case, the mass of the man is given as 65 kg and the acceleration of the belt is 1 m/s².
So, Fnet=(65 kg)×(1 m/s2)=65 NFnet=(65kg)×(1m/s2)=65N.
Coefficient of Static Friction: The maximum frictional force that can exist between the man's shoes and the belt is determined by the coefficient of static friction, μsμs, and the normal force. The normal force in this case is equal to the man's weight, which is mgmg, where gg is the acceleration due to gravity (approximately 9.8 m/s29.8m/s2).
The maximum static frictional force, Ffriction, maxFfriction, max, is given by μs×Normal Forceμs×Normal Force.
So, Ffriction, max=μs×m×g=0.2×65×9.8=127.4 NFfriction, max=μs×m×g=0.2×65×9.8=127.4N.
To keep the man stationary relative to the belt, the force of static friction must balance the net force on the man. So, the maximum acceleration of the belt at which the man can remain stationary is the acceleration at which the force of friction equals the net force.
Ffriction, max=FnetFfriction, max=Fnet
⇒127.4 N=65 N⇒127.4N=65N
Therefore, the maximum acceleration of the belt that the man can withstand while remaining stationary relative to the belt is 1 m/s21m/s2. Beyond this acceleration, the man will start sliding on the belt due to the inability of static friction to counteract the increasing net force.
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