Figure shows a man standing stationary with respect . . .

Question : Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m/s². What is the net force on the man? 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]

Doubt by Krish

Solution : 

Mass of the man (m) = 65 kg
Coefficient of friction between the shoes of man and the belt (µ) = 0.2

Let a'=maximum acceleration of the man so that he remain stationary on the belt.

The man is standing stationary with respect to the conveyor belt. (Given)

Hence, the acceleration of the conveyor belt must be equal to the acceleration of the man = 1 m/s²

Net Force acting on the Man 

F=ma
F=65×1

F=65 N

Limiting friction (f)

f=µR

f=µmg

f=0.2×65×9.8
f=127.4 N

Maximum Force on the Man (F') will be equal to the maximum force of friction (f)
F'=f
ma'=127.4
65×a'=127.4
a'=127.4/65
a'=1.96 m/s²

Hence, up to acceleration of 1.96 m/s² the man will remain stationary on the conveyor belt.