Question

Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with $1m{s}^{-2}$. 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 $=65kg$)

Answer 1

When man is stationary w.r.t. conveyor belt, his net acceleration = acceleration of conveyor $=1m/s^2$

Hence, net force by newton's second law $=ma=65\times 1m/s^2=65N$

This net force is provided by the friction between the conveyor belt and the man.

Maximum static friction $=\mu N$

Beyond this, man will move relative to the belt as per psuedo force.

At max static friction $\mu N=m{a}_{max}$

$a_{max}=\mu g=0.2\times 10=2m/s^2$