Question

Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with $1m{s}^{-2}.$ If the coefficient of static friction between the man's shoes and the belt is $0.2$, upto what acceleration of the belt can the man continue to be stationary relative to the belt? Mass of the man $=65$ kg. $(g=9.8$ m/s${}^2$)

• A. $1.96m{s}^{-2}$
• B. $0.98m{s}^{-2}$
• C. $9.8m{s}^{-2}$
• D. $19.6m{s}^{-2}$

Answer 1

The correct option is A $1.96m{s}^{-2}$

As the man is standing stationary w.r.t the belt,
$\therefore$ Acceleration of the man = Acceleration of the belt $=a=1m{s}^{-2}$
Mass of the man, $m=65kg$
Net force on the man $=ma=65\times 1=65N$
Given coefficient of friction, $\mu =0.2$
$\therefore$ Limiting friction, $f_L=\mu mg$
If the man remains stationary with respect to the maximum acceleration $a_0$ of the belt, then
$m{a}_0=f_L=\mu mg$
$\therefore a_0=\mu g=0.2\times 9.8=1.96m{s}^{-2}$