Question

The 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 $0.2$, upto what acceleration of the belt can the man continue to be stationary relative to the belt? Mass of the man $=65\text{kg}$. ($g=10{\text{m/s}}^2$)

• A. $10{\text{m/s}}^2$
• B. $5{\text{m/s}}^2$
• C. $4{\text{m/s}}^2$
• D. $2{\text{m/s}}^2$

Answer 1

The correct option is D $2{\text{m/s}}^2$

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 $a_0$ (say) of the belt, then
$m{a}_0=f_L=\mu mg$
$\therefore a_0=\mu g=0.2\times 10{\text{m/s}}^2=2{\text{m/s}}^2$