A 3-kg block of wood is on a level surface where ${\mathrm{\mu }}_{\mathrm{s}}$ = 0.25 and ${\mathrm{\mu }}_{\mathrm{k}}$ = 0.2. A force of 7 N is being applied horizontally to the block. Mark the correct statement(s) regarding this situation.

If the block is at rest, then force applied has to be greater than limiting friction force for its motion to begin.

${\mathrm{f}}_{\mathrm{L}}={\mathrm{\mu }}_{\mathrm{s}}\mathrm{mg}=0.25\times 3\mathrm{g}=7.5\mathrm{N}<{\mathrm{F}}_{\text{applied }}$

So friction is static in nature and its value would be equal to applied force, i.e., 7 N. If the body is initially moving, then kinetic friction is present $\left({\mathrm{f}}_{\mathrm{k}}={\mathrm{\mu }}_{\mathrm{k}}\mathrm{mg}=6\mathrm{N}\right)$, acting opposite to direction of motion.

As $\mathrm{F}>{\mathrm{f}}_{\mathrm{k}}$ the block is accelerated with an acceleration of $\mathrm{a}=\left[\frac{\mathrm{F}-{\mathrm{f}}_{\mathrm{k}}}{\mathrm{m}}\right]=\frac{1}{3}{\mathrm{ms}}^{-2}$ and hence its speed is continuously increasing.

If applied force is opposite to direction of motion, then block is under deceleration of $\mathrm{a}=-\left[\frac{\mathrm{F}+{\mathrm{f}}_{\mathrm{k}}}{\mathrm{m}}\right]=-\frac{13}{3}{\mathrm{ms}}^{-2}$ and hence after some time block stops and kinetic friction vanishes but applied force continues to act.

But as $\mathrm{F}<{\mathrm{f}}_{\mathrm{L}},$, the block remains at rest and friction force acquires the value equal to applied force, i.e., friction is static in nature.