Question

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

• A. If the block is initially at rest, it will remain at rest and friction force will be about $7\text{N}$.
• B. If the block is initially moving, then it will continue its motion for forever if force applied is in direction of motion of the block.
• C. If the block is initially moving and direction of applied force is same as that of motion of block then block moves with an acceleration of $\frac{1}{3}{\text{m/s}}^2$ along its initial direction of motion.
• D. If the block is initially moving and direction of applied force is opposite to that of initial motion of block then block decelerates, comes to a stop and starts moving in the opposite direction.

Answer 1

Answer: (A), (B), (C)

If the block is initially moving and direction of applied force is same as that of motion of block then block moves with an acceleration of $\frac{1}{3}{\text{m/s}}^2$ along its initial direction of motion.

If the block is at rest, then the force applied has to be greater than the limiting frictional force for its motion to begin.
$f_L={\mu }_{s}mg=0.25\times 3g=7.5\text{N}$
So, $f_L$ is more than applied force
So, the friction is static in nature and its value would be equal to the applied force, i.e., $7\text{N}$.

If the body is initially moving, then the kinetic friction is present ($f_k={\mu }_{k}mg=6\text{N}$), acting opposite to the direction of motion. If the applied force is along direction of motion, then the situation would be as shown in figure.

As $F>f_k$, the block is accelerated with an acceleration of $a=\left[\frac{F-f_k}{m}\right]=\frac{1}{3}{\text{m/s}}^2$ and hence its speed is continuously increasing.

If the applied force is opposite to the direction of motion then the block is under deceleration of $a=-\left[\frac{F+f_k}{m}\right]=-\frac{13}{3}{\text{m/s}}^2$ and hence after some time the block stops and kinetic friction is replaced by static friction as applied force continues to act.
As $F<f_L$, the block remains at rest and the frictional force acquires the value equal to the applied force, i.e., friction is static in nature.