Question

A block of mass m=1 Kg is at rest on a rough horizontal surface having coefficient of static friction ${\mu }_s=0.2$ and kinetic force ${\mu }_k=0.15$. Discuss the frictional force if a horizontal force F is applied on the block.

Sr. No.	Value of F
1.	1N
2.	2N
3.	2.5N

Answer 1

Assume no friction, the motion of the block will be in the direction of applied force. The friction opposes relative motion between two surfaces. The direction of friction will be opposite to relative motion, i.e., in leftward direction.
Now let us find the maximum friction force.
$f_{max}=f_{lim}={\mu }_{s}N=0.2\times 1\times 10=2N$
a. If F=1.0N
If the block is at rest friction acting on the block, f=F= 0.1N.
As $f<f_{lim}$, hence, friction will be of static nature and acceleration of the block will be zero.
b. If F= 0.2 N
Here the applied force equals limiting friction. The block is on the verge of slipping.
or $f=f_{lim}=2.0N$
c. If F=2.5N
Here the applied force is greater then the magnitude of the maximum nature of static friction. The nature of friction between the block and ground is of kinetic nature.
or $f=f_k={\mu }_{k}N=0.15\times 1\times 1.5N$