Question

A man of mass $m$ is applying a horizontal force in order to slide a box of mass ${m}'$ on a rough horizontal surface. It has been given that the man is not sliding. Let us assume that the coefficient of friction between the shoes of the man and the floor is $\mu$ and between the box and the floor is ${\mu }'$. What can be the conditions when it is certainly not possible to slide the box?

Answer 1

The maximum frictional force will be found by taking the product of the coefficient of friction, mass of the body and acceleration due to gravity. Find the relation between these forces by comparing the masses of the bodies and the coefficient of friction. This will help you in answering this question.

Complete step by step answer:
As we can see that it will not be possible in order to slide the box when the maximum frictional force that will be experienced on the box will be higher than the maximum frictional force that will be experienced on the man.
The maximum frictional force that will be experienced on the man can be written as,
${{f}_{m}}=\mu mg$
Where $\mu$ be the coefficient of friction, $m$ be the mass of the man and $g$ be the acceleration due to gravity.
The maximum force of friction that will be experienced on the box can be written as,
${{f}_{b}}={\mu }'{m}'g$
Where ${\mu }'$ be the coefficient of friction there and ${m}'$ be the mass of the box.
If the coefficient of friction of the box will be greater than the coefficient of friction of man. That is,
$\mu <{\mu }'$
And also the mass of the man be greater than the mass of the box,
$m<{m}'$
Hence the force of friction will be having the relation given as,
${{f}_{m}}<{{f}_{b}}$
Hence the answer has been calculated.

Note: Static friction is defined as the force that is experienced on a body at rest. Only after overcoming this static frictional force, the body can start moving the body. When the body starts to move, the friction will be acting which is given as kinetic frictional force.