Question

A man of mass m is applying a horizontal force to slide a box of mass m' on a rough horizontal surface. It is known that the man does not slide. The coefficient of friction between the shoes of the man and the floor is $\mu$ and between the box and the floor is ${\mu }^{\prime }$. In which of the following cases it is certainly not possible to slide the box?

Answer 1

It will not be possible to slide the box if the maximum frictional force that can act on the box is greater than the maximum frictional force that can act on the man.
$f_{max,man}=\mu mg$
$f_{max,box}={\mu }^{{}^{\prime }}{m}^{{}^{\prime }}g$
If $\mu <{\mu }^{{}^{\prime }}$ and $m<m^{{}^{\prime }}$, then $f_{max,man}<f_{max,box}$