1. The problem statement, all variables and given/known data 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'##. In which of the following cases it is certainly not possible to slide the box? A) μ>μ', m<m' B) μ<μ', m<m' C) μ<μ', m>m' D) μ>μ', m>m' 2. Relevant equations 3. The attempt at a solution If man applies a force F on box, due to Newton's third law, he also experiences a force F in the opposite direction. According to the question, F<=μmg and F<=μ'm'g. Also, since it is given that man does not slide, F has to be less than or equal to μmg. The box can slide if μ'm'g<F<μmg. The block never slides if μmg<μ'm'g. But I don't see how to find relation between the coefficient of friction and masses by considering the above inequalities. Any help is appreciated. Thanks!