A boy of mass M exerts a horizontal force to slide a box of mass M' across a rough horizontal surface. The friction coefficient between the boy's shoes and the floor is , while that between the box and the floor is ' . Under which of the following conditions is it definitively impossible to slide the box?

Step-by-step solution

The maximum horizontal force the boy can exert without slipping backward is given by the limiting friction between his shoes and the floor, F_ max = M g . The minimum horizontal force required to slide the box is the limiting friction between the box and the floor, f_ max = ' M' g . For the boy to slide the box, he must be able to apply a force greater than the friction on the box without slipping himself. The condition to slide the box is F_ max > f_ max , which gives M g > ' M' g , or M > ' M' . It is definitivel