# Friction in stopping a book

Let us imagine we have a book on a table. We want to push the table in such a way such that the book doesn't move with the table,instead it falls down vertically(assuming there is friction on the surface between the book and the table).This is a real life scenario which is possible. But i don't get the logic behind this happening since i deduced that the book will also move horizontally.

Let us suppose we push the table with force $$F$$. Now,we consider the free body diagrams of the book and the table seperately. Here,the table is moving forward. So,to prevent relative motion,the table will apply frictional force $$f$$ on the book. And by Newton's third law,the book will also apply force $$f$$ on the table. But here in the $$+x$$ direction,the frictional force $$f$$ is working on the block. So,won't the book always accelerate,hence move in the $$+x$$ direction? One answer i thought of that if $$f$$ is less than limiting friction,then the book wouldn't move. If we apply a force on any object less than the limiting friction, then a frictional force equal to the applied force acts in the opposite direction to nullify the applied force. But here the friction itself is being applied on the book and there is no force to act in the opposite direction to nullify this frictional force $$f$$. But such scenarios of the book falling vertically down are possible in real life. So,i want to know where i am making the mistake.