Friction and Newton's Laws 
The below figure shows a tower built by placing many rough books one on another. The coefficient of friction between each book is $\mu$.

What is the minimum force required to pull the $n$-th book from the top a little bit out while keeping all other books non-moving?

I know that this can be done practically. But when thinking with a piece of paper and a pencil a doubt comes to my mind. When we pull the mentioned book out, as a result of relative motion, friction is felt by both upper part and lower part of the tower (below and above the $n$-th block) as well as the $n$-th book. When considering only upper part for ease there is a net force on that part that can cause acceleration to the direction that we pull the below book. So why is that part not moving (according to the question and also practically)? How can I proceed?
 A: What the question is hinting to is differentiating between static and kinetic friction.

*

*If you pull with a low force (slowly), static friction keeps its hold and thus the books on top will follow along.


*If you pull with a large force (fast), you might exceed the static-friction limit and thus reach a state of kinetic friction instead. Sure, the books on top will still feel this kinetic friction and will still be pulled sideways a bit. But it might not be much - if you pull very fast, it might be unnoticable.
I would therefor think that the question is asking for how small the force can be in order to rip the book free from static friction. For that we have a static-friction formula (or inequality) that might be useful.
A: When thinking about friction forces, the first thing to do is to try to establish what the forces normal to the frictional surfaces (which are independent of friction) will be. If you can do that, you should find a way to express the friction forces in terms of these normal forces. Thus,

*

*Can you identify the frictional surfaces in your problem?

*Can you write an equation for the normal force acting between the surfaces involved?

*Can you then derive the frictional force that will develop under the assumption that the book is being extracted?

