Question

A tower has built by placing many rough books one on another(like a coin tower). The coefficient of friction between each book is μ. What is the minimum force required to pull out the n-th book from the top a little bit out while keeping all other books stationary(non-moving)?

Answer 1

The force of friction right below the coin of interest:

$$f_n=\mu nmg.$$

The force of friction on top of the n-th block caused by all blocks above:

$$f_{n-1}=\mu (n-1)mg.$$

The net force:

$$f=f_n+f_{n-1}=\mu mg(2n-1).$$