There is a pack of $N \gg 1$ identical sheets of papers lying on an infinite horizontal table. The coefficient of friction between the surface of the table, and between two sheets of paper are both equal to $\mu$. Each sheet has dimensions $L \times W$, with $L>W$. Sandra is trying to fetch the bottom-most sheet by pulling from a shorter edge of it with a constant velocity $u$ (while all the sheets lie almost exactly on top of each other, she managed to get hold of an edge of the bottommost sheet).

i  ^2.00 Sketch a qualitative graph of how the acceleration $a$ of the pack (excluding the bottom-most sheet) depends on time when (a) the speed $u$ is very small, (b) the speed $u$ is very big.

ii  ^3.00 What is the minimal speed $u_{\text {min}}$ by which it is possible to pull the bottommost sheet out (i.e. separating it completely from the remaining pack)?

iii  ^1.00 Assuming $u>u_{\text {min }}$, what is the speed of the remaining pack at the moment when the bottom-most sheet gets out of the pack (i.e. there is no longer overlapping areas)?

iv  ^2.00 Considering still $u>u_{\min }$, what is the minimal distance $l$ between the pack of papers and the edge of the table such that the pack would not slide over the edge of the table? ($l$ is the maximal allowed travel distance of the pack.)