FYKOS Year 28 Series 4 Problem 3 — unbreakable bond · FYKOS 28 #28.4.3
Physics · mechanics
Problem
Two notebooks of the type A460 we shall insert into each other so that a page of one is always followed by the page of another and we put them on a horizontal table. What is the work we have to do to seperate them if the lists act on each other only with their own weight? Assume that we pull only in the plane of the notebooks by the back of one of them and also assume that in the beginning the pages perfectly cover each other.Intuitive explanation
The key insight is that separating the notebooks requires overcoming friction between many interleaved pages, where each page pair contributes a normal force equal to the weight of all pages stacked above it. As you pull one notebook, you're not just fighting friction on one interface—you're fighting it on dozens of page interfaces simultaneously, with the friction force on each page depending on how much weight presses down on it. The work done equals the friction force integrated over the separation distance, which means calculating the total friction from all page pairs as they progressively disengage.
Intuitive explanation
The key insight is that separating the notebooks requires overcoming friction between many interleaved pages, where each page pair contributes a normal force equal to the weight of all pages stacked above it. As you pull one notebook, you're not just fighting friction on one interface—you're fighting it on dozens of page interfaces simultaneously, with the friction force on each page depending on how much weight presses down on it. The work done equals the friction force integrated over the separation distance, which means calculating the total friction from all page pairs as they progressively disengage.