Synopsis: The Strength of Interleaved Phonebooks Explained

A simple model borne out by experiments explains why it's so hard to separate a pair of phonebooks whose pages have been interleaved.  

A remarkable demonstration of the influence of friction involves a pair of phonebooks with their pages interleaved. The friction between the pages can be so great that a car can be suspended from such a phonebook pair. Now French researchers have performed experiments with smaller booklets and developed a mathematical model that explains why the friction can become so large.

Frédéric Restagno of the University of Paris-Sud and CNRS in Orsay, both in France, and his colleagues used a commercial apparatus to measure the force during the process of separating interleaved pairs of booklets with between 12 and 100 pages. The team developed a mathematical model and found that nearly all of the data lay on a predicted universal curve of force versus a single parameter that depended on the number of pages, their thickness, and the size of the overlap region.

The key to the effect is that the pages are not parallel as they fan out from the binding toward the overlap region, so that the book-separating force on each page is applied at a slight angle. Because of this angle, the separation force contributes to the “normal” force that is perpendicular to the pages. This small normal force resulting from pulling on each page contributes to the force on every page below, so the total normal force (and thus the friction) on a single inner page can be much larger than one might expect. The authors say their model may also help researchers understand complex intertwined systems such as textiles or muscle fibers.

See here a Q & A with the authors (in French), along with links to videos.

This research is published in Physical Review Letters.

–David Ehrenstein


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