The TV show Mythbusters had an episode in which they interleaved two phone books and dramatized how hard it was to pull them apart. (A long time ago, a phone book was a book that had an index of phone numbers for everyone in your city. The trick apparently also works pretty well with reasonably thick magazines.) They ended up needing two tanks to pull the phone books apart against the resistance of friction:
http://www.youtube.com/watch?v=AX_lCOjLCTo
http://www.youtube.com/watch?v=QMW_uYWwHWQ
When one of my students described this in class, it strongly violated my carefully cultivated intuition about friction, and I thought maybe the student was getting the description wrong. Actually it seems right.
Why does this work? I found the following online discussion from 2008, the same year in which the episode aired:
http://www.physicsforums.com/showthread.php?t=215857
Posts 8, 27, and 36 seem the most relevant. 36 quotes the result of a calculation, without saying what the calculation was.
Can anyone give a good analysis?
Best Answer
A year has passed since this question was posed, and as luck would have it, this week a paper appeared on the science preprint repository ArXiv discussing exactly this phenomena. The preprint (PDF) is available here.
Key to the phenomenon of spectacular friction forces between two interleaved phone books is a simple geometrical conversion of the traction force to an orthogonal component which enhances the load and thus the friction. This geometrical conversion (i.e. the huge self-created friction) is a direct consequence of the non-zero angles that the sheets make as they approach the contact region. Due to the stacking of the sheets in the contact region, the normal forces due to the geometric conversion cumulate towards the inner sheets, which results in the friction force between the interleaved books to depend exponentially on the number of sheets involved.
The fact that the anomalous geometrical amplification of friction results solely from the slopes that the sheets make as they approach the contact area, can easily be verified. As the authors state: one can realize an interleaved-book system with non-sloping sheets by removing alternating sheets in two notepads. In such a case, the books can be easily pulled apart.