Mystery of Why Interleaved Phone Books Can’t Be Pulled Apart Solved

June 3, 2016 | Joanne Kennell

Cards being shuffled
Photo credit: Traci Lawson/flickr (CC BY 2.0)

A phone book tug of war.

You may be interested to know that the task of pulling apart two humble phone books laying face up with their pages interleaved (like a shuffled deck of cards) is nearly impossible. Two cars can’t even pull them apart.

 It took 8,000 pounds of pressure from two military tanks to separate the phone books.

Physicists have known that the answer to this vexing problem must lie in friction forces, but exactly how these forces are generated has remained a mystery. Then, last year, a team of physicists from France and Canada studying tribology — the study of surfaces in relative motion — discovered that the shape of the phone books and the act of pulling the books apart is what produces the strong force.

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Previously, scientists assumed that the friction generated was proportional to the number of pages. However, the amount of friction generated by the number of pages in two phone books does not have nearly enough force to match what is happening in reality. In fact, the real force seems to rise exponentially with the number of pages. To compensate for the missing friction, scientists also included the effects of gravity and even air pressure pushing the pages together, but all failed to explain the puzzling phenomenon.

To solve the mystery, the research team built their own phone books with a specific number of pages and pages of a particular size, which were then precisely interleaved. Using the traction device to pull the books apart while measure the force needed, a mathematical model was finally put together, reported Business Insider.

It turns out the effect is quite simple. Since the pages of each book are separated by the interleaving, even though this separation is very slight, the pages end up “spreading out,” lying at a slight angle from the book’s spine. When the books are pulled away from each other, the pages want to “straighten out”, or move back closer together, and end up squeezing the interleaved pages from the other book, making it almost impossible to separate.

This effect is known as the geometrical amplification of friction, where friction forces are produced far beyond what is expected.

The authors note that understanding this material behavior can be useful for new micro- and nano-engineered materials, which are important in the medical industry, and even green technologies.

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