# Researchers explain why it's nearly impossible to separate two interleaved phonebooks

(Phys.org)—Many people are familiar with the friction enigma of two interleaved phonebooks, in which all of the pages of two phonebooks are overlapped, one by one, with the books' spines facing outward. Trying to separate the books by pulling on their spines is incredibly difficult due to the massive amount of friction between the pages. A Mythbusters episode showed that the interleaved phonebooks are strong enough to lift a car, and that nothing less than two military tanks can separate them (while tearing many of the pages).

According to a group of scientists who have studied this puzzle, many of the simple explanations of this demonstration are wrong. For instance, one explanation often given is that the weight of the pages pushing down on the pages below them is what generates the large friction force, but this explanation fails to explain why the demonstration works equally as well when carried out in the vertical or horizontal direction.

Now a team of researchers, Héctor Alarcón, et al., from France and Canada have developed a model that reveals how the amount of force required to pull the books apart depends on the number of pages, the page thickness, and the overlapping distance. These relationships were determined by performing dozens of carefully controlled experiments on a vertical pulling device.

This model confirms what has previously been suspected: the harder that a person, car, or tank pulls on the books, the higher the frictional resistance. The researchers compared this "self-induced friction amplification" effect to the Chinese finger trap toy: when you try to pull your finger out of the loosely wrapped braid, the braid tightens around your finger, making it even more difficult to get off.

"The extreme friction of the system is due to the operator," the researchers explained. "The person, car, truck, or tank will amplify the friction arising from a tiny force acting on the outermost pages of the stack that may be no more than the weight of a butterfly."

The scientists explain that this tiny force on the outermost pages originates from the paper's elasticity. The outer pages have a tendency to be flat, so they slightly resist being bowed, and bowing happens because twice as many pages must fit between the books' spines. This friction force starts off small, but the pulling amplifies it exponentially.

More evidence supporting this explanation comes from performing the experiment with two books in which every other page has been removed, so that interleaving results in completely flat . These books can be easily pulled apart.

Although the researchers did not specifically investigate methods to separate the phonebooks, their results may offer some insight into efficient separation methods.

"One way may be to blow some air from the sides while gently pulling them apart," coauthor Elie Raphaël at the École Supérieure de Physique et de Chimie Industrielles (ESPCI), Paris, told Phys.org.

The interleaved phonebook demonstration is important because it is just one example of many interleaved assemblies, and these are found in many diverse areas: surgical sutures, adhesive proteins, and the interactions between DNA and viruses all involve friction through interleaving sheets of some sort. Another more familiar example is the way that a sailor can tie a large ship to a dock post simply by wrapping a rope around the post several times. The friction between the loops of rope creates such a strong connection that no ship can pull it loose, and pulling only makes it tighter. The results may also have applications for controlling the in micro- and nano- scale mechanical devices.

More information: Héctor Alarcón, et al. "Self-amplification of solid friction in interleaved assemblies." Accepted for publication in Physical Review Letters.
Journal information: Physical Review Letters

Feedback to editors

Dec 09, 2015
I thought mythbusters already explained this. Its a combination of friction and leverage. The pages arent parallel anymore when interleaved. Since each page forms an angle, as you pull part of the vector of force tries to push each page back to their normal parallel position. As they try to move toward the center they push against each other and it increases friction. If you pull faster they push to the center faster and creates increasing friction.

Dec 09, 2015
Did anyone ever see if you could just ever so lightly pull them apart, like the solution to pulling your fingers out of a finger trap?

Dec 09, 2015
Did anyone ever see if you could just ever so lightly pull them apart, like the solution to pulling your fingers out of a finger trap?
LOL! Dude,you just fell for the Chinese Finger Trap! I can just see you - can't get those fingers out, eh? Keep trying, you might get it... (I doubt it)

Dec 09, 2015
I thought mythbusters already explained this.

If you want to get technical, Mythbusters made a conjecture.

The difference between a conjecture and an explaination is that the latter is backed up with further evidence - to see if it actually is so rather than being satisfied with what seems to be obvious. Actually, they observed a phenomenon and merely presented a guess of the most likely mechanism, which is where the inquiry ends.

Proper scientists would then insert the conjecture as a new hypothesis and set out to prove it - and that's a difference between Science with a capital S, or how it is presented on television, and science as in what the scientists are actually doing.

Adam Savage says that the only difference in science is writing it down - which is missing a whole bunch.

Dec 09, 2015
LOL - this is the same issue, as pulling a blanket or a dooner (quilt), sideways off a bed....

Pretty easy when you do it.

In very simple terms 5Kg of blanket - pulled sideways needs 10Kg of force.

But ADD in the surface friction, from the weight of ONE cat laying on the bed, which forces all the fibres to bind together, and causes an enormous rise in friction - so the covering, is HARD to pull off the bed.

Which changes to 5Kg of blanket PLUS 5 KG of cat - pulled sideways needs 30Kg of force.

Basically you have to kick the cat off the bed, so that you can pull the blanket / dooner off the bed..

I suggest introducing a travelling wave into the mix to enhance the cat removal. The cat won't appreciate it, but removing the blanket is the entire point.

Dec 13, 2015
They were able to find phone books?!

Dec 19, 2015
How large is the normal force as you approach the center of the interleaved books? Would it be large enough to be useful in "squishing" something left in the center?