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A Party Trick : How to Lift a Car With Two Phonebooks

Take two phonebooks, interleave their pages and separate them by pulling on their spines. The accumulated friction between the pages is so high that even lifting a car by the interleaved phonebooks cannot pull them apart.

Contrary to the common explanation, the weight of the pages is not the source of this frictional resistance. Rather, researchers from France and Canada have shown that the extreme friction of the system is due to the operator. The person, car, truck, or tank will amplify the friction arising from even a tiny force acting on the outermost pages of the stack that may be no more than the weight of a butterfly (see Figure 1). The authors carried out systematic experiments on booklets and have developed a model which relates the force required to separate the booklets to a single parameter. The model is validated by experiments and provides a solution to the source of extreme friction in the phonebook enigma. The study of this complex network provides insight into friction, with connections to technologies related to micro- and nano- scale mechanical devices, but also to everyday examples such as mooring a ship and even a common toy known as the Chinese finger trap.

Figure 1. Left : vehicle lifted by two phonebooks. Right : zoom of the phonebooks Copyright : France 5 / 2P2L.

To solve this puzzle, the researchers inserted sheets of paper, placed them vertically in a tensile testing machine (Figure 2, left) and measured the force required to separate them depending on the number of pages, the paper thickness and the amount of overlap between the pages. Analysis of these experiments revealed that, contrary to what was expected, the strength of the assembly increases much faster than the number of pages : for example, in some cases, a tenfold increase of the number of sheets could increase the resistance by a factor of ten thousand !

A theoretical model was developed to explain the observations. Since the overlap region of the books is twice as thick as a single book, the pages are angled accordingly (Figure 2, right). This small angle, which increases from the middle pages towards the pages on the outside is crucial to the high friction observed. When pulled in the vertical orientation, part of the force is converted into a horizontal force that squeezes the pages and enhances the friction of all the pages. In short, by a purely geometrical effect, the more one pulls the greater the horizontal force and hence the friction is enhanced. The angle is crucial, because without it, there is no horizontal force and no friction. One can easily test this at home exactly as the authors did : take a bound note book and remove every second page and interleave the pages. Now the thickness at the spine is exactly the same as at the overlap region. The enhanced friction vanishes and one can easily separate the notebooks.

Figure 2. Left : Experimental device (tensile tester) used in the laboratory to measure the friction force. Right : Schematic of the interleaved pages.

Beyond the fun aspect to this famous effect, which has been the subject of TV programs (for example Mythbusters and "On n’est pas que des cobayes" on France 5), this new study has some potential applications. Using similar geometries it is possible to measure friction coefficients with very small normal forces and the study may help to understand the mechanical behavior of more complex interleaved systems such as textiles or biological systems. Future interests lie in the design of new biomimetic nanomaterials and devices.

Reference :

Self-Amplification of Solid Friction in Interleaved Assemblies
Héctor Alarcón, Thomas Salez, Christophe Poulard, Jean-Francis Bloch, Élie Raphaël, Kari Dalnoki-Veress, and Frédéric Restagno
Physical Review Letters 116, 015502 (2016).

Contact :

Frédéric Restagno

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