# Phone book friction!

by Rhods
Tags: book, friction, phone
 P: 9 Hello All, A very interesting and entertaining video that you may have spotted recently floating around the web: http://www.youtube.com/watch?v=6sIB2kL-BWc What I am wondering is, how on earth is such a massive resistance force developed? I have a few (basic) ideas: 1. The large surface area of the inter-connected leaves of paper result in a very high coefficient of friction (relative to paper-paper COF). However, surface area is considered independent of friction resistance by Coulomb/Dry Friction, therefore, are there other 'forces' at play? 2. Very efficient load transfer through the materials:- Due to the tension force in the books, the overlapping sheets are squeezed together and by F=(Mu)R, R can be large thus F can be large. 3. A combination of the above. To your agglomerated wisdom, I ask, "What's going on?"
 Mentor P: 22,007 It's #1. And surface area isn't independent of friction coefficient, it is incorporated into it (thus the lack of a separate term for it).
 P: 15,325 Astonishing.
P: 691

## Phone book friction!

It's astonishing but understandable. Each sheet can exert a small force, and there are about 400 pages. In addition, the more you pull, the more the perpendicular forces between the pages.
 P: 235 This is actually kinda cool. After seeing the video i gave it a go myself =). I held one side and my dad the other... we couldnt pull it apart. I would never have even thought of the scenario.
 P: 816 That video is so cool, and the people in it are crazy with all their guitar solo noises at the beginning. It is the fact that the sheets are so numerous. I would agree with 1.
 P: 249 [QUOTE=Rhods;1613006] If you were to increase the force as you increased the area to keep PRESSURE the same, then increasing the area WOULD increase the frictional force between the two surfaces. Is the inter-woven phone book 'system' agreeing with the rule stated in the last sentence? QUOTE] If many pages of a book are inter-woven then the force on each page always equals the weight of all the upper pages (order of magnitude m*g). So in this experiment area is increased without decreasing pressure. We can calculate the force needed to separate two books using the formula for friction force: F=mu*Fn (mu is coefficient of friction, Fn is normal force between surfaces) Average force Fn acting on a page is: Fn=m*g/2 (half of book's weight) Since there are N pages, the maximum friction force is: F=N*mu*m*g/2 If m=1 kg, N=1000 and k=1 then: F=5000 N
 P: 363 This is how I think the phone book works Dang, I cant figure out how to post the iamge directly in my post, I used the command " " in rectengular brackets, in the past but it isnt working now
 P: 9 I have to say, I am flabbergasted by the response I have had here this far and wish to thank you all. Like all the best answers, Lojzek's is brilliantly simple (aka embarrassingly obvious), well done for lifting the fog that shrouded this myth.
Mentor
P: 22,007
 Quote by Rhods [I]Although a larger area of contact between two surfaces would create a larger source of frictional forces, it also reduces the pressure between the two surfaces for a given force holding them together.
Why would it do that?

Anyway, I think Lojzek's and Oerg's (your #2) explanations also contribute here. And there may be other forces at work as well, such as air pressure (which is the reason why the first time you open a book, it requires a little extra effort).
P: 2,751
In relation to this interleaved phone book the normal force is applied to all the pages in series instead of in parallel. In the case of friction at single interface then it's true that increasing the surface area doesn't generally help much, as force is spread over a larger area "in parallel" and, as a previous poster said, the reduction in pressure counteracts the increase in area. In this phone book case however the area is increased by interleaving many friction surfaces so that the force is applied in series to all the surfaces without the corresponding decrease in pressure. Just calculate the force per page from the formula "F = coefficient of friction x normal force" and then multiply this times the number of pages.

The video was very poor in explaining the importance of the normal (that is, the transverse compression) force here. One of the video creators "Tim" responds to a question on Utube where the strength of the tape bonding that they used to hold the two books tight is discussed. He says something along the lines of "yes we did use a layer of tape but it's strength would have been negligible compared to the overall forces the books withstood". Yes this is true but it fails to make any mention of the critical function of this binding tape in proving the normal force without which the two books could easily have been pulled apart. Exactly how much normal force was applied to compress the interleaved pages is unfortunately a total unknown in this experiment, it's seems to have been completely overlooked and not even mention by the videos creators.
Mentor
P: 22,007
 Quote by Oerg This is how I think the phone book works Dang, I cant figure out how to post the iamge directly in my post, I used the command " " in rectengular brackets, in the past but it isnt working now
Viable, but there is a little error in there - tension is constant along a string, so there is only one tension force F. The fact that both people are pulling with a force of F doesn't make for a "total tension" of 2F.
Mentor
P: 22,007
 Quote by uart The video was very poor in explaining the importance of the normal (that is, the transverse compression) force here. One of the video creators "Tim" responds to a question on Utube where the strength of the tape bonding that they used to hold the two books tight is discussed. He says something along the lines of "yes we did use a layer of tape but it's strength would have been negligible compared to the overall forces the books withstood". Yes this is true but it fails to make any mention of the critical function of this binding tape in proving the normal force without which the two books could easily have been pulled apart. Exactly how much normal force was applied to compress the interleaved pages is unfortunately a total unknown in this experiment, it's seems to have been completely overlooked and not even mention by the videos creators.
Huh, didn't notice that - yes, that's a pretty big cheat.
P: 363
 Quote by russ_watters Viable, but there is a little error in there - tension is constant along a string, so there is only one tension force F. The fact that both people are pulling with a force of F doesn't make for a "total tension" of 2F.
oops haha, and I also reliazed that i failed to take into consideration the weight of the book. Maybe if done in space and a slight correction to the tension my solution would work.
P: 9
 Quote by russ_watters Why would it do that? Anyway, I think Lojzek's and Oerg's (your #2) explanations also contribute here. And there may be other forces at work as well, such as air pressure (which is the reason why the first time you open a book, it requires a little extra effort).
Originally quoted as:

"Although a larger area of contact between two surfaces would create a larger source of frictional forces, it also reduces the pressure between the two surfaces for a given force holding them together."

Written more clearly:

"Although a larger area of contact between two surfaces would create a larger source for frictional forces, it also reduces the pressure between the two surfaces for a given force holding them together."

As in Picture - both objects have equal friction force.

It is certainly a complex situation but i do enjoy the simplicity of Lojzek's answer.