# Unlock the Secret of Phone Book Friction

• Rhods
In summary: 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 couldn't pull it apart. I would never have even thought of the scenario.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.
Rhods
Hello All,

A very interesting and entertaining video that you may have spotted recently floating around the web:

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.

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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).

Astonishing.

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.

Thank you for all your great posts, but I think we’re yet to get to the bottom of this!

In relation to Russ' comment:
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. Since pressure equals force divided by the area of contact, it works out that the increase in friction generating area is exactly offset by the reduction in pressure; the resulting frictional forces, then, are dependent only on the frictional coefficient of the materials and the FORCE holding them together.

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? Maybe, due to the phone book’s construction, gradually more leaves come into action as the loading on the phone books is increased? What makes this system special?

I guess it illustrates how important it is to consider the coefficient of friction as a system property and not solely as a material property. Also don't fix your phone your phone books together.

I do wonder what the comparative result would be if, rather than using two phone books of leaf contact areas A1 and A2, two paper sheets were used with contact areas equal to A1, A2 respectively.

Again, thank you for your interest and insight.

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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 couldn't pull it apart. I would never have even thought of the scenario.

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.

Rhods said:
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

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 http://www.youtube.com/watch?v=8BbUhlIEZEY" (aka embarrassingly obvious), well done for lifting the fog that shrouded this myth.

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Rhods said:
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).

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Rhods said:
Thank you for all your great posts, but I think we’re yet to get to the bottom of this!

In relation to Russ' comment:
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. Since pressure equals force divided by the area of contact, it works out that the increase in friction generating area is exactly offset by the reduction in pressure; the resulting frictional forces, then, are dependent only on the frictional coefficient of the materials and the FORCE holding them together.

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? Maybe, due to the phone book’s construction, gradually more leaves come into action as the loading on the phone books is increased? What makes this system special?

I guess it illustrates how important it is to consider the coefficient of friction as a system property and not solely as a material property. Also don't fix your phone your phone books together.

I do wonder what the comparative result would be if, rather than using two phone books of leaf contact areas A1 and A2, two paper sheets were used with contact areas equal to A1, A2 respectively.

Again, thank you for your interest and insight.
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.

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uart said:
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.

russ_watters said:
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.

russ_watters said:
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 http://www.theshortspan.com/photo/friction/brick.png" - both objects have equal friction force.

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

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russ_watters said:
Huh, didn't notice that - yes, that's a pretty big cheat.

Yeah here's the actual dialog.

mjsbuddha (3 days ago)
well at least the top and bottom cover had to be glued or tapped together somehow to keep the whole thing from unweaving when it came off the floor. no telling how much strength gluing together the thicker cover sheets adds.

Timacious (3 days ago)
You are right. We used an inch of tape to prevent it from unraveling. This adds of course nothing to the total strength.

I don't know exactly how this tape was applied but I suspect that they did "cheat" here by using it to provide a compressive force.

I think the tape was there to stop the pages from 'flapping around' and unravelling themselves as suggested by mjsbuddha, not to supply a compressive force - at least not a greatly influencing one (c'mon are you serious, parcel tape, 600kg...I smell a mythbusting opportunity!). Are you questioning the honesty of (the lovely) Tim and Steven?!

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Actually I am somewhat confused by Rhod's posts on pressure. The friction is dependent on the normal force and the frictional coefficient. It doest matter how big or small your area is... right?

Intersting...

Because the size of the contact area is very important in car tires as the traction is dynamic rather than static; that is, it changes as the tire rolls along. The maximum coefficient of friction can occur anywhere in the contact area, so that the greater the area, the greater the likelihood of maximum traction. Thus, under identical load and on the same dry surface, the wider tire has a greater contact area and develops higher traction,
resulting in greater stopping ability.

From the http://www.hometheaterforum.com/htf/after-hours-lounge/143245-friction-formula.html" of course.

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Rhods said:
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 http://www.theshortspan.com/photo/friction/brick.png" - both objects have equal friction force.

It is certainly a complex situation but i do enjoy the simplicity of Lojzek's answer.
The situation shown in your diagram is not the situation in the telephone books. The surfaces are stacked on each other, not next to each other. As someone else aptly put it, they are in series, not in parallel. In other words, if you place a 100lb weight on a piece of paper, the force on each surface is 100lb. If you stack 10 pieces of paper, you still have 100lb and 10x the area.

The last handful of posts neglect this concept (ie, the car tires thing is also the wrong situation) - I thought we had it before.

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Yes, I understand that, I was using the diagram to illustrate the sentence quoted in the same post, apologies for the confusion.

the frictional force and the frictional coefficient are independent of area. I read with interest the part on "the greater the area, the greater the likelihood of max. traction".'

EDIT:

The magnitude of the frictional force was found to be proportionate to the magnitude of the normal force. The constant of proportionality differs from material to material. But they both do not depend on the surface area of contact.

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Rhods said:
I think the tape was there to stop the pages from 'flapping around' and unravelling themselves as suggested by mjsbuddha, not to supply a compressive force - at least not a greatly influencing one (c'mon are you serious, parcel tape, 600kg?!
Yes, I am suggesting that! All it takes is 2 kg of force from the tape, multiplied by 600 surfaces of contact and a friction coefficient of .5.

With such a multiplier, even the weight of the paper and how much the spine has been broken in are significant factors.

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Very true, if the tape were not apparent, I suppose the pages would be held together by a suction force between the pages and possibly by the weight of the sheets themselves, depending on the phone book's orientation during testing. It would be interesting to know what the transverse force is provided the tape is not present. Over the 2kg you suggest?

If there are such forces present without tape, then in defence of the video, the tape could have been used to simply stop the sheets from falling away from the book as would naturally happen if you were to pick a book up by its spine and throw it around in a similar manner to what it was during the experiments in the video.

It's common knowledge in motorcycles and race cars that multi-plate clutches can handle more torque than single plate clutches. As posted early on, the normal force is the same for each pair of friction surfaces, and not divided as it would be with just single surface with the same total area as multiple plates. The electrical analogy would be parallel circuit as opposed to series circuit.

Formula 1 cars use very small (< 4 inch diameter) multi plate clutches to handle the 800hp (formerly 950hp for the 3 liter V10's). Most motorcycles use wet multi-plate clutches as well.

Again as posted early on, the friction factor is multiplied by the number of friction surfaces in a clutch, given the same normal force.

Well, I think I've finally got it! Thank you all for your input (and patience!).

In case anyone is interested - because you never know - I have compiled a two page report discussing this topic. It's attached as a PDF (and editable word version), entitled with probably one of the most cheesy physics puns of all time. I hope you guys don't mind me doing this.

#### Attachments

• Edit my friction.doc
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• Inseparable phone books, science fact or science friction.pdf
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Jeff Reid said:
It's common knowledge in motorcycles and race cars that multi-plate clutches can handle more torque than single plate clutches. As posted early on, the normal force is the same for each pair of friction surfaces, and not divided as it would be with just single surface with the same total area as multiple plates. The electrical analogy would be parallel circuit as opposed to series circuit.

Formula 1 cars use very small (< 4 inch diameter) multi plate clutches to handle the 800hp (formerly 950hp for the 3 liter V10's). Most motorcycles use wet multi-plate clutches as well.

Again as posted early on, the friction factor is multiplied by the number of friction surfaces in a clutch, given the same normal force.

Hi Jeff

I still dun understand. Why is the normal force not divided for every friction plate since there are multiple point of contacts?

I thought that in the phone book example, the normal foce acts through multiple surface areas, so the total normal force through all the surface areas = N x Normal force

This result still does not contradict frictional force and the frictional coefficient do not depend on the surface are of contact.

Oerg said:
mult-plate clutch, normal force is same for all
I still don't understand. Why is the normal force not divided for every friction plate since there are multiple point of contacts?
It's just like any object under compression. The compression force is the same throughout the object, and any sub-component of the object. It's similar to a series of springs linked together, the compression force is the same for all springs in a series.

I wonder what would happen if the phone books were saturated with water... if you get sheets of paper wet it makes them easier to tear but you have to peel them apart because they stick together. So would the phone books be easy to separate because the material strength is reduced or harder to separate because the friction / adhesion is increased?

CaptainQuasar said:
I wonder what would happen if the phone books were saturated with water... if you get sheets of paper wet it makes them easier to tear but you have to peel them apart because they stick together. So would the phone books be easy to separate because the material strength is reduced or harder to separate because the friction / adhesion is increased?

The friction force is so strong that the margins are torn apart even when the books are dry. If you wet the books, the paper material is weaker, and the friction force is probably enhanced, so it's easier to break the book's binding.

I think there is an aspect of this which no one has mentioned so far: there is a self-tightening effect as you pull harder on the phone books. If each phone book is 500 pages, then when you interleave them you are putting 1000 pages on top of each other: so they must be flayed outwards. When you pull on the phone books, the pages want to straighten out to be in the direction of the force. This introduces a normal force which increases the harder you pull on it.

Marty

μ = 1
Rav = |Wav| = 0.5 * (1 + 1)kg * 9.81m/s2 = 9.81N
N = Number of Contact Surfaces = Number of Sheets - 1 = (500 + 500) – 1 = 999
F = 999 * 1 * 9.81N = 9800.2N

I have a question regarding this, in the Bolded part, what does the 0.5* indicate? I'm not clever enough to deduce this :)

monish said:
I think there is an aspect of this which no one has mentioned so far: there is a self-tightening effect as you pull harder on the phone books. If each phone book is 500 pages, then when you interleave them you are putting 1000 pages on top of each other: so they must be flayed outwards. When you pull on the phone books, the pages want to straighten out to be in the direction of the force. This introduces a normal force which increases the harder you pull on it.

Marty

I would agree with that. Sounds reasonable anyway.

Are there methods to increase the resistance of the whole setup? I'm setting up my own 'phone book friction' each book consisting of ~500 pages. Now I understand that this can support about ~8000Lbs of force, now I'm wondering are there anything better than a phone book? Books with metallic pages, books with thinner pages? Would they work or rip easily?

Hi, new member here. The Mythbusters phone book video and question was just circulated around a physics teacher listserve. We've had fun with it locally.

In an effort to make a small version I shuffled together two small Post-It pads of 100 sheets. As I shuffled more pages together it felt like there is a critical number of pages to really get the thing to hold tight. The sticky parts of the pages are not touching, they serve as the "spine" of the "book". My students played around with it and finally got it to hold a 135 lb person before the connecting strings broke. One student re-engineered the connections and made them stronger. Now it can easily hold a 200 lb person hanging on it.

I made up a simple model to analyze the forces and got a maximum total static frictional force of

P*(u/3)*(a/b)*M^2

where P is the applied pulling force, u is the coefficient of static friction between the pages, a is the thickness of the pages, b is the distance from where the force is applied on one end to where the pages begin to overlap and M is the total number of pages. The coefficient of 1/3 is fuzzy because it depends on how well you can align the whole thing and distribute the pull among all the pages.

The model concentrates on describing the squeezing in of the pages as you pull on the ends. It does not include atmospheric pressure effects, which can only help the thing hold (if they do anything). The max static friction is proportional to P and the *square* of M.

Using some rough numbers for the Post-It note version, the maximum static friction is predicted to be greater than the applied force if you use more than about 60 pages. This is mostly a worst case scenario. According to this model, the pages will not slide apart in the expected manner no matter how hard you pull! However, that does not prevent the pages from ripping, strings from breaking or connecting devices from failing.

Sincerely.

Thanks for the amazing work, jbconguero! What amazes me most is actually not the friction between the pages, but that connection between the actual spine of the book and the rig won't rip apart when pulled with such strong forces.. On Mythbusters there were two cars pulling on the phone books, but the spine held up easily.. that's just amazing!

P.S I find that Magazines provides stronger resistance than thinner phone book pages. I did it with two Cleo mags (about 130 pages), and I simply can't get them to budge now. lol

## 1. What is the secret behind phone book friction?

The secret behind phone book friction is the interlocking of the pages due to the rough texture of the paper. This creates a high coefficient of friction, making it difficult to separate the pages.

## 2. How can I easily separate the pages of a phone book?

One way to easily separate the pages of a phone book is to fan the pages back and forth, creating air pockets between the pages. This reduces the friction and makes it easier to flip through the pages.

## 3. Why do phone books have rough paper?

Phone books have rough paper to increase the coefficient of friction between the pages, making it easier to flip through the pages and preventing them from slipping out of order.

## 4. Can the secret of phone book friction be applied to other materials?

Yes, the concept of interlocking and high coefficient of friction can be applied to other materials such as sandpaper, Velcro, and certain types of fabrics.

## 5. How does the secret of phone book friction relate to everyday life?

The secret of phone book friction can be seen in everyday life in various situations, such as separating sticky notes, flipping through a deck of cards, or even walking on a rough surface. Understanding this concept can help us find easier ways to perform these tasks.

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