Unlock the Secret of Phone Book Friction

[frobbe]

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 :)

 

[pallidin]

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.

 

[Zdenka]

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?

 

[jbconguero]

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.

 

[Zdenka]

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