Science


Is it possible to pull apart 2 interwoven phone books? Find out!

32 thoughts on “Inseparable phone books

  1. Completely blew me away. I figured the pages would simply “unlace” themselves. I know paper is stronger than steel when formed correctly, but I didn’t think there was enough cohesion between pages.

  2. Yeah it’s called friction. A couple of hundred pages of paper pressed up against a couple of hundred other pages of paper, you are talking a small football field of surface area.

  3. @ Dax – Umm, yeah its friction, but its not *that* much area. Certainly not a football field’s worth of surface area. Maybe 100 square metres total, depending on book size and number of pages, something of that order. Enough for lots of friction (see the video), but lets not make it seem like something its not. Unless you have some really big phonebooks or really small football fields in your area.

  4. Well, in my defense, both sides of the page are providing friction, so it’s the total area of all pieces of paper times 2. Maybe a small football field was a hyperbole, but if you do the math… (runs to google calc)

    8.5″ x 11″ (a standard piece of paper) = 93.5 square inches

    93.5 square inches x 500 pages = 46750 square inches

    46750 square inches x both sides of the page (x2) = 60.32246 m2

    60.32246 square meters = 649.305556 square feet

    That’s quite a lot of area for friction to prevent you from pulling them apart.

    And that is assuming only a 250 page phone book, around here it would be almost double that many pages.

  5. Wait a minute, isn’t the friction force essentially independent of the contact surface area? IIRC:

    F = μ * NF

    or

    Max friction force = (coefficient of (static, here) friction) * (normal force)

  6. That is indeed surprising. My hypothesis is that since these are thick phonebooks once they are woven together the middle is very thick, much thicker than the binding. So the force you exert trying to pull them apart is also attempting to close them. So the normal force is always proportional to force used to pull them apart. Meaning if the coefficient of friction is high enough there must be mechanical failure in the pages in order for them to be pulled apart. Or they cheated. Still interesting video.

  7. Regarding the force from friction being independent of surface area: that is based on the idea that increasing surface area decreases pressure (F/A). I’m not sure that applies here.

    If you stack (massless) pages underneath some weight, does doubling the number of pages decrease the normal force on each by a half? Or does each continue to experience the same force? I think it’s the latter.

    If each page continues to experience the same force as the number of pages increases, then each page provides the same frictional force, even as you add more pages. If so, doubling the pages would double the net frictional force, right?

  8. I’m pretty sure that approximation you learn in high school only really applies for perfectly ridged objects. (Like a steel wheel on a steel tabletop.)

    Something softer like rubber depends a lot on surface area.

    I’ll bet that a lot of the friction from paper comes from the individual fibers gripping each other, that would depend a lot on surface area.

  9. @Emrikol
    Unfortunately the only thing I have to go on is personal experience with high carbon steel being used (grinding, cutting, shearing, etc) against various other items. In my experience paper and wood products will dull a blade faster than when used on various other metals. I’ve whittled aluminum (and some soft steel) with less damage to a knife than when the same knife was used to cut paper. If you can find other references please let us know.

  10. Re: Friction independent of area.

    I guess it should be F = µP*A, and since P is weight/area, it’d get simplified to µ * W (actually the normal).

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