Phone Book Friction
I am attempting to do a Grade 12 physics project and chose
the topic of Phone book Friction as shown in an episode of
MythBusters. The situation is that the pages of 2 phone books are
interwoven and produces an almost inseparable book. The MythBusters
crew found that 8000 lbs of force was necessary to pull the books
apart. I am trying to find an answer as to why the phone books are
inseparable, focusing of course on friction. Could someone give me
an answer as to why this is? Preferably with some calculations to
back up the explanation.
I will give you the basis of an equation; you can work on the
calculation from it. But you will see that the force to separate
telephone books interlaced as you describe will be considerable.
A good empirical model for friction is that its magnitude is given by
Where (mu) is a dimensionless coefficient that is a property of the
surfaces in contact, and N is the "normal" force pushing them
together. In the case of your telephone books, the relevant
quantities would be a mu for phone book paper against phone book
paper, and the normal force would probably be best modeled as the
weight of phone book above the page. So each page would have a
different N, depending on what fraction of the phone books are on top of it.
That force (mu)N in particular is probably not very large. However,
there are many pages in a phone book, and each one has two
sides. So the force required to separate the phone books would not
be the frictional drag on one side of a page, but the SUM of the
drag forces on BOTH sides of ALL the pages of a book!
I believe you will see that for even small values of mu and N, the
friction force to overcome is quite large when a book has hundreds of pages!
Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
Click here to return to the Physics Archives
Update: June 2012