Fone Book Phriction
Shuffle
two phone books together like a deck of cards. Have the 'stud' in the room
pull them apart. He/she can't. Even TWO people can't pull them apart. Why?
Each page in contact has the friction caused by the weight of the pages
above it pushing down. This allows for a tremendous amount of friction.
Two BIG guys at my NJSTA Convention Workshop couldn't pull them apart!
The books are virtually IMPOSSIBLE to pull apart. The books will actually tear
apart before separating. Here's why, sorta… Think of a single phone book
sitting on a table. It's Ff = mN where, in this case, N = W. This is the
minimum force required to make the book decide to move across the table. Now,
by “shuffling” the book's pages, assuming 500 pages, you have now multiplied
the Ff by 500, sorta. The top page has only its weight pushing down, the next
page (belonging to the other book) has the weight of page one on it. The 3rd
page has 2 pages pushing down on it. The 4th has 3, the 5th has 4, . . . So,
the bottom of the book is pressed with a force equal to the weight of the
portion of pages above it. Assume, again, the pages overlap by ½ their width so
that each book provides approximately ½ its weight to the force on the bottom
pages. Then, the weight on the bottom pages is
W = (1/2 W) (2 books) = W of one book, (duh!)
The normal force between a given pair of page surfaces is = the weight of the
pages above. This N varies from zero at the top to W at the bottom, so its
average between pages is ½ W. Thus, the maximum static friction force between a
pair of page surfaces is, on average,
Ff = msN = ½ ms W
There are 999 page surfaces in contact, since the top is just exposed to air,
so the total max Ff is
Ff = 999( ½ ms W) » 500 ms W
Thus, the friction is 500 times the friction between one book and the table.
That's lots, sorta.
This was found in the book “Physics Begins with an M”, John Jewett, Allyn &
Bacon Pub.
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