### explanation

```Man Power against Paper Friction
Chris Valdez
Lavelle Blackwater
Sarah Miller
Friction
 Do you believe that is is possible for one person to pull
two (Phoenix - Metro Area) phone books apart? Ten
people? Thirty people?
 For the above questions that answer is no, it takes a
greater amount of force to pull the two phone books
apart.
Friction In a Phone Book
For this phone book pull experiment the phone
book that was used was a Phoenix-Metro Area phone
book. This type of phone book has significantly more
pages than other phone books that can be used. In the
explanation of how much friction an individual phone
book can have there will also be another example (a
GCC course guide) with similar page types.
A phone book has both static and kinetic friction.
 Static friction: this is the force that is formed from the overlaying of each page on top of
each other. (The friction that must be broke to move the object from its resting point.)
 Kinetic friction: this is the force from the movement of the pages. (The force that opposes
the applied force to the motion of an object.)
Free-Body Diagram To Find Friction
Fy = FN - mgcos = 0
Fx = mgsinf = 0
mgsin - FN = 0
mgsin - mgcos = 0
 = tan
QuickTime™ and a
decompressor
are needed to see this picture.
Finding Static Friction s of Paper
 fs = smgcos
 Example (theoretical data used):
 Assume phone is 6 lbs and 600 pages.
 Mg /page is 0.010 lbs
mg = 0.01 lbs s = 0.53
= 35º
fs = 0.53*0.01 lbs*cos(35º) = 4.34 x 10-3 lbs on any page
Finding Kinetic Friction k of Paper
 fk = kmgcos
 Example (theoretical data used):
Assume phone is 6 lbs and 600 pages.
Mg /page is 0.010 lbs
mg = 0.01 lbs k = 0.47
= 25º
fk = 0.47*0.01 lbs*cos(25º) = 3.21 x 10-3 lbs on any page
Data of the Pages
 Mass of each page is approximately .21g or 2.1 x 10-4 kg.
 Weight of each page is approximately .002N or 2.0x10-3 N.
 Normal force equation of each individual page:
FN = (# of pages in phone book)*mg
 Force applied to each page:
F = (# of pages in phone book)*smg
Data of the Pages
Example:
Number of pages: 600
Weight of the Phone book: 6.00 lbs
Weight of one page: 0.01 lbs
FN = mg = 6.0 lbs on each page
fs = µSFN = 0.81*6.0 lbs on each page = 4.9 lbs
Total Friction = 4.9 lbs/page * 600pages = 2916 lbs
Need to Know



The force on each page of the phone book has the force of the
total weight of the book acting on it. Middle pages only feel
the force of one phone book. Pages on the outside of the
phone book feel more weight than that of the internal pages.
The force of friction is doubled because of the sandwiching of
each page.
When the phone books is then pulled the full force of gravity
acts on them.
Finding the Total Force of Friction
 Ff = smg
 Fft = 2Ff x npages
 µS = .81 Weight of book mg = 1.48 lbs
 Pulling the phone books apart
Fft = 2(smg) x 2npages
Fft = 2(0.81 x 1.48 lbs) x 2(591)
Fft = 2837 lbs
How Many People Does it Take to Pull
Two Phone Books Appart?
 The force to pull two phone books apart is 2837 lbs =12.6 kN.
 Maximum value of force a human can push with both hands, no other forces only
shoulders and arm strength, 254N = 57.0 lbs.
 Now we can conclude that…
Number of people = 2837 lbs/57.0 lbs = 49.5
So about 50 people can pull a phone book. The number of people will also very
depending on the number of pages the phone book has (creating more friction).
Works Cited

http://ffden-2.phys.uaf.edu/211_fall2004.web.dir/Jeff_Levison/Freebody%20diagram.htm

http://hereandthere.us/index.php/2012/phone-book-listings/

http://msis.jsc.nasa.gov/sections/section04.htm

http://www.concurringopinions.com/archives/2007/02/are_big_search.html

http://www.apartmenttherapy.com/death-becomes-the-phone-book-164109

http://www.alternative-energy-resources.net/friction_and_lubrication.html
```