## Phone Book Friction

posted on 21 Dec 2013 by guy
last changed 23 Jun 2014

 4.333335 Average: 4.3 (6 votes) Select ratinghated itdidn't like itliked itreally liked itloved itCancel rating Your vote (click to rate)ages: 6 to 99 yrs budget: $0.00 to$0.00prep time: 15 to 60 min class time: 10 to 20 min It is possible to shuffle two phone books together in a way that they will withstand thousands of pounds of force to pull them apart. This lesson shows an example with discussion of the general principles.
required equipment: phone books
optional equipment: clamps (4), steel bar (thin)
subjects: Engineering, Physics
keywords: phone book, friction

Fig. 1: Two phone books shuffled together. Steel bars have been taped to each side of the spines in preparation for attaching clamps.

Fig. 2: Mad scientist hanging from a pair of shuffled phone books.

Take two phone books, each about 1 kg (about 1000 pages) and carefully shuffle the pages together, each page of one phone book alternating with a page of the other phone book. Overlap the pages at least half way. (See figure 1.)

You won't be able to pull the books apart. The friction force between them is so large it will easily support the weight of a grown scientist (figure 2). In principle, they could support the weight of a pickup truck, but the phone books themselves might tear apart; the spines could rip loose.

## friction

The force of friction depends on three parameters: the roughness of the surfaces, the applied pressure, and the area of contact. The roughness is different for every pair of materials, and is characterized by the "coefficient of friction". Knowing the coefficient of friction, which can often be found in engineering handbooks, the maximum friction force can be calculated as:

$$f = \mu_s P A$$

where $\mu_s$ is the coefficient of friction for the two surfaces,1 $P$ is the applied pressure, and $A$ is the area of contact.

For most paper, the coefficient of friction is in the range of 0.25 to 0.6. Phone book paper is on the rougher side, probably 0.5 or higher. Table 1 shows the static friction coefficients for some common materials.

Table 1: Coefficients of static friction for a few common materials.
materialscoefficient of friction
glass on glass0.9-1.0
rubber on dry concrete0.9-1.0
steel on steel0.74-.78
waxed wood on dry snow0.10
ice on ice0.10
teflon on teflon0.04
speed skate on ice$\approx$ 0.005

The overlap area of the two phone books in figure 1 is 10 cm by 25 cm = 0.025 m2. When sitting on the table, the average force on a page is about half the combined weight of the phone books, or 10 Newtons (2.2 lbs). The pressure on each page is then:

$$P = {W\over A} = {\rm {10 \,N\over 0.025 \,m^2} = 400 \:{N\over m^2}}$$

and the maximum friction force between the phone books is approximately:

$$f = 0.5 {\rm \left(400 \:{N\over m^2}\right)\left(0.025 \,m^2\right)\left(2000 \:pages\right) = 10,000 \,N = 2200 \,lbs}$$

Of course this value can change, depending on how the books are supported. When hanging vertically, the applied pressure is considerably weaker (but friction is still big enough to support a person's weight).

## phonebook variations

If you really want to make an effort to get the phone books apart, you'll have to attach something to the bindings to get a good grip. For the books in figure 1, we taped 1 inch wide by 1/8-inch thick steel bar on either side of the spines (to distribute the pull force across the length of the spine) and clamped them in place with C clamps.

However, if you want to use more than the weight of a scientist you may wish to use wider bars and drill holes through the books to bolt them in place.

If you don't have access to large phone books or don't have a couple spare hours to spend shuffling pages, you can still achieve an impressive demonstration with just a couple of magazines. Two 100-page magazines can provide a friction force of maybe a few hundred Newtons, more than the paper itself can support.

## teaching notes

This experiment is a little hard to believe unless you try it with your own hands. When I demonstrate this at school, I inevitably get claims that the books are glued or taped together. If students can watch you shuffle the books together (a time consuming process!) or if they can try their own hands at shuffling magazines together, skepticism will turn to astonishment in no time.

## further resources

Mythbusters have their own episodes on the phone book trick, in which they fail to pull the books apart using ten people in a tug of war (https://www.youtube.com/watch?v=AX_lCOjLCTo) but do manage to succeed using two military tanks applying 8000 lbs. of force (https://www.youtube.com/watch?v=QMW_uYWwHWQ).

Measurements of the coefficient of friction for printer paper can be found at http://www.tappi.org/content/tag/sarg/t549.pdf (table 2).

The folks at hyperphysics provide a short discussion on the principles of tire friction under various road conditions at http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/frictire.html.

• 1. We're concerned here about the case where the phone books are not slipping, which involves "static friction". The case when surfaces ARE slipping is called "kinetic friction". The coefficient of static friction for two surfaces is usually a little higher than the coefficient of kinetic friction because the surfaces tend to form microscopic bonds when they are stationary for a short length of time, making it harder to get them to slip.