Key concepts
Physics
Forces
Friction
Surface area

Introduction
Sometimes friction can be annoying. It can make it difficult to push heavy things like furniture and it can even give you a nasty scrape if you fall. But friction is actually very important—without it, you could not move around at all, or even pick things up! Try this project to find out how friction can lead to some surprising effects—such as making it almost impossible to pull two books apart.

Background
You experience friction every day. When you walk, friction is what prevents your feet from slipping on the floor. Imagine if every surface were as slippery as ice—getting around would be very difficult! Friction is a type of force, or a "push" or a "pull," that can act on objects.

In physics the frictional force between two surfaces is determined by something called the coefficient of friction. A higher coefficient of friction means that there will be more friction between two surfaces, or they will be less "slippery." For example, the rubber soles of your shoes and a carpeted floor have a much higher coefficient than ice skates on ice. The amount of friction also depends on something called the normal force. In this context "normal" means "perpendicular to the surface." A higher normal force will result in higher friction. For example, imagine two identical cardboard boxes sitting on a wooden floor. One box is empty and very light and one is full of stuff and very heavy. In both cases the coefficient of friction (between cardboard and wood) is the same. The heavier box, however, will be much harder to slide across the floor. This is because there is a higher normal force between the box and the floor, so there is more friction.

Now, think about friction between two pieces of paper. If you put two pieces of paper on top of one another, they should be very easy to pull apart, right? What will happen if you overlap a whole bunch of pieces of paper, like the pages from two books? Will they still be easy to pull apart? Try this surprising activity to find out!

Materials

• Two equal-size books (does not have to be a phone book) or two thick magazines, notepads or tablets of sticky notes

Preparation

• Take your two books or notepads and place them on a flat table so the "bound" ends are facing away from one another.

Procedure

• Open both books and overlap their back covers at least halfway.
• One by one interleave the pages of the two books by folding down a page from the left book then a page from the right book on top of that, and then a page from the left book again.
• Continue alternating in this fashion for about a dozen pages.
• Now try to pull the books apart. How easy is it to pull the books apart? Can you do it? What if you hang the books vertically by holding on to just one of them—can they support their own weight?
• Start over and interleave more pages than you did the first time.
• Repeat the testing process, trying different tests to see if you can pull the books apart. Can the books hold their own weight if you hang them vertically? Can you do "tug of war" with another person to pull them apart?
• Continue performing the tests after interleaving more and more pages until you can no longer pull the books apart. Are you surprised at how much force the books can support? How many pages did you have to interleave before you could no longer pull them apart?
• To separate the books, you might have to fold the pages back one at a time. You can also try bending the two books relative to one another, which will cause the pages at one end of the stack to start coming apart.
• Extra: Try the activity with two notepads or notebooks that have perforated, removable sheets. Remove every other sheet of paper from each notebook, then try the different tests. Are they just as difficult to pull apart, or does something change? Why do you think that might be?

Observations and results
You should have found that it was pretty easy to pull the books apart when only a several pages were interleaved. As you interleave more and more pages, however, it quickly becomes surprisingly difficult to pull them apart—until pretty soon, you cannot separate them at all! Although the classical demonstration of this project uses large phone books, it works well even for much tinier volumes, including sticky note pads. Can you figure out why this happens, based on what you read in the background section?

You know that the coefficient of friction does not change, because the surfaces remain the same material (paper). It turns out that when you try to pull the two books apart, the interleaved pages in the middle get squished together harder—this increases the normal force between them, thereby increasing overall friction. This means that the harder you pull, the higher the friction, and the harder the pages are to pull apart!

There are many demonstrations and videos of this project online but be careful when you read about it because there are several common misconceptions and incorrect explanations for how it works. One misconception is that the effect is due to the normal force from the weight of all the pages pressing down on one another. This cannot be true, however, because the activity still works if you hang the books vertically, in which case there is no normal force from the weight of each page acting on the next page. The second common incorrect explanation is that the "increased surface area" from interleaving many pages together results in more friction. This is also incorrect—a regular stack of paper will easily fall apart, even though there is lots of surface area in contact between the sheets. The effect in this activity occurs because the interleaved sheets in the middle get squeezed together as you try to pull the books apart. You can see this if you look at your books edge-on while you do the experiment. When you are not pulling on them at all—or even if you push them together a little bit—you should be able to see some small gaps between some of the pages. But when you pull on the books, these gaps quickly close and the pages flatten together. Try the "extra" step in the procedure to see how this changes if you use notepads with every other page removed. (This results in the stack of interleaved pages in the middle being the same height as the binding of either notepad, instead of twice as thick—so the pages are not pulled inward when you try to pull them apart.)

More to explore
Phone Book Friction, from Mythbusters
The enigma of the two interleaved phonebooks (pdf), from Cornell University Library
Slippery Science: Explore Friction by Launching Stuff, from Scientific American
Science Activities for All Ages!, from Science Buddies

This activity brought to you in partnership with Science Buddies