For Chapter 1, here is part B of the new stories and also the updates to the items in the book, including many video links and journal citations. If you want all the video links (hundreds) and journal citations (thousands) for this chapter, go to

http://www.flyingcircusofphysics.com/pdf/Chapter1_Ref_Com.pdf

First a list   (use "Ctrl-F" to search for a key word or just scroll down the screen)

1.56  Beds-of-nails demonstrations
1.57  Pub trick ---water and the disappearing cigarette
1.57  Pub trick --- lifting a bottle with thumb and one finger
1.57  Pub trick --- hanging spoons
1.57  Pub trick --- hanging bottle caps on your face
1.66  Stacking blocks to get an overhang
1.67  Stabilizing the leaning tower of Pisa
1.68  Domino amplifier
1.68  Human dominos for your next dull party
1.77  Bounce of the ball
1.78  Nike football commercial: real or fake?
1.81  Robbie Maddison's motorcycle jump
1.91  Pub trick --- balancing a coin on a folded paper edge
1.94  The dambusters of World War II
1.94  Stone skipping on water
1.97  Cats turning over to land in a fall


Reference and difficulty dots
Dots · through · · · indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages

Now the stories

 

1.56  Beds-of-nails demonstrations
Jearl Walker www.flyingcircusofphysics.com
Dec 2008    A long time ago, I introduced two bed-of-nails demonstrations to physics education. One (very painful) example is shown in the following photograph …

You see me sandwiched shirtless between two beds of very sharp nails while Peter Wiley (of my publisher, John Wiley and Sons) stands on top of the sandwich. (The photograph is courtesy of Cynthia Spencer, also of John Wiley & Sons.) If you have enough resolution on the photograph, you can see that in spite of the rigidity of the top bed, it is bent at the edge of my rib cage.

When Peter Wiley stepped off the top bed of nails and then helped me get up, I felt (and maybe heard) a slight suction effect as I pulled my back off the nails on the lower bed. The nails had not pierced my skin but they had been on the verge of penetration, with skin tightly folded over the points. Detaching myself from the nails may have caused a slight rush of air into the indentations in my skin.

In the second type of bed-of-nails demonstration, I am again sandwiched shirtless between the two beds but now a concrete block is positioned on the top bed. An assistant then swings a heavy sledgehammer down on the block, smashing it and momentarily compressing the sandwich, that is, compressing me between the two layers of nails, in something resembling the “iron maiden” of medieval torture.

At the end here, I give two links where you can see old videos of me performing the two types of bed-of-nails demonstrations.

The physics of someone standing on top

When one or two people stand on me, their weight is spread over enough nails in the top bed that the force on me from each nail is insufficient to pierce my skin. The force from the nails on my back is larger, because they must also support my weight. By experimenting I discovered how much weight the people can have before I am pierced. I can roughly calculate the pressure on me from each of the bottom nails by dividing the total weight by the number of nails on my back and by the area of each point on the nails. However, the calculation is only suggestive because my body is not uniform and thus I support more weight on some nails than on others. Don't think that I go without pain, because the demonstration hurts a great deal.

Here are some more photos. In the first two, student Amanda Beach is standing on me while being steadied by M. J. Saunders, the provost here at Cleveland State University. Amanda was quite worried about hurting me (but I don’t think the provost was). The second and third photos show me doing push ups on a bed of nails while wearing gloves lined with Kelvar (sold at http://www.duluthtrading.com). I could feel the points on the nails but because they did not penetrate the Kelvar, the pushups were not painful. (The photos are courtesy of T-Fiz.)

 


 
The physics of smashing a concrete block

When a concrete block is smashed on the top bed, the large block not only adds a theatrical flare to the demonstration because it shatters so nicely, but it also increases the safety in three subtle ways.

1. If I am to be squeezed hard, then the block and top bed must accelerate rapidly downward; a larger block diminishes the acceleration because of its greater mass.

2. Much of the energy in the sledgehammer goes into rupturing the block rather than into the bed's motion.

3. The fact that the block disintegrates means that the collision time (from the start of the collision to the end) is longer than if the sledgehammer hit the top bed directly. That means that the force in the collision is smaller than with a direct hit.

Both bed-of-nails demonstrations hurt and are potentially harmful, especially the one with the sledgehammer because the face can be damaged by the debris from the concrete block. I have had some scary and also some silly moments with the demonstrations. Here are some of the stories.

First time with the smashing demonstration

The first time was in a classroom. I asked one of my students to swing the sledgehammer, but quite unwisely I had him place a common small brick on top of the sandwich of nails. I told him to hit the brick hard, covered my face with one hand, and then gave him a count of 1…2…3 so that I could brace my abdomen for the impact. The student hit the brick very hard with the sledgehammer, so hard that I lay stunned on the floor for several minutes. The students in my class were shocked, but my primary thought was that this was a stupid way to die. However, the advantage of using a large concrete block was suddenly very obvious to me. Pain has a way of rapidly clarifying the physics principles.

The smashing demonstration at Oxford University

One summer I gave the Flying Circus of Physics talk at Oxford University in England to a meeting of education experts from around the world. Unfortunately, only few in the audience spoke English, much less understood my Texas-brand of humor. So, as the talk went on and I generate only slight laughter at my jokes, I became more nervous and less cautious.

When I got to the bed-of-nails demonstration at the end of the talk, I discovered that I had to perform the stunt on a bench so that everyone could see it. My assistant put the concrete block on top of the bed sandwich and then swung the sledgehammer down on the block. Because I knew that, with this unusual arrangement, the angle of swing was awkward for the assistant, I tried to steady the top bed by grabbing it firmly with one hand. When the sledgehammer hit the block, the impact drove a nail across my hand, cutting it.

I didn't realize that I had been cut until I stood up to give my closing remarks, but then the blood flow was noticeable to both me and the audience. The audience was impressed with the demonstration and especially the blood --- they required no grasp of English to know that I had hurt myself.

After packing up the equipment, I met my host at a local pub for a pint of ale, feeling somewhat relieved that at least the final demonstration of the talk had impressed the audience. Then my host told me that the disease tetanus ("lock-jaw") was a real concern in that part of England. I had not minded the pain of the cut, but the thought of contracting tetanus worried me. (The bacteria causing tetanus enters the body through a cut from, say, a dirty nail. If the bacteria are not stopped, the victim soon dies while every muscle in the body in full contraction, unable to breathe.) I put down the pint of ale and hurried over to the local hospital for a tetanus shot.

There I had to explain to the nurse how I had cut myself. As she drove the needle into my rump, she was laughing so hard that she shook. I had traveled across the Atlantic Ocean to impress educators and had ended up dropping my pants in front of a nurse laughing at me.

Demonstration at a girl’s school

Equally embarrassing was the time I gave the bed-of-nails demonstration at an all-girls high school. I figured that the woman who invited me did not want to see the sledge-hammer part of the demonstration, so I planed to do only the part where I am sandwiched in the two beds of nails with a person standing on top. Over the phone she agreed to be that person.

What I did not think about during the phone conversation was the clothing that she should wear. I did not think about that feature until I was sandwiched in the two beds with the woman about to get on top. She was wearing a short skirt and, while standing immediately next to my head, decided to talk to the audience about what she was going to do. I did my very best to turn my face to the audience instead of looking upward; the girls in the audience went wild with laughter; the woman never understood what the problem was; and I was unable to straighten out my neck for a week.

Demonstration at IBM conventions

I used the bed-of-nails demonstration not only in class and in my Flying Circus talk, but also in a series of motivational talks I gave to sales people of IBM. I began the motivational talks by being the stereotype physics professor (talking of grand things, being as boring as possible) and then slowly dropping the talk into slap-stick and then ending with the bed-of-nails demonstration. My message was that I sell a product (physics) to people (students) who often do not initially want the product, much like the sales people try to sell their IBM product to customers who may not want the product.

In part of the slapstick I did a pratfall on the stage and fell over the edge of the stage to the floor. This stunt looked like a huge mistake, and every one of the 1000 people in each audience froze with tension when I did it because mistakes are never ever supposed to happen at an IBM presentation. Only gradually would the audience realize that the fall was planned, and then for the rest of my talk they would laugh and even cheer at my stunts.

Before each of these talks I met the leading IBM executive that was there, because he was to be the one who would stand on me when I was in the bed-of-nails sandwich. Each of these executives was concerned about hurting me. I told each, "Hey, look, this demonstration is OK. Sure, your weight is going to hurt me by pressing the nails into me, but the pain is something I can endure while you are up on top. Don't worry; I've got this figured out."

At one talk the executive was especially worried because he weighed about 230 pounds, which would put me at the limit of the pain I could endure. Nevertheless, I went through my calming words. Unfortunately, when I did my pratfall during that talk, I broke a rib as I hit the floor below the stage. At the time, I did not know that a rib was broken; I only knew that my chest hurt like crazy. I continued the talk, doing the rest of the slapstick while not breathing very well. Then came the bed-of-nails demonstration and the 230-pound executive. When he stood up on the top bed of nails, the pain in my chest went ballistic and, though I could hardly breathe, I said my routine words about the stunt.

I was back in Cleveland and at my doctor's office later that day. She told me that I had broken a rib and that I should take life easy for a month. I tried to laugh (but couldn't) and said, "You've got to be kidding. I have to be back at the IBM talks next week." And I was. But thankfully the next several executives that stood on me each weighed less than 230 pounds.

Blood all over me

Once when I gave the Flying Circus talk at Western Illinois University, my assistant could not make the trip and I asked my host if he would swing the sledgehammer down on me during the final demonstration. I told him to not be timid about the swing because that would disappoint the audience. I wanted a dramatic ending, and he gave me one. He swung that sledgehammer down hard, really jarring me. However, he came in at angle that sent most of the chunks of the concrete block across my face. I had one hand guarding my teeth and eyes, but one of the large chunks cut across my exposed chin.

When I climbed out of the beds of nails and stood up to give my closing remarks, blood poured from my chin onto my pants and shoes. My host was pale with worry, but the audience was crazy with applause. That ending was the best ending I ever had with the Flying Circus talks, and at every later Flying Circus talk I secretly hoped to be cut like that again. As I said once, a long time ago, "There is no better demonstration than one in which the teacher may be hurt or killed."

To see my bed of nails demonstrations on video, go to

http://www.myspace.com/flyingcircusofphysics

and click on videos (under the photo of a festive penguin watching an electric pickle glow because of a 1.5-amp current through it).

The video that immediately begins to run shows the first demonstration, beginning at about 8.0 minutes into the video. By repeatedly clicking on the slide bar, you can quickly advance to that point.

To see both demonstrations, scroll down to Episode 1. The demonstrations occur about 19.5 minutes into the video

1.57  Pub trick --- water and the disappearing cigarette
Jearl Walker www.flyingcircusofphysics.com
July 2008 Here is a simple sleight-of-hand magic trick in which a cigarette disappears and then reappears. (You can substitute similar objects to avoid cigarettes.)

http://www.videojug.com/film/how-to-make-a-cigarette-disappear-the-david-zanthor-way-2

The saliva causes the paper on the cigarette to cling to the thumb, the same effect you might use if you wet your fingers (with either water or saliva) in order to use them to turn the page of a book.

But doesn’t that seem wrong? If you have ever slid down a water slide, you know that water is a lubricant that can almost eliminate friction. Indeed, one reason why ice is dangerous to walk on is because it is nearly always covered with a thin layer of water that makes the ice covering very slippery.

However, when water forms a very thin layer between two surfaces, especially if it can penetrate into the surfaces, it cannot flow and then it acts as a glue instead of a lubricant. When you wet your fingers to turn a page, part of the water penetrates into the spaces between the wood fibers in the paper. The water molecules not only bond to each other, but they also bond to the fibers and to your skin. Thus, the paper clings to your skin.

You can see the same physics if you dampen a small section of paper and then put into a dry ceramic bowl. The paper clings to the bowl. If you next increase the water level in the bowl, the paper is easily moved because then water can flow between the paper and the ceramic.

1.57  Pub trick --- lifting a bottle with thumb and one finger
Jearl Walker www.flyingcircusofphysics.com
Aug 2009 Here is the challenge: stand an empty glass bottle upside down on a table and then pick it up by placing one finger on the top (actually the bottom surface of the bottle) and the thumb on the side of the bottle, in a pinching motion. Try it and you’ll find that your finger and thumb merely slide along the glass surfaces, coming together at the edge. Even if the bottle is free of condensation, you still fail to pick it up. Here is a video that reveals the trick:

http://www.metacafe.com/watch/2970314/bar_trick_challenge_the_impossible_beer_lift/

And here is the physics: Your finger and thumb are naturally lubricated with secreted oil. Even if you cannot sense the oil, it lies on the epidermis.

When you pull your fingers and thumb parallel to the glass surface, you want the static friction to prevent any sliding but static friction has an upper limit. If you exceed that upper limit, your thumb and finger slide, and that is what happens.

The upper limit depends on two factors: (1) how hard you press against the surface and (2) how much the two surfaces bond in what is called cold-welding. That bonding is due to the molecular attraction between your finger molecules and the glass molecules at the various points where the two surfaces touch. Instead of considering such molecular bonding (which we cannot actually see), we just assign an experimentally determined coefficient of friction to any two surfaces. If there is almost no bonding, the coefficient is almost zero. If there is a lot of bonding (as you would find when rock climbing shoes are pressed against rock), the coefficient is high, maybe 1.2 or so.

When you initially attempt to pick up the bottle, the coefficient of friction between the glass and your skin is probably around 0.3, a fairly low value. As you naturally pinch your thumb and finger to pick up the bottle, you press hard against the glass surfaces, but the low coefficient of friction means that the upper limit to the static friction is low. Thus, you easily exceed that limit, and then your fingers slide.

If you remove the oil from your fingers (by allowing leather or cloth to absorb it or by rubbing it off with a napkin with rubbing alcohol), you remove most of the lubrication, increasing the coefficient of friction to 0.8 or so. Then the upper limit to the static friction is high and your pinching action is not enough to cause the skin to slide over the glass surfaces.

I find the adhesion and lifting is easier if I put my thumb on the top surface and my first finger on the rear side of the bottle and then adjust their orientation to make as much contact as possible (without trapping the bottle against my palm, which would not be fair).

You can also increase the coefficient of friction by a counterintuitive trick ─ you breathe onto your fingers, depositing a thin layer of moisture. Water is a good lubricant when the layer is thick enough that the water can easily move, but a very thin layer is a good adhesive because it can bond to a surface. Here the moisture bonds to both the skin and the glass, allowing you to pick up the bottle.


1.57  Pub trick --- hanging spoons
Jearl Walker www.flyingcircusofphysics.com
Nov 2009 Clean a lightweight spoon and the skin on your nose, breathe lightly onto the interior surface of the spoon’s bowl and then hold it so that the surface rests against your nose. Test for adherence by repositioning the spoon and partially releasing it. When you feel it hold, let it go. There, just what you’ve always wanted: A spoon dangles from your nose. Who can resist you now? 

Why does the spoon hang? How does breathing on it first help? Can you hang spoons from other parts of your face, or, if you’re into that kind of thing, from other parts of your body?

How long can you hang a spoon from your nose? I have long claimed that my record is 1 hour and 15 minutes, set in a French restaurant in Toronto. However, the truth is that it was actually in a truck stop in Youngstown, Ohio, where a burly member of a motorcycle gang suggested that the spoon would hang better if he reshaped my nose.

Spoon hanging has probably been practiced in pubs for as long as there have spoons and pubs. There is something a few pints of beer that makes spoon hanging compulsive. As always with the pub tricks here at the FCP site, I lay down this challenge --- anyone can do a pub trick but can you explain how it works? Well, here is the physics behind spoon hanging,

If the spoon and your nose are free of oil, there can be enough friction between the spoon and the skin to hold the spoon in place. The spoon is stable provided that the center of its mass distribution lies along a vertical line through the region where it sticks to your nose. Otherwise, gravity rotates the spoon when you release it, and the motion may cause the spoon to slide off.

Condensation from your moist breath helps glue the spoon to your nose. Normally, a water layer is a lubricant because the molecule-molecule attraction is not strong enough to resist motion. For example, if you belly flop onto a water slide, the water attached to your body can easily slide over the water layer attached to the slide --- the two layers are said to undergo shearing.

However, when a water layer is very thin, perhaps only a few nanometers thick, it acts like a glue instead of a lubricant because the water can no longer be easily sheared. Instead, it is more like an elastic solid than a liquid. With the spoon trick, your breath deposits patches of very thin water on the spoon. (Patches may already be there from condensation of the room air.) When you put the spoon on your nose, these patches bind to the two surfaces. As the spoon begins to slip down your nose, the patches may yield slightly (they are somewhat elastic) but resist further sliding (they are too much of a solid to undergo shearing).

You have used this same physics if you have ever wet your fingers in order to separate the two sides of a plastic grocery bag in which you put vegetables or fruits. The bag comes off a dispenser and must be opened at one end to make way for the food, but usually the two sides are difficult to separate. Dry fingers easily slide over the plastic, but wet fingers stick enough that you can peel the two sides apart. You might lick your fingers or dip them into water sprayed onto the vegetables or fruits. Either way, the water layer is probably thick enough to be sheared. However, when you pinch the plastic between your fingers and then move in a rubbing motion, you immediately thin the water layer and then it cannot be easily sheared. The increase in friction between your fingers and the plastic allows you to rub the plastic layers in opposite directions, opening up the bag.

If you hang spoons (either just you or a group or a class), send me a photo and I’ll post it here. Or, you could post it on your FaceBook site and then “friend me” so that I can see it. However, no spoon-hanging while driving a car or you will end up part of this month’s lead story about cars crashing into shops.
photo credits: above left, Cynthia Spencer of John Wiley & Sons; above right, Richard Howard, for the Smithsonian Magazine.

References

Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Zwicker, E., "Doing physics," Physics Teacher, 20, 181-182 (1982)
· Martin, J., How To Hang a Spoon, Turnbull & Willoughby Publ., 1985
· Wolkomir, R., "'Old Jearl' will do anything to stir an interest in physics," Smithsonian, 17, 112-121 (October 1986)
· Walker, J., "Hanging a spoon from the nose," Physics Teacher, 25, 216-217 (1987)
·· Jinesh, K. B., and J. W. M. Frenken, “Capillary condensation in atomic scale friction: How water acts like a glue,” Physical Review Letters, 96, #166103 (4 pages) (28 April 2006)
·· Feiler, A. A., J. Stiernstedt, K. Theander, P. Jenkins, and M. W. Rutland, “Effect of capillary condensation on frition force and adhesion,” Langmuir, 23, 517-522 (2007)
·· Cai, S., and B. Bhushan, “Meniscus and viscous forces during separation of hydrophilic and hydrophobic smooth/rough surfaces with symmetric and asymmetric contact angles,” Philosophical Transactions of the Royal Society A, 366, 1627-1647 (2008)
·· Kim, D-I., J. Grobelny, N. Pradeep, and R. F. Cook, “Origin of adhesion in humid air,” Langmuir, 24, 1873-1877 (2008)

1.57 Pub trick --- hanging bottle caps on your face
Jearl Walker www.flyingcircusofphysics.com
July 2010    Here is the first challenge: Hang a bottle cap (beer or soda) from your cheek or forehead. Of course, you could press the rough bottom edge so forcibly into your flesh so that it cuts a circular notch on which it can hang. But having a bunch of people with blood streaming off their faces and onto their clothes is usually not considered to be a “fun thing” to do at the pub.

Here’s a better solution.

Slightly wet the top of the cap with either spilt liquid or some of the condensation on the cold bottle. Then lightly press that surface onto the cheek. The cap will hang there for a surprisingly long time. The physics is the same as with the trick of hanging a spoon from your nose: A fairly thick layer of water acts as a lubricant because one layer of water can easily slide past the adjacent layer --- water cannot resist shearing. However, a thin layer acts as an adhesive because the water can form hydrogen bonds with the surface of both the cap and your flesh.

Here is the next challenge: How many bottle caps can you hang anywhere on your face before any of them fall? The image here shows six on my grandson’s face. Can you at least beat that? You can post photos at the Facebook site for The Flying Circus of Physics:

http://www.facebook.com/pages/Cleveland-OH/Flying-Circus-of-Physics/339329532602?v=app_23798139265&ref=ts#!/pages/Cleveland-OH/Flying-Circus-of-Physics/339329532602?v=wall&ref=ts

References
Dots · through ··· indicate level of difficulty
Journal reference style: author, title, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
· Zwicker, E., "Doing physics," Physics Teacher, 20, 181-182 (1982)
· Martin, J., How To Hang a Spoon, Turnbull & Willoughby Publ., 1985
· Wolkomir, R., "'Old Jearl' will do anything to stir an interest in physics," Smithsonian, 17, 112-121 (October 1986)
· Walker, J., "Hanging a spoon from the nose," Physics Teacher, 25, 216-217 (1987)
·· Jinesh, K. B., and J. W. M. Frenken, “Capillary condensation in atomic scale friction: How water acts like a glue,” Physical Review Letters, 96, #166103 (4 pages) (28 April 2006)
·· Feiler, A. A., J. Stiernstedt, K. Theander, P. Jenkins, and M. W. Rutland, “Effect of capillary condensation on frition force and adhesion,” Langmuir, 23, 517-522 (2007)
·· Cai, S., and B. Bhushan, “Meniscus and viscous forces during separation of hydrophilic and hydrophobic smooth/rough surfaces with symmetric and asymmetric contact angles,” Philosophical Transactions of the Royal Society A, 366, 1627-1647 (2008)
·· Kim, D-I., J. Grobelny, N. Pradeep, and R. F. Cook, “Origin of adhesion in humid air,” Langmuir, 24, 1873-1877 (2008)

 x

1.66  Stacking blocks to get an overhang
Jearl Walker www.flyingcircusofphysics.com
March 2007    Stacking blocks to make a leaning tower has long fascinated both mathematicians and normal people, including those students who have built a tower of books that leans from a library table out over an aisle, threatening to collapse onto a careless library patron. (Don’t you dare do this. Librarians are usually calm and helpful, but if you mess with their books, they transform into the orcs of Tolkien’s Middle Earth.) The standard question is, “What is the maximum overhang?” The standard answer is, “If you stack the blocks properly, there is, in principle, no limit.”
    However, M. R. Khoshbin-e-Khoshnazar of the Physics Department at the Research Institution for Curriculum Development & Educational Innovations in Tehran recently pointed out that a practical matter limits the stacking: The bottom block gets squashed by all the higher bricks and if the number of higher blocks exceeds a certain limit, the bottom block “yields,” that is, it deforms and collapses.
    If the usual stacking scheme is followed, you put the center of mass of the top block just over the outer edge of the underlying second block. Then you put the center of mass of those two top blocks just over the edge of the underlying third block. And so on. If a block has the physical characteristics of a standard rigid brick and a height of 20 cm, the maximum number of blocks for a stable tower is about 853 and the maximum height of the tower is about 171 m. If you switch to bricks with another height, the number of bricks is different but the maximum height of the stack does not change.

http://www.youtube.com/watch?v=CA-gF53jvTY Video of stacking blocks and then placing a thin rod under the center of mass of the full stack.
http://www.physics.ucla.edu/demoweb/demomanual/mechanics/center_of_mass_demonstrations/stacking_blocks.html UCLA, diagram of how to stack the blocks
http://groups.physics.umn.edu/demo/mechanics/1J1120.html Photo

· · Khoshbin-e-Khoshnazar, M. R., “Simplifying modeling can mislead students,” Physics Education, 42, No. 1, 14-15 (January 2007)

Want more references? Use the link at the top of this file.

1.67  Stabilizing the leaning tower of Pisa
Jearl Walker www.flyingcircusofphysics.com
June 2008   The famous tower in Pisa, Italy, (seen here in an image by Gregor Samsa) began to lean toward the south even during its construction, which spanned two centuries. Indeed, when the bell chamber was finally added at the top, it was made vertical in the hope of arresting the lean of the rest of the tower.

In modern times, the tower was closed to tourists after a tower in Pavia collapsed, killing four people. The danger is not so much that the tower in Pisa would actually topple over like an upright domino pushed on one side. Rather, the danger was that as the weight shifted to the south side of the tower, the support structure at the south side of the base would suddenly burst under the huge compression, and then the tower would fall over.

The tilting has been due to the uneven compacting of the underlying mud, sandy soil, and clay, with one side of the support gradually giving way as the ground shifts. During the 20^th century, the top of the tower moved southward at about 1.2 millimeters per year but the rate alarmingly shot up in 1935 when an ill-advised attempt was made to seal the foundation against water seepage by drilling into the cement and filling the drill holes with a cement grouting mixture.

In 1990, the Italian government set up a committee with the challenge of stabilizing the tower. The primary method was to remove small amounts of soil beneath the north side of the tower by means of a drilling rig angled into the ground. A pile of lead weights was also placed on the north side to encourage the ground there to slump. Very gradually the tower began to rotate back northward. However, the situation was so touchy that the tower’s motion was briefly affected by even a northerly gale and a decrease in the air temperature.

The soil removal was stopped in 1999 and the lead bars were gradually removed. Last month the committee in charge of the stabilization announced that the tower is now stabilized and should remain stable for a very long time, standing ready for the countless photos that tourists will take of it.

http://news.bbc.co.uk/2/hi/europe/7423957.stm

· Covington, R., “The leaning tower straightens up,” Smithsonian, 32, No. 3, 41-47 (June 2001)
· Barends, F. B. J., “A Dutch leaning tower saved in 1866 by the same method used for the Pisa tower,” Geotechnique, 52, No. 2, 141-142 (2002)
· Burland, J., M. Jamiolkowski, and C. Viggiani, “Preserving Pisa’s treasure,” Civil Engineering, 72, No. 3, 42-49 (March 2002)
· Burland, J. B., M. Jamiolkowski, and C. Viggiani, “The stabilization of the leaning tower of Pisa,” Soils and Foundations, 43, No. 5, 63-80 (October 2003)

Want more references? Use the link at the top of this page.

1.68  Domino amplifier
Jearl Walker www.flyingcircusofphysics.com
March 2009    A common pastime is to arrange upright dominos in a line so that when the first one is knocked over, a chain reaction is sent along the line. Although videos involving thousands of dominos are available on the web, the most impressive display I have ever seen was described in a paper published in 1983 by Lorne Whitehead of British Columbia. He called his arrangement a domino amplifier because the chain reaction went through progressively larger dominos, each one 1.5 times larger in each dimension than the preceding one. Here is a scan of his photograph of the dominos.

He toppled the first, very small domino by “nudging it with a long wispy piece of cotton baton.” It then toppled the next domino and so on, until the 13^th domino fell. As Whitehead pointed out, if he had continued the series to 32 dominos, the last one would have had a height comparable to that of a skyscraper. Thus, the slight nudge on the initial tiny domino would have resulted in toppling a gigantic block. (This would be a splendid metaphor for how we got into our current economic crisis.)

If we set up a normal domino line, we do a certain amount of work in lifting each domino to its upright position against the downward pull of the gravitational force. Our work is said to result in a gravitational potential energy associated with the elevated center (or center of mass) of the upright domino. If we topple the domino so that the center falls, the stored energy is transferred to kinetic energy during the domino’s rotation downward and then it is transferred into sound, vibration, and some very slight heating during the domino’s collision with the floor.

In a normal domino toppling demonstration, each domino hits another domino before reaching the floor and thus energy is transferred along the line, domino to domino. In each collision, some of the energy is transferred to sound, vibration, and slight heating, but much of the energy is transferred to the next domino as kinetic energy. If the dominos are identical and equally spaced, a steady amount of kinetic energy moves along the line, from domino to domino.

However, in Whitehead’s arrangement the amount of kinetic energy increases along the line (it is thus amplified). The increase is due to the progressively larger gravitational potential energy associated with the progressively larger dominos. That is, each domino is more massive the preceding one and has a center of mass that is more elevated than the preceding one. From one domino to the next, each dimension (width, thickness, and height) is 1.5 times that of the preceding domino. Thus, the center of mass is 1.5 times higher than that of the preceding domino. And the volume (and thus the mass) is 3.375 (= 1.5 x 1.5 x 1.5) times that of the preceding domino. Therefore, the gravitational potential energy (which depends on the mass and the height of the center of mass) is 5.06 (= 1.5 x 3.375) that of the preceding domino.

Here are some results:

2^nd domino has 5.06 times the energy of the 1^st domino.

3^rd domino has 5.06 x 5.06 = 5.06² = 25.6 times the energy of the 1^st.

10^th domino has 5.06⁹ = 2,100,000 times the energy of the 1^st.

13^th domino has 5.06¹² = 280,000,000 times the energy of the 1^st.

Also, as Whitehead pointed out, the energy released by that last domino is about 2 billion times the energy needed to nudge over the first domino. Of course, the energy does not come for free because someone must do work to put the dominos in their upright positions. And if the last block is as tall as a skyscraper, the work would be enormous. Still, even Whitehead’s arrangement of 13 dominos was very impressive when the last domino fell over with a mighty thud soon after I nudged over the first, tiny domino with only a slight touch. I must admit that I felt very powerful, well, for a minute or two until I faced the task of lifting all the dominos back into their upright positions.

My article about the physics of dominos and the domino effect is the “Article of the month” here at this FCP site.

http://www.flyingcircusofphysics.com/News/NewsDetail.aspx?NewsID=46

Here are other sites:

http://www.exo.net/~pauld/activities/mathematics/dominofall.html Paul Doherty’s instructions about constructing the demonstration, from the Exploratorium in San Francisco, California

http://www.physics.ubc.ca/ssp/papers/Publications/Domino%20chain%20reaction.pdf scanned copy of Lorne Whitehead’s original publication in American Journal of Physics

http://www.exo.net/~pauld/activities/mathematics/dominofall.html photo of Whitehead’s domino fall

· Daykin, D. E., "Falling dominoes," Problem 71-19, SIAM Review, 13, 569 (1971)
··· Shaw, D. E., "Mechanics of a chain of dominoes," American Journal of Physics, 46, 640-642 (1978)
· Speco, B., Jr., with B. Sugar, The Great Falling Domino Book, Warner Books, 1979
·· McLachlan, B. G., G. Beaupre, A. B. Cox, and L. Gore, "Falling dominoes," solution to problem 71-19, SIAM Review, 25, 403-404 (1983)
· Whitehead, L., "Domino 'chain reaction'," American Journal of Physics, 51, 182 (1983)
· Walker, J., "Deep think on dominoes falling in a row and leaning out from the edge of a table" in "The Amateur Scientist," Scientific American, 251, 122-130 (August 1984)
··· Bert, C. W., "Falling dominoes," SIAM Review, 28, 219-224 (1986)
··· Stronge, W. J., "The domino effect: a wave of destabilizing collisions in a periodic array," Proceedings of the Royal Society of London A, 409, 199-208 (1987)
··· Stronge, W. J., and D. Shu, "The domino effect: successive destabilization by cooperative neighbours," Proceedings of the Royal Society of London A, 418, 155-163 (1988)
··· McGeer, T., and L. H. Palmer, "Wobbling, toppling, and forces of contact," American Journal of Physics, 57, No. 12, 1089-1098 (December 1989)
··· van Leeuwen, J. M. J., “The domino effect,” (2004) available at arXiv:physics/0401018v1
··· Efthimiou, C. J., and M. D. Johnson, “Domino waves,” (2008) available at arXiv:0707.2618v1
·· Larham, R., “Validation of a model of the domino effect," (2008) available at http://arxiv.org/abs/0803.2898v1
x

1.68 Human dominos for your next dull party
Jearl Walker www.flyingcircusofphysics.com
Dec 2009    Here is some physics for your next party, especially if it is deadly dull. Set up a chain of human dominos in which the physics of instability is demonstrated by the party goers, one after another, as in this video from the Blue Peter show in the UK.

http://news.bbc.co.uk/2/hi/entertainment/8269638.stm

They use mattresses but finding a mattress for everyone at a party is not very practical. So, instead, you could just following the guide of this prank:

http://www.youtube.com/watch?v=qQKmKm4CTbk&NR=1&feature=fvwp

The idea for such toppling comes from the domino effect, in which dominos in a line are made to fall one after another after the first in the line is nudged over. As each domino falls, it trades in gravitational potential energy for kinetic energy, so that it forcibly strikes the next domino, making it fall, and so on. Setting up huge displays of falling dominos has become great sport, as in this video, where over four million dominos are toppled to set a new record.

http://news.bbc.co.uk/2/hi/7731525.stm

I must admit that I get nervous watching such displays, knowing that people have spent thousands of hours setting up the dominos and yet the toppling may reach a bad spot along a chain and stop.

In spite of my nervousness, I am fascinated by the repeated clicking made by the dominos as they strike one another. The frequency of the clicking is a measure of how fast the toppling wave (or toppling effect) sweeps along the line of dominos.

Suppose you have a very long line of equally spaced dominos. Once you begin the toppling, the wave initially accelerates and then settles down to a constant speed, and thus a constant frequency of clicks. That constant speed depends on the spacing between the dominos. A closer spacing results in a greater value for the constant speed, because each domino reaches the next one after only a short fall. A greater spacing requires each domino to fall farther to reach the next one, and that means that the wave moves slightly more slowly along the line.

Ron Larham has posted descriptions of how he was able to measure the speed of the waves by recording the clicking frequency with a Windows sound recorder, running under Windows 98. Because the recording picks up lots of noise (even from the room lights), he needed to do a Fourier analysis of the recorded data to pull out the dominant frequency of the domino clicking and calculate the speed. Here are his posted descriptions.

http://www.sas.org/tcs/weeklyIssues_2007/2007-11-02/project2/index.html

www.sas.org/tcs/weeklyIssues_2007/2007-12-07/project2/index.html

You already have an intuitive feel for the speed at which a toppling wave should move along a line of dominos. If it were to move much slower, you would immediately know that something was wrong, even though you may not immediately realize that it is the speed that is wrong. Here is an example in which the dance group The Rockettes play with our intuitive feel for toppling speeds, to amuse us.

http://www.youtube.com/watch?v=GSgmUin9vJw

Now that I have related clicking frequency and the speed of the wave, watch these mattress domino videos. You won’t hear clicking (because mattress are soft and yielding), but you can still measure the speed by the frequency of grunts and squeals of the people as they fall over, one after another.

http://news.bbc.co.uk/2/hi/uk_news/8179520.stm Bid for mattress domino record

http://www.youtube.com/watch?v=LIM6XDUUHRM Spanish TV show

And if you have lots of time to kill (for example, you are looking for an excuse not to study for that dreaded Pchem exam) and want to set up a toppling demonstration but are tired of dominos, how about vacuum cleaners, coins, shoes, DVDs, portraits, slices of toast, and almost everything else you can find around the house, as in this video:

http://www.youtube.com/watch?v=IQ5eNiq1CQY&NR=1

There you go. Now you have the perfect reason not to study for the exam --- you are simply too busy doing a physics experiment. If you post a video, send me word and I’ll put a link to it here.

More:

http://www.youtube.com/watch?v=8S7xhV9PwZw&feature=related beer commercial, a lot of fun

http://www.youtube.com/watch?v=k0PQIVbAVCo World Record human domino 145 mattresses

http://www.youtube.com/watch?v=dpEmHKXRMGs&feature=related EveryGator.com

http://www.youtube.com/watch?v=PadRPyZ5Bgg CD discs on Blue Peter TV show

http://www.youtube.com/watch?v=Hgtekdw1eyo&NR=1 over four million dominos

http://news.bbc.co.uk/2/hi/europe/7730834.stm
x

1.77  Bounce of the ball
Jearl Walker www.flyingcircusofphysics.com
November 2007   Yesterday the Cleveland Browns won their (American) football game with the arch rival Baltimore Ravens by first tying the game with a field goal kick. That last-second kick was for a remarkable distance of 51 yards, but initially the kick seemed to have failed because the football hit one of the uprights on the goal and apparently then bounced back toward the players. To score, the ball must pass through the vertical plane formed by the two uprights, and so a bounce back toward the players would not count.

However, as you can see in the videos at

http://www.youtube.com/watch?v=LPFXlTgy-yg

http://www.youtube.com/watch?v=77GkxWDOXJM&feature=related video game version

the ball actually hit the upright, passed through the vertical plane of the two uprights (thus scoring points), hit the horizontal support bar behind the uprights, and then bounced back over the crossbar and toward the players. The other team was so convinced that the kick had failed, that they left the field, only to be called back after the referees gathered to discuss the kick and then ruled that it was good. Those points tied the game and sent it into overtime, in which the Browns made another successful field goal kick and won.

Anyone can say that the bounce back over the crossbar was just freaky, because we normally expect that a ball that hits the upright and then the horizontal support bar should continue to move away from the players. What could cause it to bounce back toward the players?

Here is the physics (and notice that physics can answer the question whereas sports radio is just filled up with guesses and speculations or, if you are a fan of the Browns, tales of divine intervention). The collision of the ball with the upright gave the ball a lot of spin. Although the motion was complicated, the general direction of the spin was that the bottom of the ball rotated away from the players (the ball had backspin).

When the ball hit the horizontal support post, the spin tended to slide the ball’s bottom surface along the post, away from the players, but because the ball hit hard, it flattened on the post and could not slide. The resulting friction force on the ball from the post opposed the sliding and thus was directed back toward the players. So, when the ball recovered from the impact and began to bounce away, the friction force launched it back toward the players, sending it over the crossbar.

“Physics is everywhere” and is even in a Browns-Ravens football game.

1.78  Nike football commercial: real or fake?
Jearl Walker www.flyingcircusofphysics.com
Nov 2007 Controversy rages across sports blogs and video sites about a Nike commercial starring the famous footballer Ronaldinho, who performs four stunning shots at a goal. With each of the quick, successive shots, the ball bounces high from the crossbar on the goal and returns to Ronaldinho, who fields it and makes the next shot. Is the video real or fake? Here is the link for you to decide.

http://www.metacafe.com/watch/804642/unbelievable/ Wait until he starts shooting the ball toward the goal

If you search through the posted comments about the video, you’ll find several arguments about why the video must be fake. Some people argue that the ball control is just unbelievably good and thus cannot be real. Other people argue that slow-motion analysis reveals some inconsistencies in the video, such as the ball briefly disappearing or the background abruptly changing. Other people staunchly defend the video as being real, dismissing the doubters.

All this stuff consists of little more than opinions. The power of physics is that you can cut through opinions to get at the truth.

Here is what I see in the video. Ronaldinho kicks the ball below its center so as to send it upward to hit the crossbar. Kicking low on the ball creates backspin. That is, the top rotates back toward Ronaldinho (hence backspin) and the bottom rotates away from him. When the rotating ball hits the crossbar, a friction force acts on the ball at the point of contact. Because the front of the ball is rotating upward, the friction force acts downward on the ball, opposing the tendency of the ball’s surface to slide upward across the crossbar. Although the friction force is very brief, it is enough to flatten the rebound path, perhaps even noticeably sending the ball downward.

Racquetball players know this result well. When a player wants the ball to rebound high, the player strokes the ball somewhat across the top to give the ball topspin. Then the friction force on the ball during the collision with the wall is upward, sending the ball upward. With backspin and a downward friction force, the ball leaves the wall headed downward toward the floor. Racquetball players use topspin and backspin to confuse an opponent about the direction a rebounding ball will take.

What do we see in the football video? With each shot, the ball rebounds high (in fact, impressively high), not downward. So, sorry, I just don’t believe the video. What do you think?

What good is physics? Physics can keep you from being fooled.

· · Griffing, D. F., The Dynamics of Sports: Why That's the Way the Ball Bounces, Dalog Co., 1982 (P. O. Box 243, Oxford, Ohio, USA 45056), pages 166 ff
· · · Andrews, J. G., "A mechanical analysis of a special class of rebound phenomena," Medicine and Science in Sports and Exercise, 15, No. 3, 256-266 (1983)
· Walker, J., "Success in racquetball is enhanced by knowing the physics of the collision of ball with wall" in "The Amateur Scientist," Scientific American, 251, 215-227 + 230 (September 1984); reprinted with added notes in J. Walker, Roundabout: The Physics of Rotation in the Everyday World, Freeman, 1985, pages 8-12
· · Bridge, N. J., “The way balls really bounce,” Physics Education, 33, No. 4, 236- (July 1998)
· · · Cross, R., “Grip-slip behavior of a bouncing ball,” American Journal of Physics, 70, No. 11, 1093-1102 (November 2002)
· · · Cross, R., “Bounce of a spinning ball near normal incidence,” American Journal of Physics, 73, No. 10, 914-920 (October 2005)

Want more references? Use the link at the top of this page.

1.81  Robbie Maddison’s motorcycle jump
Jearl Walker www.flyingcircusofphysics.com
April 2009   Here is, arguably, the most impressive motorcycle jump ever made --- Robbie Maddison roared off a ramp at 80 kilometers per hour and landed on top of a replica of the Arc de Triomphe, 37 meters above ground level. And then he drove off one edge and freely fell until he slammed into a descent ramp. The danger was fascinating but something else caught my subconscious attention, something that required me to watch the video a dozen times before I understood what I was seeing.

Here are several links to the video.

http://www.metacafe.com/watch/yt-MLejkyXbJlc/robbie_maddisons_2008_new_years_eve_jump_in_hd/

http://www.youtube.com/watch?v=pbMt5ZrGtDo

http://gorillamask.net/gm_media.php?show_page=video&page_id=21027

When an object is rotating, we can describe the “amount” of its rotation with a property called angular momentum, which depends on how fast the object is rotating and how its mass is distributed around the rotation axis. It is not something for which you will have an intuitive feel, although it is behind the magic of an ice skater’s spin and a ballet performer’s tour jete.

Here is the big point.

The angular momentum of an object (this measure of the rotation) can change only if a torque (due to a force) acts on the object.

Although the ideas of torque and angular momentum are abstract, you have playground experience with them. For example, if you push on a stationary merry-go-round at its center, you cannot make the merry-go-round rotate because the torque associated with such a push is zero. The angular momentum of the merry-go-round remains zero.

However, if you push along the rim, you are applying a torque to the merry-go-round, making it rotate and increasing its angular momentum. If you then push along the rim in the opposite direction, your torque causes the angular momentum to decrease, and so the merry-go-round slows and stops.

Let’s consider Robbie Maddison and his motorcycle as a single object and consider the torques acting on it when it is airborne. When the Maddison-motorcycle object left the ramp, it had a certain amount of angular momentum because of the rotation of the wheels.
 
If we make the reasonable assumption that the air drag did not produce an appreciable torque on the object, then we must conclude that the angular momentum of the object did not change during the flight to the top of the replica. However, in the video we see that the motorcycle rotated around a horizontal axis so that it landed on its front wheel rather than its rear wheel.

Such a landing was probably essential to Maddison’s safety because landing on the rear wheel and then having the front wheel slam down on the landing platform could have caused him to crash.

But how could the motorcycle rotate in midair to a nose-down orientation? Where did the angular momentum of that rotation come from?

The gravitational force cannot provide the angular momentum because that force acts through the center of mass of the Maddison-motorcycle object. Thus, that force is like your push on the center of the merry-go-round ---- it will not cause the Maddison-motorcycle object to rotate during the flight.

When I first watched the video of the flight, I subconsciously knew that something was strange but only after watching it a dozen times did I pinpoint the rotation as being the mystery. Only then did I realize that Maddison controlled the angular momentum --- as he flew through the air, he applied the brakes to the wheels, decreasing their angular momentum. Because the angular momentum of the Maddison-motorcycle object could not change, the motorcycle itself had to rotate in order to maintain the total amount of angular momentum. Maddison very cleverly transferred rotation from the wheels to the motorcycle itself.

If, instead, Maddison had gunned the engine and dramatically increased the angular momentum of the wheels, the motorcycle would have rotated in the opposite direction, that is, nose up. Landing with the motorcycle vertical or upside down would have been disastrous.

To see the difference between applying the brakes and gunning the engine, note that in the video the wheels rotate clockwise in our view and thus have a certain amount of clockwise angular momentum when the motorcycle leaves the ramp. By slowing the wheels with the brake, the motorcycle must then rotate clockwise (bringing the nose down) in order to maintain the same total amount of clockwise angular momentum. If Maddison had gunned the engine and increased the clockwise angular momentum, the motorcycle would have had to rotate counterclockwise to offset that increase.

Some motorcycle performers bear down or pull up just as the motorcycle is leaving a ramp. Such action may have a small effect on the flight. The performer may also move away from the normal sitting position during the flight in order to affect the motorcycle’s orientation. This is certainly used by performers in X games in which a performer might almost completely lose contact with the motorcycle in midair, but I cannot see that Maddison used any technique like this.

When Maddison drives his motorcycle over the edge of the replica and free falls, the Maddison-motorcycle object again rotates to a nose-down orientation so that the motorcycle can land on both wheels almost simultaneously on the descent ramp. However, this time Maddison did not control the rotation. When he leaves the edge, the wheels are rotating only slowly. Even if he applies the brakes, there is little angular momentum to be transferred from the wheels to the motorcycle itself.

This time, the nose-down rotation was due to the way the motorcycle left the replica. As the front wheel went over the edge, the front of the motorcycle began to fall, producing a rotation around the support point under the back tire. In this case, the gravitational force does change the angular momentum because it pulls the front end of the motorcycle down while the rear end is still supported.

Once the rear wheel went over the edge, the Maddison-motorcycle object had a certain amount of angular momentum, which did not change until the motorcycle hit the ramp. The rotation was not fast but was enough to bring the motorcycle into proper orientation. Although Maddison was well experienced in rotating the motorcycle by using the brakes during a jump, he had no experience with the rotation during such a long fall. He and his staff must have done calculations on the extent of rotation as a function of the distance of falling, and then they must have adjusted the height and slope of the landing point on the descent ramp.

There is nothing better than the possibility of death to sharpen someone’s appreciation of careful physics.

http://digg.com/extreme_sports/Robbie_Maddison_s_2008_New_Year_s_Eve_jump_in_HD

http://www.ehow.com/how_2092827_jump-fences-motorcycle.html instructions

http://www.youtube.com/watch?v=EvuXT3PIRRg part 1 of a longer broadcast

http://www.youtube.com/watch?v=_xQz3Zlg_CM part 2

http://www.youtube.com/watch?v=MLejkyXbJlc

http://www.youtube.com/watch?v=6iwiVwA221Q

http://www.metacafe.com/watch/yt-6iwiVwA221Q/robbie_maddison_new_years_eve_jump_2009/

http://www.youtube.com/watch?v=b33YSVSrRVo

http://www.youtube.com/watch?v=b33YSVSrRVo&feature=PlayList&p=32E4AC8AC3B01E11&playnext=1&playnext_from=PL&index=3

http://www.youtube.com/watch?v=vyQ_e_5wAzU

http://www.metacafe.com/watch/1030860/motorcycle_jump_robbie_maddison_red_bull_experiment/ distance jump. You can see the bike orientation change.

Want more links? Go to this pdf file and scroll down to item 1.81.

1.91  Pub trick --- balancing a coin on a folded paper edge
Jearl Walker www.flyingcircusofphysics.com
February 2008   Hold a crisp (new) dollar bill upright in front of you so that the numbers are right side up. Fold the top half down onto the bottom half, and then crease the folded edge so that it both straight and sharp (the paper bends tightly around the fold). Stand the bill up on a table, with the folded edge horizontal and at the top and the splayed free edges on the table. Challenge a friend there in the bar (or the family recreational room) to balance a coin on the folded straight edge. Of course, your friend will laugh at you, saying “that’s impossible!” So, you respond with, “Well, I can easily do it. Why can’t you?”

Although in principle the coin can be balanced if its center of mass (the center of its mass distribution) is placed directly above the folded straight edge, finding that precise positioning and then releasing the coin without disturbing it is almost impossible. If the center of mass is even slightly to one side of the edge, the gravitational pull on that side of the coin exceeds the pull on the other side, and, like an unbalanced see-saw, the coin rotates around the edge. And the coin is also sure to rotate off the bill if your release gives it even a slight rotation.

Of course, if the support were wider, positioning the coin would be easier, but that is why you sharply crease the bill before you challenge your friend.

After your friend gives up, you balance the coin on one try and can even lift the bill without spilling the coin. Here is the secret: As shown in the video from easybartricks.com,

http://easybartricks.com/balancing-coin.html ,

you add another fold to the bill by folding the right side onto the left side. Sharply crease the new fold and then set the bill down on its splayed free edges so that it forms a V as seen from above. With a bit of care, position the coin with its center approximately above the apex (point) of the V. Then, pull the ends of the V in opposite directions so as to straighten out the V until the original fold is again straight. If you have steady hands, you can even lift the bill without spilling the coin.

That much is shown in the video, but the real challenge here is to explain why the trick works. Stability is very difficult to achieve if you attempt to balance something on one or two points. On one point, a chance disturbance (such as your release) can easily rotate the object’s center of mass so that it is no longer exactly above the support point, and so the gravitational force continues the rotation.

The situation is hardly better with two support points, as someone might have if walking along a stretched high-wire in a circus act. Although the object is relatively stable parallel to the line connecting the support points, it is unstable against any chance motion perpendicular to the line. This instability is not improved if there are many support points along the line, which is the situation you initially have with the dollar bill folded only once.

However, if the object is supported by three points that do not form a straight line, then it might be stable. And that is exactly what you set up if you make a second fold on the dollar bill. In fact, you have many points of support that form a V under the coin. As long as the coin’s center of mass lies above the region anywhere within the V, it is relatively stable.

When you pull the bill to straighten out the folded edge, the sharply creased second fold maintains its shape and thus the bill still forms a V below the coin. Although the V is now smaller, the coin is still stable is its center of mass lies above the region within the V. Because the V is hidden below the coin, the person you challenged cannot see it and thus can only marvel at your ability to balance the coin after you have apparently straightened out the bill.

1.94  The dambusters of World War II
Jearl Walker www.flyingcircusofphysics.com
June 2008   Last month marked the 65^th anniversary of the Allied attack on the German dams in the Ruhr, using a very unconventional weapon---a rotating bomb that skipped over the water and then rolled down the dam face to explode at a predetermined depth next to the base of the dam. The inventor was Barnes Wallis, an aeronautical engineer who designed the British R100 airship in the 1920s.

Through calculation and experimentation, he realized that the massive dams, which were vital to the German war effort, could not be breached by standard bombing. Indeed, if only one bomb were used, the bomb would have been so large that the airplane could not have taken off and carried it from England to Germany. Wallis and the RAF also knew that torpedoes could not be used against the dams because torpedo nets were stretched across the lakes to catch any torpedo dropped by an attacking airplane.

Wallis soon hit upon the idea of dropping a rapidly rotating bomb that would skip over the water like a stone thrown by a child, skipping over the nets and smacking against the dam wall. Although Wallis first considered a spinning spherical bomb, he eventually settled on a cylindrical bomb that would be given a backspin of about 500 revolutions per minute in the airplane prior to release. The rotation was set up by a system of sprockets and chains (somewhat like on a motorcycle) that was driven by the main hydraulic system of the airplane.

Here are the three points of Wallis’s argument for using rotation and backspin:

1. The rotation stabilized the cylinder during the fall and then during the skipping flight to the dam, much as rotation stabilizes a gyroscope.

2. Because of the backspin, the bottom surface rotated toward the dam and thus moved in the same direction as the bomb as a whole. That meant that the surface was moving at high speed when it hit the water, driving up a ridge of water in front of the point of impact. The bomb bounced upward and forward from that ridge. Although water is certainly fluid, when it is hit rapidly, it is almost rigid, a feature that you may have noticed if you have ever “belly-flopped” (belly first) or “cannon-balled” (rear end first) from a high diving platform into a pool of water.

3. When the bomb hit the dam wall, it was still rotating and thus rolled down the wall to the base of the wall, which is where it was designed to explode. If the bomb had exploded at the water surface, it might have broken some of the wall but perhaps only a small of amount of water would have been lost through such a break at the top. However, if the bomb cracked the wall at the bottom, the very high water pressure there would blow the wall apart. That was Wallis’s plan --- one or two carefully placed bombs could destroy what hundreds of larger bombs dropped directly on the dam could not destroy.

On May 17, 1943, three groups of Lancaster bombers left England for the attack, flying in moonlight just barely above the water in the English Channel and then barely above the trees over the land, hoping to avoid German radar. When the bombers reached a dam, not only did they have to attack the dam in only moonlight, they had to release each spinning bomb at a predetermined height and distance from the dam. The height was short, about 18 meters, or otherwise the impact would burst the bomb package. At that time, airplanes did not have altitude sensors that could measure such a short height. So, the RAF devised a surprisingly simple scheme. A spotlight was mounted under the front of the airplane and another was mounted under the belly, and the two beams were angled such that when the airplane was at the correct height, the two spots of light on the water overlapped.

The attack on the dams is depicted well in the 1954 movie The Dambusters, based on the 1951 book The Dam Busters by P. Brickhill. Below here I’ve listed several links to clips from the movie. I recommend that you watch at least the video about the attack on the first dam, the Moehne, to get a feel for the conditions. The first bomb rolled down the dam just right but failed to break it apart. The second bomb overshot the dam and exploded when it landed on the power station on the opposite side. The third bomb hit exactly right but seemingly failed to break the dam. As the next airplane made its run at the dam, the dam suddenly broke apart. Wallis was exactly right --- the shock waves from one or two bombs at the base of the dam was enough to rupture the concrete and allow the high water pressure at the base to blow out the dam.

The dams destroyed by the spinning, skipping bombs that night seriously damaged the German war effort. The attacks also resulted in significant numbers of artillery units being moved from the frontlines to the remaining dams. However, for countless people on both side of the war, the intriguing aspect of the dambusters is how the physics of a child’s game of skipping rocks could be employed in destroying massive concrete constructions.

Some of the links here take you to the movie’s version of the attack on the second dam and several old documentaries about the dambusters and their bombs, including the experiments with spherical bombs. There are also links to some original footage of the German tests with skipping bombs---they were rocket propelled as they dropped away from the airplane. (Presumably the tests were not continued because the German V-2 rockets that were bombarding England were so successful.) I’ve also included links to video about the anniversary ceremonies that were held last month. The photo here (from d1ngy_skipper) shows a Lancaster bomber at the ceremonies. 

http://www.youtube.com/watch?v=lCRIsjJFRNo&feature=related 1954 movie The Dambusters. Here is the part about the attack on the first dam.

http://www.youtube.com/watch?v=JM1VGw0wM7k&feature=related Here is the part of the 1954 movie that shows the attack on the second dam

http://www.youtube.com/watch?v=o3ohMEZ-d3I&feature=related Video of original testing, including one where the bomb exploded the airplane

http://www.youtube.com/watch?v=qrN0iVJjLgU Documentary, including original footage of the early test of the bouncing bombs and comparison between the spherical and cylindrical versions of the bomb.

http://www.youtube.com/watch?v=93AQQ9qYoQo The German version of the bouncing bomb

Dmbusters anniversary in May 2008

http://news.bbc.co.uk/2/hi/uk_news/7404052.stm video news item about the anniversary, with a Lancaster airplane flying by

http://news.bbc.co.uk/2/hi/uk_news/7405514.stm video from the cockpit of the Lancaster airplane during anniversary flyby

http://news.bbc.co.uk/2/hi/uk_news/7404447.stm News item about the dambusters

http://www.dambusters.org.uk/index.htm Dambusters web site

· Brickhill, P., The Dam Busters, Evans Brothers, London, 1951
· Stinner, A., "Physics and the dambusters," Physics Education, 24, 260-267 (1989)

1.94  Stone skipping on water
Jearl Walker www.flyingcircusofphysics.com
June 2006   Recent experiments and wonderful high-speed photos reveal the mechanics of a stone skipping over water. The stone, actually an aluminum disk, was launched by a catapult device that could control both launch speed and rotation rate. The researchers discovered (or rediscovered) that if a stone is to skip, its speed must exceed a certain threshold value or the stone merely skims (surfs) over the water top for a short distance before stopping and sinking. The stone’s rotational speed must also exceed a certain threshold value. The spinning stabilizes the stone much like spinning stabilizes a gyroscope. Then the stone maintains the same orientation (with the front end tilted upward by 10º to 20º from the water surface) for its entire skipping path. From skip to skip, its horizontal speed is almost constant, but its vertical speed (due to its being thrown upward by each crash into the water) decreases, until finally the stone just skims. A video of Kurt Steiner setting the world’s record of 40 skips can be seen at www.pastoneskipping.com/steiner.htm on the Web. 

· · ·  Bocquet, L., “The physics of stone skipping,” American Journal of Physics, 71, No. 2, 150-155 (February 2003)
·  Dume, B., “How do stones skip?” Physics World, 16, ?? (January 2003)
· ·  Clanet, C., F. Hersen, and L. Bocquet, “Secrets of successful stone-skipping,” Nature, 427, No. 6969, 29 (1 January 2004)
· · ·  Nagahiro, S., and Y. Hayakawa, “Theoretical and numerical approach to “magic angle” of stone skipping,” Physical Review Letters, 94, article # 174501 (4 pages) (6 May 2005)
· · ·  Rosellini, L., F. Hersen, C. Clanet, and L. Bocquet, “Skipping stones,” Journal of Fluid Mechanics, 543, 137-146 (2005)
·  Bocquet, L., and C. Clanet, “The mystery of the skipping stone,” Physics World, 19, No. 2, 29-31 + front cover (February 2006)

Want more references? Use the link at the top of this page.

1.97  Cats turning over to land in a fall
Jearl Walker www.flyingcircusofphysics.com
Sep 2008    If a cat falls out of, say, a tree, it somehow knows how to rotate itself to land feet first, so that its legs can act as shock absorbers. In that way, the cat takes longer to come to a stop, which means that its acceleration (which could be harmful or even lethal) while stopping might be only moderate. Here are two links to the same video (but one with slow motion) showing a cat as it falls from a tree.

http://www.youtube.com/watch?v=_q_ULVhyfJg&feature=related skip the commercial at the start. 80 ft fall. Watch the tail.

http://www.youtube.com/watch?v=ZRZimLYiO9Y Here is the same fall but with footage after the fall to show that the cat is (probably) ok.

The landing is understood but the rotation process has been controversial for centuries. In The Flying Circus of Physics book I outline the two main arguments. One of them involves the tail: The cat quickly pulls in its front legs and then whips its tail around counterclockwise. Because the cat is isolated from any torque (there is no outside force to cause it to rotate), the counterclockwise motion of the tail must be balanced by a clockwise motion of the rest of the body. We attribute this need of balance to the conservation of angular momentum. Angular momentum is a measure of the rate of rotation and the distribution of mass around the axis of rotation. The point here is that, with no outside torque to change the rotation, the rotation of part of the cat must be balanced by the rotation of the rest of the cat in the opposite direction.

Because the front legs are pulled in, the front half of the body is easier to rotate and thus rotates a bit farther than the rear half. Of course, this leaves the cat somewhat twisted. So, it then pulls in its rear legs and extends its front legs. Now the rear half rotates more than the front half. By now the cat should be approximately in a feet-down orientation so that it can land.

Cats usually do not take physics courses, but they have an intuitive feel for at least this much physics. You and I don’t have that much --- if we fell out of a tall tree, we would just wildly wave our arms and legs. A cat on the ground would surely laugh at our antics. Well, cats are actually way too smug to laugh, but they would at least inwardly grin.

· "Photographs of a Tumbling Cat," Nature, 51, 80-81 (1894)
· McDonald, D. A., "The righting movements of a freely falling cat (filmed at 1500 f.p.s.," Journal of Physiology, 129, 34P-35P (1955): special pages devoted to Proceedings of the Physiological Society for 15-16 July 1955
· · ·  Routh, E. J., Dynamics of a System of Rigid Bodies, Part 1, Dover, 1960, page 238
·  McDonald, D. A., "How does a cat fall on its feet?" New Scientist, 7, 1647-1649 (1960)
·  McDonald, D. A., "How does a man twist in the air?" New Scientist, 10, 501-503 (1961)
· · ·  Kane, T. R., and M. P. Scher, "A dynamical explanation of the falling cat phenomenon," International Journal of Solids and Structures, 5, 663-670 (1969)
· · · Essen, H., "The cat landing on its feet revisited or angular momentum conservation and torque-free rotations of nonrigid mechanical systems," American Journal of Physics, 49, No. 8, 756-758 (August 1981)
· Cooke, P., "Acrobatics: physics with a twist," Science 84, 5, 86-87 (June 1984)
· Darius, J., “The tale of a falling cat,” Nature, 308, No. 5955 (8 March 1984)
· · Edwards, M. H., "Zero angular momentum turns," American Journal of Physics, 54, 846-847 (1986)
· Laws, K., "Comment on 'Zero angular momentum turns'," American Journal of Physics, 56, 81 (1988)
· Edwards, M. H., "Reply to 'Comment on zero angular momentum turns'," American Journal of Physics, 56, 81-82 (1988)
·  Fredrickson, J. E., "The tail-less cat in free fall," Physics Teacher, 27, 620-625 (1989)
·  Galli, J. R., “Angular momentum conservation and the cat twist,” Physics Teacher, 33, 404-406 (September 1995)
Want more references? Go to the reference list for Chapter 1 of The Flying Circus of Physics book
http://www.flyingcircusofphysics.com/pdf/Chapter1_Ref_Com.pdf
and then scroll down to item 1.97
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