High School Math-Physics SMILE Meeting
08 April 2003
Notes Prepared by Porter Johnson

Ajay Gambhir [United Scientific Supplies, Inc]     Distributor of Quality Laboratory Supplies
passed around the catalog for United Scientific Supplies, Inc [http://www.unitedsci.com/] which distributes science laboratory supplies to various retail supply houses.  His company is located at 4175 Grove Avenue, Gurnee IL 60031; the telephone number is [847] 336-7556, and their FAX is [847] 336-7571; and the email address is rsoni@unitedsci.com.

Ajay passed around the company catalog, and indicated that they were interested in supplying more sophisticated laboratory equipment appropriate for high school physics classes.   His company, a wholesaler that provides apparatus to various suppliers, is also interested in evaluating interest and relevance of other equipment that is available to them.  Finally, they have a more long-range goal of developing new products, based upon the interests and requirements of teachers.  Ajay is interested in establishing relationships with physics teachers, in order to get advice as to how to proceed.  You may contact him directly if you're interested.

We appreciate your interest in us and our program, Ajay!

Don Kanner [Lane Tech HS, Physics]      Paradox and a Pair o' Docks
Don had remarked at the last meeting that, because the lateral surface area of a cylinder of radius R and height H is A = 2 p R H, whereas its volume is V = p R2 H, it should follow that the cylinder of greatest volume for a given lateral area should be one of large radius R and very small height H. To illustrate the point, Don placed three transparent cylinders so they stood upright on the table. One was tall and skinny; it was made from a single transparency sheet with its short side (width w) folded around into a circle (circumference w) and its long side (height H) standing up. Its lateral area was therefore H w. The second (medium) cylinder was only half as tall, with height H/2 and circumference 2w, and therefore lateral area of (H/2) (2w) = Hw, the same as the tall one. The third cylinder was short and squat, half as high as the second one, with a height of H/4, and circumference of 4w, and therefore a lateral area of (H/4) (4w) = Hw, the same as the first two. Don arranged them on the table to lie concentrically and coaxial with each other, ie., the tall one was surrounded by the shorter medium one, which in turn was surrounded by the short squat one, all standing with a common vertical axis. Their bottom ends were closed off by the table, but their top ends were open. What next?

Don poured rice into the tall skinny cylinder in the center, filling it completely full to its very top. He pointed out that the volume of the rice must equal the volume of the tall skinny cylinder. Then -- beautiful to see! -- Don slowly and carefully raised the tall cylinder up off the table. As he did so, the rice spilled from its now open bottom end to occupy some of the volume within the medium cylinder. Don smoothed the rice flat, and we could see that it filled the medium cylinder to just half its volume. Wow! So the medium cylinder must be capable of holding twice the volume of rice as the tall skinny one! Finally, Don slowly raised the medium cylinder to spill the rice from its bottom end to occupy some of the volume enclosed within the short squat cylinder. When he smoothed the rice flat, we could see that it occupied just 1/4 of the volume of the short squat cylinder! Don then appealed to the fact that, if this process is continued indefinitely, the enclosed volume can be made arbitrarily large, as is illustrated in the following table, beginning with a sheet of height H and width w:

Number Height Width /
pR2 H
1 H w H w w / (2p) w2/(4p) w2/(4p) H
2 H  /2 2w H w w / p w2/p w2/(2p) H
3 H / 4 4w H w 2w / p 4 w2/p w2 H / p
4 H  /8 8w  H w 4w/ p 16 w2/p 2 w2 H/ p
5 H / 16 16w H w 8w/ p 64 w2/p 4 w2 H/ p
.   .   .
¥ 0 ¥ H a ¥
 ¥ ¥

Don mentioned that zero and ¥ often occur together in physical problems; i.e,  infinite resistance goes with zero current; infinite kinetic energy requires zero time elapsed; etc.

Don, you have done as promised!  Very nice!

Fred Schaal [Lane Tech HS, Mathematics]        Green Line '92-ing!
had been playing around with his calculator while riding the el, and began studying the following problem:  For a given triangle with vertices (A, B, C), draw the following lines:

These three lines intersect to form a smaller triangle within the original triangle ABC, in general. . What is the area of that triangle, in relation to the area of the original triangle?  By trying this for different triangles, Fred found that it was difficult to make the area of the smaller triangle more than about 18% of the area of the original triangle. Is there a general result? If so, what is it, and how is it proved?

Fred, you have constructed an unusual problem! Very Good!

Karlene Joseph [Lane Tech, Physics]     Wine Glass Resonance
brought in a  wide variety of wine goblets, and filled them to different levels with water.  She rubbed with her wetted finger in a circular fashion around the rim of one, while holding its stem with the other hand. To our delight, we  heard a musical sound, or ringing, as the glass resonated.  We made the following remarks, based upon our experiences:

For additional information on wine glass resonance, see the website Crystal Goblets Can Singhttp://www.ccmr.cornell.edu/education/ask/?quid=1143.

It sounds great, Karlene!

Michelle Gattuso [Carl Sandberg HS Orland Park, Physics]        Seeing Things with Bar Magnets
showed us how to see the fields produced by magnets, using an overhead projector, along with the (transparent) Magnetic Field Observation Box, which is available from Arbor Scientific [http://www.arborsci.com/detail.aspx?ID=662]. The following information is excerpted from that webpage:

Forget the mess of iron filings and the constraints of two-dimensional representations of magnetic fields - this self-contained device reveals the proper, three-dimensional nature of magnetic lines of force. The sealed acrylic box contains iron filings suspended in a silicone oil solution. A cylindrical magnet (included) is dropped into a central chamber to create the three-dimensional field. Other magnets can be applied to the sides or ends of the box to demonstrate interesting interactions between fields. Although primarily designed for individual study, the observation box can also be placed on an overhead projector for a two-dimensional demonstration of the field (4" x 2" x 2")
Activities and uses:  Use the Magnetic Field Observation Box to study magnetic fields in three dimensions. Look at the field from a single provided magnet or bring iron or another magnet near and see the results.  Bring another magnet close to the box and insert the bar magnet in the hole.  The iron powder is magnetized in two areas showing attraction and repulsion of magnetic forces.

Michelle inserted a magnet into the hole in the box, and we saw the field lines very nicely on the overhead projector.  She placed two magnets into the hole with like poles adjacent, and later with unlike poles adjacent.  It was quite easy to see the difference in these cases, with the field lines seeming to push the magnets apart in the first case, and to pull them together in the second case.

The projector is a godsend for this demo! Way Cool, Michelle!

Gary Guzdziol [Carol Roosevelt School, Science Teacher]      Atmospheric Physics
  did a series of experiments to demonstrate the effects of air pressure.  He held an empty, opened aluminum pop can with tongs, first putting a little water into the bottom, and then heating it over a small propane torch until mist began to come out. Then, he plunged the can into a tub of water, the opened top end first.  The can promptly collapsed, its lateral surface being pushed in.  Why?  At first, this seemed to be an inevitable consequence of air pressure.  Why wasn't water forced into the can, instead of air forcing the can to be crushed?  Remarkably, it was easier for the can to collapse than for the water to be pushed into it.  Just as a chain breaks at its weakest link, the easiest mechanism for pressure reduction is the one that occurs.  Amazing, when you think about it!

Gary then produced a few boiled eggs, from which he removed the shells.  Next, he lit a small piece of paper, which he pushed into a glass gallon [4 liter] jug.  Gary promptly placed a boiled egg to cover the opening at the top of the jug.  Gradually, the flame inside went out, and the egg was sucked into the jug.  Why?  The conventional explanation, that the oxygen inside the jug is removed by the fire, is incorrect --- since Carbon Dioxide, as well as smoke and water vapor, is copiously produced.  Rather, the effect is almost entirely thermal --- hot gas initially inside the jug is cooled, thereby reducing the pressure.  It must be so! Gary was then presented with the problem of getting the egg out of the bottle. He accomplished that task by holding his lips tightly to the opening and increasing the pressure inside the jug, while quickly turning it upside down. When he took his lips off the jug, the egg was pushed out because of the temporary rise in air pressure inside the jug.  Gary repeated the experiment several times, with complete success.

Gary's final experiment involved suspending a 55 gallon [250 liter] drum, placing about 1 gallon [4 liters] of water inside it, and heating the drum with a large propane torch [used by plumbers for melting lead].  After about 15 minutes, mist began to come out of the opening on the top of the drum.  He then turned off the heat source and closed the opening tightly with a cap and wrench. He placed about 20 liters of snow [conveniently available today!] on top of the drum to speed the cooling process, and said that we should step back a little bit and wait about 15 minutes for something to happen. We waited and waited and waited, and nothing happened!  How come?  It seems as though the pressure reduction inside the drum was not quite great enough to produce the expected collapse, since the air inside had not been replaced by steam in sufficient quantity.  At the end of class Gary opened the drum with his wrench, and the sound of air rushing into the drum could be heard by all. 

Better luck next time --- you nearly blew us away! Thanks, Gary!

Carl Martikean [Wallace HS Gary, Physics]      Maintaining Balance in Mathematics
first mentioned Jack Griffin, who was the leading character in the book The Invisible Man by H G Wells.  For background information check the website: http://www.pjfarmer.com/secret/invisible/im1.htmWells claimed that the man had become invisible because the index of refraction of his body had been made equal to the index of refraction of air, so that light would pass through him just as in air, without absorption or reflection.  Carl asked the following question:  How can this man see anything?  His eyes must have that same index of refraction, and thus cannot possibly focus light.  Is this whole thing just another hoax, or what?  Porter Johnson mentioned a related point: We cannot see well when under water because the index of refraction of the fluid in our eyes is almost identical to that of water. A swim mask resolves the problem.

Carl then called attention to an article Throwing Yourself into It by Adam Summers, Assistant Professor of Ecology and Evolutionary Biology at the University of California Irvine, which appeared in the magazine Natural History.  This article pointed out that the long-jump contest in the modern Olympic games differs from the contest in the original Olympics of 2500 years ago in at least two important respects:

Very interesting ideas and insights, Carl!

Camille Jensen [Bloom Trail, Biology and Physics]      How Strong Are Beetles?
passed around a sheet prepared by Dr Robert W Matthews, Dept of Entomology, University of Georgia, Athens GA 30602.  She used that laboratory experiment as a guide for a fascinating demonstration of the strength of bess beetles, which are easily located on the floor of oak forests during the fall of the year.  Or, you can purchase a Bess Bug Penny-Pull Kit: http://www.carolina.com/bessbugs/bessbug-penny-pull-kit/144145.pr Camille rigged a harness for these beetles using dental floss, attached the other end to a petri dish, and put pennies in the dish to see how many pennies the beetles could pull while under harness.  It was important to have a rough surface [paper towels], so that the beetles could develop traction.  She described measuring the speed, amount of weight pulled, and the distance traveled, as well as computing the coefficient of friction, work done, and power.  This is quite a novel illustration of basic ideas of mechanics, using beetle power! Amazingly, the beetles could exert a force of more than 20 times their body weight in pulling this dish across the table.  For for a U-tube video see: http://www.youtube.com/watch?v=9NbBMvJoiU4 But, does this also work with cockroaches??

Thanks for this novel approach, which combines biology and physics, Camille!

Bill Blunk [100 Year Old Spinthariscope], Ann Brandon [Waves and Resonance], Leticia Rodriguez [Mass], Bill Shanks [Persistence], and Monica Seelman [Psychic Puzzle] were unable to present today because we ran out of time.  They will present  at our next meeting, 22 April 2003!

Notes taken by Porter Johnson