High School Math-Physics SMILE Meeting
22 February 2005
Notes Prepared by Porter Johnson

Walter McDonald [CPS substitute teacher]              Buoyancy
Walter presented us with two questions on Buoyancy from the book 1000 Play Thinks: Games of Art, Science, and Mathematics by Ivan Moscovitch. For details see the SMILE writeup of 24 September 2002: mp092402.html . Walter provided a clear "fish tank" reservoir filled with water, and we studied the questions and answers, drawing conclusions as given below.

  1. Playthink # 872
  2. Playthink # 874

Neat demos and good physics!  Thanks, Walter!

Fred Schaal [Lane Tech HS, mathematics]              Pump Up the Volume
Fred brought out a metallic box (appropriately decorated for holiday gifts of candy or sweets), along with a ruler.  Fred recruited an assistant, Charlotte Wood-Harrington, to make measurements of  its outside length L, outside width W, and height H. Charlotte obtained the following values:  L = 14.25 cm, W = 14.15 cm, and H = 4.50 cm.  We then treated the box as a Rectangular Parallelopiped, and computed its volume:

V = L ´ W ´ H = (14.25 cm) ´ (14.15 cm) ´ (4.50 cm) = 907.36875 cm3 » 910 cm3
Of course, a candy Aficionado or Gourmand would be more concerned about the interior volume of the box, which would be significantly less.  We estimated the difference to be 10% to 20%.  One could measure the interior volume of the box by seeing how much water it holds, using a graduated cylinder that holds up to 1000 cm3 (one liter) of water.

Porter Johnson mentioned that glasses in restaurants, cafes, and bars in Europe are commonly marked to indicate the volume of a given level of fluid.  These markings, which were a legal requirement in Germany, might be one of the following:

0,3 L = 3 dL     3 deciLiters,  or 300 cm3
0,5 L = 5 dL     5 deciLiters,  or 500 cm3
1,0 L 1 Liter,  or 1000 cm3

Watch out for those one liter beer steins!  Thanks, Fred!

Fred Farnell & Don Kanner [Lane Tech HS, physics]              Fizzing Pop Bottles
Fred and Don investigated this burning scientific and societal question: How and why do soft drinks -- which are often called "pop" in Wisconsin, "cold drinks" or just "coke" down South, "soda" in New England, and "cola" or "limonade" in Europe -- lose their FIZZ.  They put this question to direct experimental test, brought out several plastic bottles (about a half-liter in capacity) of Coca Cola™ and Dr Pepper™.  These recently purchased bottles seemed to be about the same temperature and internal pressure, since they felt "similar" when we squeezed them.  First we investigated the effects of (1) shaking the bottles a vigorously, and then allowing their contents to settle for a few seconds (until the foam disappears), as well as (2) opening the plastic caps slowly or quickly.  Here is a recording of some of our results:

Opening Speed?
- \ -
Shaken?

 Slowly Quickly
Not Shaken Slight hissing;
a little bubbling 		More Foam
Shaken Vigorously Slight hissing;
Lots of foam 		Bottle #1: lots of foam
Bottle #2: very little foam
Evidently, shaking the bottle tends to produce a more violent opening, as does opening the cap quickly.

Just what causes the violent foaming? Through class discussion, we identified the following points as likely to be relevant..

Don Kanner illustrated the phase rearrangement induced by shaking by drinking about half of the contents of one of the Coke bottles, re-tightening the cap, and shaking it vigorously.  When -- just as before -- the bottle was opened a little afterward, there was  foam all over the place! When he repeated the process of tightening the cap, shaking the bottle, and opening it several times, the amount of foaming decreased each time.  Finally, Don then tasted the contents --- flat Coke! He had removed most of the carbonation through this process. Several groups in the audience performed the same experiments, drinking some of the contents with small cups that Don had provided, with the same conclusions.  For a related discussion, see the discussion of metal cans of Guiness™ Stout  by Charlotte Wood-Harrington at the SMILE meeting of 28 September 2004: mp092804.html. Sweet science with sweet stuff!  Thanks, Fred and Don!

Bud Schultz [Aurora West HS, physics]              Dropping magnets through pipes, revisited
Bud recently obtained a set of 4 rather powerful Neodymium magnets [Item #35287 for about $3 -- for a picture click here] at a local outlet of American Science and Surplus [http://sciplus.com/].  These magnets were about 5 mm  ´ 7 mm  ´ 9 mm in size.  His presentation was an extension of those given by  Marilynn Stone, Don Kanner, and Bill Blunk, at  the Math-Physics SMILE meeting of 20 April 2004: mp042004.html. He dropped them -- first 1, then 2, then 3 -- through a vertical copper pipe 1.5 meters long, with an inside diameter about 12 mm --- standard half inch pipe. Its lower end was about 20 cm above floor level. Here are the times that we recorded for the magnets to descend and strike the floor, with various numbers of magnets attached together:

Number of Magnets Descent Time
1 6.1 sec
2 7.9 sec
3 7.7 sec
The magnets fell very nicely without coming apart -- in fact it was difficult to pull them apart.  The magnets were slowed down because of eddy currents induced in the conducting copper pipe, producing an opposing magnetic field to slow down the magnets. as described by Faraday's Law and Lenz's Law.  Interestingly, the longest time of fall occurred with to two magnets.  As the number of magnets in the array is increased, the falling time changes because of  the increased weight of the array and increased opposing eddy current forces.

Bill Blunk repeated his demonstration of the Math-Physics SMILE meetings of 20 April 2004 and of 08 September 1988 ph090898.htm, dropping an aluminum parking token through two pairs of magnets -- a configuration commonly found in coin-operated vending machines.

Ann Brandon mentioned that, at a recent meeting of the Illinois Section of the American Association of Physics Teachers [http://helios.augustana.edu/isaapt/] at UIUC, a magnet was dropped through a translucent plastic pipe with LED's attached across wire coils, which had been wrapped closely around the plastic pipe at several locations. As the magnet passed inside the pipe and through a given coil, the corresponding LED would flash. Now, there's Faraday's Law for all to see! Isn't that the Cat's Meow!

An excellent phenomenological exercise!  Thanks, Bud!

Bill Shanks  [Joliet and New Lenox environs, retired]               Laser: Cheap!
Bill showed off a new laser that he had obtained as a "remainder"  at a Cummins Tools store:  http://www.cumminstools.com/index.htm.  The device contained a red laser beam driven by 3 button cell batteries, a hologram of a swan attachable to the front, a sonic blaster, and a Green Flashing LED.  On the package it said "This is not a toy!" -- but  -- "Why does it chirp like a bird?"  We attached the hologram to the front, and looked at the resulting pattern.  Then we compared it with a more powerful and more expensive Green Laser provided by Bill Blunk.  Interestingly, one could see the path of the Green Laser beam more readily than the red one, especially by standing behind it and looking within about 10 degrees of its direction.  Of course, both beams were easily visible when chalk dust was scattered along the paths of the beams.

Very impressive gadgets!  Thanks, Bill!

Notes prepared by Porter Johnson