High School SMILE Meeting
02 May 2006


Porter Johnson (IIT physics)                  Future Plans
Porter discussed plans for more complete development of the SMILE and SMART websites over the summer. The database of academic year mathematics and physics lessons is located at AcademicYearbyCategory It has been arranged by category as follows:

  1. Mathematics:
  2. Physics (each with several sub-categories)
For several years we have maintained a guest book on the SMILE website. There are entries from e-visitors from all over the world, who have put our material to a seemingly endless variety of uses! You may view that guest book at the following URLhttp://www.iit.edu/~smile/guests/guestbook.html.  You may also add your own comments on our new guestbook link found near the bottom of the home page.

According to plans, math and physics lessons for the 2005-2006 Academic Year will be added to this database during Summer 2006.  In addition, the lessons will be further divided into subcategories and rearranged, as appropriate. In addition the recent academic year lessons in high school biology and chemistry will be organized on the SMART website.  This database will be maintained for the foreseeable future.

The SMILE website will be officially finalized and organized to include such items as The History of The SMILE Program 1986 - 2006, descriptions by staff members and participants of the impact of the SMILE Program on their professional lives, etc. Anybody who wishes to provide a written account of their personal experience in the program should send it in electronic form to me. [Porter.Johnson@iit.edu or johnsonpo@iit.edu].

Brenda Daniel (Fuller Elementary School)                    Time for Kids ®
distributed copies of the version of Time Magazine for children -- provided gratis -- to her 4th grade class. The children enjoy reading this magazine [http://www.timeforkids.com], which has dealt with scientific topics such Pluto and planet X, the effects of smoking on health, and ecological systems. The magazines also strengthen the skills needed for taking the ISAT tests. Teachers were supplied with teachers’ guides, sample projects, and the like with each issue of the magazine. Worth knowing! Thanks, Brenda.

Nneka Anigbogu (Jones College Prep, math)              Math Ideas for Non-College Prep Students
Nneka showed us a way to teach exponential decay using M&Ms® or Skittles®! We divided into three groups, each with a small bag of M&M’s and a medium sized plastic cup. We counted the number of candies in our bag and put them into the cup (53-55 were the numbers to start). Then we shook the cup and tossed the M&Ms out (like dice) and counted the M&M’s with the M showing (heads up). The candy pieces that landed with the M up were put back into the cup, which was shaken and tossed once more. Again, about half of them remained. We continued the process. Here are the data recorded in tabular form for the groups:

M&M's Toss
Trial Number  Group #1 Group #2 Group #3
1 53 55 54
2 29 25 21
3 14 08 16
4 05 08 07
5 00 04 02
6 - 02 01
7 - 01 00
8 - 00 -
One might expect the number remaining after n tosses, Yn, to decrease exponentially with n according to the formula
Yn = Y1 (1 - r)n   ...   with    r = 1/2.

She drew a graph of the number of M&M’s remaining versus the number of tosses, obtaining a profile that looked roughly exponential. She estimated the parameter r by using the formula Y2 = Y1 (1 - r), or

r = 1 - Y2 /Y1

We obtained r = 0.45, 0.55, and 0.57 for the three cases -- the extrapolated numbers using these values of r being fairly close to the actual results.

For more candy games see the M&M's website:  http://us.mms.com/us/fungames/games/. A good Phenomenological lesson -- edible too! Thanks, Nneka.

Walter Kondratko (Fenger HS, chemistry)                     Stuff From Class
showed us a crystal that was grown in his class; the kit can be ordered on the website  http://scientificsonline.com/product.asp?pn=3081666&cmss=grow+crystal. Walter then showed us a Crookes tube  http://en.wikipedia.org/wiki/Crookes_tube. A current was passed through the tube,  using a high voltage source (5000 Volts -- without the ballast circuit usually found in house fluorescent lights). A fluorescent coated strip mounted vertically within the tube allowed us to see the path of a  beam of electrons through the tube. Walter showed that the beam could be deflected up or down with a horseshoe magnet. Then he showed us a ball and stick model of an amino acid to illustrate chirality/enantiaomers [http://www.brynmawr.edu/Acads/Chem/mnerzsto/PolarimetryExercise.htm], and showed that they were mirror image isomers, which are not geometrically identical. These amino acids produce optical rotation.  The plane of polarization of light rotates  in different directions for dextrorotary (right-rotating) and levorotary (left-rotating) compounds.. For details see Stereochemistry Tutorial:  http://facultystaff.vwc.edu/~jeaster/courseinfo/Tutorials/stereochemistryl.html.
Beautiful phenomena -- quite illuminating! Thanks Walter.

Bill Blunk (Joliet Central HS, retired)              Giveaways
gave us 3 slides of pictures in an article about the release of a captured grizzly bear by the Montana Division of Natural Resources in 1987.  The culvert trap was not properly secured to the bed of the pickup truck.  When the grizzly turned and tried to attack a ranger atop the culvert track, the driver gunned the engine and drove the truck out from under the trap and ranger.  Lack of knowledge of Newton's First Law resulted in an injured driver, and the bear was subsequently killed.
Physics rules! Thanks, Bill.

Arlyn VanEk (Illiana Christian HS, physics)                 Impedance Matching
held one end of a piece of rope, and a volunteer held the other end.  Arlyn then shook his end of the rope up and down, while the volunteer held the other end fixed.  By adjusting the tension in the rope, Arlyn was able to set up a standing wave with two nodes.  He reduced the tension, and was able to get standing waves with one internal node, and with no internal nodes at all.  By moving his end in a circular path, Arlyn was able to set up a spiral standing wave. He then tied an equal length of lighter rope to the heavier one, and the process was repeated.  Arlyn was unable to produce any standing waves in this case.  With the double rope held fixed under tension, Arlyn plucked his end, and the resulting pulse traveled toward the other end. But when the pulse got to the point where the two ropes were connected, it was partially reflected and partially transmitted.  How come? Arlyn said that there was a mismatch in the (mechanical) impedance at the junction.

The mechanical impedance of a vibrating system is defined in analogy to the electrical impedance of an electric circuit [for details see T.D. Rossing and N.H. Fletcher, Principles of Vibration and Sound -- Springer Verlag 1994, ISBN 0-387-94336-6], as illustrated in the table below: [Note: i = Ö(-1) and j = -i.]


Item Electrical Mechanical
Driving Term Voltage: V0 e-iwt Force: F0 e-iwt
Response Current: I0 e-iwt Velocity: v0 e-iwt
Impedance Z(w) = V0 / I0 Z(w)= F0 / v0
Dynamics L I ' + RI + Q/C = V  mv' + Rv + kx = F
Form Z = R  + j (wL -1/(wC))     Z0 = R + j (wm - k/w)

In both cases, the relevant impedance must match for smooth transfer of energy from one system to another.

Let us consider the (small) transverse displacement of an ideal flexible string of length L that is held fixed at x = 0 and terminated at x = L. Using the formula  y(x,t) = A sin kx e-iwt, the corresponding transverse velocity is v(x,t) = -i wA sin kx e-iwt. The transverse force exerted by the string at x = L  is equal to  T ( y/ x) evaluated at x = L, which equals   kT cos kL e-iwt. The mechanical impedance is the ratio of the transverse force to the velocity x = L.  We obtain:

Z 0=  k T cos kL / [- i w sin kL ] = -j k T cot kL /w
Let us apply the relation w / k = v = Ö(T/m), where the speed of traveling transverse waves, v, is expressed in terms of the tension T and the mass per unit length m, to obtain
 Z0 =  -j kT cot kL / w = - j Ö(T m) cot kL
This input impedance must match on both sides when two ropes are tied together, for effective transfer of energy across the interface.  For details see Mechanical Impedance:  How It Works and Why You should Care on the Symposium Acoustics website: http://www.symposiumusa.com/tech2.html.

If you taper a rope gently (like a whip) you can transfer the wave all the way down to the tip of the whip. Arlyn used a real bull whip to show this, and it made a loud crack -- a sonic boom. For additional details see The Shape of a Cracking Whiphttp://www.npr.org/programs/wesat/features/2002/june/whip/index.html. The whip is an impedance transformer. A megaphone is another example of an impedance transformer, where the megaphone makes a gradual change for the air within the cone, from warm near the mouth to cooler air near the end of the megaphone.
Cracking phenomenological physics, Arlyn.  Thanks.

Erik Jurgens (Joliet West HS, physics)                            Going From a Circuit Schematic to the Breadboard
Erik made “components of circuits” molded out of toilet paper rolls and boxes (to show resistors, voltage sources, etc. with colorful yarn at either end to represent wires. With magnets attached to the yarn and the components, circuits could be illustrated on the blackboard. The students could then visualize the circuit before setting it up in the laboratory.  An example of "roll playing"!
Very interesting and useful! Thanks, Erik.

Marva Anyanwu (Wendell Green Elementary School)                     Earthquakes, and Other Things
Marva asked how many earthquakes occur in a day worldwide? It turns out that one occurs every 10 seconds (about 3 million per year that register significantly on the Richter Scale; see http://neic.usgs.gov/neis/eqlists/eqstats.html). Marva also brought in an article about the proposed 10th planet [http://www.gps.caltech.edu/~mbrown/planetlila/]. She discussed whether Pluto should be considered as a planet, and whether the number of planets should be 8, 9, or 10. Marva also passed out a table listing the densities of planets in the solar system:  http://www.enchantedlearning.com/subjects/astronomy/planets/
Fascinating, Marva!  Thanks.

Bill Colson (Morgan Park HS, math)                       Interesting  Websites
learned about the following interesting websites from  Make Magazine, Vol 05 http://www.makezine.com/:

Thanks, Bill!

Porter Johnson (IIT physics)                       Shroud of Turin Project
learned about a Shroud of Turin Project website from Steve Feld, Editor of  ThinkQuest NYC Newsletter: http://shroud2000.com/LatestNews.htm.  The site is featured on the Landmarks for Schools homepage http://landmark-project.com/index.php.  The website describes scientific investigations on the authenticity of The Shroud of Turin. It gives a link to various English and Greek Language versions of a Biblical eye-witness account in the Gospel of John, Chapter 20, verse 7, in which the shroud of Jesus is specifically mentioned [Online Parallel Biblehttp://bible.cc/john/20-7.htm]. Finally, it provides information to suggest that Leonardo DaVinci may actually have created the shroud, discussing his motivations as well as his capabilities.  A re-creation of a Shroud Image  has recently been done by Stephen Beckman, using a camera obscura -- along with other materials and technology available in Leonardo's era. This Shroud of Turin website is http://shroud2000.com/LatestNews.htm.  The website merely presents the information, allowing visitors to the website to express their own opinions on this subject.  The results of an online poll are presented.  The project provides an excellent example of Scientific Inquiry! Thanks.

The following people were unable to do their presentations because we ran out of time.  If a written version is available, we will post it. Please send it electronically to Porter Johnson at this email address:  Porter.Johnson@iit.edu.

  1. Chris Etapa               Periodic Table Patterns
  2. Fred Schaal              Collapse
  3. Larry Alofs               Voltage dividers
  4. Bud Schultz               A little air
It's been great! Thanks for the memories.

Notes prepared by Ben Stark and Porter Johnson.