Information:
• Earl Zwicker obtained an email message from a former SMILE participant and colleague, Arnold Burkert, calling attention to a presentation of how a mathematician, engineer, or scientist might write the  equation, 1 + 1 = 2, in a more "clear, scientific form". The result, then, should be more comprehensible to all concerned, shouldn't it? You may view a Microsoft Power-Point® presentation that appears on the [bilingual Afrikaans-English] website of the Department of Electrical, Electronic, and Computer Engineering of the University of Pretoria, South Africa. It may take a while to find and load this one, but it is well worth watching! Check it out! Thanks, Arnold and Earl!
  
• Deborah Koolbeck [Chicago Academy of Arts HS, physics]   discussed plans for assembling resources and services targeted specifically for high school mathematics and science teachers who are unable to obtain basic instructional support --- especially teachers in the Chicago Public School system.  These programs would be sponsored by the newly created Outreach Program Committee at Fermilab, under the guidance of its head, Dr. Chris White. [Note:  Chris is a full-time Physics faculty member at IIT,  winner of the 2002 IIT Excellence in Teaching Award, a superb phenomenological physics teacher, and a true friend and strong supporter of the SMILE program]!  The first step of this outreach program is to make an inventory of the most urgent needs of teachers, and to determine what resources can be obtained to meet some of these needs.  Specifically, Deb K [wearing her "other hat" of outreach coordinator at Fermilab] passed around a  preliminary questionnaire to survey certain specific needs of High School SMILE participants.  Fermilab has been able to obtain limited, precious resources that are specifically earmarked for Outreach. They want to have the greatest impact in providing significant, timely assistance to address the most urgent needs of beleaguered, stalwart mathematics/science teachers in local schools. By filling out and commenting upon a preliminary questionnaire, SMILE participants are serving as a vital focus group to improve the questionnaire itself, as well as to focus it upon the needs of the schools and the possibilities of developing an outreach program to address them.  Here are some of the issues in which they might be able to help you:
  • Would you like one of our technical experts to visit your school to talk to students about (1) accelerators, particles, and cosmology; (2) the daily life of our scientists/engineers; or (3)  role of computers in basic research?
  • Can we come to assist you in (1) setting up demonstration equipment or computers, or (2) presenting  basic ideas and concepts of physics to your students?
  • Would you like to have a direct email connection to an appropriate expert, so that you and/or your students could ask "far reaching" questions and obtain assistance?
  • Do you already make use of Fermilab for educational resources?  If so, how?
  • How can we help strengthen science education at your school?  How can we help you professionally, as well as in your science instruction?
  Thanks, Deb! You may also contact Deborah Koolbeck directly at her Email address:  koolbeck@fnal.gov. We look forward to working with you and Chris on these very exciting developments! 
• Michelle Jones [Morgan Park HS], a long-term participant and former staff member of SMILE whom we dearly remember, visited us to call attention to New Leaders for New Schools: TYPE 75 PRINCIPAL PROGRAM that addresses the challenge of urban school leadership.  More information, as well as an Online Application, is located on their website:  http://www.nlns.org/.  In addition, you may call the Chicago Office at 1 - 312 - 829-6547, or you may Email Michelle directly at mjones@nlns.org,  Thanks for telling us about this program. We still love you, Michelle, and hope that you have a "cross-over" hit!
• Porter Johnson asked the (not entirely hypothetical) question of whether a large (Volvo®) sedan could become "totaled" while running into the rear of a compact (Toyota®) sedan.  Interestingly enough, this can happen, since the accelerometer sensor to release the air bags is located behind the grill on some Volvo sedans, as well as on certain other cars.  If that grill is even slightly damaged, the sensor will cause both air bags to be deployed [essentially by firing explosive charges that resemble shotgun shells] --- which, in turn, often break the front windshield.  When this occurs with a relatively mature vehicle, the cost of repair becomes greater than the "replacement cost" of the vehicle less the "salvage value" of the vehicle "cannibalized" for spare parts. The vehicle is thus deemed a total loss by insurance adjustors.  This occurs, in spite of our naive assumptions based upon Newton's Laws of Motion.   Fairy tales can come true; it can happen to you ... occasionally!

Don Kanner (Lane Tech HS Physics Teacher)      Helicopter Whirligigs, General Relativity, and Forces
At our last meeting John Scavo was wondering how the number of blades on a propeller related to airflow and Richard Goberville had propeller whirligigs for all of us to take and experiment with. Don had collected all of the whirligigs from the other Lane Tech teachers at SMILE and modified them in an attempt to answer John's question. Here is the data table:

Having just used Karlene Joseph's and Dan Caldwell's paper plate and marble centripetal force demonstration in his classroom, Don showed us how to illustrate a celestial object being pulled into a black hole (sparing no expense -- ha!) using a marble whirling around inside a the top of a 1 liter plastic pop bottle held vertically with its mouth pointed toward the floor. When one stops rotating the bottle, the marble continues to whirl around the inside until it falls out the mouth. In Einstein's General Theory of Relativity, gravity corresponds to a distortion (intrinsic curvature) of the space around a mass. We are thus led to following  the question: Assuming that the mouth of the bottle is analogous to a black hole, what portion of the area near the mouth of the bottle best fits Einstein's description of space-time distortion?

Now who says that you can't teach about black holes in high school? Don referred to the classic film Frames of Reference by Hume and Ivey. The following description is adapted from information on  the website of the Department of Physics and Astronomy of the University of Victoria (BC, Canada), [http://www.phys.uvic.ca]:

FRAMES OF REFERENCE (Educational Services, Inc., 1960) 25 min, snd, b.w.
Professors Patterson Hume and Donald Ivey of the University of Toronto demonstrate the behavior of a body under the force of gravity as viewed from different frames of reference and the behavior of a frictionless puck on a rotating table in the laboratory. Two excerpts from this film are also available which present the above material in a condensed form:
1. "Excerpt 1", 7 min. QA839 F7. Shows gravitational effects.
2. "Excerpt 2", 5 1/2 min. QA839 F72. Shows rotational effects.

PJ Comment:  The idea of "tunneling into the center of force" is very old.  Isaac Newton criticized the Descartes model of the solar system, pointing out that this would be precisely the outcome of that mode.  The Bohr Atomic Model was roundly criticized during the period 1915-1925, because electrons in atomic orbits would be expected to "wind down" into the center of the nucleus, in a time of about 10^-9 seconds, because of the total power radiated by a free point charge q experiencing an acceleration of magnitude a. According to the Larmor formula

Finally, Don had a modified version of Gary Guzdziol's vacuum disk [mp111803.html]. By reducing the internal plastic disk's diameter, it was used as a washer for a nut on the end of an eyebolt to which a heavy cord was attached. Without the worry of string breaking, Don appeared to lift a stool with the device but left us wondering which force really lifted the stool.

Don also posed the challenge of how to get all the marbles to stay on a paper plate when the plate is rotated, as an extension of the lesson given by Karlene Joseph at the last SMILE meeting [mp111803.html]. Go for it, Don --- you're on a roll!

Leticia Rodriguez  [Peck Elementary School]       Chemical Tests
Leticia brought in a tray of materials which we were to categorize by their physical properties of form, color and texture.  She had put various types of food coloring close to these samples, so that SMILE participants (role-playing as third graders) could more easily distinguish them.  We were permitted to see, feel, hear, and smell them, after being assured that these particular materials passed relevant safety tests.  Here is a table summarizing our observations:

Fred Schaal [Lane Tech HS, mathematics]        Unleashing Complex Numbers
Fred extended the consideration of zeroes of quadratic functions; ax² + bx + c = 0 , which he began at the last SMILE class.  He wrote down the quadratic formula

and asked what happens in the case (a, b, c) = (1, 2, 3)?, In that case one obtains x = -1 ± Ö(-2).  This case, as well as many, many others, involves taking the square root of a negative number.  By adopting the notation  Ö(-1)  = i or  i² = -1, he introduced complex numbers and wrote the answer as  x = -1 ± 2i. He then showed, using the algebra of complex numbers, that these two complex numbers satisfy the original quadratic formula:
 

All right! So, complex numbers are not so complex, after all!  Thanks, Fred!

Porter Johnson mentioned that complex numbers were originally used merely to solve polynomial equations, after Gauss showed that every n-th order polynomial equation has n (possibly degenerate) complex roots.  Much later, a mechanical engineer named Fourier made explicit use of the Euler formula, e^ix = cos x + i sin x, to develop Fourier series for the specific purpose of  solving problems related to time-dependent heat flow in conductors.  The electrical engineers introduced the complex impedance of a circuit as a means of analysis of time-dependent circuit behavior. In addition, complex numbers play a special role in descriptions of electromagnetic waves through Maxwell's Equations of electromagnetism.  In 1925, the young physicists Schrödinger and Heisenberg independently developed Quantum Mechanics. For the first time, complex numbers played  a central and unavoidable role in that theory, and in virtually all subsequent theoretical developments in physics.  In effect, the central theoretical concept (wave function, probability amplitude, state of the system) cannot be measured directly, although its effects can be seen all over the universe!  For additional information see these St Andrews University History of Mathematics pages: Quadratic, cubic, and Quartic Equations and The Fundamental Theorem of Algebra.

Arlyn VanEk [Illiana Christian HS, physics]        Air Resistance of Swinging Block
Arlyn VanEk set up a bifilar pendulum in front of us. He explained that he had done this in his classroom. He used a wooden block (with two eye screws) on its top edge for its bob, and suspended it from the ceiling using light, inelastic cord tied to the eyes screws. He then swung the bob back in an arc, keeping the cord taut to make angle to the vertical. Then he released the bob from rest, and measured the time for it to pass through a Pasco® (http://www.pasco.com) timing gate at the bottom of its swing. Knowing the width of the block, its speed could be calculated. From this kinetic energy could be calculated at the bottom of its swing, and its gravitational potential energy could be calculated by measuring the decrease in altitude from the beginning to the bottom of its swing.

Assuming air friction is nil and noting that the motion of the block should not depend upon its mass, when he did careful measurements, he found that energy was not being conserved! Thinking that this might be due to air friction, Arlyn made a second block with a streamlined shape, resembling the head of a doubled-bladed axe. Repeating the experiment with this bob, he found this time that it had more energy at the bottom of its swing than it had potential energy at the beginning! How could this be?!

Ann Brandon and Larry Alofs remarked that the separation of kinetic energy of a moving body into rotational and translational motion can be made only corresponding to a translation of the center of mass, and rotation with respect to the center of mass.  One may thus apply the principle of conservation of energy using that principle.  Correspondingly, it is crucial to be certain that the center of mass of the pendulum moves through a circular arc, and that translational speeds are measured for the motion of that center mass.  The standard arrangement for a ballistic pendulum is to suspend  a wooden block by four strings, attached on the top side on locations symmetric with respect to the front, back, left, and right edges.  One thereby makes a bifilar pendulum, with the desired properties.   PJ also mentioned that an aerodynamic shape should more properly represent an aircraft wing --- sharp in the front and smooth in the back, rather than being front-back symmetric.  He pointed out that the winning athletes in the platform ski jumps in the 2002 Winter Olympics (in addition to being anorexic) held their skis- cross-pointed at the front, to reduce air resistance, rather than in the standard railroad track position,  to reduce air resistance.

As a sequel, Arlyn showed that two steel balls collide almost elastically when one rolls into the other at rest on a smooth table.  However, if the balls smash against one another in mid-flight and stay together, all the mechanical energy must be converted into heat.  How do we know this?  Arlyn took two solid steel balls [mass of about 500 grams each; about 5 cm in diameter], and smashed them together while a sheet of ordinary paper was held between them.   It was quite plain to see that a small hole had been burned through the paper with each encounter.  Furthermore, when the experiment was repeated in a darkened room, we could see flashes of light with each collision.  Also, the smell of burnt paper was unmistakable  Remarkable!

Finally, on a non-destructive note, Arlyn held up a Thumb Drive Flash Memory Stick with a capacity of 64 MB that can be inserted into the USB plug on his fairly new computer.  He is using this small memory stick  (normally used for a digital camera) to transfer data from the school computer to his computer at home -- the hard drive recognizes it as a formatted [ROM] disc, so that files can be moved to and fro.  Neato!

Arlyn, you showed us how it really is!  Thanks!

Fred Farnell [Lane Tech  HS, physics]     Rocket Balloons
Fred took a long, collapsed balloon, and inflated it by inserting a special straw and blowing. Then he released it into the air.  It zoomed around the room, making a "screaming" sound.  Just for amusement and edification, he sent off several more balloons, with similar effect --- except for the one that exploded during inflation.  This is an ideal party favor, which Fred had obtained from The Party Corner®, in Orland Park Shopping Center.  It was described on the package as follows:

Referring to his presentation at a previous SMILE meeting [mp111803.html], Fred promised that he would bring his daughter's old tennis shoes to SMILE in the near future, since she is nearly ready to donate them to us for scientific study. And, it's about time for her to wear winter shoes!

Those rockets really took off!  Thanks for showing us,  Fred.

Bill Shanks [retired physics teacher & member, Joliet Junior Chorale]        Clothes Pins that Light Up
Bill showed us the perfect "party gag" gift --- a pack of 50 plastic clothes pins, complete with (LED) bulbs, which light when you use the clothes pin to clamp the LED leads to make contact with electrodes on a small "dime shaped" Lithium cell, such as CL 2016, 2025, or 2032, which are rated at 2.8 Volts.
PJ Comment: A red or green LED can be lighted with a single cell, since a photon of energy 2.8 eV corresponds to a wavelength

How could you use this in class?

Bill, you must be the life of the party! Very nice!

Karlene Joseph [Lane Tech HS, physics]        Crash and Burn Website
Karlene showed us some video images of collisions of automobiles in which "crash dummies", as well as stunt drivers were sitting in the automobiles. The frame-by-frame sequence of images is quite fascinating.  It was clear to all of us that, in fact, Newton's Laws fully explain the occurrences during the crash.  In particular, when we saw the impact and damage when the head of the unrestrained occupant hit the dashboard, the warning "wear your seatbelts" was justified in graphic detail.  These images were located on the website of The Center for Injury Control, School of Public Health,  Emory University [http://www.sph.emory.edu/] on the Motor Vehicle Crash Video page.

Those daredevils and dummies showed how Newton's laws determine the course of collisions!  Thanks, Karlene!

 Notes taken by Porter Johnson