High School Mathematics-Physics SMILE Meeting
05 November 2002
Notes Prepared by Porter Johnson

Fred Schaal [Lane Tech High School, Mathematics]      TI-92 graphics calculator; Railroads
described an experiment that he had done, in which he could lay out a triangle on his calculator, and then have it determine all interior and exterior angles, as shown in the diagram below:

Note that, from the diagram, a + A = 180°; b + B = 180°; c + C = 180°.  In addition, it is true that A + B + C  = 360°, as can be seen by shrinking the triangle to a point, as shown.  By adding the first three relations, and then subtracting the fourth, we obtain a + b + c = 180°, indicating that the sum of the angles in a triangle is equal to 180°.  In addition, by drawing a line parallel to the base line at the top vertex, we  obtain the figure:
Evidently, a + b = C, indicating that the exterior angle C is the sum of the two interior angles a and b. Similarly, we can show that  b +c = A and c + a = B.

Fred noticed in his extensive travels by rail this summer that the tracks were noticeably bumpy --- presumably because freight trains also travel on the same tracks.  In addition, he observed a lateral [transverse] vibration of the train cars, and wondered why.  The consensus of the group was that the slight "play" in the  "knuckle couplers" that attach one car to another permits such transverse vibration, which can be amplified as the train travels along the track. Very interesting, Fred!

Bill Colson [Morgan Park HS, Mathematics]     Article from The Onion [http://www.theonion.com/]
distributed copies of an article from The Onion, Volume 38, Issue 39 [24-30 October 2002], entitled High-School Science Teacher Takes Fun and Excitement out of Science.  Continuing its tradition of rich satire, it described a ninth grade science teacher who does all the experiments himself, to save time, avoids difficult questions that "simply waste time", shows film strips rather than actual dissections of frogs, and constantly battles distractions in school. He is quoted as saying, "These kids are getting worse every year.  It's a wonder I get any teaching done at all." A student with prior exposure to Bill Nye and Cosmos reruns is quoted as saying "I'd heard about these cool things called Van de Graaff generators, which make your hair stand up when you touch them, and a Jacob's Ladder that makes a really huge arc of electricity.  But all we did was spend a week calculating Amperage."

Very good lesson on what not to do, Bill! Bill also mentioned that flexible LCD displays are being developed.  For details see the website New Toshiba Displays: Bigger, Smaller, Flexible  http://sci.newsfactor.com/perl/story/17864.html.

John Bozovsky [Bowen High School, Physics]    Pushing a paper straw through a potato
described an experiment in which he pushed one end of an ordinary paper straw through a potato, after first putting his finger over the other end.  Unless you close the other end, the trick will not work.  He showed the experiment to his daughter, who said "I really hate science in school, but I love Physics!" Good point, John!

Bill Shanks [Joliet Central, retired]    Mixing Colors
presented his attempts to use Christmas tree lights, which are once again available in stores, to demonstrate additivity of colors. He was motivated by an out-of-focus photograph that he took of a Christmas tree many years ago, in which the image of each bulb blurred into a colored "circle of confusion".  The idea was to use a lens to produce overlapping circles of confusion from bulbs of different colors, in order to see color mixing in regions of common illumination.  He described the general idea in the SMILE meeting of 12 December 2001; mp120401.htm. The idea is to discover whether this technique will indeed lead to these additive color relations: 

Additive  Combinations

Overlap colors Color produced
red + green yellow
red + blue magenta
green + blue cyan
To our delight, Bill did show us that red and green circles of confusion produced a yellow color in their region of overlap. (In practice, the blue light was too dim in comparison to the other lights, so that we were not able to see cyan and magenta very well.)  A wonderful and original idea, Bill!

Arlyn Van Ek [Illiana Christian HS, Physics]      Identifying Colors in a Dark Room
described an experiment that he had seen at a convention, in which a sheet of paper of unknown color was illuminated in a dark room by lights of various colors.  The goal was to determine the "true" color of the paper from its appearance with various colors of illumination.  As a sequel he mentioned that, when the American flag is viewed in intense blue light in a dark room, the red stripes appear to be black.  For an interesting discussion of the Physics of Color, see http://en.wikipedia.org/wiki/Color.  See also the Java Applet on the Color Matching Game, http://www.cs.rit.edu/~ncs/color/a_game.html, on the Introduction to Color website: http://www.cs.rit.edu/~ncs/color/. Larry Alofs mentioned that an ultraviolet LED is available at All Electronics: 

Cat # ULED-2  [5mm Ultra-violet LED. Emits blue 395nm UV light. Water-clear lens. 3.7 Vdc, 20 mA. 15 degree beam pattern. Ideal for counterfeit bill detection, detection of fluorescence in minerals, black-light light poster lighting]:  http://www.allelectronics.com/index.php

Very interesting, Arlyn and Larry

Ann Brandon [Joliet West HS, Physics]     Collisions and Momentum
applied the Bigger is Better philosophy to a freely moving, 7 kg cart. Along its path, a 25 pound [11 kg] bag of kitty litter was dropped onto the cart, slowing it down perceptibly. By pulling ticker tape with the cart, and using a spark timer to put marks on the tape every 1/60 second, she was able to determine the speed of the cart just before and just after the bag was dropped onto it.  The class verified that momentum was conserved, to a precision of a few percent.

We performed a modified experiment, in which a Pasco® cart [mass about 500 grams] with ticker tape attached to it was set into motion across the lab table.  A sealed sandbag [mass 394 grams] was dropped onto it, and it slowed down perceptibly.  The velocities just before and just after dropping were determined by measuring the length of the tape for 6 marks [0.1 second].  We obtained v1 = 13.5 cm / 0.1 sec = 135 cm/sec before dropping, and v2 = 6.9 cm / 0.1 sec = 69 cm/sec after dropping. The initial momentum was p1 = 0.500 ´ 1.35 kg m/sec = 0.675 kg m/sec, whereas the final momentum was p2 = 0.894 ´ 0.69 kg m/sec = 0.617 kg m/sec.  Momentum was thus conserved, with a precision of about 8%.  The standard PSSC experiment involves repeating this experiment with various initial masses. 

Ann also mentioned launching a tennis ball using a little lighter fluid in a tennis ball cannon.  The cannon is made from two steel cans welded together.  She warns her students against using Aluminum cans, which may burst to produce dangerous shrapnel.  For additional details see, for example, the University of Texas website, http://www.ph.utexas.edu/~phy-demo/demo-txt/1h11-20.html. Her speed record for such a launch is 107 mph, or 45 meters/second.  If you put too much lighter fluid inside the can, a flaming tennis ball is ejected.  Porter Johnson mentioned some interesting theories as to what caused the ignition of the von Hindenberg Airship at Lakehurst NJ on May 6, 1937.  For interesting theories on this matter, see the website http://americanhistory.about.com/library/weekly/aa042101b.htm. Ann actually did the physics with us.  Thanks, Ann.

Hoi Hyunh [Clemente HS]     Seeing Infinity with a Magnifying Glass
placed an object a distance d from a magnifying glass, and observed a [real or virtual] image at a distance x from the object, as indicated below:

The magnification of the image is given by the formula M = - d / (x -d) . Note that, when x = d, the magnification becomes infinite.  Note that the object distance d and the image distance d are given by the lens maker's formula, 1/d + 1/(x-d) = 1/f, where f is the focal length of the lens.  This formula may be converted from this Gaussian form to the Newtonian form, ( d - f) ´  ( x - d - f) = f2.  Very interesting, Hoi!

Notes taken by Porter Johnson