Fred Schaal [Lane Tech High School,
Mathematics] TI-92 graphics calculator;
Railroads
Fred 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/]
Bill 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
John 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
Bill 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 |
Arlyn Van Ek [Illiana Christian HS,
Physics]
Identifying Colors in a Dark Room
Arlyn 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
Ann 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
Hoi 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!