High School Mathematics-Physics SMILE Meeting
18 November 2003
Notes Prepared by Porter Johnson

Ann Brandon [Joliet West HS, physics]       Pressure, revisited
described a project that she recently completed in her physics classes, in which students compute their pressure on the ground by measuring their weight W [with bathroom scales], and the cross-sectional area A of one of their feet using graph paper, in which the large squares are square inches. They make an outline of their feet on the graph paper to measure A.  By taking the ratio P = W/A, her students obtained their "ground pressures", to be compared with air pressure of about 14.7 pounds per square inch. Ann then pointed out that airline stewardesses don't wear high-heeled shoes on the planes, because they tend to punch through the floor, causing a potential loss of cabin pressure.  Spiked heels are made with a rubber pad glued onto a steel spike, which is attached into the heel.  She also indicated that high-heeled shoes are a potential murder weapon.  [Comment by Porter Johnson:  see the film Single White Female starring Bridget Fonda and Jennifer Jason Leigh.]   In the course of discussion, the following questions arose:

Thanks for putting the pressure on us, Ann!

Fred Farnell [Lane Tech  HS, physics]     Electric Tennis Shoes 
Fred showed a pair of heavily worn tennis shoes on temporary loan from his daughter, on which lights flashed whenever the shoe experienced a strong impulse.  How come?  It was generally agreed that not much current would be required to set off the LEDs in the shoes.  There was no definitive answer as to how this was done, and it was felt that the shoes should be taken apart to determine how they function.  The following hypotheses were suggested to explain the operation of the shoes:

You tweaked our curiosity! We look forward to taking them apart, Fred!

Marilynn Stone [Lane Tech HS,  Physics]        Optical Illusions
showed a stationary image of intermeshed gears on her lap-top computer. To many of us, the gears appeared to rotate when viewed close up.  This was a novel type of optical illusion, which we all enjoyed looking at.  When our eyes are not focused, and when we view it from the side, it appears to be stationary. However, when the central part is focused upon, the outer portions seem to rotate.  Isn't this remarkable?

To see the picture, look at the image Rotating Snakes on the website: A. Kitaoka: The Latest Workshttp://www.ritsumei.ac.jp/~akitaoka/saishin-e.html.

Thanks, Marilynn!

Fred J Schaal [Lane Tech HS, mathematics]        STO FRM Not That Bad!
asked if anybody knows the standard "slope-intercept" equation for a straight line.  Somebody suggested ...

y = m x + b .
Another very familiar form is the linear relation
A x + B y = C
Dividing the latter relation by C, and adopting the notation a = C/A and b = C / B, we may write this relation as
x / a + y / b = 1
With this latter form, the x-intercept is a and the y-intercept of the curve is b. Neato!

Bill Shanks mentioned that an elliptical curve with semi-major axes (a,b) can be written in a similar form:

(x / a)2  +  ( y / b)2 = 1
Earl Zwicker extended the curve by shifting the center of the ellipse to the point (x0, y0):
[ (x  - x0)/ a ]2  +  [ ( y - y0) / b ]2 = 1
Porter Johnson pointed out that the full diamond [rhomboid] shape can be written as
| x / a|  +  | y / b | = 1
Fred also mentioned that the planet Mercury will be visible in the evening sky in about a month, just South of the brighter planet Venus.

Thanks for showing us the neat Algebra, Fred!

John Scavo [Evergreen Park HS]        How Many Blades on a Propeller??
reminded us of two important anniversaries:

According to John, the Wright brothers had determined how to make the proper size and shape of propeller. They calculated that 90 pounds of force were required for the launch, and they measured a force of 160 pounds; thus they decided to fly! For more details see the NASA website Wright 1903 Flyer -- Propeller Propulsionhttp://wright.nasa.gov/airplane/propeller.html and the Nova:  http://www.pbs.org/wgbh/nova/wright/flye-nf.htmlJohn mentioned that the P-51 Mustang fighter plane, champion of the skies in World War II, could fire its guns at their maximum rate for only 15 seconds before running out of ammunition.

How many blades are optimal for a propeller?  The answer depends upon many factors, such as the pitch of the blades, their operating speed, their size and shape, the weight, shape, and cruising speed of the plane, etc.  The problem is different for a windmill, which converts wind energy into more useful forms.  For details see An Illustrated History of Wind Power Development: http://telosnet.com/wind/index.html .  See also the science project Number and Size of Blades on Wind Turbine vs Electrical Outputhttp://www.selah.k12.wa.us/SOAR/SciProj2000/JohnH.html.

Interesting questions, John!

Richard Goberville  [Joliet Central HS, physics]        Newton's Third Law
showed us the video of a failed jump from a ladder resting against the top edge of a fence, in which the jumper missed landing into a swimming pool, but ended up falling straight down onto the ground, instead.  The ladder was nearly twice as tall as the fence, so when the jumper pushed off from a rung well above the fence top, the ladder went one way and the jumper the other, but not as far as he had expected.  The video had appeared on a Canadian Cable TV Channel called Captain Video, and Maximum Exposure.  Good physics at the heart of this sad outcome, Richard!  He also passed out plastic jumping frogs, as well as flying pencil whirligigs, which he had obtained in large quantities from Oriental Trading Company: http://www.orientaltrading.com/.

Thanks for sharing your physics toys, Richard!

Karlene Joseph [Lane Tech Park, physics]        Launching Your Marbles
showed us an inquiry-based learning exercise obtained from her colleague Brian Scane.  She passed around paper bowls and plates, as well as marbles. Karlene asked us to put a marble in the bowl, and make the marble move in a circle within the bowl. After some practice, most of us were able to make the marble go around in the bowl, although if the marble left the dish, it appeared to move oddly. In particular, when the marble left the bowl it moved in a straight path, even though its motion had been roughly circular before its departure.  We also tried the same exercise with a paper plate.  It was much more difficult to get the marble to stay on the plate.  Finally, she asked us to cut one quadrant out of the plate, and predict how the marble would movel when it left the plate after making three-quarters of a revolution.  Good physics insights, Karlene!

Bill Shanks [Joliet Central, physics, retired]        Plumb Bobs
referred to a recent Chicago Tribune cartoon that showed a Plumb Bob being pulled from the vertical toward a large person named Tiny, with the caption: "Hey Tiny, you're throwing off my plumb bob again!"  Bill asked some non-scientific friends whether they thought this cartoon was funny, and then realized that most people do not understand the effect of gravity.  He commented that, although gravity affects our everyday lives, it is not intuitively obvious to most people as to how this occurs.  Bill pointed out that the earth attracts the sun and moon, which in turn attract the earth.  In fact, every object is attracted gravitationally by every other object.  We believe this implicitly, but how do we actually show it.  Can you feel the gravitational attraction of your hands to one another? No,  because it is too small!  Then, how do we show that gravity is present between everyday objects?  The competing effects of air pressure, electrostatic attraction, and air currents would have to be eliminated. Bill mentioned the classical Cavendish Experiment, involving motion of a torsion pendulum in response to motion of a large mass nearby, as described in the Harvard Uniersity experiment: http://www.fas.harvard.edu/~scdiroff/lds/NewtonianMechanics/CavendishExperiment/CavendishExperiment.html Pasco Corporation [http://www.pasco.com/] provides a very nice a Gravitational Torsional Balance; AP-8215http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=51879&Detail=1. See also the Leyboldt-Didactic GMBH site http://www.leybold-didactic.com/data_e/index.htmlfor [332101] The Gravitational Torsional Balancehttp://www.leybold-didactic.com/phk/produkte.asp?L=2

Thanks for making us aware, Bill!

Gary Guzdziol  [Carol Rosenwald Specialty School, science]        Air Pressure Collapse
put a small amount of water inside a clean metal one gallon can (about 4 liters), and with the cap off he placed it on a ring-stand.  He heated the container with a propane torch for a few minutes, until the water inside began to boil.  Then he turned off the torch, and tightened the lid on the can, wearing insulating cloves.  The can began to make creaky noises as it cooled and contracted, and this process continued until the can had clearly collapsed in on itself.  How come? The villain here, as with his large steel drum [mp110403.html], was air pressure.  Next Gary showed  a rubber pad about 3/8 inch (1 cm) thick, which he had obtained from a flooring store.  He had cut the pad into a circle, about 10 inches [25 cm] in diameter, with a small hole punched through its center.  He had pushed a string through the hole, and tied it to a small hard plastic ring a few cm in diameter.  Holding the string, he dropped the rubber pad onto the floor. When  Gary pulled up on the string, the pad stuck to the floor -- air pressure again.  Gary was also able to pick up a fairly heavy table with the string when the pad was dropped onto it.  He calculated the downward force of air pressure as the area of the pad (about 80 square inches) multiplied by air pressure (about 15 pounds per square inch) to be around 1200 poundsGary also showed us a rubber "dent puller", which  can also be used for carrying large glass sheets, as well as presumably for climbing large buildings.

Gary also showed us that this collapse under air pressure has occurred on a larger scale with railroad cars that were sealed too quickly after steam cleaning.  For details see the DR SLIME website:  The Can Crush Demo with a Real Life Examplehttp://www.delta.edu/slime/cancrush.html.

Very dynamic and interesting, Gary! Thanks.

Notes taken by Porter Johnson