High School Mathematics-Physics SMILE Meeting
18 November 2003
Notes Prepared by Porter Johnson
Announcements
• Professor Eduardo De Santiago [IIT Civil and Architectural Engineering Department], an expert in structural engineering, will present a special lecture providing insight into designing a strong, light bridge at the next meeting, Tuesday 02 December.  Bridge kits will be available until 5 pm on this date at the IIT Office of Admissions, 101 Perlstein Hall.  The 2004 Chicago Regional Contest will be held Tuesday, 10 February 2004, at IIT.
• Rudy Keil [retired teacher] called attention to an excellent set of photographs of the Northern Lights, taken recently in Iceland, on the website http://science.time.com/2013/02/28/dazzling-northern-lights-over-iceland/.

Ann Brandon [Joliet West HS, physics]       Pressure, revisited
Ann
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:

• How do snow shoes work?
• What about earth shoes? Are they better for our backs, and why?
• Shouldn't guys have to wear high heels once in their lives? [Comment by Porter Johnson: For an illustration of the difficulties encountered by a man recently transferred into a woman's body, see the performance by Ellen Barkin in the film Switch.]
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:

• Piezoelectric film inside to produce voltage, firing an LED?
• Battery plus triggering spring?
• Magnet and coil to produce current when triggered by spring?
You tweaked our curiosity! We look forward to taking them apart, Fred!

Marilynn Stone [Lane Tech HS,  Physics]        Optical Illusions
Marilynn
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!
Fred
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??
John
reminded us of two important anniversaries:

• Seventy-fifth Anniversary of Mickey Mouse. A physical unit called Mickey Count corresponds to the movement of a computer mouse by 1/200 inch. Isn't that fascinating?
• December 17, 2003: Hundredth anniversary of the flight of the Wright Brothers at Kitty Hawk NC.
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
Richard

Thanks for sharing your physics toys, Richard!

Karlene Joseph [Lane Tech Park, physics]        Launching Your Marbles
Karlene
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
Bill
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
Gary