High School Mathematics-Physics SMILE Meeting
14 December 2004
Notes Prepared by Porter Johnson

Lee Slick [Morgan Park, physics]          Film Canister Optics (a give-away available in large quantities)
Lee  showed us how to use a film canister and push pin to show inverted optical images, along the lines of his presentation at the MP SMILE class of 10 December 2002mp121002.html, from which the following is excerpted:

"Image Inverter:  Lee passed out a cylindrical film canister, complete with plastic cap, along with a plastic push pin,  to each of us.  We used the push pin to poke one hole in the center of the cap, and then put three holes very close together at the center of the base, to form a triangle.  We then pushed the pin through the lateral surface of the canister, in order to grasp it.  When we looked at a bright region on the wall through the single hole in the cap, we saw the three hole triangle in the base.  However, when we rotated the canister about a vertical axis passing through the center perpendicular to the lateral surface, we observed that the triangle had become inverted.  How come? For additional details see The Human Eyehttp://www.mit.edu/~danz/marti/intro.html and The Quaker Oats Canister: http://sdsu-physics.org/assets/PDFs/oatmeal_pinhole_camera.pdf. Karlene Joseph remarked that she also used the canister lid as a pin hole camera.  When we moved the push pin across the field of view and on the other side of the hole in the lid, we saw it move in its direction of actual motion.  However, when we moved it in that direction while held between our eye and the hole in the lid, it appeared to move in the opposite direction.  Very interesting, Karlene ..."

Thanks, Lee.

Larry Alofs [Kenwood HS, physics]           Inductance
set up his mini video-camera, attached it to our small TV, and focused it upon a rather sophisticated TVM:  Transistor Voltmeter.  Now we could all see the readings on the small TV.  The TVM could be used to measure voltage, current, and resistance --- in addition it could be used to determine Capacitance and Inductance, using special plugs called C and CX for Capacitance, and L and LX for Inductance.  He set the meter to its most sensitive scale for inductance (mH: milliHenry), and attached a long piece of wire to the special plugs L and LX.  When the wire formed only one loop, the meter read an inductance L = 0.001 mH.  When he looped the wire around several times in the same direction (lasso style), the inductance reading increased, up to 0.016 mH.  When he folded these loops at the middle, so as to double the number of loops, the inductance again increased. Then he formed a smaller loop with the same number of turns, and we saw that the inductance decreased to 0.007 mH.  He then put an aluminum bar inside the coil, and there was no observable difference in the inductance. But when he placed a (soft) iron bar inside the coil, we saw the inductance increase from 0.016 mH to  0.022 mH.  As he put more iron bars inside the coil, the inductance steadily increased.  Here are the data for the inductance versus the number of turns of wire, with one iron bar inside:

Number of Turns     Inductance (mH)
1 0.001
5 0.001
10 0.003
15 0.010
20 0.016
25 0.022
30 0.030
35 0.037

Larry next took a large air core solenoid, consisting of about 500 turns of wire with inner radius about 5 cm.  He measured the inductance of the coil.  When he placed an iron bar inside the coil, the inductance increased -- the more bars, the greater the inductance.  Here are the data:

Number of bars inside    Inductance
0 4.83 mH
1 8.22 mH
2 11.67 mH
3 14.75 mH
Larry then took a much heavier coil of wire and repeated the experiment of measuring its Inductance with and without iron bars in its core.  Here are the data:
Number of bars inside       Inductance
0 0.812 H
1 1.28 H
2 1.69 H
3 2.05 H
Larry added an aluminum bar into that coil, and we saw that its measured inductance decreased slightly How come?  Could diamagnetism be at work? Or is it Lenz's Law? Eddy currents?

Larry next passed around a 1.5 Volt dry cell battery, along with wires coming from one side of a transformer.  Larry mentioned that there is no problem in connecting the leads from the primary coil in the transformer to the battery, but that when the leads are removed a spark often develops.  The effect is explained by Faraday's Law, relating the induced electromotive force EMF to the time rate of change in F, the magnetic flux:

EMF = - DF / Dt = - L DI / Dt.
We passed the device around the room, and were occasionally able to draw a spark. Much to our surprise, we got quite a shock as a high voltage pulse passed through our bodies. Amazing!

For his next encore, Larry took an ordinary 40 Watt light bulb, and calculated its internal resistance from the formula relating (RMS) power P to (RMS) Voltage V and resistance R:

P = V2/ R ... or ... R = V2/ P = 1202 / 40 = 360 W.
First Larry put the light bulb into a socket, and plugged the leads of the socket into the house current. The bulb lit normally. Next Larry hooked the big coil in series with the light bulb, and then plugged it into the house current. The bulb was much dimmer than before. How come?! Larry told us that the big coil had a DC electrical resistance of 80 W -- which would not be enough to explain the dramatic change in brightness of the bulb, since 80 W is a small fraction of 360 W.

We decided that the villain here was Inductive Reactance, a term in the Complex Impedance [http://www.ndt-ed.org/EducationResources/CommunityCollege/EddyCurrents/Physics/impedance.htm] produced by inductance. Inductive Reactance is the resistance to alternating current caused by the Inductance of a coil.  The Inductive Reactance X =  2pfL. Since L = 0.812 H for the coil and f = 60 Hz, then X = 2p (60 Hz) (0.812 H) = 310  W, so that the inductive reactance is more important than the DC resistance in this case.  Larry showed that, as he stuffed more and more and more iron bars into the coil, the bulb became dimmer and dimmer and dimmer, because of the steady increase in Inductance, and therefore Inductive Reactance.

A superb phenomenological exercise, from which we all enjoyed and learned a great deal! Thanks, Larry!

Paul Fraccaro [Joliet Central HS, math & science]           Best Paper Size? 
Paul showed a geometrical construction that permits the precise alteration of an ordinary sheet of notebook paper (width W = 216 mm (8.5")  by length L = 279 mm (11") into one of the same length, with W = L / Ö2  = 198 mm. According to Paul, this paper corresponds to the international standard scale.  Furthermore, he claims that it is the ideal size for making paper airplanes. Here is the construction:

Paper folding

  1. Fold side AB (about angle ABD) onto side BD, and mark the point E on BD where A lies.  The length BE will thus be equal to AB.
  2. Unfold the paper.
  3. Draw the line AE, and fold side AC (about angle CAE) so that it lies along the line AE.  Mark the point on line AE that corresponds to the end of line AC; call it F
  4. Draw a line (GFH) parallel to side BD, passing though point F.
  5. Cut off the paper along the line GFH.
  6. Stop; you're finished!

Standard A4 paper sheets, used for letters, printers, and copying machines, are approximately 210 mm wide by 297 mm long, corresponding to an area of about 1/16 square meters.  Note that 297 / 210 ~ Ö2 = 1.414.

For more information on International Standard Paper Sizes, see the website http://www.cl.cam.ac.uk/~mgk25/iso-paper.html, from which the following is abstracted:

"... In the ISO paper size system, the height-to-width ratio of all pages is the square root of two (1.4142 : 1). This aspect ratio is especially convenient for a paper size. If you put two such pages next to each other, or equivalently cut one parallel to its shorter side into two equal pieces, then the resulting page will have again the same width/height ratio.

ISO 216 defines the A series of paper sizes based on these simple principles:

For instructions on making various types of paper airplanes see Alex's Paper Airplane website http://www.paperairplanes.co.uk/.

Does this really give us the best gliders? Very interesting, Paul!

Roy Coleman [Morgan Park HS, physics]           Weighing Bridges for the Bridge Contest
Roy's  students have been asking him how to determine whether their bridges weigh less than 28 grams, as required under the rules for the 2005 Chicago regional bridge-building contests [http://bridgecontest.phys.iit.edu/].  He showed a simple balance set up with a meter stick balanced with its center on a cylindrical ball-point pen lying horizontally on the table. A few nickel coins served as "precision weights".  The mass of each nickel is very close to 5 gramsRoy took the bridge materials kit, placed it on one end of the meter stick balance, placed 6 nickels on the other end of the stick, and found a good balance.  He therefore concluded that the mass of the bridge materials was approximately 30 gramsRoy showed that, by placing 5 nickels at an end of the meter stick and one at 20 cm from that end, one can determine whether the finished bridge weights less than 28 gramsRoy mentioned that this was a good place to introduce a discussion of torques and their role in static equilibrium.

Nifty and nice, Roy!

Arlyn van Ek [Illiana Christian HS, physics]           Air Zooka™ Vortex Launcher 
Arlyn showed off his new physics toy, the Air Zooka Vortex Launcher, which he had ordered from a recent Teacher Source Catalog [http://www.teachersource.com] by Educational Innovations Inc for around $15. [http://www.teachersource.com/catalog/page/Physical_Science_Physics/Mysteriously_Flowing_Fluids/].   Here is a description of the vortex launcher from that source:

"This amazing device launches a powerful vortex of air up to 20 feet. Powerful enough to blow out a candle from across the room! Safe for classroom use because it launches no projectile, only a strong puff of air. Easy to use and requires no batteries. Colors may vary."
We tested the device by lighting a cigarette lighter in the back of the room, and then blowing it out with the vortex generator from across the room, more than 6 meters away. It worked!  Arlyn also got a Wizard Stick Fog Generator from that same source.  Similar devices are available at the K-Mart ZeroToys website:  http://zerotoys.com/newsite/products.htm, and to obtain the best price one can use Google-Froogle [http://froogle.google.com]. 

Great gadget! Thanks , Arlyn!

Bill Shanks [Joliet environs, happily retired]           LED Lantern with 12 Super Bright White LED's
Bill showed us his latest lantern, which he obtained recently at Sam's Club.  The lantern is advertised for about $15 on the Amazon.com website [http://www.amazon.com], from which the following has been excerpted:

"Light up the night with this unique power lantern. With 12 individual light emitting diodes (LED), this lantern provides bright illumination that's built to last. Unlike old style lantern bulbs, LEDs rarely burn out and can glow for up to 100,000 hours! The Power Lantern includes a dimmer switch that allows you to set your own level of illumination--from low-level reading light inside your tent, to an ultra-bright torch to help light your path."

That's a nice one! Thanks, Bill!

We did not have time for Ann Brandon to make her presentation titled: Scotch Tape ElectrostaticsAnn will be scheduled for the beginning of the first SMILE meeting of the Spring Semester, which will occur on Tuesday 25 January 2005See you there!

Notes prepared by Porter Johnson