High School mathematics-Physics SMILE Meeting
11 March 2003
Notes Prepared by Porter Johnson

Announcements:

Ann Brandon [Joliet West  HS, Physics]      Producing Current in a Coil of Wire
Ann
hooked a coil of wire in series with a fairly sensitive galvanometer, and then passed a cow magnet back and forth through the center of the coil.  The galvanometer needle moved in response, indicating that an electric current was passing through the wire as the cow magnet moved.  This is a direct illustration of Faraday's Law, in which the change of magnetic flux passing through a current loop is equal to the induced Voltage.  Ann also described dropping a cow magnet through a hollow, vertically held Aluminum tube 5 meters in length.  Normally the magnet would drop that distance in about 1 second in free fall, but it took about 11 seconds for the magnet to travel down the tube. This is because the falling magnet induces a current in the tube.  The current -- in turn -- produces a magnetic field of its own, which opposes the field of the falling magnet, thus slowing its descent. [Lenz's Law: http://regentsprep.org/Regents/physics/phys08/clenslaw/default.htm]. Cow magnets are wonderful, although they don't look very appetizing!

Most interesting! We can always depend on Ann!

Carl Martikean [Wallace HS, Gary, Physics]  Ding-a-Long:  You Conduit [Con-du-it] Yourself
Carl
had been successful in constructing his own set of one octave chimes, using a 10 foot [3 meter] section of C4 thin wall, galvanized steel conduit, which can be found at any hardware store.  He suspended the chimes, cut at appropriate lengths for the chromatic scale, using 10 pound test fishing line.  Carl played some notes for us by hitting the suspended pieces with a wooden striker, producing an almost recognizable melody. Carl also showed us how to make a closed end pipe, using lengths of hollow PVC tubing, attached at the base on Craft Foam through the use of a Hot Glue GunCarl pointed out that you could make a base consisting entirely of solidified hot glue, without using the craft foam as a substrate at all.  Carl also showed us how to make a mallet, using a wooden ball with a hole in it and a dowel rod.  Materials can be found at Hobby Shop stores, for example.

A serious discussion arose as to whether air vibrating inside the tube, or vibrations of the tube itself, were responsible for the vibration.  We concluded that the tube was vibrating, since the sound was damped when you held it in place, and since the sound did not change very much when one end of the tube was taped over.

Clever, Carl! You almost had us fooled!

Arlyn van Ek [Illiana Christian HS, Physics]      Power to the People
Arlyn
illustrated that Power P = Voltage V ´ Current I, using Fred Schaal as his hapless volunteer / victim.  Fred was instructed to hold on to a small resistor until it became too hot to hold.  With a current of 1.0 Amp and Voltage  of 3.1 Volts, corresponding to a power of 3.1 Watts, Fred was able to hold on for about 12 seconds.  With a Voltage of 4.8 Volts and a current of 1.5 Amp, corresponding to a power of 7.2 Watts, Fred released the wire after only 5 seconds.  Interestingly, the total amount of heat [H] generated in the wire was about the same in the two cases:  36 Joules.

H = P t = (3.1 W) (12 s) » 36 J » (7.2 W) ( 5 s)    ---    WOW!
Arlyn then showed an array involving 3 identical light bulbs, with two placed in series and hooked in parallel with the third one.  We guessed correctly that the single bulb would be much brighter than the pair in series, when we hooked the array to the Voltage source.  In fact, because the two bulbs in parallel each have half the Voltage drop and half the current, each one is 1/4 as bright as the bulb in series.  Do you believe that?

Arlyn next brought out the Genecon Generator [http://www.arborsci.com/detail.aspx?ID=543], obtained from Arbor Scientific, which he had showed us at the 11 April 2000 SMILE meeting [mp041100.htm].  By turning a crank, we convert mechanical energy into electrical energy, providing current to light the bulbs.  When current passes through one bulb, it becomes much more difficult to turn the crank --- the more electrical energy one makes, the more difficult it is to turn the crank to supply mechanical energy. We cannot readily see the stress placed on a battery when it converts chemical energy into electrical energy, but we can feel the stress in our own hands when we we turn the crank to make electricity!. Beautiful!

An electrifying demo on a hot topic, Arlyn!

Betty Roombos [Gordon Tech HS, Physics] and Karlene Joseph [Lane Tech HS, Physics]     Skating Around the Issue
Betty
and Karlene showed us how a student could gain insight as to how an object moves when dropped out of an airplane. We watched .Karlene skate in line across the room holding a soccer ball, which she threw into the air and then caught.  Karlene threw the ball straight up, and caught it as it came straight down, as viewed from her reference frame.  However, in our frame we saw the ball travel up and down along an inverted parabolic arc.  Karlene then dropped the ball from above her head, while rolling across the room at roughly constant speed.  We saw the ball fall in a parabolic arc. Karlene next tried a bombing run, in which she held the ball high and then dropped it while moving in order to hit a fixed target on the floor.  On the third try she gauged the proper release point and hit the target, a styrofoam™ cup -- which shattered -- which won our applause!  Stupendous shooting, Karlene!

Next Betty pulled Karlene across the room with a piece of bungee cord that she kept stretched by a calibrated amount, thereby applying a constant force to KarleneBetty had to move faster and faster to maintain this state of constant force, which produced a constant acceleration. Betty suggested other experiments  with (a) two bungee cords to double the force, and/or (b) pulling two kids to double the mass. Also, Betty mentioned that the amount of frictional drag actually could be measured.

What great ways for students to gain insights into Newton's Laws.  Pretty stuff, Betty and Karlene!

Don Kanner [Lane Tech HS, Physics]      Update on Jug Investigation
Don
described experiments he had done with several pop bottles of various sizes, which had the same size opening.  By measuring the resonant frequency, f, with various amounts of water in the bottles, he learned that the resonant frequency was dependent only upon the volume, V, of air in the bottle  In fact, he found this approximate formula for the frequency f [Hz] in terms of the speed of sound [c= 35,000 cm/sec] and  V [ in cubic centimeters]:

2 p f = c / ÖV
At this point Don checked the facts on Helmholtz Resonators, which indicated that area, A, and height, H, of the opening column, along with V, were relevant for the resonant frequency: 2 p f = c / Ö(A/HV). For these bottles, the sizes and shapes of the openings are the same, and thus the answer for f depends only on the volume V.  In fact, one might expect to find that  A/H is about 1 cm, for consistency.

Great work in combining Physics with your musical avocation, Don!

Fred Schaal [Lane Tech HS, Mathematics]      TI Interactive Software
Fred
had intended to transfer images from his laptop computer to the screen in order to display TI Interactive Software, but discovered that, without a projector, there was no hope of doing so.  Such transfers of images from one type of system to another are always problematical, and the safest step is to use your own system for the entire process.  Thanks for trying, Fred!

Bill Blunk [Joliet Central HS, Physics]      Space Shuttle Tile
Bill
passed around a trapezoidal piece that was a Space Shuttle Tile on a previous, successful mission.  The exterior of  the tile was made of a hard, dark ceramic material, whereas there was a light foam-like interior, and the tile was very light.  He held the interior with his hand and heated the exterior with a propane torch, until the exterior began to glow bright orange.  Interestingly, he could still hold the edge of the exterior with his hands, while this was being done.  Bill was not certain whether it is still possible to get such tiles, but will check on this

A remarkable demonstration of the insulating properties of the tiles.  Thanks, Bill!

Bill Shanks [Joliet Central HS, Physics, retired]      Fuel Efficiency of a Bicycle in mpg
Bill
calculated the fuel efficiency of a bicycle from data presented at a previous SMILE class, which indicated that 30 kilocalories [kcal] of food energy are required to ride one mile on a bicycle at a speed of about 18 miles per hour -- 30 kilometers per hour.  He used the fact that 3700 kcal of food energy can be obtained from 1 pound of body fat, so that one may travel 3700/30 = 120 miles per pound of body fat. A gallon of fat should weigh about the same as a gallon of water --- approximately 8 pounds, so that one theoretically should be able to travel about 1000 miles per gallon of body fat.   Who would have thunk it?

Bill also passed around an article by Charles Leroux in the 11 March 2003 issue of the Chicago Tribune, defining the Body Mass Index: BMI, which is computed in terms of a person's weight W [ in pounds] and  height H [in inches] as

BMI = 703 ´ W / H2

A BMI of 18-25 is considered Normal, 25-29 is considered Overweight, and above 30 is considered Obese.  It was unclear as to where this number comes from, since it surely does not represent an accurate measure of a relevant parameter such as fat percentage.

An insightful combination of ideas, Bill!

Bill Colson [Morgan Park HS, Mathematics]      T. G. I. P. --- Thank God It's Pi Day!
Bill
called our attention to the following websites from a recent National Council of Teachers of Mathematics News Bulletin, which are appropriate for the up-coming Pi Day [3.14]:

Thanks for the timely reminder, Bill!

We ran out of time before Ben Butler could make his presentation: What's a Million?  Ben will present at our next meeting, 25 March 2003!

Notes prepared by Porter Johnson