High School Mathematics-Physics SMILE Meeting 1997-2006 Academic Years Teaching Exercises

27 October 1998: Ann Brandon [Joliet West HS]
She reviewed the difference between Scalars and Vectors.
She asked which of the following are vectors (V) or scalars (S):
Distance: (S)
Displacement:(V)
Speed:(S)
Velocity:(V)
Acceleration:(V)

She also showed a game in which velocity vectors are illustrated. There was a sort of maze through which two players should travel in a race without hitting the walls. They could change the x- and y-components of velocity by only one unit from the previous move. The winner goes through in the least number of moves without hitting the wall.

10 November 1998: Alex Junievicz [CPS Substitute]
He made 2 comments, First he brought a maze that helps get the difference between Distance/Displacement across. Find the route through the maze, measure it in meters (expand the relationship of cm to m) and the figure out the displacement (direct vector route) in meters and direction. remember North is zero...or use the meteorological ESE East-South-North-West, etc.

Second, he mentioned a way of keeping electrical meters from being destroyed. By placing at least 2 silicon diodes in opposite directions across the movement, thus the voltage should not exceed 0.6 V saving the meter. if 0.6 V affects the full scale readings, 2 can be put in series--1.2 V. Another device used for protection is the neon bulb which fires at about 90 V depending upon ambient light.

06 April 1999: Karlene Joseph [Lane Tech HS]
She asked the question: How do you get a balloon completely inside a 500 cc Florence Flask? The students in her class had various opinions, which were interesting to consider from the viewpoint of basic physics and "common sense". She then got a balloon to go inside by putting a little water [" 50 cc] inside the flask, and boiling away most of it. Then, she took the flask off the heating element and put the balloon around the lip of the flask. After a few seconds the balloon was pulled inside the flask, and as more of the water vapor condensed the balloon filled up with air. Verrrrrrry interesting!

Next she demonstrated an OCARINA, which she had obtained from the craft store at Berea College in Berea, Kentucky [Latitude: 37o 34.2', Longitude: 84o 17.6']. She played on octave on the instrument, and then asked how to explain the sounds from the size and shape of the holes. Of course, nobody knew!

Addition information has been obtained by Lilla Green [Hartigan School]

I was in TN for some years and know a little about the Ocarina. It is sometimes referred to as a "globular flute." I think it is actually a very ancient instrument, although many cultures have embraced it and put their own touches to it. I think it originated with Native Americans, who made them out of clay. Now, they are made from wood or Terra Cotta or even plastic. They are made in all kinds of shapes, like animals or faces. The "sweet potato" Ocarina is also common (It's just shaped like a blob basically). I have seen them in antique stores and little gift shops, but I have never heard one played. If I were to guess, though I would say the physics is very similar to the flute or recorder, where you blow in and change the frequency that comes out by obstructing various outlets.

--Aubrey T. Hanbicki; The James Franck Institute; University of Chicago

Also, see following website: http://www.ocarina.co.uk/.

02 February 1999: Bill Colson [Morgan Park HS]
How is it possible to suck spaghetti into your mouth?

The audience experienced the phenomenon with samples of foul-tasting pseudo-spaghetti, and drew these conclusions:

There is a pressure difference and the spaghetti will enter the mouth because the friction of the spaghetti will allow the spaghetti to be pushed by the pressure difference toward the lower pressure inside region.

See Readers Digest for January 1999.

01 February 2000: John Scavo (Richards Career Academy)
(handout - see http://mypages.iit.edu/~smart/scavjoh1/lesson1.htm or http://www.ed.gov/pubs/parents/Science/soap.html) placed a pan on the table and filled it half full of water. Then he cut a small boat shape (about 5 cm long) from an index card. After using a paper punch to make a hole at the center of the boat, he used scissors to cut a narrow slot from the back of the boat to the hole - making a "keyhole" in it. We gathered around to see him place the boat on the water, and then he squeezed one drop of dishwashing soap into the hole, and the boat was rapidly propelled from one end of the pan to the other! A soap-powered boat! Actually, the soap reduces the surface tension of the water at the back of the boat, and the surface tension forces on the boat become unbalanced, propelling it. Neat!

14 March 2000: Bill Blunk (Joliet Central HS)
set up the Millikan Oil Drop Experiment on the table. It is a dandy piece of equipment sold by Sargent Welch, and expensive, so his school could afford only one, Bill explained. So when he sets it up for his students, only one at a time can look through the telescope to see the oil drop(s).

He then showed us a new addition to his technology - a small video camera that he had bought for \$90 at the ISPP meeting at New Trier HS. (It's the sort of thing being used on computers these days when people are "talking" to each other.) It was now connected to a large TV set in front of us, and when Bill aimed the camera at us, we could see ourselves on the TV.

He reviewed for us how the Millikan Oil Drop Experiment [http://en.wikipedia.org/wiki/Oil_drop_experiment] works; a pair of horizontal, parallel conducting plates are placed about 1 cm apart, and an electric charge is placed on them. Then some "oil drops" are squirted into the space between them (using an atomizer with a hollow needle such as for inflating a basketball).

Some of the drops become charged and may have 1, 2, 3, etc electrons on them. (Millikan used oil drops because he found small water drops evaporate rapidly, oil drops don't.) With the aid of a dandy diagram on the board which showed a charged sphere and a rod nearby, Bill showed us how opposite charges attract and repel. He used colorful magnets that had the + and - charge signs on them. They stuck to the board on the diagram and Bill could move them around to show how charges respond to each other -- a la Bill Shanks.

Bill Blunk also explained that nowadays fairly uniform latex spheres averaging 913 nm in diameter and carried by water drops from the atomizer are what he squirts into the space between the plates. A sphere (drop) with one electron negative charge would be attracted toward the upper positively charged plate. If a drop had 2 electrons and twice the negative charge (assuming they are all alike), then it would move twice as fast. By observing the motion of the drops through the telescope against a reticule (grid), one could calculate their speeds.

At this point, Bill placed the video camera to "look" right into the telescope, and we could then see the drops on the TV screen! With the voltage off (no charge) the drops would gradually move upward (which was really down, since the telescope inverts the image) under gravity. But with the voltage on, some would move down (actually, up, as seen on the TV!). But they moved with different speeds, and the differences between their speeds was always the same amount, which means that the electron charges on the drops always differed by the same amount. Bill could now show this to the entire class at once with the aid of his new video camera. Great! And it is affordable!

11 April 2000: Carl Martikean (Wallace HS, Gary, IN)
placed a capped jar with a greenish liquid in it on the table, then wrote on the board: Pediculus humanus capitus. "Does anyone know that this is?" he asked, referring to the writing. One person raised her hand. "What's the answer?" asked Carl. To which she replied, "Head lice!" And Carl said, "Right! Head lice!" Carl said that the liquid in the jar was sewer water, and twisted off the cap. Then he opened a plastic bag that he said contained new insects that live in sewers, and dumped some into the jar of sewer water. "Just look!" Carl said, pointing to the jar. "They come to life almost immediately!" -- as the particles moved up and down in the jar. "Would anybody like to drink some of this?" asked Carl. With no volunteers, Carl said, "OK - I'll drink some myself!" - and much to our disgust and astonishment - he did! "More?" asked Carl. And then he drank down half the jar. Of course, by now most of us guessed it was a fake. Carl explained that the "sewer water" was really a mix of ginger ale (for carbonation) and Frosh (a soft drink for green color). The "insects" from the plastic bag were really dried currants. "Kids will believe almost anything you tell them," Carl said. He explained that he wants his students to question him (and what they see on TV and elsewhere) about everything, and this is one way he tries to make skeptics of them.

05 September 2000 Don Kanner (Lane Tech HS)
showed us Galileo's inclined plane experiment. Galileo used a source of water drops as a clock (equal time intervals between drips) in order to time how long it took for an object to move down a plane inclined at a measured angle above the vertical. To have calibrate elapsed time, one would measure the amount of water collected in 10 seconds. One would do this for increasing angles of inclination, and make a graph of acceleration down the plane vs angle of inclination. As the angle approaches 90 deg (ie, vertical), the acceleration would approach that of an object in free fall, the acceleration due to gravity, which can be inferred from extrapolation on the graph. The inclined plane, in a sense, "dilutes" the acceleration due to gravity so that motion may be measured over the long time intervals available on a water clock of that era. Great ideas! Thanks, Don!

10 October 2000 Don Kanner (Lane Tech HS)
showed us a "Test Tube Black Box." He held up a cardboard tube about 45 cm long and 7 cm in diameter. About 2 cm from the left end, a string passed through the tube through a pair of diametrically opposed holes.  (On each end of the string were small metal rings to prevent the string from coming free of the tube.) Another string passed through the tube at its right end, in an identical manner, except it was longer. Looking at us with a grin, Don pulled down on the left string, and the string on the right end shortened. When he pulled down on the right end string, the left end string shortened. But then he pulled UP on the right end string - and it moved straight up until it was stopped by its bottom ring. And the left end string did not become shorter or move at all! How was this possible!? After showing us again with some variations, Don challenged us to come up with an explanation or make our own version. He explained that a chemistry colleague at Lane Tech  uses this to catch the attention of his students and to make them put their minds to work. So ... how about us!? Any ideas? Maybe Don will show us more next time.

30 January 2001 Ann Brandon (Joliet West HS)
presented an exercise entitled Millikan's Eggs. The idea is to determine how many plastic chickens [of identical mass] are inside each plastic egg [plastic shells of identical mass, not counting the chickens inside].  The students are to weigh each egg carefully, and then organize the data in such a form (a bar graph is helpful) as to determine the number of chickens and the mass of a chicken.  If an egg has n chickens, each of mass m, and if the plastic shell has mass M, then the mass of that egg will be

Mass(n) = M + n ´ m .

This exercise is analogous to  the analysis in Millikan's Oil Drop Experiment, to determine how many extra electrons are on an oil drop, and thereby the charge of one electron.  The students found it surprisingly difficult to get started on the analysis.

27 March 2001 Don Kanner (Lane Tech HS, Physics)
mentioned a self-checking graph, associated with the Toilet Flushing Experiment designed circa 20 years ago by Roy Coleman.  Working in pairs, students were asked to flush a toilet, and to record the depth of water in the reservoir behind the toilet seat, as a function of time, in intervals of roughly two seconds. Most students got a graph like that appearing on the left below, which resembles a check mark.  Upon occasion, student teams would obtain a graph like the one on the right below.  Those students, who had not followed instructions properly, were measuring water depth in the wrong chamber!

01 May 2001 Estellvenia Sanders (Chicago Vocational HS) Teeing for Angles
made a rectangle on the floor about 2 ft wide and 10 ft long using masking tape. She marked the tape at 1 ft intervals. She then gave each of three volunteers a toy plastic golf club and plastic ball. Each volunteer was asked to putt the ball to see the distance it would go before it either stopped or went out-of-bounds. A chart was drawn on the board, with each person's name displayed on the vertical-axis, and the distance on the horizontal-axis. Each distance was located as a dot on the chart. Straight lines were drawn to connect each pair of dots on the chart as data was obtained. The lines made various angles with each other, which the we were asked to identify as obtuse, acute, right angle, etc. A geometry vocabulary was thus motivated by this game: angle, point, plane, line, etc. Estellvenia uses hand signing to communicate with her deaf students, and this kind of activity proves quite helpful. Thanks, Estellvenia!

25 September 2001 Ann Brandon (Joliet West HS, Physics)
Ann gave the following handout sheet of 4 graphs of distance versus time D-T, velocity versus time V-T, and acceleration versus time A-T.

The problem was to match them up.***see below.

Ann continued her presentation of  the11 September 2001 SMILE meeting, in which she dropped a transparent plastic tennis ball tube, with washers attached to  its inside bottom end with rubber bands.  Using the Video camera, Jami English carefully recorded the tube as it fell through the air, so we could see more clearly when and how the washers fell inside the tube.  The following tentative conclusions were made:

• It seemed that the washers jump inside the tube after the tube is dropped, say, 0.5 meters, and well before it hits the floor.
• When the tube was thrown up and caught before it started to come back down, the washers were still pulled inside the tube!  It is the downward acceleration, rather than the downward velocity, that causes them to be inside.  In addition, the upward-moving tube slows nearly to rest when the washers are pulled inside, making it easier for our eyes to see it happen.

These conclusions are tentative, pending examination of the video.

Roy Coleman (Morgan Park HS, Physics)
indicated that  an up-to-date SMILE CD ROM is available from him for \$10, plus any shipping costs.  You may send him an email at "coleman  AT iit DOT edu". Also, he announced that the next ISPP Meeting will be held Wednesday, 17 October 2001, at Morgan Park High School, starting at 6:30 pm.

Bill Shanks (Joliet Central HS, retired)
began a presentation, but promptly discovered that the apparatus was broken.  He will do it next time.

See you Tuesday, 25 September!

*** The Answers:  D, B, C  ... C, A, A or D ...  B, C, A or D ... A, D, B

05 February 2002: Roy Coleman (Morgan Park HS, Physics) Various:

• Dropping a Hammer:
A former student, now a lawyer, asked Roy how to describe the damage done by dropping an 8 lb [3.5 kg] sledge hammer through a height of about 16 feet [5 meters] onto somebody's skull.  They decided to describe the effect through the work energy theorem.  The potential energy lost by the hammer, mgh, was about 8 lb ´ 16 feet = 128 ft lb [170 Joules].  Assume that the skull can deform about 1 cm [0.5 in or 1/24 ft] without breaking.  The average force on the skull would then be about 128 ´ 24 lb = 3000 lb  [17000 NT].  The skull will surely break under those conditions.
• Millikan Eggs:
He described putting a different number of  identical objects (say; marbles) inside various empty  Leggs Egg Shell containers, and  then measuring the mass of each of the containers, to obtain data such as the following [in grams]:  15, 61, 52, 42, 23, 34, 24, 24, 23, 23.
Questions[1] What is the mass of a shell? [2] What is the mass of each of the identical objects inside? [3]  How many objects are inside each shell?  Solution to this problem is very similar to analysis of data for the Millikan Oil Drop Experiment to determine the charge of an electron.
Porter pointed out that this will not work with real eggs from chickens, since [1] shells of double yoked eggs are usually somewhat larger than ordinary shells and [2] You can see inside a chicken egg by a process known as "candling", or holding the egg over a shielded bright light.  Alas, the day in which each family has a chicken house and keeps a Bantam Rooster for entertainment purposes has passed for most Americans.
• Special 2-inch plastic eggs [and other interesting items] are described in the recent Oriental Trading Center Catalog [Write OTC, P O Box 2328, Omaha NE 68103-2200,  or call 1 - 800 - 875-8480, or check the website http://www.orientaltrading.com]
• No Gravity Day [01 April]:
Roy described elaborate and bizarre procedures which were employed on a recent April 01.  Several days in advance, he prepared an "official announcement" of NO GRAVITY DAY, with an "official permit" from the "city department of governmental control".  He passed out a sheet with several suggestions for how to manage on that day, which included the following items:
1. Do not flush the toilets!
2. Hold onto the railing on steps!
3. Obey the traffic signal light on the third floor!
4. ...
5. ... april fool ...
6. ...
7. Be sure to wear a rope around your wrist.
A hapless substitute math teacher became quite confused after seeing a staged levitation experiment, and left school after a few minutes in a quite disturbed state.
Let's hope the second law of thermodynamics isn't repealed also.  Very fine, Roy!

08 October 2002: Fred Farnell [Lane Tech HS, Physics]     A Slow Train
Fred
used traction feed computer paper to lay out a 27 meter "track" on the floor of his classroom.  He released a slow-moving, battery-operated toy train engine [He got it at Radio Shack; it requires 4 batteries for operation.], which students kept on the paper track by pushing it occasionally with a stick.  Students were located along the track with stop-watches to record the time required for the train to travel to their locations.  A distance-time graph was constructed from the data, which was a fairly straight line of slope 0.5 meters/sec.  [A smaller, faster toy made the 27 meter trek in about 13 seconds.]  The speed-time and acceleration-time graphs were constructed from the distance-time graph by taking slopes.  He signaled the students to begin timing by lowering a rod that he held over his head --- this method of initiation is similar to the music conductor's downbeat, which signals the orchestra to begin playing a piece.  A fresh approach, Fred.  We knew that bigger is better, and sometimes slower is better, as well.

05 November 2002: 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!

25 February 2003: Monica Seelman [St James School]      Surface Tension with Cheerios
Monica
has always enjoyed eating Cheerios™ cereal for breakfast, and was particularly fascinated by the fact that these pressed toroidal cereal pieces tend to clump while floating on milk. How come?  At Monica's invitation, in groups of 2, we put some milk into a bowl and began to add a few Cheerios, which floated on the surface.  Monica had expressed some concern that she had only been able to get 2% milk, versus her usual skim milk at breakfast, and wondered how it would work.  We found that it worked very well, and that it worked at least as well, and possibly better, with water.  The cereal pieces floated on the surface until they came close, and then seemed to stick together along their edges.  Presumably, the surface energy, which is proportion the surface perimeter between cereal and fluid, is reduced by having the cereal pieces to adhere. The same principles apply to adhesion of algae in a pond, clotting of blood, etc.

Very interesting --- even though you haven't been eating your Wheaties™, Monica!

25 March 2003: Ben Butler [Laura Ward Elementary School, Science Teacher]        What's a Million?
Ben
showed several exercises that he has presented to his students.

1. First he showed us two capped containers [about 2 gallons or 10 liters] that contained colored, tiny plastic beads.  He remarked that each container contained 1 million individual pieces. The container with yellow beads contained one black bead.  Surprisingly, it was fairly easy to find that bead, since it migrated to the top as we shook the container.  Ben shook it to the tune of the chorus [Bounce-Bounce-Bounce- ... ] of the R Kelly rap song, Ignition. without the lyrics. [Ben occasionally does this chant in class, to let the students know that he is not totally ignorant of their world.]  Ben passed around another container with a million blue plastic pieces, and one black one, which is much harder to find.
2. Ben next showed us the mechanism for a bar stool turntable.  First he used it  to demonstrate the relation between the radius R and circumference c of a circle: c = 2 p R.  He measured the radius (6" or 15 cm) with a ruler, and then calculated the circumference.  He demonstrated the expression by putting 3 sheets of notebook paper [11" or 33 cm each] around the edge, and then showing that he needs just a little more to make the circumference [37.7" or 96 cm]
3. Ben next had a volunteer to stand on the mechanism, and Ben rotated him around several times. He asked us how far the edge of the mechanism had moved in, say, 5 complete revolutions --- more than 15 feet or nearly 5 meters.  The participant got very dizzy while being spun around, for some strange reason!
4. The volume of a cylinder of radius R and height H is V = p R2 H, and the area of its lateral surface is A = 2 p R H. Starting with two  8.5" ´ 11" transparency sheets, Ben folded one into a long, 11" tall cylinder, and the other into an 8.5" short cylinder. With their bottom ends blocked off, which way  cylinder would hold the greater volume?  Most students expect that the taller cylinder will have a greater volume than the shorter one.  Ben stood both cylinders inside a large transparent container, with the shorter one encircling the taller one.  Then Ben showed us the answer by using Uncle Ben's Rice™ to fill the long cylinder completely. He then lifted the long cylinder, so that the rice inside it spilled into the shorter cylinder  --- which was then only partially filed with rice. Ben was able to add quite a bit more rice in filling the shorter cylinder! In the interest of full disclosure, Ben pointed out that he has no relation to either Uncle Ben™ or his rice!

A good set of ideas, Ben!

25 March 2003: Don Kanner [Lane Tech HS, Physics]      Proclamation Concerning Areas and Volumes
Don remarked that, because the lateral surface area of a cylinder of radius R and height H is A = 2 p R H, whereas its volume is V = p R2 H, it should follow that the cylinder of greatest volume for a given lateral area should be one of large radius R and very small height H. Do you believe this?

Don promised to prove it next time! We await edification, Don!

08 April 2003: Don Kanner [Lane Tech HS, Physics]      Paradox and a Pair o' Docks
Don had remarked at the last meeting that, because the lateral surface area of a cylinder of radius R and height H is A = 2 p R H, whereas its volume is V = p R2 H, it should follow that the cylinder of greatest volume for a given lateral area should be one of large radius R and very small height H. To illustrate the point, Don placed three transparent cylinders so they stood upright on the table. One was tall and skinny; it was made from a single transparency sheet with its short side (width w) folded around into a circle (circumference w) and its long side (height H) standing up. Its lateral area was therefore H w. The second (medium) cylinder was only half as tall, with height H/2 and circumference 2w, and therefore lateral area of (H/2) (2w) = Hw, the same as the tall one. The third cylinder was short and squat, half as high as the second one, with a height of H/4, and circumference of 4w, and therefore a lateral area of (H/4) (4w) = Hw, the same as the first two. Don arranged them on the table to lie concentrically and coaxial with each other, ie., the tall one was surrounded by the shorter medium one, which in turn was surrounded by the short squat one, all standing with a common vertical axis. Their bottom ends were closed off by the table, but their top ends were open. What next?

Don poured rice into the tall skinny cylinder in the center, filling it completely full to its very top. He pointed out that the volume of the rice must equal the volume of the tall skinny cylinder. Then -- beautiful to see! -- Don slowly and carefully raised the tall cylinder up off the table. As he did so, the rice spilled from its now open bottom end to occupy some of the volume within the medium cylinder. Don smoothed the rice flat, and we could see that it filled the medium cylinder to just half its volume. Wow! So the medium cylinder must be capable of holding twice the volume of rice as the tall skinny one! Finally, Don slowly raised the medium cylinder to spill the rice from its bottom end to occupy some of the volume enclosed within the short squat cylinder. When he smoothed the rice flat, we could see that it occupied just 1/4 of the volume of the short squat cylinder! Don then appealed to the fact that, if this process is continued indefinitely, the enclosed volume can be made arbitrarily large, as is illustrated in the following table, beginning with a sheet of height H and width w:

 Number Height Width / Circumference Lateral Surface Area Cylinder Radius R Cylinder Area pR2 Cylinder Volume pR2 H 1 H w H w w / (2p) w2/(4p) w2/(4p) H 2 H  /2 2w H w w / p w2/p w2/(2p) H 3 H / 4 4w H w 2w / p 4 w2/p w2 H / p 4 H  /8 8w H w 4w/ p 16 w2/p 2 w2 H/ p 5 H / 16 16w H w 8w/ p 64 w2/p 4 w2 H/ p .   .   . ¥ 0 ¥ H a ¥ ¥ ¥

Don mentioned that zero and ¥ often occur together in physical problems; i.e,  infinite resistance goes with zero current; infinite kinetic energy requires zero time elapsed; etc.

Don, you have done as promised!  Very nice!

06 May 2003: Roy Coleman [Morgan Park HS, Physics]        Using Marbles to Determine the Size of the Monster Behind Door
Roy
handed out a sheet containing the following information:

The Size of a Monster
There is a very hungry monster in an almost completely closed room.   There is a door to enter and a thin horizontal slit at the bottom along the entire length of a side.  Before you enter the room you must determine the width of the monster. You also have a large supply of small rocks.

Using a monster that looks remarkably like a soft drink can and rocks that look like marbles, you are to determine its experimental width and compare that value to its actual width.  Each time the monster is hit it grumbles (klinks?) and moves, never touching any of the walls.

A couple of hints:

1. Each group will need to throw at least 200 rocks randomly through the slit into the room.
2. What is the probability of hitting the monster if it is half the size of the room?
3. Look up information on the Rutherford Scattering experiment.
4. Does the size of the rock itself make a difference?

Good luck in gauging the size of the monster, Roy. Thanks!

09 September 2003: Fred Farnell [Lane Tech HS, physics]        Balancing an Egg on End
Fred
began by describing this activity as an illustration of the application of the Scientific Method.  He showed a dozen fresh eggs, which he had asked his class to vote on the following hypothesis concerning balancing an egg on end:

 `Choices: ` `Number of Votes` Not possible 45 Only on vernal equinox 34 Only on autumnal equinox 7 Broad end only 35 Pointy end only 1 On either end 10 Only at equator 1
Four eggs were successfully  balanced on their broad ends, by  Marilyn Stone and Betty Roombos [twins!].  Others tried to balance the eggs, without success.  The moral is that it requires patience, steady nerves, and effort to balance an egg. It is also possible to balance an egg on its pointy end. This question is discussed in the book Bad Astronomy: Misconceptions and Misuses Revealed, from Astrology to the moon-landing hoax by Phillip Plait [Wiley 2002, ISBN 0-4714-09766].  Note that some of the choices are not reasonable, such as the fact that balancing can be done on the vernal equinox, but not on the autumnal equinox.  Still, there are many people who believe in such pseudo-scientific folklore.  For details see the Egg Balancing Website: http://www.badastronomy.com/bad/misc/egg_spin.html.

Thanks for sharing this with us, Fred!

23 September 2003: Roy Coleman [Morgan Park HS, physics]        Pulling on a Spool with a String
Roy
brought in a very large wire spool [rough dimensions: outer diameter 40 cm, inner diameter of 15 cm, height 40 cm]. He wrapped a heavy cord around the inner portion, and went through the classic demonstration of pulling the cord, as described on the website Julien C Sprott: Physics Demonstrations: Motion [http://sprott.physics.wisc.edu/demobook/chapter1.htm, item 1.12].  He made the spool come toward him, go away from him, stand still and slip, and slide toward him, just by pulling with various orientations of the cord. Roy then rolled the gigantic spool on the chalk tray of the board, attaching a marker to the edge.  The marker traced a cycloid on the board -- Beautiful!

Bigger spools are better, definitely!  Neat, Roy!

Roy also called our attention to the American Association Physics Teachers [AAPT] High School Photo Contest, as described in the Fall 2003 issue of the AAPT Announcer [Vol 33, No 3].  [also, see the website http://www.aapt.org/Contests/pc03.cfm]  The First Place winner by Jared Hill of Durham NC, is shown on its front cover.  It  shows a hard-boiled egg spinning in a thin layer of water.  The water is creeping up the side of the egg until it is thrown outward, creating a fountain effect. See the journal article "Fluid flow up the Wall of a Spinning Egg" by Gutiérrez, Fehr, Calzadilla, and Figueroa, American Journal of Physics 66, 442-445 (May 1998).  Our own Ann Brandon is a guiding spirit of this contest!

07 October 2003: Imara Abdullah [Douglas Academy,  science]        Posters
Imara
provided us with poster paper, colored markers, and tape, and asked each of us to prepare a poster to illustrate some concept or process in mathematics or science.  We came up with the following displays:

 Name Display description Concept or process illustrated Porter Johnson blank sheet of paper Vacuum, empty space, cosmic void Bill Colson Flow chart 3 ® 1 3 conditions for triangle congruence Roy Coleman I'm a p r2 (big wheel) Area and circumference of circle Elizabeth Roombos Rock hurled off cliff Projectile motion Marilynn Stone Click-clack apparatus Momentum conservation Monica Seelman 45°-45°-90° triangle Pythagorean Theorem Earl Zwicker Sequential images of ball on inclined plane Galileo experiments in mechanics Imara Abdullah Walking dog around block Perimeter John Bozovsky Kneeling carpenter drilling into wall Niels Bohr (kneeling and boring) Larry Alofs Rectangle at new IIT student center Golden rectangle  -- or not? Jane Shields Colored strips on paper Northern lights Babatunde Taiwo Rocks thrown simultaneously up and down Do they hit the ground at the same time? Walter McDonald Headlight beam image Illumination: Inverse square law Rich Goberville Projectile shot from cannon Action-reaction Forces Bill Shanks Plumb bob demons Universal gravitation Fred Farnell Light charged balls on strings Coulomb's Law: Electrostatics Leticia Rodriguez See-through skeleton Systems in human body John Bozovsky Truck accident How the Mercedes bends
Imara showed us how to display individual posters, using two sheets of transparent Plexiglas™ sheets, held by two binder clips.  Nifty, eh!

We were all on our feet and involved!  Beautiful Activity, Imara.
dynamite, Gary! Thanks.

04 November 2003: Monica Seelman [ST James Elementary School, science]        How much paper is there in a roll?
Monica
brought a wrapped cylindrical roll of paper about 1.36 meters in height.  The roll had an inner circumference of  11.6 cm, an outer circumference of 23.6 cm, corresponding to an average circumference of 17.6 cm.  The thickness of a stack of 25 sheets was measured to be 0.6 cm, corresponding 0.024 cm per sheet. Since the paper was 2.0 cm thick on the roll, Monica felt that there were about 83 sheets in the roll.  Thus, she estimated the roll to be 14.7 meters long --- and with a height of 1.36 meters, this corresponds to an area of 20 square metersLarry Alofs suggested an alternative method of estimating the amount of paper, by weighing a small piece of paper of known area, and then weighing the entire roll.  This might have been more accurate, in practice.  We could have done both, and then rolled the paper out to see how long it actually was.

Thanks for showing us the way, Monica!

06 April 2004: John Scavo  [Evergreen Park HS, Physics]         Cub Scout Science
John
passed around copies of an article, Amazing Science Tricks by Michio Goto, which appeared in the April 2004 issue of Boy's Life® http://www.boyslife.org/, official magazine of the Boy Scouts of America®.  See also the book Amazing Science Tricks by Michio Goto: http://www.a1books.com/AMAZING-SCIENCE-TRICKS-KIDS-PARENTS/4770024924/catalogJohn called particular attention to the lessons entitled Keeping Water Separate, A Candle that Sucks Water, Bending Light through Water, and Toothpick Torpedo.  He demonstrated the bending of light through water by poking a hole in a 2 liter soft drink bottle with an awl, and then filling it with water.  When the bottle was placed on the table (in an aluminum oven pan!) in an upright position with the cap off, water flowed out of the hole in a steady stream.  He held a flashlight at the level of the hole and on the opposite side of the bottle, and turned it on.  Light shined through the bottle, and came out into the stream of water, and was totally reflected internally along the stream.  Beautiful!  He showed us the Toothpick Torpedo.  First John dabbed a little shampoo on the blunt end of a wooden toothpick, and dropped the toothpick horizontally into a pan of water. The toothpick began moving in the direction of the sharp end.  Why?  Shampoo reduces the surface tension in the fluid near the blunt end of the toothpick, and thus the floating toothpick experiences an unbalanced force, and goes forward.

Isn't Science Amazing?  Thanks, John

07 December 2004: Sally Hill [Clemente HS]           Physics Catapult Project  (handout)
The following has been extracted from the handout passed out by Sally:

1. Goal: Create a device that will launch a ball at a target with proper distance and accuracy.
2. Competition Rules
• groups may be no larger than 3 students
• you may use any safe materials you wish
• no explosives or dangerous air compression devices
• your project must be able to fit through a classroom door
• you will launch the tennis ball (provided on test date)
• the ball must hit the target on a fly
• your device must be powered only by energy stored in it, and may not be aided by a 'helping hand'
3. Testing Procedure
• Each group will line up behind the launching line and send their tennis ball toward the target 25 feet (8 meters) away.
• Each group will be given 3 shots, with each shot graded by "distance missed"
Sally brought in a winning catapult, and used it to fire a tennis ball across the room.  Stretched fabric was used to provide the potential energy needed for launch.  We found that the catapult was more powerful when a large, strong rubber band was wrapped around the pivot point of the catapult -- the tennis ball went about 8 meters across the room.

14 December 2004: 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!

08 March 2005: Fred Schaal [Lane Tech HS, mathematics]              RANDINT(1,14,4)+50
Fred
used the Pseudo-random Number Generator RANDINT, which is programmed into the TI-83 calculator. He generated a random, equally-distributed set of 200 integers from 1 through 14, and obtained the following number-of-occurrences of the generated numbers:

 Generated Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Number-of-occurrences 13 12 13 18 17 14 20 15 13 13 17 10 13 12
Does this appear to be a "random" set of numbers? The answer is "Yes", despite the fact that the number-of-occurrences ranges between 10 and 20. On statistical grounds, we would expect the average number of occurrences to be about 200/14 = 14.3, with a spread (standard deviation) of Ö14.3 = 3.8.  Thus, about 2/3 of the number-of-occurrences should lie between 11 and 17. That is consistent with the spread in the data. Curiously, only the number "6" occurs exactly 14 times.

Porter Johnson mentioned that "everybody knows" that it is unlikely for a randomly flipped coin to come up H (Heads) ten times in a row. However, not everybody realizes that the alternating sequence H T H T H T H T H T is equally unlikely. Furthermore, it is quite unlikely that in 1000 coin flips, Heads will occur exactly 500 times.

For a general discussion of Pseudorandom Number Generators see the Wikipedia webpage: http://en.wikipedia.org/wiki/Pseudorandom_number_generator.

Fred also brought in his metal candy box, for which we had taken exterior measurements last time. to determine a volume of about 910 cm3.  We took a graduated cylinder filled with water, from which we were able to pour about 800 cm3 of water before the box became full. Our estimated volume was too large by over 10%. Why?

Fred also pointed out that the planet Mercury would be visible next to the New Moon just after sunset in the next few days. Thanks for the ideas, Fred!

10 May 2005: Roy Coleman appeared on the Channel 5 (NBC) news on Monday 09 May.  His classroom work with college-bound students was shown on that program, in keeping with his wide-spread, well-deserved reputation as an excellent physics teacher. You looked great, Roy!

20 September 2005: Roy Coleman (Morgan Park HS, physics)               Using Spools to Teach Physics
Roy
followed up on Karlene's presentation on cycloids last week by placing a piece of chalk into a hole near the edge of a circular face (on one side or the other) of a large spool, about 50 cm in diameter.  When that face of the spool was held against the board and rolled without slipping along the chalk tray at the bottom of the blackboard, the chalk traced its own cycloidal path on the board.

Roy then wrapped a string around the axle of the spool, placed the spool on a horizontal table, and slowly pulled on the string.  In which direction does the spool begin rolling?  Well, it depends upon the direction of the torque produced about the axis of rotation.  This actually is the horizontal axis through the line of contact of the spool with the table. There is a critical angle at which there is zero torque about the contact point.  This happens when the string points directly at the axis of rotation.  The spool simply slides along without rotation when the string is pulled with a force sufficiently large to overcome static friction. For details see the Rolling Spool entry on the Oberlin College Physics Demonstration website:  http://www.oberlin.edu/physics/catalog/demonstrations/mech/spool.html. Good show!  Thanks, Roy.

20 September 2005: Carl Martikean (Proviso Math and Science Academy, physics)    Module:  Learning to see Behind
Carl
has developed some Project-Based Learning Modules in his new school. He passed out one such module, which presented the following problem:

"Your task is to devise a scheme that uses the three car mirrors so that there are no blind spots --- or at least minimal ones."
The analysis proceeds through the following steps:
1. Summarize your state of knowledge using a KTN table. A KTN organizer is a list of the following things:
• K: Things you Know.
• T: Things you Think you know.
• N: Things you Need to know.
2. Draw the ray diagrams for your plan.  Be sure that any blind spots are clearly marked.
3. Write out a set of steps that can be used for any vehicle.  Be sure to include a complete explanation of why this is a proper method of mirror adjustment.

Here were some items on our KTN table:

 Know Think we know Need to know There are 3 mirrors. The left mirror is closer. Head of driver can move. The mirrors are adjustable. Different people of different sizes have different problems with the blind spot. Views from the 3 mirrors must overlap. Mirrors show us things that are behind us. Different height cars may result in complications. What is a ray and how do we draw it? How does light react with a mirror? How big are the the mirrors? Do passengers obstruct the view from the rear view mirror? Do other obstructions, such as small windows in the rear, complicate the problem?
For detailed directions with ray diagrams see the following website:  http://www.gws-mbca.org/features/AdjustingMirrors.html.  In addition, the Canadian Direct website http://www.canadiandirect.com/Auto/Safe_Driving_Tips/Blind_Spots.aspx has both directions for mirror adjustment and ray diagrams. Neat lesson! Thanks, Carl.

04 October 2005: Don Kanner (Lane Tech HS, physics)             Who Lives Where?
Don
handed out the following problem:

I have been very fortunate in being able to make arrangements for all my staff. Alf, Bert, Charlie, Duggie, Ernie, Fred, and George, as well as my chauffeur, Hubert, and my secretary, Judith, to live in houses (all different) on Domum Road. This road has houses numbered from 1 to 55. My employees all made statements about the numbers of their houses as follows:
• Alf said that his number was 23 more than Bert's.
• Bert said that his number was 16 less than Charlie's.
• Charlie said that his number was 19 less than Duggie's.
• Duggie said that his number was 12 more than Ernie's.
• Ernie said that his number was 30 more than Fred's.
• Fred said that his number was 17 less than George's.
• George said that his number was 37 less than Hubert's.
• Hubert said that his number was 12 more than Judith's.
• Judith said that her number was 10 more than Alf's.
I discovered afterwards that one of these statements was not true. Find the numbers of the houses in which all my nine employees live.
This problem was taken from the book Puzzles for Pleasure by E R Emmet [Emerson Books 1972, ISBN 0-87523-178-0]: http://www.mathpropress.com/mathBooks/Emmet.html. It can be analyzed by writing a large number of simultaneous equations and solving by brute force. Don showed us a "graphical" way of solving it that was simpler and more fun. Don drew a number line, with each number (integer) represented by a dot. Starting with the first statement (Alf and Bert) and walking up and down the number line, on arbitrarily marked positions, he marked the position of Bert's house with a B at the origin, and the position of Alf's house with an A at +23. He continued this process to mark the position of Charlie relative to Bert, etc, until he had used all the information from the nine statements. From this it became apparent that the one false statement is: "D is 12 more than E". This is the only way for a single inconsistency to occur. Simply powerful! Try it!

Don then stated The Four Laws of Scitechnoliterarydynamics:

• The Zeroth Law (Vocabulary Skills)
Time and care must be taken to determine the meaning of all new words, within the context of the material being read.
• The First Law (Visual-Verbal Skills)
Time and care must be taken to visualize all that is verbal and verbalize all that is visual.
• The Second Law (Organizational Skills)
Time and care must be taken to organize everything that is organizable.
• The Third Law (Translational Skills)
Time and care must be taken to summarize the essence of what is being read in plain English.
Don then explained Roy Coleman's infamous self grading experiment, which he gives out as a makeup exercise -- see below.  Great stuff! Thanks, Don.

04 October 2005: Roy Coleman (Morgan Park HS, physics)                  Bathroom Physics
The idea is, using a ruler and stop watch, to plot the depth of the water in a toilet tank as a function of time as it is flushed and then refills. Students routinely obtain three distinct types of plots, which he described.  Which one was correct, and why?  We were able to identify the correct one and to figure out why the students got incorrect curves (meter stick in the tank upside down; meter stick in the toilet bowl -- not the tank!).  Roy does the above activity (as well as having students calculate the volumes of their bathrooms, in cubic meters) the night before parents' night.  This in-home exercise is a good icebreaker, since parents have seen the students the night before working together on this unconventional activity.

Roy called attention to an amazing internet picture of the shock wave ahead of the sonic boom, around a supersonic airplane; see http://antwrp.gsfc.nasa.gov/apod/ap010221.html. Wow!  Thanks, Roy!

18 October2005: Ann Brandon (Retired, Joliet West)            Halloween Math  +  Straw Stuff
Ann
had a roll of ticker tape to illustrate Halloween Math -- specifically to determine what one gets when one divides the circumference of a pumpkin by its diameter.  As surrogates for pumpkins we used round plastic jar caps of various sizes. Pieces of ticker tape the length of the circumference and the length of the diameter were measured and torn from the ticker tape roll. Each person then had  a diameter and a circumference for their "pumpkin".  Ann attached a magnetized meter stick vertically to the blackboard, which was used to mark the distances for each person's ticker tape pieces.  It also served as the Y-axis for a set of coordinates on the board. The length of each circumference was the Y-value and the length of each diameter the X-value for a point with coordinates (X,Y) -- one data point per person.  This produced points that traced out a straight line, the slope of which was p, ie, the function which describes the line is Y = p X.  That is, the circumference of a circle is p times its diameter: c = p d

Ann also pointed out that with tape each student could tape his/her diameter strip on the X-axis, with the circumference strip taped at right angles starting at Y = 0 and the right end of the diameter strip, leaving the top of the circumference strip at the place where the corresponding point will be.  Using the best fit, we calculated the slope of the line to be 64.3 cm / 20.5 cm = 3.1366! Pretty close to the real thing-- now let's eat some real Pumpkin p

Ann then showed two old cardboard boxes filled with Swan paper straws (probably dating back to the 1970s).  There are things you can do with paper straws that you cannot do with plastic straws.  Paper straws are reportedly still available from a coffee supply company or at a Hard Rock Cafe™ . They can also be ordered from art supply catalogs, commonly used by art teachers in schools.  She cut an inverted V into the flattened end of a straw, forming  a double reed, like an oboe.  Ann then blew continuously into the straw, producing an oboe-like sound.  As she did this, she used scissors to cut successive pieces from the end of the straw. We heard the pitch of the sound getting higher -- usually, but not always.Ann then showed how you can make smoke (which you may need for a demonstration with a LASER, etc) by lighting the end of the straw and letting it burn down a bit. Then she blew into the straw, causing the smoke to puff out of the lit end by squeezing the unlit end of the straw.  Neat stuff, as always!  Thanks, Ann.