Mathematics-Physics High School SMILE Meeting
01 February 2000
Notes Prepared by Earl Zwicker

Earl Zwicker (IIT) showed us a topological puzzle. He cut a sheet of paper (8.5x11) into the shape of a plus sign (+), after first folding it in half one way, then the other. The folds were used as a visual guide, and Earl cut a good half inch on each side of each fold, leaving a + shaped piece of paper with each leg a good inch wide. He then folded the vertical legs to meet in a loop, and taped them together. Then the horizontal legs to make another loop (taped) lying below the first (& naturally perpendicular to the first loop). Next, he used a scissors and cut each loop in half "longways" - along its circumference. Behold! The result was a rectangle, like a picture frame!

Next, he held up what appeared to be two intertwined hearts. This was the result of making a half-twist before taping the legs together to make a Mobius strip of each loop. Then cutting as before along the "circumference" of each. Try it!

John Scavo (Richards Career Academy) (handout - see 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!

Bill Colson (Morgan Park HS) held up a book: Two-Fisted Science, an historical reference (ISBN 0-9660106-04 Ottaviari et al), and mentioned Feynman among others. Holding up another book, The Kingdom of Infinite Numbers (ISBN 0-7167-3388-9, Benjamin Bunch), Bill read from a piece by W.H. Auden - inspiring! Fred Schaal (Lane Tech HS) invited a number of us up front, gave us each a piece of polar graph paper (paper with a set of concentric circles on it, and radii drawn in every 10o). He had each of us cut out a segment of angle, one of us 10o, next 20o, then 30o, etc. We then taped the edges together to form a set of cones. Fred proceeded to lay out a set of equations for the lateral area (LA) of a cone, and ended up with a result that the altitude of a constructed cone lying on the table is:

h = R( k/180 - k2/3602 )0.5
where k is the angle (in degrees) of the cut-out segment.

We used sticks of spaghetti to poke down through our cones' tops to the table below, marked the stick, and got an experimental value of h. And then we calculated h from the above expression. Both observed and calculated values matched surprisingly well! A beautiful phenomenological math lesson! Thanks, Fred!

Larry Alofs (Kenwood HS) wrote on the board: Reasons why water doesn't boil ...and he asked us for answers. Some answers were:

• Not hot enough (too little molecular kinetic energy);
• Too much pressure.
Then a question was asked,"What's the difference in evaporation and boiling?" On the board, Larry sketched water molecules, showing their polar nature and the subsequent attraction between them. What does it take to break the attraction and produce evaporation?...boiling?

Larry took an Erlenmeyer vacuum flask and filled it half with water. A one-hole stopper with thermometer was placed in the top opening so the thermometer dipped into the water. He hooked up an aspirator to the water faucet and demonstrated that a vacuum resulted with the water running. With the water off, he connected the aspirator to the tube at the top end of the flask, and read the temperature of the water as 45o C. He then turned on the water, the aspirator reduced the pressure in the flask, and before long, the water inside was vigorously boiling! "Where are the bubbles forming?" asked Larry. Observation showed they formed near the surface of the water, rather than at the bottom as when placed on a hot plate. After a few minutes of discussion, Larry disconnected the flask from the vacuum, and observed that the water temperature was now 38.5o C. How come? Discussion concluded that the water molecules with the greatest energy were boiled off, leaving behind those with lower energy, and therefore lower temperature - temperature being a measure of their average energy. Beautiful, Larry!

Arlyn Van Ek (Illiana Christian) sketched a bell jar setup to evaporate water from a watch glass under vacuum (with conc. sulfuric acid to absorb evaporated water molecules). This would result in lowering water temperature and pressure to and past the triple point, where all three states of water (solid ice, liquid water, and gaseous water vapor) are in thermal equilibrium.

He drew the P-T phase diagram on the board and identified the triple point temperature as 0.01o C.

This led Earl Zwicker to show us a triple point cell which is used to obtain the triple point temperature of 0.01o C as a calibration point for very accurate thermometry. My, how one thing leads to another!

Ann Brandon (Joliet West HS) showed us a demo that she picked up at a national AAPT workshop. With a Radio Shack amplifier-speaker in one hand, and connected by wire to a small photoresistor at its other end, Ann held the photoresistor near fluorescent and incandescent light sources, and we heard very faint 120 Hz hum. Then she took a TV remote and aimed it the photoresistor - producing a series of rapid "clicks" or "pops" when she activated the remote. The remote was sending its coded IR signal and it was detected by the photoresistor which we then heard as sound generated by the amplifier-speaker. Great!

Finally, a flame (lighter) was held near the photoresistor, and Ann ran a hair comb back and forth so its teeth interrupted the IR coming from the flame to the photoresistor. This produced a sound like sawing a piece of wood, much to our amusement! Much fun, and good physics! Thanks, Ann!

Great ideas! Don't miss the next meeting! SEE YOU THERE!