High School Mathematics-Physics SMILE Meeting
06 May 2003
Notes Prepared by Porter Johnson

Don Kanner [Lane Tech HS, physics]        Question on Hydraulic Rams
passed out this summer homework problem assignment, taken from the classic text Elements of Physics by R F Millikan and  H G Gale:  A copy of the problem can be seen by clicking here:

Information concerning Hydraulic Rams can be obtained from these sources:

  1. Hydraulic Ram pumps: http://www.bae.ncsu.edu/programs/extension/publicat/wqwm/ebae161_92.htm
  2. Hydraulic Ram http://www.cat.org.uk/catpubs/tipsheet.tmpl?sku=07
  3. How does a hydraulic ram pump work?: http://www.howstuffworks.com/question318.htm.
Don wants our answers when we come back on September 9.  We'll think about this one.  Thanks, Don!

Bill Shanks [Joliet Central HS, retired]        Persistence of Vision + Other things
showed us his latest toy, a Skyliner Electronic Message Maker, which he got recently at WalMart.  It can also be ordered on the websites:  http://www.clubthings.com/product318.html or http://www.ravehaven.com/products/Sale-Items/SkyWriter-Electronic-Message-Maker_665.html. When the device is turned on, it plays a tune, and two sets of blinking LED's are lit.  When it is twirled in a circle in the vertical plane, the persistent images of words are created.  Fifteen phrases, such as SMILE and BE HAPPY are programmed into the device  -- each with a different distinctive and possibly recognizable tune!  Or, you can program you own messages.  To operate it, spin it around in the air --- the words magically appear before your eyes!

Bill briefly discussed the phenomenon of persistence of vision, which explains how this device works -- as well as the image on a television screen.  The visual cortex lays out an image in the brain, which persists during loading, so that we can get the big picture, or at least the big perception.  Bill quoted a former physics teacher, who recommended saying  "So it seems to be now the thing I think I see", rather than "Now I see".

Bill then passed around LED Pens of various colors, which he obtained at Walgreens --- which also can be ordered at http://www.morsex.com/misc/pens.htm. He showed us three LED Pens --- red, yellow-green, and blue, which he used as light sources.  He turned on various combinations in the darkened room, and showed us the color circles they projected on the white board in front of the room.

Bill then showed his next toy, a search light with two white light sources, one green LED, and a xenon bulb., which he had obtained from Berland's House of Tools: http://www.berlandstools.com.    This device is similar to the Trident Headlamp: http://www.nextag.com/streamlight-trident-headlamp/stores-htmlBill intended to use this device as a skunk repellent, and did so with limited success. The eyes of many forest animals reflect light back to the source, so that the eyes appear to glow in the dark.  For details see the websites How Exactly Do Animals See in the Dark?http://www.ccmr.cornell.edu/education/ask/index.html?quid=589 or Why do cats eyes glow in the dark?http://dspace.dial.pipex.com/agarman/bco/fact4.htm.  [Unfortunately, this technique might work only on the four-legged variety of skunk!].  Bill used the white light to demonstrate retinal fatigue, by shining it on a magenta sheet of paper on the white board in the darkened room.  After a minute or so, we looked away from the sheet, and we saw a green image in the shape of the paper sheet.  Fascinating!

We think we see the light now!  Thanks, Bill!

Arlyn Van Ek [Iliana Christian HS]        Resonance Show
partially filled a wine glass with water, held it by the stem with one hand, wet his finger on the other hand, and rubbed it around the rim.  This set up a stick-slip motion, which produced a fairly high-pitched sound, in the kiloHertz range.  He poured some water out of the glass and repeated the process, producing a higher pitched sound.  As he continued to pour water out of the glass, the pitch continued to increase.  How come?  Earl Zwicker reminded us that the frequency f of oscillation of a mass m attached to a spring of spring constant k is given by f = 1/(2 p) Ö(k/m). Earl suggested that -- analogously-- the effective spring constant k is determined by the oscillations at the rim of the glass. Since one can clearly see the water vibrating inside the glass, the effective mass m includes water, so that m decreases as the amount of water in the glass decreases.  Hence the frequency increases as the glass is emptied. Very nice!

Arlyn then showed a video tape of a Washington DC street musician, who was very proficient in playing tunes, using a different glass for each note.  He did a rather impressive job on Ode to Joy, Chorus of 9th Symphony 4th Movement by Ludwig van Beethoven [http://www.all-about-beethoven.com/symphony9.html], as well as various sailing tunes.  This particular street musician was quite talented, and several of us asked Arlyn to make copies of the performance. For more information see How Can You Make a Wine Glass Sing?http://www.howstuffworks.com/question603.htm.

Arlyn continued by demonstrating resonance using a kit of solid Singing Rods, available for about $20 from Arbor Scientifichttp://www.arborsci.com/CoolStuff/cool13.htm#SingRod. Arlyn held a rod at its center, and produced a high-pitched sound that increased in intensity as he rubbed the rod by grasping it between forefinger and thumb and sliding [rubbing] them along the length of the rod [stick-slip motion with his fingers].  When he held it at 2/3 and 3/4 of its length,  still higher pitches were produced.  The sound was produced by resonant longitudinal oscillations of the rod, with a vibrational node at the holding point.  The sound was not spectacularly loud, unless you hold the rod at a node corresponding to a normal mode of vibration of the rod --- in which case it really wakes everybody up!

Pretty physics, Arlyn!

Monica Seelman [ST James School]      Psychic Puzzle
Monica presented her solution of the puzzle that appears on the Psychic Powers website:  http://mr-31238.mr.valuehost.co.uk/assets/Flash/psychic.swf.  On that website, you are to pick a number, such as 47, say.  Then, calculate the sum of the digits, 4 + 7 = 11.  Next, subtract the sum of the digits, 11, from the original number, 47.  The answer is 36.  In fact, the answer will always be a multiple of 9:  9 - 18  - 27 - 36 - 45 - 54 - 63 - 72 - 81.  This fact provides the explanation for the apparent demonstration of ESP on that website, since the images associated with multiples of 9 are always identical.  Check it out for yourself!  [Similar explanations were provided by Art DiVito and Ken Schug via handout.]

Monica next handed out a multiplication table, which would have looked like this, if only the one's place had been written, with any numbers in the ten's place left out, so that 7 ´ 7 = 9, etc.

´  :   0  1  2  3  4  5  6  7  8  9  0
 -      -   -  -  -  -  -  -  -  -  -
 0  :   0  0  0  0  0  0  0  0  0  0  0
 1  :   0  1  2  3  4  5  6  7  8  9  0
 2  :   0  2  4  6  8  0  2  4  6  8  0
 3  :   0  3  6  9  2  5  8  1  4   7   0 
 4  :   0  4  8  2  6  0  4  8  2  6  0
 5  :   0  5  0  5  0  5  0  5  0  5  0
 6  :   0  6  2  8  4  0  6  2  8  4  0
 7  :   0  7  4  1  8  5  2   9  6  3  0
 8  :   0  8  6  4  2  0  8  6   4  2  0
 9  :   0  9  8  7  6  5  4  3  2  1  0
 0  :   0  0  0  0  0  0  0  0  0  0  0

The following symmetries of this table almost appear to leap out of the page:

Porter Johnson pointed out that this multiplication procedure is called multiplication modulo 10, and that we have noticed some of the symmetry properties of this group of ten elements.  MODULO 10 ADDITION can also be performed (7 + 6 = 13 ® 3, etc) -- leading to a different table --  which also defines a group of 10 elementsWould the tables -- for multiplication and for addition -- be identical in form [isomorphic]?  For additional information see the website Modular Arithmetichttp://www.cut-the-knot.org/blue/Modulo.shtml.  Mathematics is about discovering patterns in things around us, and sometimes [as in playing chess, GO,  or bridge] the specific numbers are either irrelevant,  or play only an incidental role.

So that's how you do ESP with numerology!  Very nice, Monica!!

Roy Coleman [Morgan Park HS, Physics]        Using Marbles to Determine the Size of the Monster Behind Door
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!

Ben Butler [Laura Ward Elementary School]        Dry Ice
brought a supply of dry ice [the solid form of Carbon Dioxide -- C02], which he had obtained from the ice house at Harrison Street and Pulaski Road on the way to class.  He broke off a piece of the dry ice and put it into a glass of water.  The mixture boiled vigorously and produced a great deal of a cloudy vapor, just like boiling beakers in scary moviesDry ice passes from the solid phase to the gas phase at atmospheric pressure.  However, at a pressure of about  3 atmospheres, the liquid phase can also be produced.  Ben produced the liquid phase in a clear flexible tube with a valved opening at one end and attached to a pressure gauge at the other end.  He put a small piece of dry ice inside the tube, and closed the valve; then the pressure steadily increased as it vaporized.  When the pressure exceeded about 3 atmospheres, we saw small droplets of the liquid phase of C02Beautiful!  The apparatus was obtained from Flinn Scientifichttp://www.flinnsci.com/.

What an elegant experiment to show the three states of CO2! Now, Why does dry ice feel dry?  Very slick, Ben!

Peter Smagacz [Lane Tech HS, Physics]       Isolating Rotational Kinetic Energy
discussed using a YoYo to describe various forms of mechanical energygravitational potential energy, kinetic energy of translation, and kinetic energy of rotation::

E = PEg + KEr + KEt = m g h + ½ I v2 + ½ m v2
Unfortunately, his designated Yoyo expert (his son) was unable to attend the class, so that he could not demonstrate the effects.  The idea is that, when the YoYo leaves your hand and falls, gravitational potential energy is converted into kinetic energy, and when the YoYo is "sleeping" at the bottom of its path, it has only rotational kinetic energy.  When the expert gently tugs on the cord, the string wraps around the YoYo shaft and the YoYo rises almost to its original position.  Very interesting discussion -- but can you "walk the dog"?

Interesting ideas, Peter!

John Bozovsky [Chicago Design Academy -- the school formerly known as Bowen HS -- Physics]       Vibrating String Apparatus Revisited
showed us a vibrating string apparatus made out of a cast-off battery operated electric razor, which was attached to a board.  A string was connected to the razor head, and tied at its other end to a Pinch Clamp, which would normally be used in the lab for closing rubber hose.  The pinch clamp was also attached the board, so that the tension in the string could be adjusted by turning the adjustable screw in the pinch clamp.  The razor vibrated at a fixed frequency f of about 100 Hz, as estimated from the hum of the razor.  The length L of the string was fixed at about 30 cm.  By varying the tension, various standing wave patterns could be produced. As the tension T was decreased, the speed of vibrations on the string decreases, and the wavelength l also decreases. Thus, one can fit more nodes on the string of length L, since n l = 2 L, n = 1, 2, 3.  See the writeup for Ann Brandon in the previous class:  mp042203.html This is a cool system, without doubt!

John also showed us a home-made, Adjustable Resonance Tube Apparatus, in which the height of a column of water is varied by raising a reservoir filled with water, with rubber tubing attached to a nipple at the bottom of the tube, as well as to one at the bottom of the reservoir. This device is a variation of the commercially available devices available from science supply houses  We heard the resonant sounds very well!

Plunk your magic twanger, Froggy [http://michelesworld.net/dmm/frog/gremlin/memory.htm] --- er, John! You were in tune with the physics!

We did not have time for the presentations of Gary Guzdziol [video recording of oil drum implosion in his garage on a snowy day] and Fred Schaal [92-ing on the Green Line].  They will be first on the schedule at our first meeting of the Fall Semester 2003, Tuesday, 09 September 2003.  See you there!

Notes taken by Porter Johnson