High School Mathematics-Physics SMILE Meeting
06 April 2004
Notes Prepared by Porter Johnson

John Scavo  [Evergreen Park HS, Physics]         Cub Scout Science
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.thejapanpage.com/html/book_directory/Detailed/329.shtmlJohn 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

Peter Smagacz [Paul Robeson HS, Physics]         Drift Velocity
asked how fast electrons are traveling when a large electric current is passing through a wire.  Some people might guess that they move at the speed of light.  Surprisingly, the electrons are slowly drifting through the wire, at less than one millimeter per second, when, say, current is passing through the starter motor in an automobile.  How come? The answer lies in the fact that the density of electrons in a conductor is very large (n = about 1029 per cubic meter), so that a very large current per unit area J is produced even when the drift velocity is fairly modest.  Specifically, J = I / A = n e0 vD. Thus, when vD = 0.001 m/sec, we get

J = 1029 ´ (1.6 ´ 10-19) ´ 0.001 = 1.6 ´ 107 amp/m2.

If the battery cable has a cross sectional area A= 2´10-5 m2, the current flow would be I = J A = 320 amps. Peter illustrated this with an analogy by lining up some small stones (electrons) in a trough. When he pushed another stone into the trough at one end, a stone at the other end fell out.  Thus, while the stones did not move rapidly, the effect of a stone entering at one end was rapidly communicated to a stone at the other end.

Thanks for sharing this, Peter!

Roy Coleman [Morgan Park HS, Physics]           Diodes and Bulbs 
Roy took 40 watt and 75 watt light bulbs, and showed us that the 40 watt bulb produced less light than the 75 watt bulb, when screwed into a 110 volt socket -- presumably because of the higher resistance of the 40 watt bulb.   Then he reminded us of Ann Brandon's demo from the last SMILE meeting, in which the lower wattage bulb produced less light than the higher wattage bulb, when placed in series across the 110 volt supply.  He then asked us whether the same thing would happen here.  Curiously enough, when he placed two knife switches in series with the bulbs, one bulb would light only when the first switch was closed, whereas the other bulb would light only when the second was closed.  How can that possibly be true??  Roy explained that he had "improved" the switches and the bulb sockets by placing diodes under them, as shown in the circuit below (handout).

NOTE: diodes are wired in opposing directions 
The same principles apply to low voltage lights, but the diodes involved should have higher current ratings than those in the high voltage case.

We see the light(s)!  Thanks, Roy!

Bill Blunk [Joliet Central, Physics]           Jacob's Ladder + Signaling with Plane Mirrors
  began by showing us Jacob's Ladder, which is described on the Science First website in the article Constructing a Jacob's Ladder http://members.tripod.com/shady_hollow/Projects/jladder.html. A Neon Sign Transformer is used to set up a high voltage arc between a pair of vertical, nearly parallel wires.  The wires were about 30 cm long, and closer at the bottom end (about 5 mm), tapering gradually farther apart toward the top.  The arc begins at the bottom end of the wires, and it moves slowly and erratically up the wires, and then disappears at the ends --- as with the angels of Jacob's ladderHow come?  The arc is hot, ionized air, and -- being less dense than the surrounding air -- it is buoyed up, and rises.  Bill fanned the air around the arc as it began to move upward, and it reversed its course, because the ion path was pushed downward by fanning.  Very interesting! Bill put a piece of paper through the arc, and moved it quickly around for a second or two.  We saw that the paper had many small holes burned into it --- those are produced at the rate of 120 per second by the alternating current.  Fascinating!

Bill then reminded us of Colin Fletcher, whose travels through the Grand Canyon are described in the book The Man Who Walked through Time.   He took a mirror along to signal aircraft by reflected sunlight, and so notify them of his location, so that they could drop food to him.  However, he had great difficulty in hitting the aircraft with the reflected image of the sun, and was forced to build a large fire to identify his location.  How could he have reflected the sunlight to the aircraft?  Bill set up a central light source (a fiber optic illuminator -- a bright light), and passed around some signal mirrors, which are polished stainless steel plates with a hole at the center. The idea is to look through the hole in the mirror at the object to be illuminated (aircraft). While keeping the object in view, turn the mirror. Sunlight coming through the hole in the mirror appears as a spot of light. Turn the mirror so that you can see the spot on your face by its reflection from (your side of)  the mirror.  Adjust the mirror so that the bright spot falls on  the hole of the mirror and in the line of sight of  the airplane.  Then, the reflected sunlight will hit the aircraft, as indicated in the diagram below:


| P (aircraft)

| /

(bright spot on face)* | * (image of bright spot)

\ | /

\ | /

\ | /


hole -->


/ | \

/ | \

(eye) O | \ (Sun)


Bill, this one really hit the spot!

Bud Schultz [West Aurora HS,  Physics]           Interactive Physics Simulations -- SIMS
Bud has been using the Interactive Physics simulations in his classroom.  He had loaded the module, Rocket Sled 2, into his laptop PC, and -- with the aid of a projector -- displayed the image of the computer screen on the blackboard screen.  In this module, the masses and initial speeds of two sleds could be varied, as well as the nature of the collision between the sleds.  The sleds (one lined up behind the other) were initially located near the edge of a canyon, and the objective was to see what initial conditions would enable one or both sleds -- one colliding from behind into the other -- to jump over the canyon and land on the other side.  Very often, one or both of the sleds went into the canyon, as Bud showed us.

Information on Interactive Physics Simulations can be obtained at the website http://www.design-simulation.com/IP/index.php.  Other modules in the series include Coconut Kick, Newton's Mountain, and AsteroidBud showed us the last of these on his laptop.  In particular, a projectile launched with the proper velocity will move in a circular orbit around the spherical asteroid because of gravitational attraction. What is the proper velocity?

Bud called attention to gaps in understanding of students (and some teachers!) in the application of mathematics to solve problems.  He deals with this issue by giving extra-credit problems, such as the following:

Given the equations
a x2 + b x + c = 0 ;
x = [ - b ± Ö ( b2 - 4 a c) ] / (2 a) .  
Show that these equations are the same.

You really took us over the edge!  Good, Bud!

Ann Brandon  [Joliet West, Physics]           Forming Images with Plane Mirrors
As we watched Ann used chalk to draw a semicircle on the front desk -- concave facing us.  She used a large wooden protractor as a guide. She placed about a dozen, small mirrors (10 cm high and 3 cm wide) side-by-side around and tangent to the chalk semicircle.  The mirrors were held vertically -- 10 cm side up -- on wooden blocks, facing the center of the semicircle.  She then placed a lit candle at the center of curvature.  Ann picked out a person at the back of the room, and asked him to help her adjust each mirror, so that he could see the reflected image of the candle in each of the mirrors.  We then saw that the mirrors had been re-arranged at regular intervals along a parabolic arc, and the candle was at the focus of that arc! Great!  Thus, we can focus light with an array of flat mirrors, by adjusting the location of each image appropriately.  We each walked by the location of the image, to verify that it had been focused there.  We then placed a light source at the back of the room, and saw that reflected light bathed the candle itself.  Furthermore, there was a bright reflected image produced by each mirror, in which we could see the candle superposed on the light source. Neato!

Beautiful images, Ann!

Don Kanner was unable to attend to make his presentation on the Vandegraaff Electrostatic Generator.  It will be scheduled at the beginning of our next class, Tuesday 20 April 2004 See you there!

Notes prepared by Porter Johnson