High School Mathematics Physics SMILE Meeting
05 September 2000
Notes Prepared by Earl Zwicker

Bill Colson (Morgan Park HS)
treated us to a classic bit: Tom Lehrer's "New Math" playing out a neat pair of speakers and radio-recorder-player. Entertaining and somewhat informative perspective.

Ann Brandon (Joliet West HS) gave each group of two of us an eye dropper and a dixie cup half-filled with water. We provided our own penny, and Ann told us to find out how many drops of water the penny would hold. She posted results on the board as we found our answers:

 Heads 22 21 30 34 24 28 13 17 Tails 28 45 30 31 24 18

In our curiosity to explain the results, the concepts of area and surface tension were brought up and discussed, and we enjoyed a good review and multiple insights into these topics. A good classroom investigation - Thanks, Ann!

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!

Fred Schaal (Lane Tech HS)
told us to look due East about one hour before sunrise, and observe the sky. Watch the planets in the pre-dawn sky! They form a triangle: Saturn, Jupiter, and ?? (Do you know?) The beauty and pleasure of astronomy. Thanks, Fred!

Bill Blunk (Joliet Central HS)
showed us the Orbitron magnetic toy. (Manufactured by Binary Arts, and available at the website of The Toy Box: http://www.toyboxligonier.com/tbx/orbitron.html.  See also the Wizmo Orbitron, available at  http://www.parents-choice.org/product.cfm?product_id=1839&award=xx&from=ThinkFun). Essentially, it was made with two chrome-plated heavy wire rings, of equal diameter (about 27 cm), held coaxially a fixed distance apart (by a frame of some sort). A small but massive metal top had magnetized axles, which held it onto the pair of rings.

If the rings were held with axis horizontal, and the top place at rest at the highest position, the top would gradually start spinning as it moved down and around the pair of rings until it reach the bottom, then continued on up the other "side" - but not all the way. Some energy had been lost. Bill told us how he tried to increase the speed of the top to reach the point at which the magnetic force keeping it in contact with the rings would no longer supply sufficient centripetal force to keep the top moving in a circle, so it would then "fly off" -- but there were problems.

Next, Bill showed us another toy (Lumberjack Toys,7651 Herrington NE Belmont, MI 49306) which used a tethered ball one could project up toward a small basketball hoop, and try to make a "basket." Shows transition of kinetic energy into gravitational potential energy, as well as being fun. The toy is available at the following location:

Amazing Toys
319 Central Avenue
Great Falls MT 59401
(406) 727-5557 [Bob Pechlin]
http://www.amazingtoys.net

Thanks, Bill!

Carl Martikean (Wallace School, Gary, IN)
showed us 2 sharp pencils, 4 sheets of Cartesian graph paper, 1 tire pressure gauge, and asked - How can we weigh a car using this stuff?

Answer - drive the car with each one of the four tires standing on a sheet of the graph paper. Trace the footprint of the tire on the each paper. Use the gauge to measure the pressure in each tire. With the graph papers on the table, measure the areas of the footprints. The force on each of those footprints must equal the pressure in the tire multiplied by the area of the footprint. One must use the absolute or total air pressure in the tire, which is the pressure measured by the gauge plus atomospheric pressure. For example, if the pressure gauge reads 26 pounds/square inch, then we must add 14.7 pounds per square inch to 26, for an absolute pressure of 40.7 pounds per square inch. Multiply by the area of the footprint (suppose it is 30 square inches), and we have about 1200 pounds. If each of the 4 tires is identical, then the total force being held up (the weight of the car) is 4800 pounds! Thanks, Carl!

At this point those in the SMART Program left to a meeting and we who remained enjoyed Lee Slick (Morgan Park HS), who wrote down the squares of numbers ending in 5:

 52 = 25 152 = 225 252 = 625 352 = 1225 452 = 2025 etc.

With Lee's help, we saw a pattern: All the results end in 25. If we multiply the ten's digit by the next higher digit, we get the number to place before the 25. To square 35, for example, multiply the 3 by 4 to get 12, and we have 1225 as the result. More neat ideas! Thanks, Lee!