ANNOUNCEMENT:

        OUR NEXT MEETING...

...will be the start of the Fall semester on September 5, Tuesday.
You will receive a reminder in the mail. You may already have
registered...

Bill Colson (Morgan Park HS)
handed out an article from the Chicago Reader, from the pages of the Mad Scientist, Spring, 1999, Zine-O-File, and an excerpt from Science Runs Amok? Time Travel - A Medical Nightmare? by Robert Vanderwoude. It points out the biological consequences of time travel, among them being that the antibiotic resistant microbes in time travelers of today could be transferred to people of, say, the 1950s. Also, an article "How Big Are the Planets," Parade Magazine, April 30, 2000, Marilyn Vos Savant -- giving an idea of scale. Use and Keep these in your file!

Fred Schaal (Lane Tech HS)
did the Law of Sines with us as an exploration by hand-held calculator. He drew a triangle on the board and identified its three angles as A,B,C, and the lengths of the sides opposite as a,b,c, as shown:

Choosing values for A, and keeping c and B fixed but letting the side a increase with A, he obtained the following table of values, which he wrote on the board:

Triangles were actually drawn for the various values of A, and a was then measured, and the above ratios were calculated based on these experimental measurements. Fred noted that the ratio does not change much, and wondered at this.

Fred set up the calculation of the curve for x(T), y(T), where

He displayed the result as a set of points with the aid of a TI graphing calculator, a transparency projector and LCD display. The graph looked like a roll of carpeting viewed end-on, a kind of spiral around the origin. Most interesting! A good example of how to connect the abstract to the concrete so as to make math "real" for students!

Bill Lilly (Kenwood HS)
gave us a handout titled "Pendulum," which was a lab exercise. Using a TI CBR Sonic Ranger, high frequency sound from the Ranger was reflected from a swinging balloon [held on the end of string by Pearline Scott (Franklin School)]. The output from Ranger (for 10 s) was stored in the calculator and shown on the projector screen as a graph with the aid of Fred Schaal's LCD display. It looked like a sine wave, and Bill described how students could analyze the data for frequency, effect of shortening string, lengthening string, amplitude effects, velocity minima and maxima with position, etc. Another beautiful example of concrete/abstract connections!

Roy Coleman (Morgan Park HS)
held up the power line cable that Earl Zwicker had discussed with us last meeting, and then he described a house wiring problem that he was involved with that had occurred many years ago. Strange things happened: The dog would do a flying leap over the threshold when coming back into the house, which necessitated his continuing on down the basement stairs, then back upstairs to get in. Why? When some lights were turned on, other lights would become dim. Why? A water pipe in the basement corroded and had to be replaced, and the problems became worsened. An electrician called in to find the problem gave up after 2-3 hours, shaking his head, and never sent a bill. Roy drew a circuit diagram on the board showing a stepdown power transformer and the low-voltage secondary with center-tap to ground and its + and - 120 VAC ends going to serve the house power. What they finally discovered could be seen only from a second-story bedroom window. The ground wire from the secondary of the stepdown transformer passed through a tree next to the house, and it had broken. Thus, the entire house wiring was "floating" with respect to ground, and any connections to the grounded power transformer primary were being made through grounded water pipes, etc. Com Ed was called, and they got out there and fixed it in record time once the problem and its consequences were made clear. Most interesting!

Bill Blunk (Joliet Central HS)
showed us a physics "toy" called a ROMP [Randomly Oscillating Magnetic Pendulum], which came from Edmund Scientific. It is item CR82-172, available for $13.95. See the website http://www.edsci.com/. (It is also available at American Science Center. See the website http://sciplus.com/.) It has a flat metal base about 8 in square. A pendulum with a length of about 12 inches is suspended above the base so that, when at rest, its end is about 1 inch above the center of the base. The pendulum is made from a rigid, slender plastic rod, and it has a disk-shaped magnet (about 1 cm diam) at its end. There are 9 identical disk magnets stuck to the base by magnetic attraction; they can be arranged on the base in any pattern one desires. Bill placed them in two concentric circles with one at the center. When he held the pendulum out at an angle and released it, it swung in an erratic pattern over the magnets on the base. He used it as a model for nuclear forces. The magnet on the end of the pendulum he likened to a neutron, and the other magnets on the base represented particles in the nucleus. When he held the pendulum at a high angle to represent a neutron with high energy, the pendulum swung in its erratic pattern. But when he lowered the angle to represent a neutron with smaller energy, the "neutron" magnet became "captured", and centered itself over the magnet at the center of the base. Neat!

Fred Farnell (Lane Tech HS)
asks his students to estimate how fast an egg can be thrown into a vertically-held blanket without breaking the egg. He also asks from what height h could an egg be dropped onto a hard surface (about 5 cm) or a cushion (about 2 m) without breaking. What is the speed of the egg when it strikes the surface?

Larry Alofs (Kenwood HS)
gave us a handout from Science News, April 1, 2000, describing the new golden dollar bearing the likeness of Sacagawea, "...the young Shoshone woman who guided Lewis and Clark..." The metallurgy involved was tricky; the new coin will not require the retooling of vending machines. The make-up of other US coins was listed out on the same page. A most useful reference for physics teachers. Thanks, Larry!

Arlyn van Ek (Illiana Christian HS)
showed us an interesting 50 minute video available from NOVA. See the website http://www.pbs.org/whatson/press/winspring/secrets_medsiege.html. Titled Medieval Siege, it sells for about $26 (1-800-949-8670). He uses it when he must be out of the classroom. He showed us some excerpts about the WARWOLF [the atom bomb of the 14th century] and the Trebucket (like a catapult with a sling on its end), and how a group of people experimented building several models, many to full-scale, to test whether they had the range and power to knock down the thick defensive walls of a medieval castle. They had some problems until they put wheels on it, like old engravings showed them to be built. The wheels, counter-intuitively, increased the range of the projectiles and stability of the trebucket! Most interesting physics involved. Thanks, Arlyn!

Janet Sheard (West School, Glencoe)
showed us Build It, Move It, a kit on Force and Motion (ETA catalogs)/ 4th grade. She said the materials could be adopted to a wide range of levels. The inexpensive but effective apparatus came in a plastic storage box. Many investigations into forces: What are they? Sources of? Motion, Friction, Inertia, Machines. Janet had not yet used the kit, and we ran out of time, but maybe Janet will show us how some of it works next Fall. Essentially "Physics for Every Kid." Inspiring!

ANOTHER GREAT MEETING! SEE YOU NEXT FALL!

Porter Johnson

Using EXCEL to Study Volume of Cut-out Cone
See Notes for 28 March 2000 HS Math-Phys Class

If you take a sheet of paper with a circle of radius R, and cut out a sector of opening angle k^o, as described in the 28 March 2000 SMILE HS Math Physics Notes, the volume of the cone formed by that sheet is

The formula may be simplifying by defining the ratio x = k^o/360^o, so that for radius R = 1

One may show by elementary calculus that the volume is maximized by the choice

corresponding to angle k = 293.9388^o. The maximum volume is

Here is a set of steps that will result in the data table and the graph: First, type these descriptive words in lines #2 and #3

• In Cell A2 type cone vol
• In Cell A3 type angle
• In Cell B3 type x
• In Cell C3 type angle
• In Cell D4 type volume

• In Cell A4 type 290
• In Cell B4 type = A4/360
• In Cell C4 type = A4
• In Cell D4 type = PI() * B4^2 / 3 * SQRT(1 - B4^2)

• In Cell A5 type 291

At this point you should save the EXCEL table [after all, you've worked hard to create it!].

• Take the mouse and "enclose" [i.e. "highlight"] both cells A4 and A5, which contain the numbers 290 and 291, respectively. If you pull downward on the lower right corner of the rectangle with a + sign there, you will get evenly spaced points as far down as you pull; say, 290 to 310.
• Now, enclose the cell B4, and pull down on the + sign at the lower right corner, so as to fill cells in column B as far down as column A is filled.
• Similarly, enclose cell C4, and pull it down.
• Finally, enclose cell D4 and pull it down.

• Using the mouse, capture the data in column A, and then in column D.
• From the toolbar menu, click on the "chart wizard" ikon.
• Pick the "xy scatter" option
• Then pick the "smooth curve" option
• Include the "major grid lines" and "minor grid line" options for x and y
• Finish drawing the graph.