02 May 2000

Notes by Porter Johnson

**ANNOUNCEMENT:**

Nobel Laureate in Physics and

Chair, Teachers Academy for Mathematics and Science

Monday, 22 May 2000

Perlstein Auditorium [33rd & State, NW Corner]

for a discussion about

**The Essential Transition from 19 ^{th} to 21^{st}
Century
**

High School Science Education

buffet supper 6 pm

discussion 7 pm

**RSVP to (312) 567-8820 or parson@iit.edu**

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:

Then

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:

A | a / sin A |
---|---|

6^{o} |
16.3 |

19^{o} |
14.4 |

46^{o} |
17.8 |

83^{o} |
15.4 |

99^{o} |
20.2 |

153^{o} |
16.3 |

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

y = T[1+1/(2p) ] sin T

for 0 < T < 20p.

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
__

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
__

*** | A | B | C | D |

1 | _____ | _____ | _____ | _____ |

2 | _____ | _____ | _____ | _____ |

3 | _____ | _____ | _____ | _____ |

4 | _____ | _____ | _____ | _____ |

5 | _____ | _____ | _____ | _____ |

__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**

*** | A | B | C | D |

1 | _____ | _____ | _____ | _____ |

2 | cone vol | _____ | _____ | _____ |

3 | angle | x | angle | volume |

4 | 290 | .805556 | 290 | .402645 |

5 | 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.__

*** | A | B | C | D |

1 | _____ | _____ | _____ | _____ |

2 | cone vol | _____ | _____ | _____ |

3 | angle | x | angle | volume |

4 | 290 | .805556 | 290 | .402645 |

5 | 291 | .808333 | 291 | .402830 |

6 | 292 | .811111 | 292 | .402963 |

7 | 293 | .813889 | 293 | .403042 |

8 | 294 | .816667 | 294 | .403066 |

9 | 295 | .819444 | 295 | .403035 |

10 | 296 | .822222 | 296 | .402946 |

11 | 297 | .825000 | 297 | .402798 |

12 | 298 | .827778 | 298 | .402589 |

13 | 299 | .830556 | 299 | .402320 |

14 | 300 | .833333 | 300 | .401986 |

15 | 301 | .836111 | 301 | .401588 |

16 | 302 | .838889 | 302 | .401123 |

17 | 303 | .841667 | 303 | .400590 |

18 | 304 | .844444 | 304 | .399987 |

19 | 305 | .847222 | 305 | .399313 |

20 | 306 | .850000 | 306 | .398564 |

21 | 307 | .852778 | 307 | .397739 |

22 | 308 | .855556 | 308 | .396837 |

23 | 309 | .858333 | 309 | .395855 |

24 | 310 | .861111 | 310 | .394791 |

__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.__