24 February 2004

Notes Prepared by Porter Johnson

**Porter Johnson**passed out a table obtained from the website**Beaufort Scale of Wind Force and Its Probable Wave Height:**http://www.zetnet.co.uk/sigs/weather/Met_Codes/beaufort.htm. The**Beaufort Scale**is the international standard for describing**wind velocity**( as measured**11 meters**above the surface -- called "**Wind Force**" by**Marine Meteorologist**s) and relating it to steady-state**probable**and maximum (crest to trough)**wave heights**on deep, open water. For example,**Wind Force 4 (Moderate breeze)**corresponds to winds around**7 meters/second**and average wave heights of about 1**meter,**whereas**Wind Force 8 (Gale)**corresponds to**20 m/sec**winds and**6 meter**waves, and**Wind Force 12 (Hurricane threshold)**corresponds to**35 m/sec**winds and**14 meter**waves. For more details check the website, as well as other sites linked to it.**Earl Zwicker**called attention to the**Spring 2004**meeting of the**ISAAPT**[Illinois Section of the American Association for Physics Teachers] on**23-24 April 2004**, at the**University of Illinois**,**Urbana-Champaig**n. For details consult the**ISAAPT**website: [http://helios.augustana.edu/isaapt/].**Fred Schaal**mentioned that both Venus and Mars are visible in the evening sky --- and the moon would have been between them on our meeting day!

**Arlyn Van Ek [Illiana Christian HS,
Physics]
The Gravity Probe B Mission**

**Arlyn** set up his laptop computer and played a **DVD** he had
obtained about the joint **NASA - Stanford University** project
called **Gravity Probe
B, ** which is scheduled to be launched soon on a polar orbit
about the earth. We
saw beautiful graphical images describing this exciting project. In
addition, he
passed around an article appearing in the ** November 1 2003 **issue
of ** Science
News** . Here is an excerpt from that
article (p 280):

"A satellite designed to test one of the more twisted predictions of Albert Einstein's general theory of relativity is finally at its launch site after 40 years of preparation. The probe will look for evidence of a gravitational effect known as frame dragging. Just as a dipper drags honey along as it twirls in a honey jar, any spinning body in space, including Earth, ought to drag some space-time along with it. That was Einstein's prediction, anyway. The effect has never been convincingly observed. ... To create gyroscopes sensitive enough to register such minute rotations, the GP-B team has crafted niobium-coated, solid quartz spheres the size of ping-pong balls. Nowhere do these silvery orbs deviate by more than 40 atoms from perfect sphericity. In each gyroscope, one of these balls will spin at 10,000 revolutions per minute while floating weightless within a chamber."In addition see the

In **
Einstein's theory of General Relativity**, gravity is not
merely a "force" of usual variety (i.e., electric, magnetic, etc).
Rather, it is treated as a distortion of the fabric of space and time
(metric
tensor), resulting in an intrinsically curved space-time, as described
by **
Riemann** geometry, rather than ** Euclidean** geometry. The
theoretical situation
is briefly summarized on the** ST Andrews [UK] Mathematics History **websites,
on webpages **Non-Euclidean Geometry** [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html#67],
as well as **General Relativity**: http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/General_relativity.html#23
--- from which the following has been excerpted:

" ... In 1907, two years after proposing the special theory of relativity,Einsteinwas preparing a review of special relativity when he suddenly wondered how Newtonian gravitation would have to be modified to fit in with special relativity. At this point there occurred toEinstein, described by him as thehappiest thought of my life,namely that an observer who is falling from the roof of a house experiences no gravitational field. He proposed theEquivalence Principleas a consequence:... 'we shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame.'..."

Unfortunately, **Einstein's** theory has been **notoriously
difficult**
to test in full detail, because its effects are extremely small in the
"weak" gravitational field of the earth.

**A real mind-opener, Arlyn!**

**Carl Martikean [Crete Monee HS,
Physics]
Galileo's
Study of Motion (handout)**

**Carl** pointed out that, in **Galileo's **time, the subject
of algebra
was very new to Europeans -- even the well-educated elite. The
scientists
of his and **Isaac Newton's **time were more comfortable with
geometrical
arguments, since the study of Euclidean geometry was part of their
education. Thus, ** Galileo's** analysis of **Accelerated
Motion** [in
effect, blocks sliding down inclined planes] was given in the language
of
geometry. ** Carl ** discussed ** Galileo's** proof of the
following proposition:

[Today we are more comfortable in describing such motions using algebra:"The spaces described by a body falling down from rest with a uniformly accelerated motion are to each other as the squares of the time intervals employed in traversing these distances." Theorem II, Proposition II

**Thanks for sharing this new insight, Carl.**

**Larry Alofs [Kenwood HS,
Physics]
"Armstrong" Flashlight**

**Larry** held up a transparent, plastic flashlight, called the "**Eternal
Flashlight"**. When he shook it back-and-forth along its
principal
axis, it would generate enough energy to light up. We could see a
solenoid
coil near its center, and a magnet that shuttled back-and-forth along a
tunnel
passing through the solenoid. So the changing magnetic flux
within the
coil would generate an **EMF **producing a current which charged a
capacitor
storing energy to light the bulb. Visit the **Heartland America**
website http://www.HeartlandAmerica.com,
search for product number 95784 --- about $15. **Larry** then held
up an **LED**
flashlight, purchased for about $10 on the **Harbor Freight**
website: http://www.harborfreight.com.
The flashlight that he showed us had 3 AA batteries and 2 **LEDs**,
The
current drawn for this **LED** flashlight was very low, and it
would operate
continuously for essentially the shelf life of the batteries!

**You really brightened up
our day ... and our nights! Thanks Larry!**

**Ann Brandon [Joliet West HS,
Physics]
Figuring
Physics: Light Bulbs**

**Ann** called our attention to the **March 2004 **issue of **The
Physics Teacher** [http://scitation.aip.org/content/aapt/journal/tpt],
an official publication of the **AAPT: American Association
of Physics Teachers:**[ http://www.aapt.org]/.
The monthly
column ** Figuring Physics by Paul Hewitt** contained questions
about two light bulbs,
** A **
and **B. **They were in sockets connected in series across a **
DC** source (battery). **Bulb A is definitely brighter than
bulb B**.
What happens when the positions of the two light bulbs are
switched? We
took the following "**straw poll**":

A will be
brighter |
17 Votes |

B will be brighter |
1 Vote |

No Idea |
4 Votes |

**Ann** then asked which bulb would burn brighter when they were
each placed
directly across the battery? ** Curiously enough,
bulb B burned brighter than bulb A** in that situation. **
Why? **

The
result can be understood with the formulas relating
the ** voltage V, current I, resistance R, and power P ** for a
resistor:

**You really lit us up! Thanks, Ann.**

**Camille Gales [Coles Elementary School,
Math]
A question from "The Chicken from Minsk ... "**

**Camille** passed out the following problem, which was taken from
an
out-of-print (?) book mentioned by **Bill Colson** at the High
School Physics **SMILE** meeting of
**08 September 1998**
[ph090898.htm]. Here is the question:

" ... Two mathematicians,Can anybody helpIgorandPavel, meet on the street. 'How is your family', saysIgor. 'As I recall, you have three sons, but I don't remember their ages.' 'That's easy', saysPavel. 'The product of their ages is 36.'Igorstill looks confused, soPavelpoints across the street. 'See that building? The sum of their ages is the same as the number of windows facing us.'Igorthinks for a minute and says, 'I still don't know their ages'. 'I'm sorry, saysPavel,'I forgot to tell you: my oldest son has red hair'. 'Now I know their ages', he says.

Do you?... "

Source:The Chicken from Minsk and 99 Other Infuriatingly Challenging Brain Teasers from the Great Russian Tradition of Math and Science, by Yuri B. Chernyak and Robert M. Rose

**Fred Farnell [Lane Tech,
Physics]
The
Dissection of the Twinkling Shoes**

**Fred** held up his daughter's tennis shoes, the same ones that he
had
showed us at the **18 November 2003 SMILE**
meeting [mp111803.html].
The lights embedded in the shoes **still **flashed on and off when
he struck
them.. His daughter's shoes had outgrown their usefulness, and **Fred
** was allowed to study /
destroy them to determine how they work. He polled the audience
on
hypotheses as to how they work. Here is the "**official tally**":

Mechanism |
Number of Votes |

Switch plus battery | 8 |

Capacitor plus battery | 0 |

Piezoelectric device | 5 |

Spring plus battery | 4 |

Magnet plus coil | 1 |

**You
really got to the sole of the issue! Very nice, Fred.**

There was not time
enough for **Walter McDonald** to present his work on mathematics
problems
that involve "sailing". He will be scheduled at the beginning of
our next class, **Tuesday 09 March 2004**. ** See you there!**

**Notes prepared by Porter Johnson
**