Don Kanner [Lane Tech HS,
physics]
Question on Hydraulic Rams
Don
passed out this summer homework problem assignment, taken from the
classic text Elements of Physics by R F Millikan and H G
Gale:
A copy of the
problem can be seen by clicking here:
Information concerning Hydraulic Rams can be obtained from these sources:
Bill Shanks [Joliet Central HS,
retired]
Persistence of Vision + Other things
Bill showed us his latest toy, a Skyliner Electronic Message
Maker,
which he got recently at WalMart. It can also be ordered
on the
websites: http://www.clubthings.com/product318.html
or http://www.ravehaven.com/products/Sale-Items/SkyWriter-Electronic-Message-Maker_665.html.
When the device is turned on, it plays a tune, and two sets of blinking
LED's are
lit. When it is twirled in a circle in the vertical plane, the
persistent
images of words are created. Fifteen phrases, such as SMILE
and BE
HAPPY are programmed into the device -- each with a
different
distinctive and possibly recognizable tune! Or, you can program
you own
messages. To operate it, spin it around in the air --- the words magically
appear before your eyes!
Bill briefly discussed the phenomenon of persistence of vision, which explains how this device works -- as well as the image on a television screen. The visual cortex lays out an image in the brain, which persists during loading, so that we can get the big picture, or at least the big perception. Bill quoted a former physics teacher, who recommended saying "So it seems to be now the thing I think I see", rather than "Now I see".
Bill then passed around LED Pens of various colors, which he obtained at Walgreens --- which also can be ordered at http://www.morsex.com/misc/pens.htm. He showed us three LED Pens --- red, yellow-green, and blue, which he used as light sources. He turned on various combinations in the darkened room, and showed us the color circles they projected on the white board in front of the room.
Bill then showed his next toy, a search light with two white light sources, one green LED, and a xenon bulb., which he had obtained from Berland's House of Tools: http://www.berlandstools.com. This device is similar to the Trident Headlamp: http://www.nextag.com/streamlight-trident-headlamp/stores-html. Bill intended to use this device as a skunk repellent, and did so with limited success. The eyes of many forest animals reflect light back to the source, so that the eyes appear to glow in the dark. For details see the websites How Exactly Do Animals See in the Dark?: http://www.ccmr.cornell.edu/education/ask/index.html?quid=589 or Why do cats eyes glow in the dark?: http://dspace.dial.pipex.com/agarman/bco/fact4.htm. [Unfortunately, this technique might work only on the four-legged variety of skunk!]. Bill used the white light to demonstrate retinal fatigue, by shining it on a magenta sheet of paper on the white board in the darkened room. After a minute or so, we looked away from the sheet, and we saw a green image in the shape of the paper sheet. Fascinating!
We think we see the light now! Thanks, Bill!
Arlyn Van Ek [Iliana Christian
HS]
Resonance Show
Arlyn partially filled a wine glass with water, held it by the stem
with
one hand, wet his finger on the other hand, and rubbed it around the
rim.
This set up a stick-slip motion, which produced a fairly
high-pitched
sound, in the kiloHertz range. He poured some water out
of the glass and
repeated the process, producing a higher pitched sound. As he
continued to
pour water out of the glass, the pitch continued to increase.
How
come? Earl Zwicker reminded us that the frequency f
of
oscillation of a mass m attached to a spring of spring constant
k
is given by f = 1/(2 p) Ö(k/m).
Earl suggested that -- analogously-- the effective spring
constant k is determined by the
oscillations at the rim of the glass. Since one can clearly see
the water
vibrating inside the glass, the effective mass m includes
water, so that m
decreases as the amount of water in the glass decreases. Hence
the
frequency increases as the glass is emptied. Very nice!
Arlyn then showed a video tape of a Washington DC street musician, who was very proficient in playing tunes, using a different glass for each note. He did a rather impressive job on Ode to Joy, Chorus of 9th Symphony 4th Movement by Ludwig van Beethoven [http://www.all-about-beethoven.com/symphony9.html], as well as various sailing tunes. This particular street musician was quite talented, and several of us asked Arlyn to make copies of the performance. For more information see How Can You Make a Wine Glass Sing?: http://www.howstuffworks.com/question603.htm.
Arlyn continued by demonstrating resonance using a kit of solid Singing Rods, available for about $20 from Arbor Scientific: http://www.arborsci.com/CoolStuff/cool13.htm#SingRod. Arlyn held a rod at its center, and produced a high-pitched sound that increased in intensity as he rubbed the rod by grasping it between forefinger and thumb and sliding [rubbing] them along the length of the rod [stick-slip motion with his fingers]. When he held it at 2/3 and 3/4 of its length, still higher pitches were produced. The sound was produced by resonant longitudinal oscillations of the rod, with a vibrational node at the holding point. The sound was not spectacularly loud, unless you hold the rod at a node corresponding to a normal mode of vibration of the rod --- in which case it really wakes everybody up!
Pretty physics, Arlyn!
Monica Seelman [ST James School]
Psychic
Puzzle
Monica presented her solution of the puzzle that appears on the Psychic
Powers website:
http://mr-31238.mr.valuehost.co.uk/assets/Flash/psychic.swf.
On that website, you are to pick a number, such as 47,
say. Then,
calculate the sum of the digits, 4 + 7 = 11. Next,
subtract the sum
of the digits, 11, from the original number, 47.
The answer
is 36. In fact, the answer will always be a multiple of
9: 9
- 18 - 27 - 36 - 45 - 54 - 63 - 72 - 81. This fact
provides the
explanation for the apparent demonstration of ESP on that
website, since the
images associated with multiples of 9 are always identical. Check
it
out for yourself! [Similar explanations were provided by Art
DiVito
and Ken Schug via handout.]
Monica next handed out a multiplication table, which would have looked like this, if only the one's place had been written, with any numbers in the ten's place left out, so that 7 ´ 7 = 9, etc.
´ | : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
- | - | - | - | - | - | - | - | - | - | - | ||
0 | : | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 0 |
2 | : | 0 | 2 | 4 | 6 | 8 | 0 | 2 | 4 | 6 | 8 | 0 |
3 | : | 0 | 3 | 6 | 9 | 2 | 5 | 8 | 1 | 4 | 7 | 0 |
4 | : | 0 | 4 | 8 | 2 | 6 | 0 | 4 | 8 | 2 | 6 | 0 |
5 | : | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 | 5 | 0 |
6 | : | 0 | 6 | 2 | 8 | 4 | 0 | 6 | 2 | 8 | 4 | 0 |
7 | : | 0 | 7 | 4 | 1 | 8 | 5 | 2 | 9 | 6 | 3 | 0 |
8 | : | 0 | 8 | 6 | 4 | 2 | 0 | 8 | 6 | 4 | 2 | 0 |
9 | : | 0 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
0 | : | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
The following symmetries of this table almost appear to leap out of the page:
Porter Johnson pointed out that this multiplication procedure is called multiplication modulo 10, and that we have noticed some of the symmetry properties of this group of ten elements. MODULO 10 ADDITION can also be performed (7 + 6 = 13 ® 3, etc) -- leading to a different table -- which also defines a group of 10 elements. Would the tables -- for multiplication and for addition -- be identical in form [isomorphic]? For additional information see the website Modular Arithmetic: http://www.cut-the-knot.org/blue/Modulo.shtml. Mathematics is about discovering patterns in things around us, and sometimes [as in playing chess, GO, or bridge] the specific numbers are either irrelevant, or play only an incidental role.
So that's how you do ESP with numerology! Very nice, Monica!!
Roy Coleman [Morgan Park HS,
Physics]
Using Marbles to Determine the Size
of the Monster Behind Door
Roy handed out a sheet containing the following information:
The Size of a Monster There is a very hungry monster in an almost completely closed room. There is a door to enter and a thin horizontal slit at the bottom along the entire length of a side. Before you enter the room you must determine the width of the monster. You also have a large supply of small rocks.Using a monster that looks remarkably like a soft drink can and rocks that look like marbles, you are to determine its experimental width and compare that value to its actual width. Each time the monster is hit it grumbles (klinks?) and moves, never touching any of the walls.
A couple of hints:
- Each group will need to throw at least 200 rocks randomly through the slit into the room.
- What is the probability of hitting the monster if it is half the size of the room?
- Look up information on the Rutherford Scattering experiment.
- Does the size of the rock itself make a difference?
Good luck in gauging the size of the monster, Roy. Thanks!
Ben Butler [Laura Ward Elementary
School]
Dry Ice
Ben brought a supply of dry ice [the solid form of Carbon
Dioxide -- C02],
which he had obtained from the ice house at Harrison Street and
Pulaski Road
on the way to class. He broke off a piece of the dry ice
and put it into a
glass of water. The mixture boiled vigorously and produced a
great deal of
a cloudy vapor, just like boiling beakers in scary movies.
Dry ice
passes from the solid phase to the gas phase at
atmospheric pressure. However, at a pressure of about 3
atmospheres, the liquid phase can also be produced. Ben
produced the
liquid phase in a clear flexible tube with a valved opening at one end
and attached to a
pressure gauge at the other end. He put a small piece of dry
ice inside the
tube, and closed the valve; then the pressure steadily increased as it
vaporized. When the pressure exceeded about 3 atmospheres,
we saw small droplets of the
liquid phase of C02. Beautiful!
The apparatus was obtained from Flinn
Scientific: http://www.flinnsci.com/.
What an elegant experiment to show the three states of CO2! Now, Why does dry ice feel dry? Very slick, Ben!
Peter Smagacz [Lane Tech HS, Physics]
Isolating Rotational Kinetic Energy
Peter discussed using a YoYo to describe various forms of
mechanical
energy: gravitational potential energy, kinetic
energy of
translation, and
kinetic energy of rotation::
Interesting ideas, Peter!
John Bozovsky [Chicago Design Academy -- the school formerly
known as Bowen
HS -- Physics]
Vibrating String Apparatus Revisited
John showed us a vibrating string apparatus made out of a cast-off
battery
operated electric razor, which was attached to a board. A string
was
connected to the razor head, and tied at its other end to a Pinch
Clamp,
which would normally be used in the lab for closing rubber hose.
The pinch
clamp was also attached the board, so that the tension in the
string could be
adjusted by turning the adjustable screw in the pinch
clamp. The razor
vibrated at a fixed frequency f of about 100 Hz, as
estimated from the hum of
the razor. The length L of the string was fixed at about
30 cm. By
varying the tension, various standing wave patterns could be
produced. As the
tension T was decreased, the speed of vibrations on
the string decreases,
and the wavelength l also decreases.
Thus, one can fit
more nodes on the string of length L, since n l = 2
L, n = 1, 2, 3. See the writeup for Ann Brandon
in the previous
class: mp042203.html This is a cool
system, without doubt!
John also showed us a home-made, Adjustable Resonance Tube Apparatus, in which the height of a column of water is varied by raising a reservoir filled with water, with rubber tubing attached to a nipple at the bottom of the tube, as well as to one at the bottom of the reservoir. This device is a variation of the commercially available devices available from science supply houses We heard the resonant sounds very well!
Plunk your magic twanger, Froggy [http://michelesworld.net/dmm/frog/gremlin/memory.htm] --- er, John! You were in tune with the physics!
We did not have time for the presentations of Gary Guzdziol [video recording of oil drum implosion in his garage on a snowy day] and Fred Schaal [92-ing on the Green Line]. They will be first on the schedule at our first meeting of the Fall Semester 2003, Tuesday, 09 September 2003. See you there!
Notes taken by Porter Johnson