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Porter W Johnson Illinois Institute of Technology
Department of Biological,
Chemical, and Physical Sciences
Chicago IL 60616-3793
Everybody knows that birds can fly, but this particular bird can balance on its
nose! Actually, the rubber-coated bird has heavy weights near the ends of the
wings, and can balance on its nose, since its center of mass lies below that
point. As an application of the same idea, a tight-rope walker usually carries
a long, slightly bent, pole which substantially improves his/her balance.
The familiar crack of the bull whip is heard in "Cowboy" movies, but what
actually causes that crack? That extensively debated issue has recently been
settled: the crack corresponds to the fact that end of the whip actually
exceeds the speed of sound. It is an example of a "sonic boom", familiar to
those living near air force squadrons or near those airports at which the Super
Sonic Transport [SST] aircraft are permitted to land.
One can, in effect, overcome the effect of gravity by swinging a bucketful of
water over one's head. If the bucket maintains sufficient speed on its arc, the
water will not spill. A more dramatic demonstration can be done with a
[plastic] wine glass, a thin aluminum pie pan, and two pieces of string of
length about 2 meters. The strings should be tied together at the middle, the
pie pan should be held up by the strings, the glass filled with water and placed
on the pie pan. Sling it like a slingshot, and be careful until you get the
feel for it!
LED Current Indicator
We tell students that "direct" current through a wire flows only in one
direction, whereas "alternating" current continually changes direction. These
simple ideas can be demonstrated by a device consisting of a pair of light-
emitting diodes connected in parallel to a wire with probes on each end. When
direct current passes through the system [9 Volt battery] only one diode is lit,
whereas with alternating current [use a 9 Volt AC power supply for safety] both
diodes go on. The device may be obtained from an electronic supply house, such
as Radio Shack.
The windmill, used as a pump, made it possible for early settlers to get water,
and in that sense it "conquered" the West. One can make a simple device to
convert wind energy into mechanical energy with a pencil, a straight pin, and a
piece of paper cut into blades. The device spins when one blows upon it, as
well as when it is moved through the air.
Rattle-Back: One-Way Rotator
The plastic Rattle-Back is flat on one side and has an assymetric oval shape on
the other side. When placed on a smooth planar surface on the oval side, it
readily rotates in one direction, will stop and reverse direction when rotated
in the opposite sense. Certain pocket knives also have the right shape. This
effect is described in laborious detail in some classic textbooks on advanced
The traditional function of the slinky is to walk down stairs when started, as a
demonstration of energy, momentum, and angular momentum. One innovative use is
to stretch it out to ten to twenty times its natural length on the floor, with
two people holding its ends, and to use it as a medium for waves. Longitudinal
and transverse waves may be set up, and it can easily be demonstrated that they
travel with different speeds.
The water from a slightly open tap initially forms a stream, but it breaks into
droplets after the stream falls some distance. The children's toy contains two
immiscible liquids, the heavier one being dark-colored. When the device is
inverted the heavier liquid passes through a hole and falls as droplets. The
droplets accumulate on the bottom and gradually form a continuous fluid.
Happy Balls and Sad Balls
Assemble a variety of balls and drop them from fixed height onto a smooth
horizontal surface, noting that the degree of "bounce" is almost independent of
the appearance or surface features. The "happy ball---sad ball" kit consists of
two black balls, the happy one [darkened ping-pong ball] bounces rather well,
but the sad one [hard polymer] does not bounce at all.
Super Ball Launch
Drop the little and big super balls separately, and show that they bounce to
approximately the same height, indicating that the collisions with the surface
are about equally elastic. However, when we drop them together with the little
ball riding on top of the big ball, the little ball acquires almost all of the
energy after the bounce. Hint: You may wish to cut a small indentation in the
big ball, so that the little ball will stay in place as it falls. In addition,
there is a device in which the balls ride downward on a stick before being
launched by impact from the floor.
Note: All materials are readily available at science supply houses, such as the
American Science Center.
II. Phenomenological Exercise with Super Balls:
Part I: Drop the super ball from a height, h, of 50 cm, as measured from
the smooth horizontal surface to the bottom of the ball. Measure the
bounce height, b. The ratio, b / h, is called the coefficient of
restitution. Determine that parameter. Repeat the experiment by dropping
from a height of 100 cm, and compare the values.
Part II: This "performance based" exercise involves learning how to make
the ball bounce "back and forth" about the same spot. Release the ball
from a height of about 1 meter, giving it horizontal speed and "spin" find
the right combinations of speed and spin.
III. Cryptography Exercise:
This is a "simple replacement" code, in which one letter is replaced by
another throughout the message. It is the simplest of codes, and which can
readily be "cracked" if the message is long enough.
Zpxvx jg ywx myvw xhxva cjwlzx.
Ix pqhx wyzpjwn zy rxqv xbuxsz rxqv jzgxkr.
Qgd wyz ipqz aylv uylwzva uqw fy ryv ayl. Qgd ipqz ayl uqw fy ryv aylv uylwzva.
Ayl uqw ymgxvhx q kyz ma olgz kyydjwn.
Njhx cx kjmxvza yv njhx cx fxqzp.
Gpx iqkdg jw mxqlza, kjdx zpx wjnpz.
J pqhx q fvxqc.
Q pylgx fjhjfxf qnqjwgz jzgxkr uqwwyz gzqwf.
Zpxvx jg wyzpjwn wxi lwfxv zpx glw.
J vym mqwdg mxuqlgx zpqz jg ipxvx zpx cywxa jg.
J qc wyz q uvyyd.
Gsxqd gyrzka, mlz uqvva q mjn gzjud.
Zy mx yv wyz zy mx; zpqz jg zpx tlxgzjyw.
Fqwux kjdx q mlzzxvrka; gzjwn kjdx q mxx.
Zpx myyd yr wqzlvx jg ivjzzxw jw zpx kqwnlqnx yr cqzpxcqzjug.
Frequencies of Occurrence of Letters
A 15 B 01 C 08 D 13 E 00 F 10
G 16 H 07 I 07 J 33 K 12 L 20
M 15 N 11 O 01 P 22 Q 40 R 10
S 02 T 01 U 13 V 27 W 34 X 60
Y 39 Z 49
ETAOIN SHRDLU was known to every mechanical printer or type-setter, because
it contains the twelve letters that appear most commonly in written
English, in the order in which they naturally occur. In other words, "e"
is the most common letter in English, "t" is next, and so forth. By
counting the number of occurrences of each letter, we can presume that the
most common letter [X] might be "E" in transposition, whereas the next most
common letter [Z] might be "T", and so forth. In this way, one can crack
the transposition code. Here is the message:
There is one born every minute.
We have nothing to fear except fear itself.
Ask not what your country can do for you. Ask what you can do for your country.
You can observe a lot by just looking.
Give me liberty or give me death.
She walks in beauty, like the night.
I have a dream.
A house divided against itself cannot stand.
There is nothing new under the sun.
I rob banks because that is where the money is.
I am not a crook.
Speak softly, but carry a big stick.
To be or not to be; that is the question.
Dance like a butterfly; sting like a bee.
The book of nature is written in the language of mathematics.
Replacement Code [to be executed horizontally; not Chinese style!]
x to + e to x z to e t to z
q to t a to q y to a o to y
j to o i to j w to i n to w
g to n s to g p to s h to p
v to h r to v f to r d to f
k to d l to k u to l c to u
m to c b to m + to b
Such a simple replacement message was found in the novella "The Gold Bug" by
Edgar Allen Poe, and in the story it was deciphered by the technique described
Cryptography, a branch of mathematics, is a very important in our society for
encryption codes and the like, which form the basis for financial transactions,
national security codes, and information transfer. No numbers are involved in
cryptography, except in an incidental way, since Mathematics deals with
patterns, and not just with numbers.
An interesting multi-cultural component is to identify the person who said each
of these things, and the context.