The Student and The Barometer

Some time ago I received a call from a colleague. He was about to give a student a zero for his answer to a physics question, while the student claimed a perfect score. The instructor and the student agreed to an impartial arbiter, and I was selected.

I read the examination question: "Show how it is possible to determine the height of a tall building with the aid of a barometer." The student had answered: "Take the barometer to the top of the building, attach a long rope to it, lower it to the street, and then bring it up, measuring the length of the rope. The length of the rope is the height of the building."

The student really had a strong case for full credit since he had really answered the question completely and correctly! On the other hand, if full credit were given, it could well contribute to a high grade in his physics course and certify competence in physics, but the answer did not confirm this.

I suggested that the student have another try. I gave the student six minutes to answer the question with the warning that the answer should show some knowledge of physics. At the end of five minutes, he hadn't written anything. I asked if he wished to give up, but he said he had many answers to this problem; he was just thinking of the best one. I excused myself for interrupting him and asked him to please go on.

In the next minute, he dashed off his answer, which read: "Take the barometer to the top of the building and lean over the edge of the roof. Drop the barometer, timing its fall with a stopwatch. Then, using the formula x=0.5*a*t^2, calculate the height of the building." At this point, I asked my colleague if he would give up. He conceded, and gave the student almost full credit.

While leaving my colleague's office, I recalled that the student had said that he had other answers to the problem, so I asked him what they were. "Well," said the student, "there are many ways of getting the height of a tall building with the aid of a barometer. For example,if the sun is shining you could measure the height of the barometer, then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a simple matter of proportional arithmetic to work out the height of the skyscraper.

"Fine," I said, "and others?"

"Yes," said the student, "there is a very basic measurement method you will like. In this method, you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units." "A very direct method."

"Of course. If you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum, and determine the value of g [gravity] at the street level and at the top of the building. From the difference between the two values of g, the height of the building, in principle, can be calculated."

"On this same tack, you could take the barometer to the top of the building, attach a long rope to it, lower it to just above the street, and then swing it as a pendulum. You could then calculate the height of the building by the period of the precession".

"Finally," he concluded, "there are many other ways of solving the problem. Probably the best," he said, "is to take the barometer to the basement and knock on the superintendent's door. When the superintendent answers, you speak to him as follows: 'Mr. Superintendent, here is a fine barometer. If you will tell me the height of the building, I will give you this barometer."

At this point, I asked the student if he really did not know the conventional answer to this question. He admitted that he did, but said that he was fed up with high school and college instructors trying to teach him how to think.

The name of the student was Niels Bohr, who later received the Nobel prize for Physics.

Cartoon Laws of Physics
Cartoon Law I
=============
Any body suspended in space will remain in space until made aware
of its situation.

Daffy Duck steps off a cliff, expecting further pasture land.  He
loiters in midair, soliloquizing flippantly, until he chances to
look down.  At this point, the familiar principle of 32 feet per
second per second takes over.

Cartoon Law II
==============
Any body in motion will tend to remain in motion until solid matter
intervenes suddenly. Whether shot from a cannon or in hot pursuit
on foot, cartoon characters are so absolute in their momentum that
only a telephone pole or an outsize boulder retards their forward
motion absolutely.  Sir Isaac Newton called this sudden termination
of motion the stooge's surcease.

Cartoon Law III
===============
Any body passing through solid matter will leave a perforation
conforming to its perimeter.

Also called the silhouette of passage, this phenomenon is the
speciality of victims of directed-pressure explosions and of
reckless cowards who are so eager to escape that they exit directly
through the wall of a house, leaving a cookie-cutout-perfect hole.
The threat of skunks or matrimony often catalyzes this reaction.

Cartoon Law IV
==============
The time required for an object to fall twenty stories is greater
than or equal to the time it takes for whoever knocked it off the
ledge to spiral down twenty flights to attempt to catch it
unbroken.

Such an object is inevitably priceless, the attempt to catch it is
inevitably unsuccessful.

Cartoon Law V
=============
All principles of gravity are negated by fear.

Psychic forces are sufficient in most bodies for a shock to propel
them directly away from the earth's surface.  A spooky noise or an
adversary's signature sound will induce motion upward, usually to
the cradle of a chandelier, a treetop, or the crest of a flagpole.
The feet of a character who is running or the wheels of a speeding
auto need never touch the ground, especially when in flight.

Cartoon Law VI
==============
As speed increases, objects can be in several places at once. This
is particularly true of tooth-and-claw fights, in which a
character's head may be glimpsed emerging from the cloud of
altercation at several places simultaneously.  This effect is
common as well among bodies that are spinning or being throttled.
A `wacky' character has the option of self-replication only at
manic high speeds and may ricochet off walls to achieve the
velocity required.

Cartoon Law VII
===============
Certain bodies can pass through solid walls painted to resemble
tunnel entrances; others cannot.

This trompe l'oeil inconsistency has baffled generations, but at
least it is known that whoever paints an entrance on a wall's
surface to trick an opponent will be unable to pursue him into this
theoretical space.  The painter is flattened against the wall when
he attempts to follow into the painting.  This is ultimately a
problem of art, not of science.

Cartoon Law VIII
================
Any violent rearrangement of feline matter is impermanent.

Cartoon cats possess even more deaths than the traditional nine
lives might comfortably afford.  They can be decimated, spliced,
splayed, accordion-pleated, spindled, or disassembled, but they
cannot be destroyed.  After a few moments of blinking self pity,
they reinflate, elongate, snap back, or solidify.
 
Corollary: A cat will assume the shape of its container.

Cartoon Law IX
==============
Everything falls faster than an anvil.

Cartoon Law X
=============
For every vengeance there is an equal and opposite revengeance.

This is the one law of animated cartoon motion that also applies to
the physical world at large.  For that reason, we need the relief
of watching it happen to a duck instead.


    Cartoon Law Amendments
 ----------------------------

Amendment A:
A sharp object will always propel a character upward.

When poked (usually in the buttocks) with a sharp object (usually
a pin), a character will defy gravity by shooting straight up, with
great velocity.

Amendment B:
The laws of object permanence are nullified for "cool" characters.

Characters who are intended to be "cool" can make previously
nonexistent objects appear from behind their backs at will.  For
instance, the Road Runner can materialize signs to express himself
without speaking.

Amendment C:
Explosive weapons cannot cause fatal injuries.

They merely turn characters temporarily black and smoky.

Amendment D:
Gravity is transmitted by slow-moving waves of large wavelengths.

Their operation can be witnessed by observing the behavior of a
canine suspended over a large vertical drop.  Its feet will begin
to fall first, causing its legs to stretch.  As the wave reaches
its torso, that part will begin to fall, causing the neck to
stretch.  As the head begins to fall, tension is released and the
canine will resume its regular proportions until such time as it
strikes theground.

Amendment E:
Dynamite is spontaneously generated in "C-spaces" (spaces in which cartoon laws hold).

The process is analogous to steady-state theories of the universe which postulated that the tensions involved in maintaining a space would cause the creation of hydrogen from nothing. Dynamite quanta are quite large (stick-sized) and unstable (lit). Such quanta are attracted to psychic forces generated by feelings of distress in "cool" characters (see Amendment B), which may be a special case of this law), who are able to use said quanta to their advantage. One may imagine C-spaces where all matter and energy result from primal masses of dynamite exploding. A big bang indeed.

Amendment F:
Any bag, sack, purse, etc. possessed by a cool character is a tesseract - any number of objects of any size may be placed in it or removed from it with no change in its outer dimensions.

Amendment G:
Characters can spin around and change into any set of clothes appropriate to the situation.

Amendment H:
Rabbits can dig a burrow from here to there in less than 20 seconds and emerge spotlessly clean.

Amendment I:
Movements are accompanied by funny sound effects.