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Skyscraper Height
The following question appeared in a physics degree exam
at the University of Copenhagen:
"Describe how to determine the height of a skyscraper with
a barometer."
One enterprising student replied: "You tie a long piece of string
to the neck of the barometer, then lower the barometer from the
roof of the skyscraper to the ground. The length of the string plus
the length of the barometer will equal the height of the building."
This highly original answer so incensed the examiner that the
student was failed immediately. The student appealed, on the
grounds that his answer was indisputably correct, and the
university appointed an independent arbiter to decide the case.
The arbiter judged that the answer was indeed correct, but did
not display any noticeable knowledge of physics; to resolve the
problem it was decided to call the student in and allow him six
minutes in which to verbally provide an answer which showed at
least a minimal familiarity with the basic principles of physics.
For five minutes the student sat in silence, forehead creased in
thought. The arbiter reminded him that time was running out, to
which the student replied that he had several extremely relevant
answers, but couldn't make up his mind which to use.
On being advised to hurry up the student replied as follows:
"One, you could take the barometer up to the roof of the
skyscraper, drop it over the edge, and measure the time it takes
to reach the ground. The height of the building can then be worked
out from the formula H =3D 1/2gt squared (height equals half times
gravity time squared). But bad luck on the barometer.
"Two, 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.
"Three, if you wanted to be highly scientific about it, you could tie a
short piece of string to the barometer and swing it like a pendulum,
first at ground level and then on the roof of the skyscraper. The
height is worked out by the difference in the gravitational restoring
force (T = 3D 2 pi sqr root of l over g).
"Four, if the skyscraper has an outside emergency staircase, it
would be easy to walk up it and mark off the height of the skyscraper
in barometer lengths, then add them up.
"Five, if you merely wanted to be boring and orthodox about it, of
course, you could use the barometer to measure air pressure on the
roof of the skyscraper, compare it with standard air pressure on the
ground, and convert the difference in millibars into feet to give the
height of the building.
"Six, since we are constantly being exhorted to exercise independence
of mind and apply scientific methods, undoubtedly the best way would
be to knock on the janitor's door and say to him 'I will give you this
nice new barometer, if you will tell me the height of this skyscraper.'"
The arbiter re-graded the student with an 'A.'
Skyscraper Height
The following question appeared in a physics degree exam
at the University of Copenhagen:
"Describe how to determine the height of a skyscraper with
a barometer."
One enterprising student replied: "You tie a long piece of string
to the neck of the barometer, then lower the barometer from the
roof of the skyscraper to the ground. The length of the string plus
the length of the barometer will equal the height of the building."
This highly original answer so incensed the examiner that the
student was failed immediately. The student appealed, on the
grounds that his answer was indisputably correct, and the
university appointed an independent arbiter to decide the case.
The arbiter judged that the answer was indeed correct, but did
not display any noticeable knowledge of physics; to resolve the
problem it was decided to call the student in and allow him six
minutes in which to verbally provide an answer which showed at
least a minimal familiarity with the basic principles of physics.
For five minutes the student sat in silence, forehead creased in
thought. The arbiter reminded him that time was running out, to
which the student replied that he had several extremely relevant
answers, but couldn't make up his mind which to use.
On being advised to hurry up the student replied as follows:
"One, you could take the barometer up to the roof of the
skyscraper, drop it over the edge, and measure the time it takes
to reach the ground. The height of the building can then be worked
out from the formula H =3D 1/2gt squared (height equals half times
gravity time squared). But bad luck on the barometer.
"Two, 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.
"Three, if you wanted to be highly scientific about it, you could tie a
short piece of string to the barometer and swing it like a pendulum,
first at ground level and then on the roof of the skyscraper. The
height is worked out by the difference in the gravitational restoring
force (T = 3D 2 pi sqr root of l over g).
"Four, if the skyscraper has an outside emergency staircase, it
would be easy to walk up it and mark off the height of the skyscraper
in barometer lengths, then add them up.
"Five, if you merely wanted to be boring and orthodox about it, of
course, you could use the barometer to measure air pressure on the
roof of the skyscraper, compare it with standard air pressure on the
ground, and convert the difference in millibars into feet to give the
height of the building.
"Six, since we are constantly being exhorted to exercise independence
of mind and apply scientific methods, undoubtedly the best way would
be to knock on the janitor's door and say to him 'I will give you this
nice new barometer, if you will tell me the height of this skyscraper.'"
The arbiter re-graded the student with an 'A.'
