How to Measure the Height of a Skyscraper by a Barometer?
During the physics exam of Copenhagen University, students were expected to answer this question:
“How to measure the height of a skyscraper by barometer?”.
An interesting answer to this question was:
“Firstly, you tie a rope to a tip of barometer. After that, you release the barometer until the bottom of the skyscraper. If you sum the rope’s length with the barometer’s length, the result will be the height of that skyscraper.”
As a result of this answer, the student has failed, and he objected to the administration. A teacher assigned to solve the issue and that teacher decided the fact that even though the answer that was given by the student was right, it wasn’t including enough information based on physics. So, s/he decided to give this student six minutes time to explain the details. The student improves his/her answer as:
“Firstly, you take the barometer to the top of the building and you calculate the time passed until it reaches the bottom. The height of the building can be calculated by using the formula h=1/2gt2. However, since the barometer is a cylindrical, this method is an inappropriate choice. If the weather is sunny, you can measure the length of barometer’s shadow by setting it up on the ground. If you measure the length of the barometer too, you can apply a simple proportion (Thales relation) on the barometer and the skyscraper. Yet, if you want a more logical and scientific answer, you can tie a string to the tip of barometer and you can wave it as a pendulum: firstly at the ground level, secondly at the top of the building. The length can be calculated by using the difference between the two results of
. Or, if there is a fire escape outside of the building, you can use your barometer as a ruler and while you are climbing to the top of the building, you can calculate the height in the unit of barometer and turn it into other units. If you really want to that much boring and traditional, surely you can measure the pressure at the top and bottom of the building, and find the difference in the unit of milibar and turn it into feet. This would give you the height of that skyscraper. On the other hand, since we are always encouraged to use the mental independence and scientific methods together, the best way would be knocking the door of the person who does cleaning and runs errands and asking him whether he wants a new barometer or not and telling him that we can give this barometer to him if he tells the height of that building. “
. Or, if there is a fire escape outside of the building, you can use your barometer as a ruler and while you are climbing to the top of the building, you can calculate the height in the unit of barometer and turn it into other units. If you really want to that much boring and traditional, surely you can measure the pressure at the top and bottom of the building, and find the difference in the unit of milibar and turn it into feet. This would give you the height of that skyscraper. On the other hand, since we are always encouraged to use the mental independence and scientific methods together, the best way would be knocking the door of the person who does cleaning and runs errands and asking him whether he wants a new barometer or not and telling him that we can give this barometer to him if he tells the height of that building. “The name of the student who gave these answers was NIELS BOHR, the person who gained first Nobel Physics Award and the only famous quantum physicist that was educated in Denmark.
References
Nobel Lectures, Physics 1922-1941, Elsevier Publishing Company, Amsterdam, 1965
http://www.mentors.ca/bohr.html
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