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I read a story in which an it was asked in an exam to show how it is possible to determine the height of a tall building with the aid of a barometer.

This story is quite famous I guess, and the student gave several non-conventional answers (which were all correct) because he was fed up of instructors trying to teach him how to think. Here is a link to the story. In the end the student says that he knew the conventional answer to the question.

I was trying to figure out what should have been the conventional answer or the answer instructor wanted from students?

Qmechanic
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Bhaskar Vashishth
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3 Answers3

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I like throwing it of the roof and count the seconds the most, but what the instructors wanted to hear is most likely to apply the barometric formula, which reads $p(h)=p_0 \exp (\frac{-mgh}{k_BT})$, assuming the same temperature hat level $p_0$ and $p(h)$

rtime
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With a tall building there will be a difference in air pressure between the top and the bottom. Near ground level, the pressure drops about 10% per 1000m (it levels off gradually). See Wikipedia's entry on Atmospheric pressure for more details.

So, if you measure the pressure at the top and the bottom, you can use the difference to compute the height. If the building is 200m high, you'll see the barometer drop 2%.

hdhondt
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Determine the height of a tall building with the aid of a barometer.

  1. Look at the building's facade and windows and determine how many floors the building has. Consider whether the ground floor actually counts as two floors (etc.) high. Example: 52 floors. Note that in the case of many extremely tall buildings, the architect may use a trick where what looks like one floor is actually two, to make the building appear more inviting and less menacing (common in Las Vegas Strip Hotel Casinos).

  2. If the barometer is mounted to a board or plaque, estimate the height of the barometer itself, 10" for example, then use it to measure a portion of the side of the building. If the first floor is actually about the height of two floors, then measure 1/4 way up the first floor knowing this is half of a floor, or equivalent.

  3. Perform basic math to come up with a statement: "One floor is 120" high.

  4. Multiply that times the number of floors you came up with earlier. 52 floors at 120" high each = 6,240, / 12 inches = 520' tall. That's your answer. It's gotta be just as accurate as using the barometer at the top of the building vs. the ground level. And, well, you used the barometer.

Farrara
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