How to measure the height of a building using a barometer

Sir Ernest Rutherford, Nobel laureate in physics and chairman of the Royal Academy, once said the following story:

One day a friend telephoned me. He was just about to fail one of his students for the wrong answer to the physics question, but he insisted that he should get the maximum number of points. Both agreed that this matter should be decided by an independent judge and that I was chosen for that purpose.

So I read the exam question: “Show how you can determine the height of the building using a barometer.” The

student replied: “We take a barometer to the top of the building, attach the barometer to the rope, lower it onto the street, roll back and measure the length of the rope used. Its length corresponds to the height of the building. “

In fact, his demand for the maximum number of points was fully justified, because his answer was the most correct! On the other hand, it would mean granting him the highest grade in physics, while his answer did not confirm such knowledge. I suggested that he try again. I gave him six minutes to think about it, but I stipulated that the answer should contain some element of knowledge in physics.

After five minutes I noticed that he did not write anything. So I asked if he wanted to give up, but he replied that he knew many solutions and wondered about the best. I apologized to him and told him to continue. After another minute, the answer was ready:

“We take a barometer to the top of the building and lean over the edge of the roof. We drop the barometer to the ground, measuring the time of its flight with a stopwatch. Then, using the formula x = 0.5 * a * t ^ 2, we calculate the height of the building. ”

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At this point, I asked my friend if he wanted to give up. He nodded his head and gave the student almost the highest mark.

When I left, I called the student back to myself and asked him about the other answers he was thinking about.

  • Well – he answered – there are many ways to determine the height of the building with the help of a barometer. On a sunny day you can, for example, measure its height, then the height of its shadows and the building, and in a simple proportion determine the height of the building itself.
  • Okay, what about those other methods?
  • If you want, you can calculate it the basic method of measuring altitude. We take a barometer and start to go up the stairs of the building. During this climb, we measure the length of the barometer on the wall and reaching the top we know its height in the barometer lengths.
  • Pretty direct method.
  • Indeed. If you would like something more sophisticated, we can tie the barometer to the end of the string and use it like a pendulum. We measure the force of gravity at the height of the street and then at the top of the building. You can easily calculate its height from the difference of these results.

In the same way, we can attach the barometer to the rope and leave it to the street level and then calculate the height itself from the swinging periods.

And finally probably the best method. We take a barometer, go to the basement and knock it at the manager’s door. When he opens us, we say: “Mr. Manager, I have a great barometer here. If you tell me the height of this building, the barometer is yours. ”

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At that moment I asked the student if he knew the conventional answer to this question. He admitted that he knew her, but he was fed up with telling him through school, teachers and colleagues about how he was supposed to think.

The student’s name was …

Niels Bohr

He was awarded the Nobel Prize in Physics from 1922.