Educational Stories 01 - The Barometer Problem

I'm going to use this blog to also collect some really educational stories which can be used in class to inspire students. Let me begin this series with the famous Barometer Problem which I used in all my physics classes when I lecture on pressure.

During an exam, students were asked to explain how to measure the height of a building using a barometer.

*Now if you are a student of mine, you should be able to answer this after the lesson on pressure but let me just run through the proper "textbook" answer.

Pressure = density x gravitational acceleration x height

So if you measure the pressure difference from the top of the building and below, you can divide it by the density of air and the gravitational acceleration to get you an approximate height difference. This is assuming that density of air and gravitational acceleration is constant over the height of this building.*

Now in this exam, there was a student who looked extremely puzzled/constipated when he was tackling the problem. When the teacher started marking the papers he noticed that boy's answer.

Ans: I would take a string and tie it to the barometer. I will lower the barometer to the ground and measure the length of the string.

DOH! The boy wasn't wrong. BUT he did not demonstrate any knowledge of pressure which was the aim of the assessment. Furious yet tickled at the same time, the teacher summoned the boy to his office.

He asked the boy to re-do the problem but this time to use concepts he thought in class. The boy became more puzzled. He replied: "Which concept? I have many answers!"

The teacher was astonished. He asked the boy "Many answers? Tell them to me."

The boy answered:

"Method 2: I could use units. I walk up the building in the stair case and mark on the walls each time i pass the height of the barometer and count how high the building is in terms of barometers. After measuring the height of 1 barometer with a ruler, I can convert that height form barometer lengths into standard units.

Method 3: I could use Kinematics. I release the barometer from the top of the building from rest and measure how long it takes to reach the ground with a stopwatch. Using the formula taught:

x = ut + 1/2 at^2

I can deduce the height of the building x by substituting u = 0, a = 10m/s^2 and t the time measured on the stopwatch.

Method 4: I could use Period of pendulum by constructing a huge pendulum of length equal to the building and measure the period of the pendulum when swinging it from the top of the building.

T = 2pi root(length of pendulum/g)

Measuring the period, the height of the building could be calculated for the equation above.

Method 5: Similar triangles. I place the baromter standing on the floor and measure the ratio of the height of the baromoter to its shadow. I can calculate the height of the building with respect to its shadow.

Of course, the easiest answer would be to just give the building manager the barometer in exchange of information about the building."

The teacher was dumbstruck and gave the boy an A.

You can find this story in many websites attributing the boy to Niels Bohr but that isn't true. Nevertheless, this makes a great story to inspire students and to round up basic mechanics in Physics or Similar triangles in mathematics.