Physicists prefer to share the legend that a professor who asked students exactly how they can determine the elevation of a structure using a barometer.

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The story goes on come list some of the means you could do that. You can drop the barometer from the roof and also record the moment it takes come hit the ground. Or you can offer the barometer as a bribe to the building manager and ask him the height.

Of course, this isn't yes, really a story around finding the elevation of a building, but rather a lesson on finding inventive solutions—the allude being the teachers must not discourage students from thinking of brand-new ways to solve a problem. (Even if that does do grading test trickier.)

In short, a barometer actions atmospheric pressure. This pressure changes as weather systems move through one area—storms an outcome in lower barometric pressure. The simplest barometers use mercury and also looks something prefer this:


The tube on the right has actually a higher mercury level, with a sealed top and also a vacuum over the mercury column. The column on the left is open up to the atmosphere. Notification the dotted line. In order because that the mercury below this line continue to be in equilibrium, the air push pushing down on the left should be same to the press of the mercury pushing down on the right. By measure up the elevation of the column, you have the right to calculate the atmospheric pressure. In basic the push in a liquid (like mercury or air) rises with depth and also can be calculated as:


In this expression, h is of food the depth that the mercury and g is the gravitational field (with a worth of 9.8 N/kg). The ρ represents the thickness of the fluid. But what if the atmospheric press changes? With rise in pressure, the setting will push down on the open up tube and cause the mercury to increase until the 2 sides of the tube achieve equilibrium.

You usually uncover mercury in barometers because it has a thickness of 13,560 kg/m3 i beg your pardon is significantly greater than the density of, say, water (1000 kg/m3). Because normal atmospheric pressure is about 105 N/m2 (or 105 Pascals), friend would need a mercury shaft of 0.76 meter (or 760 mm—a usual unit for pressure). Utilizing water would call for a pillar 10 meters tall. That's just too high to it is in practical.

Now because that the fun part. Expect I usage a barometer to measure up the atmospheric push on the floor floor the a building. Together ride the elevator up, the atmospheric pressure decreases. Why? because that the same reason the pressure transforms with various heights of mercury. Assuming the density of waiting remains consistent (a reasonable assumption, offered the small change in altitude), the adjust in push from the soil floor come the roof would certainly correlate come the elevation of the building. This equation is similar to the one to calculation the push from the mercury other than that it uses the density of waiting (1.2 kg/m3). Ascending a 30-meter structure would watch the push decrease through 353 N/m2. The represents a tiny fraction of the atmospheric pressure, which explains why you require a extremely sensitive barometer. Fortunately, mine iPhone has actually one.

Yes, the iPhone features a integrated barometer. That doesn't use mercury, though. It supplies an electrical sensor. I can also record push readings. Number of iOS apps carry out this, however I prefer SensorLog. It appears to work reasonably well.

I newly attended a conference in a structure with one elevator. Of course I supplied my iphone to calculate the elevation of the elevator as a duty of time using the press data:

In order to prevent an unfavorable height values, I collection the lowest value to zero meters. Also, notice that return the app records data in ~ 100 Hz the doesn't seem favor the press values readjust as fast. This is what to produce those measures in the over graph. Unfortunately, this method that it would certainly be difficult to find the acceleration that the elevator. I guess it's a great thing the iPhone also has one accelerometer in it, right? maybe the following step is to usage the accelerometer to measure up the height. Ns will save that because that a future post.


Rhett Allain is an associate professor that physics at Southeastern Louisiana University. He enjoys teaching and also talking around physics. Periodically he takes points apart and also can't placed them back together.

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