Lab Activities No. 1 & 2

Last Monday (Feb. 2), we discussed measurements. We said that measurements are inherently uncertain, and they are uncertain for particular reasons.

For one, the nature of the quantity being measured affects its uncertainty. If I told you to measure the exact position and momentum of an electron in space at a specific time, then you would have a hard time. We all know this because of Heisenberg's Uncertainty Principle, which states that the product of the uncertainty of measurement of a small object's (such as the electron) position and momentum should always be equal to or greater than half h-bar. So the more precise you measure the electron's position in space, the more uncertain your measurement for its momentum becomes.

Another thing, the judgement of the experimenter deals with the measurement. Intuitively, our minds estimate the measurements if the thing we are measuring doesn't follow the calibration of the measuring device used. If I told you to measure a 2.5in line using a ruler calibrated only at integers (means to say 1in, 2in, 3in, and so on), one side of your head would say 2in, or 3in. But in hindsight, your brain is really telling you that that line is indeed 2.5in. So our judgement on the thing measured gets in the way of the certainty of the measurement.

Lastly, our measurements are inherently uncertain because the measuring device we use has limits. Any measuring device existent on this planet has limitations (everything has limitations, but let's not get deeper on that point), and this affects our measurement. For example, we have a 1in line and we use different rulers to measure it. The thing though, is that one ruler was calibrated at integers (1, 2, 3, etc.), and the other divided the inch into tenths (1.0, 1.1, 1.2, etc.). Both rulers will give you a reading of 1in. However, the only difference in this measurement is what you actually get using either ruler. The ruler calibrated at integers gives a reading of 1in, and the other 1.0in. What makes 1.0in different from 1in? According to Sir Batac's discussion, 1.0in tells you that the line is not 0.9in or 1.1in. And 1in tells you that the line is not 0in or 2in. So our measuring device also gets in the way of our measurements. So we must be careful with these.

After that discussion, we talked about the different types of errors: Uncertainty, and Deviation.

In Uncertainty, our reference value is the mean of the data, usually denoted by the label for the measured thing enclosed by angled bars '<h>'. And the thing significant about this is that the lower the uncertainty is, the more precise your measurements are.

For Deviation, on the other hand, our reference value is some external value independent of the experiment done. These values are usually the standard values, or definitions. Also, the lower your deviation is to the accepted values, the more accurate your measurements are.

The last thing we discussed was on the Order of Approximations.

There are five orders of approximations that we use. They are the Order of Magnitude Approximation, Significant Figures, Limited Measurements, and Based on the Distribution Function. I won't go in detail here because I think you're already struggling with the length of this blog. So let's get to the meat of the lab session.

The 'big' thing we did during the lab was to measure rice grains using a vernier caliper. I was already introduced to this when my uncle used it to help me do a project last semester, but I wasn't really able to use it that much so this is actually a good thing. I learned on how to exactly measure things with a caliper that I want to have one. Anyway let's not get to that.

For most of the time now we only measured the length of Long Jasmine Thai Rice. Our objective was to collect the data from every group in the class to see a distribution curve where we'd be able to see, on average, what the length of grain of rice (Long Jasmine Thai Rice) was. It was fun to measure singular, and small, grains of rice - but worth it. In the end we were able to measure the length of 50 grains and Sir plotted it in his computer and showed the class our data. One thing that he mentioned to us though is that we didn't really measure the grains to two decimal places and assumed that they measured in exact tenths. This was not preferable because our measurements might become biased, and that wouldn't be good. So, I took note of that (it is extremely important). Therefore, next time, we must make sure to measure objects more carefully, not missing details as they are.

Then we were told that we would be finishing the experiment next week. So that ends my blog pretty much.

PS Here is a plot of our data (as done by yours truly). The x-axis is the length of the rice grain in millimeters (mm), and the y-axis the frequency of that length occurring: