November 19,2010, 8:30-11:30, NIP room 108
It was the first official Physics 101.1 lecture for the semester, and I was a bit nervous because I was one of the only 2 non-NIP students enrolled in the class. With physicists-to-be as classmates, I expected very bright (and scientific) minds to surround me constantly, thereby I had to try to match their supposed intellect by reading the given handouts in advance. The topics for the morning were Measurement and Error Propagation, two essential topics considering Physics 101.1's main concentration: experimentation.
As I entered the laboratory, I tried to absorb everything around me- the equipment, the tables and the students. As a BS BAA student planning to shift to Applied Physics, everything to me was foreign yet exciting. Corollary to that, I thought that physics was the field where I ought to be, not the world of business.
As a product of a private (not science) high school, I feel as if I am not on a level playing field with my peers, primarily because the science topics we discussed in HS were, as far as I know, not on par with those in science high schools. But still, physics was my second favorite subject in high school, and I loved it with a passion.
As the instructor entered the room, I focused my entire attention on the lecture at hand.
The first topic was measurement, its importance in the realm of physics, significant figures, and the different orders of approximation. Measurement is very important because, as people again and again say, physics is an experimental science. The instructor did a very good well explaining the importance of measurement and reporting data with the correct number of sigfigs. One error I remember is the digital weighing scale with .1 as the least count but the value reported was a value with something-hundredths.
The zeroth order of approximation is by using order of magnitude (10^x). This is used to give a general overview of the measurement of something, in a situation when accuracy isn't really something important. One application of order of magnitude is the Fermi questions. A fermi question is a question wherein an answer is given by very rough estimations. I remember my Physics 10 class under May Lim, since that was the first time I heard about Fermi questions.
The first order of approximation is by using significant figures. Rules on what are considered sigfigs were discussed as well as the rules on addition/subtraction, multiplication/division and constants.
Significant figures are something that I've studied for a long time, but it was only recently that I understood its importance in the world of science. In high school, sigfigs were studied as a single topic, and after that, they weren't applied to computations. The convention in our high school was to round all final answers to 2 decimal places, thereby sigfigs did not matter. In Physics 101.1 and Chem16 Lab, sigfigs became something to take note of because of the the experimental nature of the subjects, thereby the uncertain nature of measurements is involved directly.
Admittedly, I am still quite confused with sigfig rules regarding long computations. When we did the activity after the lecture on Measurements, I was very very nervous because some rules were still vague to me.
The second order of approximation is the use of best estimates, expressed by the expectation value (mean of the data) added or subtracted to the computed uncertainty (given by max| highest or lowest value -mean| or, in some cases, the least count). This order of approximation is used when an experiment involves a number of trials, so as not to give a single answer, but a range of possible values, which is a better description of the data.
The third order of approximation is the statistical treatment, which makes use of integration, a tool in mathematics I have never tackled. I did not completely understand what the formula entailed, but I do know that this approximation is used for continuous data, wherein the intervals between the data are too miniscule to be noticed. When we tackle integration in Math 53, I plan to go back to the statistical treatment and understand the formula in its entirety.
As I've mentioned earlier, we had an activity right after the first part of the lecture. We were asked to report given data in 3 sigfigs, answer basic arithmetic and report the answers with the correct no. of sigfigs, and give the best estimate of some data presented. The first and third parts of the activity were easy to answer, it was the second part where I was quite nervous. But luckily, the majority of my answers were correct, but I need to reread the notes.
The second part of the lecture was about error and error propagation. Error is inherent in all measurements, so the only thing we can do is to minimize it and report data recognizing this inherent error. There are actually two types of error, uncertainty and deviation. Uncertainty is the error correlated to precision while deviation is correlated to accuracy. Absolute and relative error were also differentiated.
Accuracy and precision are closely related albeit largely different. Accuracy pertains to the closeness of data to a given value, say the gravitational constant G 6.67x10^-11 m^3/kg*s^2. Precision, on the other hand, is the closeness of given data with one another. It does not depend on an accepted value, but on the data gathered. So, it is possible for data to be precise but not accurate, vice versa, both or neither. The darts analogy illustrated everything clearly to me.
For a measurement to be acceptable, the deviation should be less than or equal to the uncertainty, so that the measured data would fall upon the accepted value. This makes perfect sense to me, because if the uncertainty is less than the deviation, then the value would not be accurate at all.
Finally, error propagation was discussed. It is necessary to minimize error propagation so as to report data correctly, and if operations are done among measured values, the principle of maximum pessimism holds. This principle states that the error does not decrease as a result of mathematical operation. It may only increase or stay put. The rules of this principle were also discussed.
We were supposed to answer an activity sheet but time seemed to be elusive. Thereby, we were tasked to answer it at home.
All in all, the first lecture of Physics 101.1 was important and very informative for me. The importance of sigfigs and principles of error propagation were highlighted as key points in my mind. I admit that I am not really that good with measurements and experimentation, but I will try to do my best for the sake of this class.
