Saturday, December 11, 2010

On Graphical Analysis

December 10, 2010; 8:30-11:30; NIP R108

Recovering from the arduous task of measuring rice that we did the last two meetings, we were thrust to a new topic which was graphical analysis.

Graphical analysis is basically understanding the relationship between two or more quantities displayed in graphical form. Bar graphs and pie charts were discussed as graphs that are used to show the distribution of a particular set of data. Scatter plots are graphs that show how one quantity changes as the independent quantity is changed. This could be explicitly presented as a function.

The elements of the scatterplot (the ind. and dependent variables, error bars, and the line of best fit) were also discussed. We were also taught how to graph scatter plots in Microsoft Excel, and how to implement error bars and best fit lines in our graphs.

Linearization was also discussed. The idea of this topic is to express higher order functions as linear functions, or functions of the form mx+b because linear forms are generally easier to handle and it is very easy to see the relationship of variables and constants with this form.

Getting back to our activities for the day, we didn't really get a chance to directly implement the things that we learned because we unfortunately didn't bring a laptop for our group. Thus, we were reduced to go to another group and observe. The first line of business was to plot a set of data given x, y, and uncertainty in x. The plots to done were x vs y, x^2 vs y and x^3 vs y. Admittedly, I think that I am very proficient in making spreadsheets in MS Excel, but I learned that day that I lacked knowledge in graphing in Excel. After this, the line of best fit and error bars were applied.

Another set of data were to be graphed after that. This set of data involved the moment of inertia and distance. The formula for the moment of inertia is:
I= I(cm) + md^2,
we were tasked to find m and I(cm).
We applied linearization to the equation by plotting d^2 as x, and I as y, getting the linear form of y=mx+I(cm). In this, the slope of the line is the mass, while the y-intercept (or constant) is the I(cm).

After this, we started the activity that we would perform next week- taking the time it takes for a small cart to get to the other side by applying a constant force.

This lab meeting was a jam-packed day. Unfortunately, we didn't really get the chance to make the most out of the lessons because of our lack of laptop. There were certain times today that I got bored, not because the things that we did were boring, but because of the aforementioned problem.

Almost everything that we learned this lab meeting was new to me, most notably the error bars and line of best fit. Linearization also appealed to me as a very interesting topic. I plan to experiment with MS Excel to better understand scatter plots and linearization.

Saturday, December 4, 2010

On Vernier and Micrometer Calipers, Part 2

December 3, 2010; 8:30-11:30; NIP R108

We continued the activity that we started last week, which was the difficult task of measuring the length (L) and thickness (T) of 100 grains of rice with both vernier caliper and micrometer caliper. Picking up from last week, we finished measuring the L and T of 70 grains of rice with the vernier caliper, leaving us with 30 more grains of rice to be measured with the vernier caliper, and 100 grains of rice to be measured with the micrometer caliper.

Before starting with measuring, Sir Pacho distributed the handouts for the fourth activity, which was all about graphical analysis. To a certain extent, I am quite weak with the topic, most notably when I am analyzing x-t, v-t and a-t graphs. But this was not our main focus for the meeting, for we have yet to finish the third activity.

We decided to implement strategy with measuring the rice. Two of the three of us measured the rice with each of the vernier and micrometer calipers simultaneously while the third member recorded the measurements obtained. Then, we rotated posts so that we would be familiarized with handling both devices.

It was an arduous task, yet we were able to measure 105 grains of rice for the vernier and micrometer calipers. Thereby, I deemed this activity to be successful.

Sir Pacho then told us to coordinate with other groups and combine all of our measurements together so that the sample space would be greater.

After finishing the activity, I felt a deep sense of accomplishment. I learned not to give up just because a task seems to be quite laborous. I also learned that great coordination with your group mates is a vital factor to perform an activity with the least amount of time and effort.

Saturday, November 27, 2010

On Vernier and Micrometer Calipers

November 26, 2010; 9:00-11:30; NIP R108

A Vernier and micrometer caliper were assigned to each group of 3 (which was determined last meeting; my groupmates are Mac and Peter). After the preliminary survey regarding the previous topics, Sir Aleo discussed about how to properly read caliper and micrometer readings. It is described by:

M.S. + F.S. * L.C. - Z = actual reading

M.S.= main scale reading
F.S.= fractional scale reading
L.C.= least count
Z= zero reading

My experience on vernier calipers could be traced back to my 4th yr HS Physics Lab class. It was only then wherein we were introduced to vernier calipers and micrometer calipers, devices which offer greater precision than standard rulers and meter sticks. In our school, only calipers were available, and not micrometers. Thereby, before this physics meeting, I knew how to use vernier calipers, and not micrometer calipers.

It was the first time ever wherein I lied my eyes upon the micrometer caliper, a peculiar device that looked like a stick with an arch on one end. I also had a hard time comprehending how to use the device since it was the first time that I've seen it in my life.

After the lecture, we were given our activity sheet as a group. The activity entailed three sets of mini-activities. The activity's premise is basically the measurement of the length (L) and thickness (T) of rice using the vernier caliper and micrometer caliper, and then applying our knowledge on best estimates and Gaussian distribution.

The first mini-activity is the measurement of L & T of a single grain of rice, measured with both the vernier and micrometer calipers. Using the vernier caliper was easy, but the micrometer caliper proved to be excruciatingly difficult. The micrometer caliper's mechanism involves a screw which needs to be rotated over and over again so that the measured object would lock into place for measurement. Since a grain of rice is very irregular in shape and relatively soft, it was difficult to lock it into place. Therefore, we resorted to perform the 3 mini-activities with the vernier caliper first, then when we finish, with the micrometer caliper.

The second mini-activity is the measurement of L & T of 10 grains of rice, and then presenting the final measurement as a best estimate. We took turns measuring with the vernier caliper, and it seemed that we had good chemistry as a group.

The third mini-activity is the measurement of L & T of 10^2-10^3 grains of rice, and then presenting the final data as a Gaussian distribution. At first, it appealed to me as a joke because it was very tedious to measure 10 grains, what more if the number of grains is in the second or third order of magnitude. We took turns yet again, and eventually reached 70 grains with the vernier caliper.

We finished the lab meeting with tired arms and a hungry stomach. Even if the activity was a bit tedious, it allowed us physics students to gain insight on what experimenters feel. Measuring a great number of specimens is difficult, that's for sure.

We will continue the activity next meeting, and when we reach 100 grains for vernier caliper, we would start everything again for the micrometer caliper.

Wednesday, November 24, 2010

On Measurement and Error Propagation

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.

The First Meeting

November 12, 8:30-10:30, NIP room 108

The distribution of the syllabus and the diagnostic exam were the activities of the first ever Physics 101.1 meeting. More importantly, it was the first time that I chanced a glance upon my fellow classmates and the class instructor, Sir Aleo Pacho.

When I think about Lab classes, I can’t help but recall my High School days. Lab classes were fun, yet were something I didn’t think I excelled in. But right now, I am invigorated to excel, primarily because this is a different ball game- this is a lot more serious. A UP lab class is ought to be taken more seriously than a normal HS lab class.

When I entered the room with my friend Mac, what caught my eye almost immediately was the instructor. He did not look like a conventional instructor, due to the fact that he had really really long hair. I admit that I was intimidated at first, but it was only for a short while. When he started talking and explaining stuff, I realized that he was a cool guy, and a really good instructor.

The diagnostic exam was easy, but there was one part that confused me. It was something like ‘draw the scatterplot’ of a given set of data. I, then, recalled my Microsoft Excel. There was a certain graph in Excel called ‘scatter’-something that entailed that the given data was ‘scattered’ yet exhibited a pattern. And so, I scattered the data given to me. After the exam, I realized that what was only asked was a simple line graph, and I laughed at my apparent idiocy.