Pulling the Trigger

New experiment. New toys. New knowledge to gain. The activities we are doing in the lab seem to be getting more and more interesting as time flies by. For today, we analyzed the mechanism of a projectile motion. We use new sets of instruments such as the projectile gun and a metal bullet. Other instruments were meter stick, tracking paper, and marker. The experiment was divided into two parts. The first one is analyzing the trajectory of a body in a projectile motion and the second one is analyzing the relationship of the angle of projection of the metal ball to the horizontal distance it covers after it was launched. Since projectile motion has a theoretical background, it is also our mission to analyze the adherence of the results of our experiment to the theoretical one.

We managed to do “division of labor” to effectively work on the experiment. Each of us did a turn in setting up the projectile gun because it would be grueling for anyone to do it all alone all throughout the experiment. For the first part of the experiment, we recorded the height of the trajectory by tracking the marks that metal left as it hits the paper posted in the wooden block. We recorded several trials for the different distances of the wooden block from the projectile gun.

For the second part of the experiment, we recorded the horizontal distances that were travelled by the metal ball in different degree of projection of the gun. We also did several trials for each of the degree of inclination.

Physicists, meet the papers!

We've gone to a dipper topic for today, one that is very relevant for us physicists: writing technical papers. Writing scientific papers is not new for almost all of us since many of my classmates including me have had already the experience since we were in high school level. I can still remember how grueling it was writing those papers... when you will burn the midnight oil just to finish a single page and by tomorrow you would only taste the words of criticism from your teacher when you didn't get what they want… the voluminous revisions that blotted so many red inks in my paper. Oh! How fresh those memories are to me. That's why I’m feeling a little anxious when the discussion opened up and we were told that we were going to write our own scientific paper based on the activity that we did on air track. I tell you that I’m no good in writing. Actually it is my frustration to write because i easily run out of words. And not just words, oftentimes, it is the motivation to write that lacks in me.

But for us to become a full-pledged scientist, we all need to learn how to write and express or show our ideas, analyses, and findings, and apply it for the betterment of mankind. I know a lot of famous scientists who rose to stardom because of the impact of their publications. For an instance, Albert Einstein, a clerk on a Swiss patent office strucked the scientific community and the world with his paradigm-shifting revision of Classical Physics and many other great discoveries in 1905, which is often termed as the "miracle year". His works on General Relativity served as an avenue for the existence of what they call the “Modern Physics”. Einstein would have remained a lowly clerk hadn't he published and shared his works to the humanity. On the other hand, Principia Mathematica, one of the greatest scientific papers in human history ever published was written by Sir Isaac Newton, one of the pillars of Classical Physics. Publications, indeed is a significant part of being a physicist to the point that it serves sometimes as the sole basis of how productive a scientist is.

OMg! ( Oh My Gravity!)

Our experiment for today dealt with mechanics. We used some cool instruments (if you may call them instruments) such as the air track and the glider. The principle behind the near frictionless surface of the surface of the air track is just easy to comprehend. The upward force that lifts the glider off the track causes the car to move in a seemingly frictionless surface. The only friction that the glider dealt with is the air friction which is not so strong compared to the friction that it may work against when in contact with the aluminum track. The mechanism of the instrument used is comparable with how the maglev train works only that it is the magnetic repulsion that lifts off the train in maglev and not the upward force of gushing air from a "electromechanical blower" that can be found in the air track. Anyway, the objective of our experiment is not about understanding how the air track works. Our real mission is to derive the value of the magnitude of acceleration due to gravity (g) empirically and compare it to the conventionally accepted value which is 9.8 m/s2. We also want to know the effect of differences of angle of inclination of the air-track to the motion of the glider as it slides down the air-track.

For this experiment, we used a ruler, stopwatch, marker, recording paper, a glider and the air-track. We prepared four different set-ups of the experiment corresponding to the degree of inclination of the air-track: flat (0°), 2°, 4°, and 6°. In each of the set-ups, we also assigned distances to be travelled by the glider. A recorder was assigned to record the time it took the glider to cover the distance measurements we assigned. For the set-up where the degree of inclination is zero, we recorded ten trials for each of the distance measurements. To jumpstart the motion of the glider, we used the force of the spring of a retractable ballpoint pen. In this way, we can make it sure that the force we exerted is constant in all of the trials. For the set-ups with the degree of inclination of 2, 4, and 6, we only had 5 trials for each of the distance measurement. Unlike the first set-up, we no longer used the spring of the ballpoint pen to jumpstart the motion of the glider because it readily slides down when it was laid in the inclined air-track.

With a first glance on the data we gathered, we did notice that the time it took the glider to cover the assigned distances gets shorter as the degree of the inclination increases. This means that the glider moves faster as the air-track went steeper.

The data that we got from the experiment will also be utilized to compute the acceleration of the glider along the air-track and the magnitude of the acceleration due to gravity. We will heavily rely on the Newton’s Second Law of motion in deriving the said quantities given by ∑F=ma. I can’t wait to see the results!

The Best-Fit Line

For today, we studied the best fit line. This topic does not only encompass algebra but includes a lot of statistics.  By definition, a best-fit line is a line that best fits the scattered points plotted in a graph. It is just looking the line that represents the trend of a scattered points.  In determining the best fit line, its slope must be computed first. There are several ways in determining the slope of  a best fit line. Among these are the ordinary least squares line, the ratios of medians line, the ratio of arithmetic means line, the regression-through-origin least-squares line, and the arithmetic mean of ratios. Statistically, determining the best fit lines lies heavily in determining the mean value or median value of the x and y variables.

Friedrich Gausse, the Caliper, and the Rice Grains

In our lab activity for today, we worked on rice. Oops! If you think we did something biological work for today, you are definitely wrong. We still did physics! In our lesson on Gaussian distribution, our professors handed us a set of rice grains for us to measure and represent the diameter and length of a typical rice grain. We used some devices that were not so familiar with us yet: the micrometer caliper and the vernier caliper. These devices are used in measuring lengths that are in a micrometer scale and commonly cannot be measurable in an accurate manner by a typical ruler. He taught us first how to use the said devices and we started measuring the rice grains one at a time. Using the micrometer caliper in measuring the diameter of rice grains is manageable enough for us but not the length. The tip of the rice just slipped off the grip of the caliper so we resorted to using a ruler instead. Using the said device meant some changes in the uncertainty of our measurement since the two devices have different level of accuracy.

In determining the dimensions of a typical rice, we are going to use three different orders of approximation such as the first order of approximation, second order of approximation and the third order of approximation. The number of the samples utilized determines what order of approximation is used. For the first order of approximation, only a single sample was used. For the second order of approximation, there were only 10 samples. For the third order of approximation there were 100 rice samples used. We are to asses which of the three order of approximation is reliable enough in determining the dimensions of a typical rice grain. And we can do it by analyzing the graphical distribution of the lengths and diameters or rice samples.

Measuring Measurement

How accurate are you in measuring quantities? This is the question that our professor wants us to ponder last Wednesday. For all we know, measurement is very important in our everyday living. From the simple way of measuring the right amount of food we're about to consume in every meal to measuring the pixel size of our uploads, we are very dependent on measurement. As a student studying physics, the accurate and reliable way of measurement is a fundamental thing to master. In fact, as our professor said, the meticulous way of measurement in physics sets it above from other disciplines with the likes of chemistry, biology, etc.

However, measuring is not as ordinary as we think it would be. The way of measurement that our professor wants us to learn is more than using a ruler or any measuring device in measuring quantities. Since measuring devices and humans have some flaws in their selves, we cannot guarantee a perfectly accurate kind of measurement that we want to attain. However, through the use of some techniques that our professor shared to us, we can somehow reach a considerable accuracy that will significantly help us attaining the data that we need.

Our discussion last Wednesday started with the introduction of the concepts of scientific notation, rounding off values, and significant figures. Since we already tackled these concepts since in my freshman level in high school, I found no problem dealing with them.The discussion eventually tackled the central topic which is the order of approximation.  The first order of approximation deals with the use of significant figures and their operations (e.g. addition, subtraction, multiplication and division). The second order of approximation deals with “Best Estimates”. The second order of approximation is commonly used in measuring irregular or fluctuating quantities. From these, terms like expectation value and uncertainty were introduced. Expectation value ‹Q› is the average of the trials obtained while uncertainty “gives the idea of the range of values where the actual value can fall”. Best estimate Qbe of a quantity is given by Qbe=‹Q› ± ΔQ. The third order of approximation is the Statistical approach. We didn’t tackle much of the third order of approximation because it deals with higher math which are not yet appropriate for us in the moment.  My professor gave us activity sheet regarding the first and second order of approximation. We accomplished half of the activity and left the other half to be considered as homework.

The second part of the discussion deals with error in measurement. Errors in measurement are an inevitable thing. It denotes “how far a measured value is with respect to a reference value”. There are two types of error with respect to a reference value. The first one is “uncertainty” (also called random error) or error with respect to the mean of the data. The other one is “deviation” or error with respect to a standard or accepted value. Uncertainty and deviation may be recorded in two different ways: either absolute error or relative error. Absolute error is the “actual absolute difference between the quantity and the reference value” while relative error is a “number that describes how large the error value is compared to the reference value. Absolute error has the unit of the quantity involved while relative error is usually reported as percentage.

At the third part of the discussion, we discussed the issues about the precision, accuracy, acceptability, and practicality of measurement. Our professor explained to us the difference between being “precise” and being “accurate” by showing some illustrations of darts placed in different manner on the target. Darts that are closer to one another and located at the bull’s eye represent both accuracy and precision. Those that are close from one another but far from the bull’s eye represent precision only while those at the bull’s eye but a bit far from one another represent accuracy. However, those that are neither close from one another nor near from the bull’s eye are considered neither precise nor accurate. From these representations, we can define accuracy as the closeness of the values (represented by the location of darts) to the standard value (represented by the bull’s eye). Precision, on the other hand, can be defined as the closeness of the measured values to each other.

Uncertainty and deviation has indirect relationship with precision and accuracy, respectively. The “lower the uncertainty of a given set of data, the more precise the measurement is.” Similarly, the lower the deviation of the given set of data, the more accurate the measurement is.

Is the data measured should be considered? This is the question that can be answered by the parameter of acceptability. From our discussion, the acceptability of the given measurement has something to do with the relative values of deviation and uncertainty of the given measurement.  A measurement can be accepted when the “uncertainty is small enough and the deviation is smaller than the uncertainty”.

The other condition that must also be considered is “practicality”. The most practical measurement will be the “one that yield a maximum error value that is within the specified margin.”

At the last part of our discussion, we tackled error propagation. Error propagation says that error propagates when an unknown quantity is measured by means of computation of given quantities and not by directly measuring the unknown quantity with a specific device. Since the individual quantity has in itself an uncertainty value, then the uncertainty value will only combine with one another once different operations are applied to them. In other words, as the principle of maximum pessimism states, “ the error of computed quantities must be greater than or equal to the individual quantities used to obtain it”. There are different approaches on adding, subtracting, dividing, or multiplying the uncertainties in best estimates.

Our professor once again gave us activity sheet about the lessons above and homework as well.

Reference:Physics 101.1 Handout