On the Center of Mass and Torque

February 18, 2011; 8:30-11:30; NIP R108

For the nth time, we were late this meeting because we had to finish the technical paper. Fortunately for us, though, the experiment this meeting was not really that demanding. We finished quite quickly and made up for the lost time brought about by us being late.

The goal of the experiment this meeting was to calculate the mass of a meterstick in a set-up wherein the meterstick was suspended from a height and was supported in its fulcrum point. We first had to determine the meterstick's center of mass (the point where mass is concentrated) by finding the right spot in its body wherein the meterstick, being suspended mid-air, was balanced. After that, we changed the fulcrum point and added weights to both sides, then carefully finding the positions of the weights that would balance the meterstick. We performed this part two times and took the average.

The mass of the meterstick could be calculated by equating all the torque (clockwise and counterclockwise) to 0, since the whole set-up is in equilibrium. The only missing term in the equation is the mass, and it could be derived with simple algebra.

Using an electronic balance, we measured the true mass of the meterstick. To our pleasant surprise, our calculated mass was only off by less than 1 percent.

After this, we were tasked to make the mass of the meterstick nonuniform - which was done by placing a weight on it- and then calculate the mass of the meterstick+weight by adding weights and by equating the torque with the aforementioned condition (torque=0). We only performed one trial because we were quite confident of our calculations. We, then used the balance to calculate mass, and once again, we were only off by less than 1 percent.

My friend and I made a promise that we would not be late next meeting. In turn, it was also a promise that we would not rush our technical paper and cram the night before.

On Harmonic Motion and Pendulums

February 11, 2011; 8:30-11:30; NIP R108

Because I was quite late this meeting, it was quite disorienting to see my other labmates already starting a new experiment as I entered the room. The setup that I chanced upon seeing involved a stand, a pendulum, a set of weights and a string. Immediately, simple harmonic motion entered my mind - this week's experiment was all about pendulums. It was something very familiar to me since I already did a variation of this experiment back in High School.

Mac and I formed a new group, since both of us were late. Peter, our other group mate, was absent this meeting. We went upstairs to the physics instruments room to get the setup and what greeted us inside the room was a very upset and grumpy man who handled the materials. I don't want to rant about the old man but it seemed as if he was grumpy for no apparent reason. It irritated me a bit as to how he acted- it was unethical, yes, and also quite unnecessary.

After getting the materials, we went back to the room and started the experiment. Basically, what we were supposed to do was to vary the length of string, angle of displacement, and weight of bob one at a time to see their effect on the period of oscillation.

Since there were only two persons in our group, both of us had to do something. Mac measured the period of oscillation, while I fixed the angle of displacement and released the bob. Like all the other experiments that we have performed, this one was very routinary and involved trial upon trial.

The motion of a pendulum could be described by a mathematical equation:

T=2*pi*sqrt(L/g)

where T=period, L=length of string, and g=gravitational acceleration.

As we can see from the formulation, the only major contributing factor to the period is the length of string. Their relationship is direct- increasing L increases T. After some research, I also discovered that T is also affected, to some extent, by the angle of displacement, i.e. the equation only works for small angles of displacement. For large angles, more complicated mathematical formulations that involve Taylor expansions and infinite series are required.

The data that we gathered, as far as I can remember, are not that concise with the theoretical expectations. We measured slight increases in period of oscillation as we increased the mass. This could be attributed to error in release of bob or in measurement of time.

Since we were late for the meeting, we were unable to test the scenario wherein the length was very, very high, thereby we had to merge with Robby's group to share with their data. It was very fun because the setup was too big for R108; we had to go to the second floor and hang the pendulum from that height. Admittedly, the setup was quite dangerous since the bob could fling from the string and hit bystanders, but still, it was very fun. For this setup, I was assigned to measure the period of oscillation.

I prefer this experiment to the two previous projectile motion experiments because

1. I was reunited with my old group, even if the other member was absent

2. I was more useful in this experiment

3. the setup was generally more fun (particularly the large L setup)

This new experiment implied that we had to, again, submit a technical report next meeting, something that I'm really not that enthusiastic about.

On Projectile Motion, Part 2

February 4, 2011; 8:30-11:30; NIP R108

This meeting was basically another one devoted to experimentation concerning projectile motion. This time, we were tasked to measure the y-component (height) of the projectile as we vary the x-component (range) while, in turn, varying the angle four times (0, 15, 30 and 45 degrees). This was arguably an easier task since the ball (projectile) was flung to the wall, therefore it did not go to far-off places like last meeting.

If we know the x and y components and the angle of the projectile, its initial velocity could be computed. From my last post,

Y=X*tanA-0.5g*(X/(Vi*cosA))^2

We know X, Y and A, therefore the only missing term in the equation is the initial velocity.

We encountered difficulty with the "projectile gun" or whatever it is called because it disassembled itself every now and then, therefore the tightness of the spring in the gun varied, in turn, varying the force (and the initial velocity) in which the ball was released. This arose when we were measuring the height with the angle of inclination at 30 degrees. We had erratic data during this part, i.e., the distance fluctuated up and down (due to the varying force) where it was supposed to resemble a parabola with simply one peak.

We were very efficient as a group, finishing ahead of time and encountering little difficulty apart from the aforementioned problem. I was also more useful this lab meeting- I was responsible for recording and encoding the data for my new group. I also became less shy with my group mates, mainly because they were very friendly with me. The initial awkwardness I felt with them last meeting was gone, and I hope that when we begin writing the technical report, I hope that my awkwardness with them would be gone, too.

This meeting made me realize how demanding physics research is. It was very tedious to repeat the same steps over and over again, therefore experimentation could be regarded as a test of endurance- it shows how dedicated one is as a scientist.