Lab 1: Finding a Relationship Between Mass and Period for an Inertial Balance
Chris Ceron and Amy Chung
The purpose of this experiment was to find a relationship between mass and period using an inertial balance that is used to measure the inertial mass. We used this instrument to find the relationship without depending on gravity. Our inertial balance was composed of a tray that is attached to two springy pieces of metal. We began our lab by being provided a power-law formula:
We used our inertial balance by oscillating the tray in between a device called Photogate that measures the period of oscillation. Once we confirmed that the data Logger Pro was receiving was reasonable, we added weights to the balance to record the different periods of oscillation based on the amount of weight that was oscillating.
We collected nine different weights and oscillation periods to ensure an accurate relationship between the mass and oscillation period. We then set up a table that would establish a correlation between the natural log of the Period with the natural log of the sum of mass between the tray and any additional weights. The purpose of this table was to find our unknown variables and to be able to use the Power-Law formula.
Once the table was set, we plugged in all the data we collected and provided an educated guess of the mass of the tray. We continued to provide educated guesses until the correlation coefficient between the period and sum of the masses is very close to 1. Once we found a weight that was 0.9998, we tested the maximum and minimum masses that the tray could equal so the correlation would stay at 0.9998. Maintaining this correlation was crucial to using the most accurate relationship between the mass and period of oscillation.
We found that our tray was between 290 grams and 340 grams, and used 315 grams as a midpoint for additional data:
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| Lowest mass - 290g |
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| Highest mass - 340g |
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| Midpoint of lowest and highest mass - 315g |
We used Logger Pro to evaluate the missing variables A and N of the given formula by using the slope and the y-intersection that was calculated from our inputted data. From there, we were able to use the Power-Law formula to find the mass added onto the tray.
We found that our calculations were accurate by using a scale to find the mass of the unknown object.
This is mostly complete.
ReplyDeleteIn no particular order, some things that would make things more clear, for future blogs (or this one):
Put the picture of the inertial balance first, so the reader knows what the device is right when you first mention it. The device is a mystery until a little bit into the blog.
Go into more detail about the whole taking the natural log so that the equation looks like that of a straight line, and what will be on the x and y axes and why; that the goal was to get the best straight line and so you adjusted the value of Mtray until the correlation coefficient was as high as possible (you wrote "once we found a weight that was 0.9998", which is not really clear what that means); that since a variety of masses gave this same highest correlation, you actually have a range of values for Mtray and thus for A and n.
It would be clearest to show, in addition to your calculations (well done) a table of your results, showing clearly that your mathematical model gives results that do or do not match what you get from the electronic balance.
Discuss sources of uncertainty in your results. Just because things are in range does not mean that there is no uncertainty. This is a big deal in labs. It means that you understood the assumptions and idealizations that you made and what factors that you decided to ignore. (For instance, in a free fall lab we usually ignore air resistance. Sometimes that is a safe assumption and sometimes not.)
The photogate gave timing results to four or five significant figures. You only report two or three.
The lab explicitly asked you to used a stopwatch to measure and record the time for some number of oscillations to verify that the photogate was timing correctly. You say you did it, but I don't see that data here.