Lab Partners: Kevin Tran, Jose Rodriguez
Date lab was performed: 27-Feb-2017
Purpose: The purpose of the experiment is to develop a mathematical model of the relationship between period and added mass by measuring and collecting data of the period of oscillations for different known masses. The mathematical model will then be used determine unknown masses of several objects.
Theory/ Introduction: In order to develop a mathematical model of the relationship between period and added mass, we assumed that the period is related to mass by a power-law equation.
For mass of the tray, we needed to plug in a range of numbers until we got a straight - line plot. We plugged in numbers for mass of the tray until the correlation coefficient is at 0.9998. The reason why the correlation coefficient must be very high is because a high correlation coefficient represents a very strong relationship between period and mass. We wanted a very strong relationship between period and mass in order to accurately measure unknown masses of several objects later on in the experiment. If we successfully measured the correct mass of our objects with unknown masses, that meant that the mathematical model we developed was accurate.
When we plugged in a range of values for mass of the tray, there were several values that give a straight line plot with correlation coefficient value of 0.9998. Since different values of mass of tray gave different values of A and n, we recorded the minimum, middle, and maximum value of mass of the tray that gave the correlation coefficient value of 0.9998. The reason why we recorded several values of the mass of the tray is that it actually gives us the range of masses for the objects with unknown masses since there is some uncertainty in our mathematical model for the relationship between mass and period.
A Summary of apparatus/ experimental procedure: First we prepared the equipment necessary for this experiment. We set up the lab using a C-clamp, inertial balance, masking tape, photo gate, and Logger Pro application. The C-clamp is used to hold down the inertial balance on the tabletop. The masking tape was folded taco-shaped and placed on the end of the balance and set up the photo gate so that the tape passes through the beam of the photo gate. The masking tape was folded taco-shaped so that the photo gate can accurately record the oscillations of the balance.
The photo gate was used to keep track of the period of the balance by keeping track of the tape as it passes through it. After we set up the lab, we placed known masses in increasing increments of 100 grams and ran the Logger Pro program and got several corresponding values for T.
We stopped placing masses after recording the period for 800 grams. After finding the values for T, we plugged in the values recorded in order to create a straight line plot. We then estimated the mass of the tray by plugging in values until we got a straight line plot and minimum, middle, and maximum values of the mass of the tray that gives the correlation coefficient value of 0.9998.
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| Although the values are not clear in this picture, the correlation value reads 0.9998 |
This picture gives an example of the value of the mass of the tray that yields a correlation value of 0.9998. After we found the minimum, middle, and maximum values for the mass of the tray, we were able to use the equation "T=A("mass added" + "Mass of tray")^n" to solve for the unknown mass of an object.
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| In this picture, we found the mass of the phone by finding the period of its oscillations and solving for "mass added." We then placed the phone and wallet (no picture available) on the tray to find its unknown mass. After solving for the unknown mass, we weighed the phone and wallet individually on an electronic balance to find its true mass and compared it to our values to see if our mathematical model is accurate. Lists/ Tables of measured data: 
List/ Table of Calculated results/ graphs of data:
  
Explanation of graph/Analysis:
 
We graphed the values of period measured on excel to get this straight line plot. The students made this graph in order to get the value of n, which is the slope of this line. Students can also get the value of "A", which is the y-intercept of this line. Although this picture is unclear, the white box in the highlighted portion of the graph gives the value of slope and y-intercept. The "theory/introduction" portion explains what the students have to do in order to derive useful information from this graph.
Conclusion:
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For the purpose you are trying to come up with a mathematical model for the relationship between mass and period for an inertial balance. You might consider putting a picture of it (maybe your third one in the blog) up near the top so that a 4A student reader would know what apparatus you were talking about.
ReplyDeleteYour description of the mathematical approach could be more complete. You might try telling the story this way:
--Power law equation
--ln form
--what will be plotted on the y axis and on the x-axis
--what the slope and y-intercept of that graph will tell you
--how you are going to find the mass of the tray
Instead of saying "Students will weigh" you can say "We weighed", partly because it was YOU and not some generic student doing the lab, and partly because lab blogs describe what you actually did (past tense) and not what someone will do in the future.
The photogate is used to measure the period as the tape passes back and forth through it.
Not clear in your blog why a high correlation value is important.
The lab handout had a suggested format for showing your results.
I don't think you positioned the wallet "incorrectly". The masses you used to make your model were cylinders centered on the tray. The "unknown" objects that you tested were different shapes. We didn't test to see if the same mass placed differently or with a different shape gave us different results.
A lot of the elements of a good lab blog are here. What I'm not getting is the sense of reason for each step.