Partners: Matthew Ibarra, Billy Justin
Date of Lab: 12 October 2016
Lab 13 Magnetic Potential Energy
Mission Statement:To demonstrate how simple harmonic motion and oscillations work.
Theory: Every
kind of calculation is in truth an approximation, and the tolerance of
uncertainty depends on the application the calculation will be for. When
multiple calculations are involved, then the uncertainty ripples, or
propagates, through to the final result. Learning the method by which
this kind of propagated uncertainty is determined is the essence of this
lab.
Experimental Procedure:
We were first given a single spring with a certain k and tasked with identifying said k. We concluded
that we should use the effective mass of 115 grams ( 1/3 mass of spring [13.8 g] + mass
of hook [3.7 g] + hanging mass [107 g]) to aid in this calculation of k before comparing with the results of other groups.
The methodology of our calculation went as follows: in order to obtain the k constant, we first found the displacement without the hanging mass and then displacement with the hanging mass. Since k = W/x we used the delta in weight / delta of displacement from absent hanging mass to present hanging mass, shown below.
next we required the oscillation time for our spring. To this end,
we counted the time for our spring to oscillate 10 times after being displaced 2
cm, conducting 5 trials and taking the average time, shown below.
Dividing our average oscillation time by the number of oscillations, we determined our period of oscillation to be 0.550 seconds.
With our contribution completed, we collected the data amassed by the other groups, shown below.
With this data now in hand, we proceeded to plot our collective k vs T graph, making sure to employ the power fit option so as to make sure our period took the desired form of 1/k^1/2, shown below to be the B value.
Following this exercise, we continued on to the second part of the lab where we varied the effective mass and found the accompanying
period. After inputting the pertinent data, we made the graph of mass vs period to see if the period is indeed
m^1/2 as expected. To measure the period of oscillation, we used the same method as for the previous part.
our effective mass variation is noticeably small, possibly affecting our graph, shown below.
This time, we got the b value to be 0.7323, which is not quite the value we are looking for, which is 0.5, resulting in a percent error of 46.46%.
Conclusion:
The predominate source of error in our opinion is most likely attributable to other groups, for we feel very confident in our own procedure and results. Furthermore, besides human error, other error could be from the mass variation not being big enough.
Despite not getting the value we are hoping for, we still developed a model nonetheless, and understand the relationship between period , k and mass.
Experimental Procedure:
The methodology of our calculation went as follows: in order to obtain the k constant, we first found the displacement without the hanging mass and then displacement with the hanging mass. Since k = W/x we used the delta in weight / delta of displacement from absent hanging mass to present hanging mass, shown below.
With our contribution completed, we collected the data amassed by the other groups, shown below.
Conclusion:
The predominate source of error in our opinion is most likely attributable to other groups, for we feel very confident in our own procedure and results. Furthermore, besides human error, other error could be from the mass variation not being big enough.
Despite not getting the value we are hoping for, we still developed a model nonetheless, and understand the relationship between period , k and mass.
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