Lab 3 Espenell V01039829
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School
University of Victoria *
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Course
PHYS-110
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
Pages
5
Uploaded by BaronEagle3666
Project 3 Worksheet
1.
Include a photo of your raw work, including your TA’s signature. Failure to include this data will result in a grade of zero for the entire lab report. 2.
Create a table for your data and angles, as described in the Analysis & Submission section of the lab manual. (Don’t forget to convert units, especially for the final column.) Section ij R
i
(± 0.073 cm) ∆R
ij (± 0.073 cm) θ
ij
(± 0.017 rad) a
ij
(m/s
2
) 1-2 8.6 2.8 0.33 0.92 2-3 8.8 2.7 0.3 0.81 3-4 8.9 2.7 0.3 0.81 4-5 9 2.7 0.31 0.84 5-6 8.9 2.7 0.3 0.81 6-7 8.7 2.9 0.31 0.9 7-8 8.3 3 0.33 0.99
8-9 8.1 3 0.35 1.1 9-10 8.9 2.9 0.37 1.1 10-11 8.1 2.8 0.33 0.92 11-12 8.3 2.7 0.31 0.84 12-13 8.6 2.9 0.31 0.9 13-14 8.9 2.6 0.3 0.78 14-15 9 2.7 0.31 0.84 15-16 9 2.6 0.28 0.73 16-17 8.9 2.5 0.28 0.7 17-18 9 2.6 0.3 0.78 18-19 8.8 2.7 0.33 0.89 19-1 8.7 5.6 0.66 3.
Show your calculation for the average radius and its uncertainty, as well as θtot and T . 4.
Calculate the centripetal acceleration using Ravg, θtot and T for the whole path of the arc angle, along with its uncertainty.
5.
Calculate the mean centripetal acceleration from your table, along with its uncertainty, for the discretization data. 6.
Calculate the gravitational acceleration and its uncertainty from your two values of centripetal acceleration.
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7.
Perform a statistical comparison between the g values determined via the two methods, and then comparing each of these to the accepted value of g separately. (Note: If the statistical tests do not agree, ideally an experimenter would try to figure out why they did not agree. This is the proper process for performing a test with an expected result.)
8. Respond to the following questions/instructions using complete sentences: (a) Identify as many assumptions that you can that were used in this lab activity design. This could include assumptions about physical effects that can be neglected, assumptions about validity of approximations, or anything else. In this lab activity, we assumed that the path of the pendulum moved in a perfect circular motion and that the circular motion was uniform, or at a constant velocity. We also assumed that we started and stopped the spark timer right when the pendulum crossed our initial point, which could be inaccurate because it’s common to produce error in an experiment that depends on “eyeballing” any measurements. (b) Which method for determining g was more precise? Justify your answer. Method 1, taking the average acceleration over the whole path and using that value to find g, was the more precise of the two methods because the uncertainty of a
avg
, which was 0.019 m/s
2
, was slightly smaller than the uncertainty of a
ij
,
,
which was 0.020 m/s
2
. (c) Which method for determining g was more accurate? Justify your answer. Method 1, taking the average acceleration over the whole path and using that value to find g, was the more accurate of the two methods because the value of g that I calculated (before rounding), 13.8 m/s
2
, was slightly smaller than the value of g taken from the discretization data, which was 14.3 m/s
2
, and therefore closer to the true value of g, which is 9.8092 m/s
2
. (d) Which is the superior method for determining g - the single calculation of the total motion of the pendulum or the combination of calculations from discretization? Justify your answer. Based on the data from our experiment, the single calculation of the total motion of the pendulum is the superior method for determining g since it gave the more precise and more accurate results of the two methods. (e) What could you do to improve (decrease) the uncertainty in this experiment? To improve the uncertainty in this experiment, we could do a few trials with multiple sheets of paper with circles of the same radius, and calculate the mean acceleration and g value between those trials to get more precise calculations, or we could more precisely measure the length of the string by using a more precise measuring tool than a metre stick, which would decrease the uncertainty for L and therefore for g. Using a more precise measuring device to measure the radii of the circle would also result in less uncertainty for the R values, which would create a more accurate g value as well.