Measurement and Error Analysis Lab

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1420

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Physics

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Apr 3, 2024

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Physics 1420 Section A1 Measurement and Error Analysis Lab Avinash Subramanian Micheal Flaherty Date Performed: 2/6/23 TA: Hao Zhu

Abstract: The purpose of this lab was to practice good measurement techniques and be able to calculate different uncertainties of quantities. This experiment used many tools but most notably the experiment had used a photogate head and connector as well as a GLX Xplorer Tool to measure the relationship between T and L. The results described a fairly accurate analysis with a standard error of 0.01 of the diameter of Bob and a 0.05 standard error with the top of the Bob to a fixed point. The result had ended up with a percent error in gm of 0.51% which is fairly low as well as calculating a gm value of 9.86. The slope ended up being 0.04 which is a positive correlation between T^2 and L. This shows that as the Pendulum Length had increased the Period Squared or the time would increase which is what the experimenters had expected to happen. Data Sheets: Within Lab Pages Questions: 1. When you measure the period of the pendulum there is some uncertainty in the measured results. Why is it useful to measure more than one period? It is useful to measure more than one period for the experiment as it will be more likely to be accurate through being able to take the average of several trials instead of just having one period on the Xplorer GLX. Taking only single period samples would be affected greatly by circumstances like the accuracy and precision of the Xplorer GLX tool. Taking measurements of more periods would allow for an experimenter to be able to take these measurements and prove that they are more reproducible and also likely make more precise and accurate measurements because of it. 2. What are the two most significant reasons for a difference between your measured acceleration and the accepted value? How do these reasons impact your results? One significant reason for a difference between the measured acceleration and the accepted value of 9.8m/s^2 was due to how the pendulum stand would not directly hold the string and our measurements had a very small angle put on the string. This could cause the measurements to be slightly skewed as the slippage would add centimeters of the pendulum that was not measured. Another significant reason for how the difference would be is the disparities in the angle of release with each trial with a different pendulum length. A large angle would result in a larger average time and a smaller angle would result in a smaller time respectively. This would affect the slope of the data as it could bring another confounding variable into our consideration for measurement. Sample Calculations: Percent Error: % error

Percent Error=|MeasuredValue−AcceptedValueAcceptedValue|∗ 100=| 9.86m/s2−9.81m/s /9.81m/s2|∗100=0.51 Slope: best fit lineΔ yΔ x=y2−y1x2−x1Δ yΔ x=(3.550 m-2.002m)/(90.53 s2-51.65 s2)/=0.04 s2/m Acceleration due to gravity= (4π2)/kg=(4π2)/4.0 s2/m=9.86 m/s2

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