Yuchan Make-Up Lab for Lab 2_ Paper Drop - Notebook

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University Of Chicago *

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131000

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Apr 3, 2024

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Make-up Lab: Paper Drop Autumn 2023 Student Name: Yuchan Ahn Date: 20th Oct, 2023 Course: 13100/2 Lab Section / TA Name: 2L05 / Joseph Noonan A reminder : when completing your lab notebook, it’s preferable to answer in short sentences and bullet points rather than long paragraphs, and to use color to separate your answers from the question text. You don’t need to use full sentences or any formal format… this record is for you , and the TA is just looking for it to be complete. For example… -Is this a question? Yes -How about this! No -- questions end in a question mark. That’s an exclamatory statement. A note on symbols and equations : Inserting symbols and equations into your notebook is possible, but not always quick and easy (especially if you’ve never had to do it before). We don’t want you to spend a lot of time figuring out formatting when you could be spending that time on physics. So consider the following shortcuts as you fill out your notebook. -You can insert an equation by selecting “Insert: Equation” from the menu bar -If you can’t find a symbol in the “Insert: Special Characters” menu, then spell then spell the symbol out (for example... pi, delta_x, B_exp, +/-) -If you need to do a long block of math, it may be quicker to write it out on a piece of paper and take a picture. Department of Physics, University of Chicago
Part 1 Paper drop observations Summarize the observations you make as well as the procedure you chose. Include photos, drawings, and/or sentences to describe your setup and what you see. Height of release point was measured using a meter stick. To make sure there’s no initial lateral velocity, I held the paper upright on my finger and waited for it to be stable. The location of the point on the floor directly below the release point was determined as the bottom of the meter stick which was used to measure the 60cm height on the wall. Department of Physics, University of Chicago
The location of the point on the floor directly below the release point was marked with a thin piece of post-it and the lateral displacement of the paper was determined by measuring the distance from center of the paper to the post-it. Record your data. What format should it take? Trial Lateral Displacement (cm) 1 9.0 2 7.0 3 17.5 4 16.8 5 19.8 6 10.0 7 20.4 8 0.0 9 20.3 10 13.5 Trial Lateral Displacement (cm) 11 14.4 12 13.0 13 24.0 14 21.5 15 11.3 16 7.2 17 10.1 18 16.9 19 9.2 20 14.0 Department of Physics, University of Chicago
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Paper drop analysis What was the mean displacement of your slips of paper? (The standard deviation? The standard deviation of the mean?) Are there any outliers that might have affected your results? ● Mean displacement cm = 13. 80 ± 0. 05 Since the only source of uncertainty comes from the uncertainty of measurement in lateral displacement which was made using the ruler, I take half of the smallest tick mark of my ruler to be the uncertainty of my values (=0.05 cm). ● Standard deviation cm = 5. 97 ● Standard deviation of the mean cm = 1. 34 There were no outliers (values further than 3 standard deviations away from the mean). A possible source of systematic uncertainty in my measurements is the uncertainty associated with my ruler. Since it is a flexible ruler and is very worn out, measurements taken by the ruler come with inherent uncertainty due to the inaccurate ruler. Comparison with others How does your result compare with your two imaginary lab parters? Agreement: ● Angela ( cm) and Me ( cm): 𝑑𝐴 = 20. 7 ± 1. 2 𝑑𝑌 = 13. 80 ± 0. 05 Department of Physics, University of Chicago
○ |t’|=5.74 ○ Angela and my results disagree ● Mario ( cm) and Me( cm): 𝑑𝑀 = 15 ± 4 𝑑𝑌 = 13. 80 ± 0. 05 ○ |t’|=0.30 ○ Mario and my results agree ● Angela and Mario ○ |t’|=1.35 ○ Mario and Angela’s results are inconclusive Part 2 Continuing the experiment As you collect data for Part 2, record your process and your results here. For the same reasoning in part 1, all of the lateral displacement values below are determined to have an uncertainty of half the smallest tick mark of my ruler, 0.05 cm. 75cm Trial Lateral Displacement (cm) 1 18.0 2 9.8 3 12.1 4 2.9 5 25.0 Avg 13.56 70cm Trial Lateral Displacement (cm) 1 22.4 2 7.2 3 9.5 4 18.4 5 3.5 Avg 12.2 Department of Physics, University of Chicago
65cm Trial Lateral Displacement (cm) 1 3.6 2 1.0 3 17.4 4 11.0 5 3.2 Avg 7.24 60cm Trial Lateral Displacement (cm) 1 9.8 2 3.0 3 8.1 4 6.8 5 20.2 Avg 9.58 55cm Trial Lateral Displacement (cm) 1 17.3 2 4.9 3 20.9 4 14.8 5 8.5 Avg 13.28 50cm Trial Lateral Displacement (cm) 1 21.3 2 18.1 3 20.8 4 13.3 5 16.5 Avg 18.0 Department of Physics, University of Chicago
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45cm Trial Lateral Displacement (cm) 1 7.0 2 10.0 3 10.8 4 13.9 5 7.6 Avg 9.86 Plot below is the mean lateral displacement plotted against respective drop heights. Department of Physics, University of Chicago
Linear (blue) and square root (red) model fitted onto the data points. Plot below is constrained such that there is zero displacement at zero height. Plot below does not have the constraint of zero displacement at zero height. Either of the second plot (one without zero displacement at zero height constraint) models my data best. While collecting the data, I realized that there was an inverse relationship between the drop height and the respective lateral displacement (i.e. higher the drop height, smaller the lateral displacement). The constraint of zero displacement and zero height in the first model Department of Physics, University of Chicago
forces the model to show a direct relationship between the drop height and lateral displacement. Without the displacement, the model is able to show that the relationship between the variable and collected value is inverse which is more compliant with what I observed. However, the second model does suggest that near 0 drop height, the lateral displacement will be greatest which seems counterintuitive. Despite the counterintuitive suggestion of the second model, it best presents what I observed in the experiment and it best shows the relationship of the variables and values. Department of Physics, University of Chicago
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