Standing Waves Results

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School

George Mason University *

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Course

246

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

docx

Pages

4

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RESULTS Group Lab Report * Title of Experiment: Standing Waves Date: 1/24/2024 Class, Section & Lab group: Phys 246 - 2D2 group 4 Recorder (consolidates report and submits into dropbox): Group Members PRESENT: Lily Vega, Khadijat Shodeinde, Mariam Sabah * Before beginning, save this report on your desktop with the Recorder's last name appended. Tables: Table 1: Table comparing the number of antinodes to their respective frequency Table 2: Table which includes the mass on the pulley, the number of antinodes, force, and tension of a string.
Graphs: Graph 1: Antinodes (n) vs. Resonance Frequency (Hz) with trendline included. Graph 2: Antinodes vs. Tension with trendline included. Analysis Questions: 1. Create graphs of the antinode vs. frequency and antinode vs. tension in Excel. 2. Using the trendline feature in Excel, choose the appropriate fit for the two plots and fit your group’s data. Make sure the fit equations show on the two graphs. 3. Predict the value of the constant. = (2 /mg ) for frequency = 0.2482 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐿∗ 𝜇
4. Now, for all linear data – compare the slope value from Excel to the constant value shown in the theory section. How does your data compare to the predicted constant value calculated? Discuss. The slope for the frequency vs. antinodes graph is 0.0876. The calculated constant value for frequency came to be 0.2482. The calculated value is significantly greater than the constant value retrieved from the graph made with the excel data. This could be because the frequencies given in the data set are not 100% linear, resulting in a skew of the constant value. 5. If the data is not linear – compare the calculated constant value for the proper equation shown on page 5 to the fit constant from the Excel trendline feature. How does your data compare to the predicted constant value calculated? Discuss. 6. The value of µ is only known to 2.5% precision. Is this uncertainty sufficient to state that your Excel fit constants equal the calculated constant value for these experiments? Explain. It is important to understand the accepted uncertainty in the environment of this experiment. The value collected from the Excel data is not within a close range of the calculated constant value. The slight variation in the density of the string most likely had no effect on the constant value that was determined from the Excel graph. 7. Discuss in your group the impact of the pulley friction. How does your group predict this friction, if present, would impact data results? Explain reasoning. The pulley friction can impact results in a number of ways. If the pulley has a large amount of friction then it can reduce the tension of the string. The gravitational force acting on the object may be underestimated due to this. Additionally, friction may cause the pulley to rotate in a slower motion, which would affect the results obtained by timing the motion of the object. In order to minimize the impact of the friction on the data results, it is vital to use a pulley with low friction. It is also important to measure the speed of the object as accurately as possible. The impact of the friction can be predicted by considering the coefficient of the friction between the pulley and the string and the force that acts on the pulley. The lower the coefficient, the more likely it is to have a lower friction force. The type of pulley, materials and conditions in which the experiment is conducted must also be considered when making the prediction. 8. Discuss the stretchy string – if the µ changes during the experiment with changing masses would its value tend to increase or decrease? Explain.
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If the coefficient of the friction changes during the experiment with changing masses, it would impact the accuracy of the data. The increase in the coefficient would increase the force needed to keep the string moving. The string should have consistent properties such as the force of the action, or the value of the coefficient. The elasticity of the string can affect the accuracy of the measurement in a pulley system, so it is important to maintain constant properties throughout the procedure. The change in coefficient can be measured in order to properly analyze the data. Summary/Conclusion: An experiment was performed where a string was attached to a pulley system with different weights attached. The frequencies and tension values were recorded and analyzed against their specific antinode values. Based on the analysis performed, the constant value retrieved from the slope of the graph created came out to be 0.0876. This is lower than the calculated expected constant value of 0.2482. This is potentially due to the inconsistency of the force generated on the pulley. The force may skew the values, leading them to not be proportional. Another possible effect would be the elasticity of the string used. If the elasticity is not consistent in all trials, then this would potentially change the value of the constant.