Louis Thomas Detoro Lab 5_ Uniform Circular Motion

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Arizona State University *

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122

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Mechanical Engineering

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Apr 3, 2024

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Title of the Experiment: Uniform Circular Motion Student’s name: Louis Thomas Detoro Section SLN: PHY 122 - 14231 TA’s Name: Ayush Kumar Singh, Yash Patil Week of the experiment: 5 1

Objectives: The objective of this lab is to investigate how friction behaves in circular motion, while also examining the relationship between mass, velocity, radius, and centripetal force. Experimental Data: (Figure 1. Force vs Mass Graph of 4 points) Part 1a. Force vs Mass Radius = 10.1 cm = 0.101 m Speed = 0.321 m/s From Graph of F vs. m : Slope ± slope = 1.015 2

(Figure 2. Force vs Velocity Squared graph of 9 Points) Part 1b . Force vs velocity Radius = 10.1 cm = 0.101 m Mass (kg) = 180.40 g = 0.18040 kg From Graph of F vs. v 2 : Slope ± slope = 0.881 3

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(Figure 3. Force vs 1/Radius Graph of 5 points) Part 1c: Force vs Radius Cylinder Mass = 180.40 g = 0.18040 kg Speed = 0.188 m/s From Graph of F vs. 1/r: Slope ± slope = 0.007 Data Analysis : Part 1a. Calculate the theoretical value of the ratio v 2 /r using equation (1) from the lab manual. What is the experimental value of the ratio v 2 /r based on your graph from part a? Calculate the percent error between the theoretical value and your experimental value for the ratio v 2 /r. Experimental Value = 1.015 m/s 2 4

Theoretical value = v 2 /r v = 0.321 m/s r = 0.101 m Theoretical value = (0.321)^2 / 0.101 = 1.020 m/s 2 Percent Error = |Experimental Value - Theoretical Value| / Theoretical Value * 100 Percent Error = |1.015 - 1.02| / 1.02 * 100 = 0.49 % Part 1b. Calculate the theoretical value of the ratio m/r using equation (1) from the lab manual. What is the experimental value of the ratio m/r based on your graph from part a? Calculate the percent error between the theoretical value and your experimental value for the ratio m/r. Experimental Value = 0.881 m/s 2 Theoretical value = m/r m = 0.18040 kg r = 0.101 m Theoretical value = (0.18040 kg) / 0.101 m = 1.786 m/s 2 Percent Error = |Experimental Value - Theoretical Value| / Theoretical Value * 100 Percent Error = |0.881 - 1.786| / 1.786* 100 = 50.7 % Part 1c. Calculate the theoretical value of the product mv 2 using equation (1) from the lab manual. What is the experimental value of the product mv 2 based on your graph from part a? Calculate the percent error between the theoretical value and your experimental value for the product mv 2 . Experimental Value = 0.007 m/s 2 Theoretical value = mv 2 m = 0.18040 kg v = 0.321 m/s Theoretical value = 0.18040 kg * (0.321m/s) 2 = 0.019 m/s 2 5

Percent Error = |Experimental Value - Theoretical Value| / Theoretical Value * 100 Percent Error = |0.007 - 0.019| / 0.019* 100 = 63.2 % Results Part 1. Experimental ( units ) Theoretical ( units ) Discrepancy (%) v 2 /r 1.015 m/s 2 1.020 m/s 2 0.49 % m/r 0.881 m/s 2 1.786 m/s 2 50.7 % mv 2 0.007 m/s 2 0.019 m/s 2 63.2 % Discussion and Conclusion: The objective of this lab is to investigate how friction behaves in circular motion, while also examining the relationship between mass, velocity, radius, and centripetal force. Through the data collected it is possible to see the relationship between them. By looking at the data collected for the first part of this experiment, it can be concluded that mass and force have a linear relationship. This was possible due to the fact that during this part of the experiment mass and force were isolated. This same technique is used to show the relationship between force and velocity squared, and force and 1/radius. For part 1a, the data collected was used to show the relationship between mass and force. Through the data and graph, it shows that the relationship between force and mass is linear. Using this data the discrepancy between the experimental and theoretical values was found to be 0.49 % which proves that the data given and used to calculate this relationship can be considered accurate. For part 1b, the relationship between Force and Velocity squared were found with the given data. For this part of the experiment, mass and radius were kept constant in order to isolate force and velocity. By using the data given, the experimental and theoretical values were found and then used to calculate the discrepancy of the data which came out to be 50.7 %. From the discrepancy percentage it can be determined that the results of part 1b are deemed to be not accurate as the discrepancy of the data is over 50%. For part 1c, the relationship between force and radius were found with the provided data. During this part of the experiment, mass and velocity were held constant in order to isolate radius and force. From this part of the experiment it was calculated that the discrepancy percentage is 63.2 %. From that result it can be determined that the data is not accurate as the discrepancy between the data is very large. 6

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In conclusion the objectives of this lab were not met due to the gap in discrepancy between the data in part 1b and 1c. If the discrepancy between the data were smaller, the data and experiment as a whole could be deemed as successful in meeting the objectives of the lab. 7