Lab 6 Atwood's machine

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Florida International University *

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2048L

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Physics

Date

Dec 6, 2023

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pdf

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5

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Lab #6 Lab partner-2: Alexia Reyes ID: 6313144 Lab partner-3: Anna Schieferdecker ID: 6304351 Title: Atwood’s Machine Preliminary Question Answers: 1) If two objects of equal mass are suspended from either end of a string passing over an alight pulley, there would be no motion because there be a force of gravity strong enough on one weight to overcome the friction in order to move. T T 2) 3) The two masses have the same magnitude acceleration because in an Atwood’s machine, the two masses are connected via string which passes over the pulley. The tension from the string exhibits equal and opposite forces that act on each mass. This is supported by Newton’s Second law, which states that when all forces and masses are equal, the acceleration will also be equal. This is represented as F=ma. 4) Analysis: 1) Look at table for part 1
2) Look at table for part 2 3) The graph shows a positive slope, as mass difference increases the acceleration also increases. 4) The graph has a positive slope with the x-axis as 1/m T , so as total mass decreases the acceleration increases and vice versa. 5) Our results are consistent with the theoretical expression given. The theoretical expression is a=( )g. With mass (𝑚1 − 𝑚2)/(𝑚1 + 𝑚2) difference in the numerator there is a directly proportional relationship with acceleration which means as mass difference increases the acceleration increases and vice versa. With total mass in the denominator there is an inversely proportional relationship with acceleration which means that as total mass increases the acceleration decreases and vice versa. 6) The slope of the Part 1 graph is 0.0232. Using the equation “gravity = slope (total mass),” gravity can be calculated to be 9.28 m/s^2 according to the Part 1 data. This value has a 5.40% difference from the actual value of around 9.81 m/s^2. Using the data from Part 2, gravity can be calculated using “gravity = slope / change in mass,” resulting in a value of 8.36 m/s^2. This value has a 14.8% difference from the actual value. While the value from Part 1 is very similar to the actual value with an under 10% difference, the value from Part 2 is less similar. In both cases, the discrepancy can be attributed to similar factors. The small amount of data points result in less accuracy, since small outliers can have a large impact on the slope of the graph. Additionally, factors like friction, air resistance, and the gravitational variances dependent on location can make the data different from the ideal or standard values. The pulley could have also been slightly uneven, throwing off the data because the weights weren’t equally balanced. Data Tables: 1. Part I Constant Total Mass Trial M1 (g) M2 (g) Mt, m1+m2 (g) Acceleration (m/s^2) mdiff , m1-m2 (g) 1 200 200 400 0 0 2 210 190 400 0.4196 20 3 220 180 400 0.8969 40
4 230 170 400 1.368 60 5 240 160 400 1.850 80 Part II Constant Mass Difference Trial M1 (g) M2 (g) MT, m1-m2 (g) Acceleration (m/s^2) MT, m1+m2 (g) 1/mT (g^-1) 1 160 150 10 0.2525 310 3.23x10^-3 2 170 160 10 0.2264 330 3.03x10^-3 3 180 170 10 0.2170 350 2.86x10^-3 4 190 180 10 0.2053 370 2.70x10^-3 5 200 190 10 0.1938 390 2.56x10^-3 Graphs: Part I Constant Total Mass
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