Lab report 5

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Wilfrid Laurier University *

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Mechanical Engineering

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Jan 9, 2024

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Lab 5: Torque and the Principle of Moments Conducted: November 16, 2023 Submitted: November 23, 2023 Lab Coordinator: Hasan Shodiev Brandon Silva 169041212 Lab Partner: Aidian L10 2:30-4:20 Understanding variables of torque Purpose The purpose of this experiment was to observe and analyze how differences in weight, angle, position, and distance can affect the torque of an object (the force that causes an object to rotate about its axis). During this experiment, two different meter sticks were used: a uniform metre stick and an ununiform meter stick with holes through half of the stick. This demonstrated how constant and unconstant weights throughout a system can significantly affect torque. Results Table 1: Testing the Principle of Moments Quantity Symbol Value Uncertainty Units Position of metre stick’s center of mass rs 49.80 ± 0.1 cm Total mass a ma 36.11 ± 0.01 g Total mass b mb 69.80 ± 0.01 g Distance reading at mass a ra 19.70 ± 0.01 cm Distance reading at mass b rb 66.50 ± 0.02 cm

Distance a a 30.10 ± 0.02 cm Distance b b 16.70 ± 0.02 cm Torque counterclockwise (ccw) tau(ccw) -0.109 ± 0.001 J Torque clockwise (cw) tau(cw) 0.117 ± 0.001 J The clockwise and counterclockwise torques Sample calculation 1: Torque counterclockwise calculation: m a a = torque counterclockwise CONVERT G TO KG AND CM TO METRES 0.3611(0.301) = tau(ccw) tau(ccw) = 0.1086911J → -0.109J (ccw direction creates a negative number) Sample Calculation 2: Torque clockwise calculation: m b b = TorqueClockwise CONVERT G TO KG AND CM TO METRES 0.698(0.167) = tau(cw) tau(cw) = 0.116566J → 0.117J Table 2: Mass Determination from a Single Equilibrium Setup Quantity Symbol Value Uncertainty Units Zero error of digital scale z 0 ± 0.00 g Total mass a ma 222.90 ± 0.02 g Total mass of system M 395.00 ± 0.02 g Metre stick mass (calculation) m 172.10 ± 0.02 g Metre stick mass (measured using digital scale) m(th) 153.65 ± 0.02 g

The measured and calculated values agree or don't agree Sample calculation 3: Metre stick mass calculation: Total mass of system - Total mass a = Metre stick mass 395.00g - 222.90g = 172.10g Table 3: Centre of mass distance for the Non-Uniform Metre Stick Quantity Symbol Value Uncertainty Units Zero error of digital scale z 0.00 ± 0.00 g Total mass a ma 222.900 ± 0.001 g Distance reading at mass a ra 18.00 ± 0.01 cm Position of metre stick’s center of mass rb 36.86 ± 0.01 cm Distance at suspension point rs 30.00 ± 0.01 cm Distance a a 12.00 ± 0.01 cm Distance b b 6.86 ± 0.01 cm The measured and calculated values agree or don't agree Sample calculation 4: calculating distance b: maA = mb 222.90(12) = (390)b 2674.8 / 390 = (390)b / 390 6.85846 = b → 6.86cm = b Sample calculation 5: calculating the mass of the system: m = (a/b)ma m = (12/6.86)222.90

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m = 389.91cm Sample calculation 6: calculating the position of the metre stick’s center of mass: rb = rs + b rb = 30 + 6.86 rb = 36.86cm Discussion The torque counter clockwise was relatively similar to the torque clockwise, which can infer that the system was close to being perfectly balanced, however since the values were not equal, the system was not one-hundred percent balanced. Therefore, it can be inferred that the system did not completely obey the principle of moments. Also, the calculated mass of the metre stick (m) and the analytical balance weight of the mass of the metre stick (m(th)) were not identical, meaning, they did not agree with each other. This could mean that the systems weight changed, which could have skewed the data. This could have been caused by and experimental error of incorrect weighing from the analytical balance, or a human error of misimput of imformation (highly unlikely). Lastly, the measured position of the centre mass was found to be 36.86cm, which does agree with the value calculated in table 3. Conclusion In conclusion, this experiment was a success due to the fact the original goal for this experiment was achieved. Overall the concluding findings were, the counterclockwise and clockwise torques (tau ccw and tau cw) were -0.109 (tau ccw) and 0.117 (tau cw). The measured and calculated values of the metre sticks masses did not agree, the calculated m was 172.10g and the measured m(th) was 153.65g. Lastly, rb was found to be 36.86cm, distance b was 6.86cm, and the total mass of the non-uniform metre stick was 222.90g. Overall, this experiment was ran pretty thoroughly but still could have been conducted better with the use of move professional equipment. Overall this experiment was able to evaluate

how torque is dependent on the weight of objects and the equilibrium of systems. Data Sheets

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