young's modulus lab

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Wilfrid Laurier University *

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142

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Mechanical Engineering

Date

Dec 6, 2023

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pdf

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5

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Determining Young’s Modulus of Elasticity of a Wire Shaylan Mahase-Singh 169026841 Lab Partner: Isabella Williams PC 142, Lab 7 Lab Instructor: Hasan Shodiev Lab IA: Oliver Oczos March 23 rd , 2023
Purpose: The purpose of this experiment was to determine Young’s modulus of elasticity of a wire by stretching it using weights. Young’s modulus is the ratio of the longitudinal stress, which is force per unit area, to the longitudinal strain, which is the proportional deformation. When the value for Young’s modulus is low it means that the object is elastic, when it’s high it means that the object is stiff (inelastic). Hooke’s Law is also used in this experiment as well, where it’s the proportionality between deformation and applied force. Both Young’s modulus and Hooke’s Law are intertwined, where Hooke’s law can be used to derive Young’s modulus for a linear elastic material. The goal of this experiment is to observe the relationship between the apparatus and the weights given to determine is elasticity. Results: Table 1: Elongation Data Instrument Reference (Name) Optical Lever Units Cm Precision Measure 0.01 Zero Error N/A Hanging Mass (Kg) Scale Reading Trial Number 1 2 3 6 5 4 3 2 1 3.58 2.41 0.42 -0.43 -1.56 -3.54 3.64 2.42 0.40 -0.42 -1.50 -3.54 3.63 2.44 0.45 -0.42 -1.54 -3.59
Table 2: Average Scale Readings of Hanging Masses Hanging Mass (Kg) Average Scale Reading (Cm) 6 3.62 5 2.42 4 0.42 3 -0.42 2 -1.53 1 -3.56 Graph 1: Elongation e (cm) vs Hanging Mass (kg) Calculations: Sample Calculation 1: Calculating Young’s Modulus Elongation of Average Hanging Mass for Trial 1: (3.58 + 3.64 + 3.63) / 3 = 3.62 cm Slope e/M: 0.7108 y = 0.7108x + 3.3874 R² = 0.9869 0 1 2 3 4 5 6 7 -4 -3 -2 -1 0 1 2 3 4 Elongation e (cm) Average Hanging Mass (kg) Elongation e (cm) vs Average Hanging Mass (kg) Elongation e (cm) Linear (Elongation e (cm))
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Young’s Modulus Equation: Y= (M*g/πr 2 ) / (πr 2 e) M: 6 kg 6000 g g: 981 cm/g2 r: 0.7108 cm e: 3.62 cm Y= ((6000 g)(981 cm/g 2 ) / π (0.7108 cm ) 2 ) / (π (0.7108 cm) 2 (3.62 cm)) = 6.37 x 10 6 g/cm 2 Sample Calculation 2: Percentage Error Measured Value of Young’s Modulus of Steel: 1.9 x 10 9 g/cm 2 % Error = (|Measured Value-Actual Value|) / (Actual Value) x 100% = (|1.9 x 10 9 6.37 x 10 6 |) / (6.37 x 10 6 ) = 297.3% In-Lab Question: A reasonable uncertainty for D would be 0.01 because it is in agreement with the precision measure of the optical lever. Discussion: This experiment was unsuccessful in determining the value of Young’s Modulus of elasticity of a wire. The value of Young’s Modulus calculated was 6.37 x 10 6 g/cm 2 . The weights that were used, along with the wire that was part of the apparatus were measured and recorded in Table 1, and its average elongation e was calculated and placed in Table 2. From there the elongation e vs average hanging mass graph (Graph 1) was created. The relationship between elongation e and the hanging load is that they have a directly proportional linear relationship. As the mass of the weights decreased, the elongation decreases as well (Table 1). It also shows in Graph 1 as well, where the equation was y- 0.7108x +3.3874 and the R 2 value was 0.9869. The
value of R 2 being high shows that since its close to being to 1, the linear relationship is strong. When calculating Sample Calculation 2, the percentage error was 297.3%, which is a very high percentage. Conclusion: In conclusion, the experiment was done successfully, but the results were unsuccessful. Even though Young’s Modulus of elasticity of the wire was found, the percentage error between the accepted value of Young’s Modulus of Steel was 1.9 x 10 9 g/cm 2 and the calculated value was 6.37 x 10 6 g/cm 2 which led to a very big percentage error of 297.3%. References: Sturtevant, T. (2022). PC141 Lab Manual. Wilfrid Laurier University