DoM and HL LR

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School

University of Illinois, Urbana Champaign *

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Course

102

Subject

Mechanical Engineering

Date

Apr 3, 2024

Type

pdf

Pages

9

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Experiment one: Density of Matter 1. Introduction: The purpose of this experiment was to study the density of solid objects. The greater the volume of an object, the smaller the density of an object as they have an inversely proportional relationship. In this lab, density will be found from found masses and volumes calculated from measurements taken during the lab. The mathematical equation used to calculate the volume of cylindrical solids is: V = (1) Π𝑟 2 ? where V is the volume of the cylinder, is the ratio of the circumference of a circle to its Π radius, r is the radius of the cylinder, and l is the length of the cylinder. The mathematical equation used to calculate the volume of a solid rectangular prism is: (2) 𝑉 = ??ℎ where V is the volume of the rectangular prism, l is the length of the rectangular prism, w is the width of the rectangular prism, and h is the height of the rectangular prism. The mathematical equation used to calculate the density of an object is: (3) ρ = 𝑀 𝑉 where is the density of an object, M is the mass of the object, and V is the volume of an ρ object. 2. Experiment procedures: The materials and equipment used for this lab included the following: 3 aluminum cylinders of varied sizes, 3 cardboard rectangular prisms of varied sizes, a balance, and vernier calipers. Part 1: - Step 1: The balance was turned on and zeroed. - Step 2: The mass of a cylinder was measured on the balance. - Step 3: The radius and height of the cylinder were measured by putting the cylinder in between the ends of the vernier calipers. - Step 4: The volume was found by multiplying the square of the radius by the height of the cylinder by pi. - Step 5: The density was calculated by dividing the found mass of the cylinder by the found volume of the cylinder. - Step 6: Steps 1-5 were repeated twice for two other cylinders.
Description: The aluminum used were smooth, opaque, silver cylinders. Part 2: - Step 7: Steps 1 and 2 were repeated for the rectangular prism. - Step 8: The height, length, and width of the prism were measured by putting the prism in between the ends of the vernier calipers. - Step 9: The volume was found by multiplying the length by the height by the width of the cylinder. - Step 10: Step 5 was repeated. - Step 11: Steps 7-10 were repeated twice for the other rectangular prisms. Description: The rectangular prisms used were made of cardboard. The largest was red, the second largest was yellow, and the smallest was blue. They were hollow and opaque with a semi-matte finish. 3. Results, analysis, and questions: Table 1: Table one shows the mass, length, radius, volume, and density of the aluminum cylinders. Column 1 mass (grams) length (cm) diameter (cm) radius (cm) volume (m^3 x10^-6) density (kg/m^3) cylinder 1 27.52 7.7 1.1 0.55 7.32 3760 cylinder 2 12.56 3.1 1.1 0.55 2.95 4258 cylinder 3 6.36 7.5 0.6 0.3 2.12 3000 Based on table 1, the graph illustrated the relationship between volume versus mass of the cylinders. Graph 1:
From graph 1, the slope of best fit was 0.000254, which demonstrates (based on equation 3). 1 ρ Therefore, the density of aluminum is theoretically 3,979 kilograms per meter cubed. The average experimental density of the aluminum cylinders was found to be approximately 3,673 kilograms per meter cubed, which means that there was around a 7.69% error. The coefficient of determination was calculated to be 0.981. This demonstrates that the data from this part of the experiment was relatively accurate. A likely source of error was from measuring the cylinders with the vernier calipers, where the cylinder may not have gripped tight enough for accuracy. Table 2: Table 2 shows the mass, height, length, width, volume and density of the blocks. Mass (grams) Height (cm) Length (cm) Width (cm) Volume (m^3 x 10^-3) Density (kg/m^3) Block 1 (red) 134.18 303 74 150 3.36 40 Block 2 (yellow) 86.6 75 152 152 1.73 50 Block 3 (blue) 50.01 146 73 73 0.78 64 Based on table 2, the graph 2 illustrates the relationship between mass and volume of the blocks.
From graph 2, the slope of best fit was 0.0308, which demonstrates (based on equation 3). 1 ρ Therefore, the density of cardboard was 32.47 kilograms per meter cubed. The average experimental density was 51.3 kilograms per meter cubed, giving a 36.8% error. The coefficient of determination was calculated to be 0.994. This demonstrates that the data from this part of the experiment was precise, but not accurate. A source of error was likely due to the inexact measuring of the blocks due to a tightened grip on the vernier calipers. It is possible that the cardboard may have been compressed, making the measurements more inaccurate. 4. Conclusion: Through this experiment, the density of solid objects was studied. A deeper understanding of laboratory procedures and precise measurements were also examined. The density of solid objects was studied. One was calculated with the volume of a set of cylinders, and the other was calculated using a set of cardboard blocks. was used in both parts of the ρ experiment to represent density. The errors in this lab stemmed from improper measuring. To be repeated with greater accuracy, the lab should be redone with measurements taken on a flat surface. 5. Data Sheet: Next Page under Density of Matter
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