Lab 1 manuscript

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Texas A&M University *

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Mechanical Engineering

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Dec 6, 2023

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Density of Cubes, Matteo Greco, Aiden Burke, Lab 1: Measurement and Uncertainty, 9/15/23, section 333 Density is an innate property of matter that can be useful in identifying various materials. The purpose of this experiment was to determine the materials that composed 10 individual cubes of unknown materials. By finding the density of each cube at room temperature and comparing it to the density of known materials, we should be able to roughly determine possible materials that each cube could be composed of. First, we examined a collection of 10 different cubes of unknown materials. Then, we measured the length, width, and height in centimeters of each cube using a vernier caliper to obtain the dimensions in order to calculate the volume of each cube. We then repeated this process using a ruler in case of error using the caliper. Next, we used a digital scale to measure the mass of each cube in grams. Using the calculated volume of each cube and measured mass, we were able to determine the density of each cube using the equation d = m/v, where d is the density, m is the mass, and v is the volume. Finally, using the calculated density, we compared the densities of each cube to known materials in order to come up with possible material they could be made of. Using the measurements of each cube, we created figure 1. Figure 1 The table shows the data collected from each cube, as well as the calculated density of each cube. The densities were calculated by multiplying the length, width, and height of each cube to find the volume, then dividing the measured mass by the volume. Then, the uncertainty for each density was found to account for possible errors in the collection of the data. The density could then be used to compare to known material densities in order to identify the material of each cube. Sample Calculations: Density (cube 1) d= 9.999g / (2.550cm * 2.435cm * 2.510 cm) = 0.6416 g/cm 3

Uncertainty (cube 1) 𝑈 = 0. 6416𝑔/𝑐𝑚 3 ( 0.001𝑔 9.999𝑔 ) 2 + ( 0.005 𝑐𝑚 2.550 𝑐𝑚 ) 2 + ( 0.005 𝑐𝑚 2.435 𝑐𝑚 ) 2 + ( 0.005 𝑐𝑚 2.510 𝑐𝑚 ) 2 = 0. 0022 𝑔/𝑐𝑚 3 Based on the data collected and calculated density, cube 1 could have been charcoal (with a density of 0.6 g/cm^3 1 ) or oak wood (with a density of 0.6 g/cm^3 1 ). Cube 2 could have been cork (with density 0.55 g/cm^3 1 ) or plywood (with density 0.54 g/cm^3 1 ). Cube 3 could have been nylon (with density 1.14 g/cm^3 1 ). Cube 4 could have been copper (with density 8.96 g/cm^3 1 ) or brass (with density 8.78 g/cm^3 1 ). Cube 5 could have been polyacrylonitrile (with density 1.18 g/cm^3 1 ). Cube 6 could have been cadmium(with density 8.64 g/cm^3 1 ) or pinchbeck (with density 8.65 g/cm^3 1 ). Cube 7 could have been steel (with density 7.82 g/cm^3 1 ). Cube 8 could have been graphite (with density 2.26 g/cm^3 1 ). Cube 9 could have been pine wood(with density 0.74 g/cm^3 1 ). Cube 10 could have been aluminum(with density 2.7 g/cm^3 1 ). Thus, the initial hypothesis of being able to identify each material by comparing measured densities to known densities was proven true because we were able to determine possible candidates for each cube. However, some of the values calculated could have been impacted by human error. Some sources of this error could have been misreading the vernier caliper, improperly writing or reading a recorded value, or a mistake in performing calculations. 1. Solids - Densities. https://www.engineeringtoolbox.com/density-solids-d_1265.html (accessed 2023-09-21).

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