Error Analysis Lab

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Introduction

In this lab, the density of 20 glass beads were determined using two different methods and the results were compared to see how close the values were to each other. In first method the volume of each individual bead was measured using the diameter of each bead, along with the mass. In the second method the beads we treated as a whole unit. The total mass was measured and volume was measured based on the amount of water that was displaced in a graduated cylinder. Then, the beads were swapped with 20 different glass beads of the same type. The procedure was repeated and the results were compared to the data of the first bead set to look for any systematic errors that may have occurred. During the experiment, the data was used to see whether the diameter, mass, and density were constant between the individual beads. However, the main goal of the experiment was to answer the question of whether or not individual density average agreed with the bulk density.

Analysis
Through error analysis, the data found was used to determine if the calculated densities were the same when comparing twenty individual beads versus the entire set of twenty beads treated as one unit. For the first data set, the average diameter is 1.42 cm. The average mass is 3.90 g. The average density is 2.62 g/cm3. The average variation of the diameter is 0.04 cm. This amount shows how much the beads varied in diameter. The average variation of the mass is 0.28 g, which shows how much the mass of the beads varied from one another. The average variation between the densities of the individual beads is 0.06 g/cm3. The average percent variation of the diameter is 2.8%. The average percent variation of the mass is 7.2%. The average percent variation of the density is 2.4%. The uncertainty for the diameter in the first data set is 0.005cm and the percent uncertainty is 0.37%. The uncertainty of the mass is 0.005g and the percent uncertainty is 0.15%. Since the percent of...
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