# 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…show more content…
The measured difference between the beads is less than the measured tolerance, therefore, the two density values agree. The measured density of the bulk beads in the second data set is 2.63g/cm3. The uncertainty of the density measurement is 0.02g/cm3 and the percent uncertainty is 0.83%. Again, the average density from the individual bead measurements in this data set is 2.57g and the percent of uncertainty is 0.36%. The percent of uncertainty is higher with the bulk beads; however, the measured densities are similar. The measured difference between the bulk and individual beads is 0.06g/cm3. The measured tolerance of the density between the bulk and individual beads is 0.077g/cm3. The measured difference between the beads is less than the measured tolerance, therefore, the two density values agree. Conclusion For the first data set (Group 6), the density and the uncertainty of its value (ρ ± Δρ) is 2.62 g/cm3 ± 0.06. For data set two (Group 4) this estimate was 2.57 ± 0.06. Overall, the data shows that when considered individually, neither the diameter, mass, nor density of the beads was constant. In the end, the individual density average agreed with the bulk density. The same was found for the second group of beads that were