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Data: Table 1: Measurements and Uncertainties. d (cm) Trial d (cm) 1 1.596 11.00 2 1.589 10.50 3 1.591 10.00 4 1.585 9.50 5 1.595 9.00 6 1.587 Average ΔL (cm) L (cm) 8.50  h= d = d = h = Table 2: Densities; V (cm3) Trial d (cm) L (cm) M (g) 1 1.596 11.00 31.1 2 1.589 10.50 21.8 3 1.591 10.00 28.1 4 1.585 9.50 19.7 5 1.595 9.00 25.4 6 1.587 8.50 17.6 7 1.595 8.00 22.5 8 1.583 7.50 15.6 9 1.595 7.00 19.8 10 1.587 6.50 13.5 11 1.592 6.00 17.1 12 1.585 5.50 11.5 13 1.595 5.00 14.3 14 1.582 4.50 9.4 15 1.593 4.00 11.3 ( g ) cm 3 Material Miami Dade College/North Campus PHY2048L/PHY2053L Lab 1 “Density of Unknown Material: Measurements and Graphing.” Purpose: To find the mathematical and graphical relationship between mass and volume of unknown cylinders, while practicing measurements with the correct number of significant figures and applying the rules for uncertainty determination. Materials: • • • • Mystery Density Set Triple beam or electronic balance Ruler or Caliper Computer with Logger Pro Pre Lab Questions: 1. In your own words define density and explain what would you determine the density of an object? __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ __________________________________________________________________________________________ 2. On the Space below, draw or sketch a low density object and a higher density object, explain your drawings. Procedure: I. Measurements averages, absolute errors, and relative error. a. Select the six largest cylinders from the set; b. Use the caliper to measure their diameter (d) in centimeters. Record your measurement in table 1, including the uncertainty given by the measuring tool; c. Use the ruler to measure their height (h) in centimeters including the uncertainty given by the measuring tool. Record your measurements in table 1. d. Calculate the average diameter and the average height of the cylinder set. Remember unweighted N average is found as: x = x i i N ; e. Determine the absolute error in your set of measurements, to do so first find the absolute value of the difference between each measurement and their average, record that on table 1. Then find the N average of the difference, basically: x = x i i N −x ; f. Record your diameter and length using the average, absolute error format, ( x = g. Determine the relative error in your measurements; x = h. Determine the average Volume ( V = d 2 4 x  x ); x ; x h ) of the cylinders and it corresponding absolute error. II. Density of Materials. a. Use the caliper and ruler to measure the diameter and length of each of the 15 cylinders, record your measurements in data table 2; b. Calculate the volume of each cylinder, record your results in data table2; c. Use the triple beam balance or the digital scale to determine the mass (M) of each cylinder, record your measurements in data table 2; d. Calculate the density (ρ) of each cylinder, record your result in data table 2; e. Use Logger Pro and graph Mass vs. Volume for your cylinder sets; and f. Determine the mathematical relationship between mass and volume. Data: Table 1: Measurements and Uncertainties. Trial d (cm) d (cm) h (cm) h (cm) 1 2 3 4 5 6 Average d =  h= d = h = Table 2: Densities; Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 d (cm) L (cm) V (cm3) M (g) ( g ) cm 3 Material Analysis: 1. Why is the relative error of the length, larger than that of the diameter? 2. What is the meaning of the slope of the lines in your Mass vs. Volume graph? 3. Based on your results from table two and your graph, are all cylinders made out of the same material? Explain 4. Some cylinders are made out of acetyl and others out of polystyrene, their corresponding densities are 1.04 g/cm3 and 1.42 g/cm3: • Complete the last column of Table 2, by identifying the material used in making a given cylinder; • Determine your percentage errors in your slopes; • Determine the average density for each set of six cylinders and its absolute error. Conclusions: For all conclusions make sure to follow Appendix A and B. • Definitions • Equations • Meanings of Slope and Y-intercept • Discussion of sources of errors • Sources

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