A student made five successive measurements to determine the density of copper.

Question

A student made five successive measurements to determine the density of copper. He obtained the following values: rho_1 = 6.3 g/cm^3, rho_2 = 7 g/cm^3, rho_3 = 9.1 g/cm^3, rho_4 = 9.2 g/cm^3, and rho_5 = 9.8 g/cm^3. 1. Calculate the average density rho_ave = 8.28 2. Calculate the standard deviation sigma_N - 1 (rho) = 1.53 3. Calculate uncertainty in density measurement Delta rho = -685 4. State the percent variability in the density measurement: percent variability = 1850 % 5. Given the accepted (known) density of copper to be rho_cu = 8.96 g/cm^3, what is the percent difference in the density measurement: percent difference = 7.589 %

Explanation / Answer

1. Average value is (6.3+7+9.1+9.2+9.8)/5 = 8.3 g/cm3.

2. Standard deviation = 1.5 g/cm3.

3. Uncertainty in density measurement = (1.5 / sqrt(5)) = 0.7 g/cm3.

4. Percent variability = (0.7 x 100 / 8.3) = 8.4%

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