Question:

1. What percent error is sustained in your final value (for the density of the solid) by the method of Archimedes' principle if you merely take the value for the density of water as 1.00 g/cm3 and neglect the variation with temperature? Show the calculation.

2. Which method of determining density do you prefer? Which is more accurate? Which is more precise? What are the advantages and disadvantages of each method?

3. For each method, what are some possible systematic errors you encountered?

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BASIC NIEASUREMENTS - THE DENSITY OF A SOLID OBJECT: To determine the density of a solid = mass / volume. The volume is determined by one of two methods: 1) by simple measurement of its dimensions, and 2) by Archimedes' principle. More importantly, this experiment is concerned with errors. The random error of each measurement will be either calculated or estimated, and the overall error in each value of density calculated. Class results of the densities will be compared, revealing the actual errors. EDUCATIONAL PURPOSE: To learn how to use instruments such as the vernier caliper, micrometer, and beam balance; to become competent in the estimations and handling of errors; to discuss systematic errors that may affect the experiment. SUGGESTED READING: OpcnStax Univcrsity Physic-s'Violumc 1, Chapter 14, Section 4 REQUIRED EQUIPMENT: Beam balance (light, capacity 311 g or heavy, cap 2610 g) Steel cylinder (light, diameter 18 mm or heavy, diameter 25 mm) Vernier calipers, micrometer Beaker, string, etc THEORY: The density of a solid is, of course, the mass divided by the volume. We can determine the volume in two ways: (1) By measuring its physical dimensions and (2) By Archimedes' principle. For a precisely-made cylinder the rst method is easy - we just measure the height (h) and diameter (d) with a pair of calipers and use the formula V = (1) 9. Calculate the density of the cylinder to 4 signicant gures. ANALYSIS: (Note: The following calculations should appear in the Data and Observation section of your lab report. ** DETERMINE THE ESTIMATED ERROR IN THE DENSITY ** 1. First estimate the random error in one reading of mass (m). (A good place to begin is one half the smallest division.) Express this error in both the absolute and relative form. e.g. m = 44.90 i 0.005 g = 44.90 g i 0.011% since 0.005f44.9 = 0.00011 The absolute error will also be the error in the mass of the fluid (m') for method 2. What is now the error in the difference, (m - m')? Express the latter in the relative form. (See introduction to lab manual, page 7.) e.g. m - m' = (44.90 i 0.005 g) - (39.20 i 0.005 g) = 5.70 i 0.01 g = 5.70 gt 0.1? % 2. Using your 5 sets of measurements for the height and the diameter calculate the standard error of the mean for each. Calculate random error (relative form) in each quantity. (See P. 9 of the lab manual for an example.) d = 18.80 i 0.005 mm = 18.80 mm i 027% since 0.00511 8.8 = 0.0026 h = 20.60 i 0.006 mm = 20.60 mm i .029% since 0.006f20.6 = 0.0029 3. Using the formulas on page 9 and 10 of your lab manual, calculate the expected (random) error for the density of the cylinder both for method 1 and method 2. e.g. Totai % error = 0.011 + 2(0.027) + 0.029 = 0.095% (Method 1), and " " " = 0.011 + 0.175 = 0.186% (Method 2) QUESTIONS: 1. What percent error is sustained in your final value (for the density of the solid) by the method of Archimedes' principle if you merely take the value for the density of water as 1.00 g/cm3 and neglect the variation with temperature? Show the calculation. 2. Which method of determining density do you prefer? Which is more accurate? Which is more precise? What are the advantages and disadvantages of each method? 3. For each method, what are some possible systematic errors you encountered