Measurement Error Prelab Assignment

Name:_________________________ Lab Section:________ 4-digit Code Number:____________

Read Taylor Error Analysis, Chapters 1 and 2.

1. How many significant figures are in each of these measurements?
1. __________ 22.03 grams
2. __________ 22.30 grams
3. __________ 0.005 kg
4. __________ 1.005 kg
5. __________ 0.080 cm
6. __________ 100.0 m
7. __________ 3.0 miles
8. __________ 6.010 cm3
9. __________ 0.9 kg/m3
10. __________ 0.500 sec
11. __________ 1.500 sec
12. __________ 6.3 x 103 m
13. __________ 6.3 x 105 m
14. __________ 1.70 x 10-4 J
15. __________ 6000 miles ± 100 miles
16. __________ 6000 miles ± 10 miles
17. __________ 6000 miles ± 1 mile

2. Describe a way to measure (not calculate) the circumference of a cylinder to the nearest 0.1 mm using only a nonflexible ruler graduated in millimeters. Do not use the formulae C=2 radius or C= diameter; measure the circumference directly. Also note that the required measurement uncertainty is 0.1 mm while the ruler itself is graduated in whole millimeters and has a reading error of 0.5 mm (five times larger than requested). Think of a way to reduce the uncertainty.

3. Let R be the ratio of circumference to diameter R = C/ d. Derive the error propagation formula for the uncertainty in R (denoted R), like we did for the area last week in lab.

4. Pay attention to significant figures in this problem. Suppose that the Earth is a perfectly smooth sphere of radius RE = 6.37 x 106 meters. A rope encircles the Earth at the equator.
1. What is the length of the rope?

2. A second rope is to encircle the Earth above the equator, but at an altitude of 1.00 meter above the ground. What is the length of the second rope?

3. What is the difference in length of the two ropes? Are you surprised by this result? Explain.

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