Name:_______________________________ 4-digit Code Number:_______________________________

Read Taylor *Error Analysis*, Chapters 1 and 2.

- How many significant figures are in each of these measurements?
- __________ 22.03 grams
- __________ 22.30 grams
- __________ 0.005 kg
- __________ 1.005 kg
- __________ 0.080 cm
- __________ 100.0 m
- __________ 3.0 miles
- __________ 6.010 cm
^{3} - __________ 0.9 kg/m
^{3} - __________ 0.500 sec
- __________ 1.500 sec
- __________ 6.3 x 10
^{3}m - __________ 6.3 x 10
^{5}m - __________ 1.70 x 10
^{-4}J - __________ 6000 miles ± 100 miles
- __________ 6000 miles ± 10 miles
- __________ 6000 miles ± 1 mile

- 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.

- 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.

- Pay attention to significant figures in this problem.
Suppose that the Earth is a perfectly smooth sphere of radius
R
_{E}= 6.37 x 10^{6}meters. A rope encircles the Earth at the equator.- What is the length of the rope?

- 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?

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

Go to the lab

- What is the length of the rope?