PROBLEMS
- Which three of the seven fundamental units are useful to mechanics this first semester?
- Convert the radius of the earth to km.
- How old are the roots of the current world timekeeping system?
- A hydrogen ground state electron radius is 52.9pm. How many meters is that?
- Which tends to make the better marksman: Accuracy or precision?
- How many significant digits do the following numbers have: 300, 409, 17.03, 0.0032, 1.56x1011, 1.003, 1.000?
- A person stands on a scale that reads whole pounds. The result is 161 lb. What is the absolute error of the measurement? Relative error?
- For the scale in the problem above will the absolute error change for a different person? Relative error?
- What is the quantization error in a 10 bit microcontroller with a FSR of 5.0V? Absolute error?
- What is the quantization error on a standard ENGLISH ruler? Absolute error?
- What three types of errors exist? Which is related to calibration? Which is inherent in devices?
- You measure the blackbody temperature of the night sky three times and read: 7.3C, 9.1C and 8.7C. Assuming the temperature fluctuation is due to your device, how should you represent this result with its associated error if we assume a 95% confidence interval? Feel free to use GeoGebra for this.
- Does the standard deviation of a population change dramatically as more data comes in? Standard error?
- How might we use a low-precision device to make a precise measurement of some natural constant like the speed of light in vacuum?
- The mean of a data set is 3.45 and the standard error is 0.003. How should the result be written using a 95% confidence interval?
ANSWERS
1. meters, kilograms, seconds
2. 6370 km
3. around 5000 yrs old
4. 5.29x10-11m
5. precision
6. 1, 3, 4, 2, 3, 4, 4
7. 1/2 lb, 0.00313 lb
8. no, yes.
9. 0.0049, 0.0024
10. 1/16 inch, 1/32 inch
11. systematic, random, blunders. systematic. random.
12. 8.4 +/- 0.9 C
13. no. yes.
14. make many measurements. The error will shrink as
15. 3.450 +/- 0.006. If you have a non-zero digit for the thousandths place on the mean, use it.