Name: Significant Digits, Unit Conversions, Graphing and Uncertainties in Measurements =========================================================== Choose the best answer. (30 pts total) 1. Do the following calculation and express the result with the correct number of significant digits and in scientific notation: 36.94-25.2 + 100.81 =??? a. 112.55 b. 112.6 c. 1.1255 x 10 2 d. 1.126 x 10 2 e. 1.126 x 10-2 2. Express 3300 g/cm 3 in kg/m 3. a. 3.3 x 10 2 kg/m 3 b. 3.3 x 10 9 kg/m 3 c. 3.3 x 10 3 kg/m 3 d. 3.3 x 10 6 kg/m 3 3. When drawing a graph, it is best to draw it small, so it takes only a small part of the graph paper and the data points are crammed together. In physics, we like to maximize the error in our graphs and measurements and make things hard to read. a. True b. False 4. Assuming all data points are of equal quality, which of the following is the best fit line? a. b. c. d.
5. Do not mix units in a graph or they won t cancel properly in the slope (Δy/Δx). Use the same type of units for the same type of number on both axes. Which of the following sets of units is NOT ok to use? [Remember: N = kg m/s 2 ] a. y-axis = N and x-axis = m/s 2 b. y-axis = g cm/s 2 and x-axis = cm/s 2 c. y-axis = N and and x-axis = cm/s 2 6. When it is acceptable to use a data point as a slope point? a. if the data point appears to fall upon the line b. if the data point appears to fall upon the line and if it falls at the extreme end of the page c. NEVER, because this tends to influence the positioning of the best fit line. 7. To find the best possible value for the slope of a graph (while minimizing uncertainty), the two slope points should be (as much as reasonably possible) which of the following? a. at extreme ends of the page of paper c. at the intersection of the grid lines b. never a data point d. You want answers a, b and c 8. Which is the incorrect formula for calculating the slope (Δy/Δx) with the slope points (x 1, y 1 ) and (x 2, y 2 )? a. (y 1 y 2 ) / (x 1 x 2 ) b. (y 2 y 1 ) / (x 2 x 1 ) c. (y 1 y 2 ) / (x 2 x 1 ) 9. How do you find the y-intercept of your graph if your graph does not include the origin (0,0)? a. See where your best fit line crosses the vertical axis. b. See where your best fit line crosses the horizontal axis. c. Use the equation of a line to solve for the y-intercept algebraically. Questions 10-11: The data in your experiment is governed by the formula: A = (BC/D) E You graph A on the y (vertical) axis and C on the x (horizontal) axis. 10. What is the slope theoretically equal to? a. B/D b. A/E c. E d. C/A e. C/D 11. What is the y-intercept theoretically equal to? a. B/D b. E c. E d. C/A e. C/D Questions 12 and 15 refer to Uncertainty of Electronic Meters. Refer to the Appendix B table of your lab manual or ask your instructor for help. 12. A student measured a DC current using a Fluke 87III meter. What does the table in Appendix B show for the meter uncertainty? a. 0.05% + 1 digit b. 0.2% + 2 digits c. 1.0% + 2 digits d. 2.0% + 2 digits Questions 13-15: A student measured an AC current of 0.152 Amps using a Fluke 8000A meter. The student knows that this meter has an uncertainty of 1.0% + 2 digits for AC current. 13. What is the least significant figure (LSF) in the student s AC current measurement? a. 0 b. 1 c. 5 d. 2
14. What is the decimal place of the least significant figure (LSF) in the student s AC current measurement? (You need to know this for the # digits part of meter uncertainty.) a. tenths place b. hundredths place c. thousandths place 15. What is the meter uncertainty of the current measurement in Amps? (Remember to round your final answer for uncertainty properly. See Do s and Don ts #26 for help or ask the instructor) a..003 A b..004 A c..002 A d..001 A e..01 A Questions 16-17: You are using a ruler to measure lengths. Assume that you can reasonably measure to one-half of the smallest division. This means you can see if the length of the object is closer to one of the tick marks, half-way between two tick marks, or closer to the following tick mark. (If you can t tell if a measurement is closer to a tick mark or half-way in between, then you can only reasonably measure to the nearest whole of the smallest division). This is your instrumental precision (instrumental uncertainty). 16. If the smallest division on your ruler is 1 mm (= 0.1 cm), what is the numerical value of your instrumental precision (instrumental uncertainty)? a. 1 mm b. 0.1 cm c. 0.05 cm d. 0.05 mm 17. If a rod is exactly three centimeters long, how would you record the length to reflect the precision of the instrument (and therefore, how well you can measure the length)? a. 30 mm b. 3.0 cm c. 3.00 cm d. 30.00 cm Questions 18-19: A student made the following six measurements of the mass of an object: m = 56.6 g, 56.6 g, 56.6 g, 56.6 g, 56.6g, 56.6 g. The instrumental uncertainty is δ inst = 0.1 g. 18. What is a reasonable estimate of the sample uncertainty, δ samp? a. 0.0 g b. 0.1 g c. 0.6 g d. 56.6 g 19. What is a reasonable estimate of the uncertainty of the measurement, δm? To determine this, look at both the instrumental and sample uncertainties and choose the larger value. a. 0.0 g b. 0.1 g c. 0.6 g d. 56.6 g 20. A student made the following nine measurements of the wavelength of a standing wave: l = 14.4 cm, 15.1 cm, 14.2 cm, 14.6 cm, 14.4 cm, 14.8 cm, 13.7 cm, 13.9 cm, 14.9 cm. Assume the instrumental uncertainty is 0.1 cm. What is a reasonable estimate of the sample uncertainty, δ samp? (Read all the choices before you choose the best answer) a. 0.1 cm b. 0.4 cm c. 0.5 cm d. 0.7 cm e. 1 cm f. Answers c and d are both reasonable estimates. 21. A student measures a coefficient of linear expansion of (14.2 ± 0.8)x10-6 C -1 for a steel tube and the accepted value for commercially available steel is 11.3 x10-6 C -1 to 13.5x10-6 C -1. How would you describe the two values/numbers? (Consider whether the ranges overlap.) a. They do not agree. b. They are close but do not quite agree. c. They agree within uncertainty.
Questions 22-24: The following questions test your knowledge of some of the terminology used with the identification and propagation of uncertainty. Use the following x = (10.8 ± 0.4) cm 22. What is the best estimate of x? 23. What is the absolute uncertainty of x? 24. What is the relative uncertainty of x? Questions 25-30: Propagating Uncertainty through a calculation Use the Rules for Propagating uncertainty (step-by-step method) to solve the following calculations including uncertainty. Pay attention to units! It is usually better to convert units before you do the calculation. Remember to convert the uncertainty if you convert the best estimate. The final answer should be rounded properly following the Rules for reporting experimental values (Appendix C of the Phy 121L/131L lab manual OR see Do s and Don ts of Physics Lab Reports #26). Reduce rounding error by keeping at least two extra non-significant digits in intermediate calculations, and only round severely in the last step. A = (10.0 ± 0.1) mm; B = (5.00 ± 0.10) cm; C = (8.0 ± 0.1) mm; D = (4.2 ± 0.2) cm 25. Convert C to cm. a. (0.8 ± 0.1) cm b. (8.0 ± 1.0) cm c. (0.80 ± 0.01) cm 26. B + C =? a. (13.0 ± 0.2) cm b. (5.80 ±.11) cm c. (58.0 ± 0.2) mm 27. B D =? a. (0.8 ± 0.3) cm b. (0.80 ±.21) cm c. (0.8 ± 0.1) cm 28. AC =? a. (80.0 ± 0.02) mm 2 b. (80.0 ± 1.8) mm 2 c. (80.0 ±.2) mm 2 29. B 2 =? a. (25.0 ± 1.0) cm 2 b. (10.0 ± 4.0) cm 2 c. (25.0 ± 0.2) cm 2 d. (25.0 ± 0.01) cm 2 30. ½D =? a. (4.2 ± 0.1) cm b. (2.10 ± 0.05) cm c. (2.04 ±.10) cm d. (2.1 ± 0.1) cm
Extra Credit: Propagating Uncertainty through a multistep calculation with hints *** Up to 10 points EC but a maximum score of 35 out of 30 on Review Assignment *** Do following multistep calculations including uncertainty. Write out your final answer (value with its associated uncertainty) following the Rules for reporting experimental values (see Appendix C of the Phy 121L/131L lab manual or Do s and Don ts #26). Reduce rounding error by keeping at least two extra non-significant digits in intermediate calculations. Show all work to receive credit, including converting absolute to relative uncertainties (%) or relative uncertainties to absolute uncertainties where needed. EC#1. [(34.35 ± 0.05) g (30.35 ± 0.05) g] (9.80 m/s 2 ) =??? Answer = EC#2. [(7.73 ± 0.01) cm] [(19.0 ± 0.1)mm] 2 =??? Give final answer in cm 3. Hint: first step is to make both length measurements have the same units (mm cm). Answer =