Chapter1 measurements from rpg
- 1. Measurements slides courtesy of Dr. Gamag
- 2. Learning Goals • Be familiar with the SI units. • Be familiar with the frequently used prefixes for SI units. • Change units.
- 3. Learning Goals Differentiate accuracy from precision Differentiate random errors from systematic errors
- 4. Units How many people are in this classroom? What’s the temperature at the moment? What’s your height? How long does it take to walk from here to the bookstore? How heavy is the Physics textbook? Measurements
- 5. Standard Unit (SI / MKS) meter kilogram second Measurement Approximate value Size of cells in most living organisms 1 x 10-5 m Distance of Earth to nearest star 4 x 1016 m Electron mass 9 x 10-31 kg Sun’s mass 2 x 1030 kg Time between normal heartbeats 8 x 10-1 s Measurements
- 6. Prefixes
- 7. Prefixes
- 8. Unit Conversion Choose a conversion factor that will make the units cancel, leaving the answer in the correct units. Convert 1.34 kg to grams: 1.34 kg 103 g 1 kg = 1340 g Convert 43 km/h to m/s: 43 km 1 h 103 m 1 km 1 h 60 min 1 min 60 s = 12 m s
- 9. Uncertainty in Measurements Scientists share their results that are reported with an uncertainty. A new measurement that is within the margin of uncertainty confirms the old measurement. Acceleration due to gravity is g = 9.80 ± 0.02 m s2 Acceptable measurements range from 9.78 − 9.82 m s2
- 11. Significant Figures Multiplication or Division : fewest significant figures Addition or Subtraction : fewest digits to the right of the decimal point
- 13. Accuracy vs. Precision How precise and accurate are the measurements of the three students? Spring elongation measured by three students. Data averaged over five trials.
- 14. It is the degree of exactness of a measurement. Student 3’s measurements are the most precise, within ±0.1 cm. The measurements of the other two students are less precise because they have larger uncertainties. Precision depends on the instrument and technique used to make the measurement. Device with the finest division on its scale produces the most precise measurement. Precision: how close are the data to each other?
- 15. Precision: degree of exactness of a measurement Least count: smallest value that can be measured by the instrument. Measured values are good only up to this value. Precision: Least Count
- 16. Accuracy how well the results of a measurement agree with the “real” value If the real length of the spring had been 14.8 cm, then student 2 would have been most accurate and student 3 least accurate. Student 3 may be precise in measuring but he is the least accurate.
- 17. Precision versus Accuracy Precision: closeness of the measurements to each other Accuracy: closeness of the measurements to the true value
- 18. Systematic Errors vs. Random Errors Systematic Errors - consistent inaccuracies in the result of an experiment that may be incurred due to the equipment or faulty experiment procedure e.g. misalignment, wrong calibration, negligence of friction Random Errors - errors in measurement due to the precision of the instrument or the experimenter’s inability to do the measurements uniformly e.g. stop watch’s precision, response time of experimenter
- 19. Chapter 1 Exercise a) Convert the following measurements to SI units i. 42.3 cm ii. 214 μg iii. 57 ns b) Rank the following mass measurements from least to greatest: 11.6 mg, 1021 μg, 0.000006 kg, 0.31 mg. c) The length of a room is 16.40 m, its width is 4.5 m, and its height is 3.26 m. What is the volume enclosed by the room?