Measurement in Physics: Fundamental Units, Accuracy, and Precision

1. Physics 1710—Section 4 Instructor—Matteson Session #2 Chapter 1 Measurement

2. Physics 1710—Chapter 1 Measurement Joe College Seat# 53 1/14/02 Session #1 Foolscap “Quiz” Name_______ Seat # ____ Date _______ Session #2 Response Card # ________ (Tell me if you do not have one) E-mail address _______@____.___ (if you did not receive message from Matteson@unt.edu)

3. Physics 1710—Chapter 1 Measurement Fact: The earth has a circumference of approximately 40 million meters (4. X 107 m). How fast must one move on average to travel around the world in 80 days?

4. Physics 1710—Chapter 1 Measurement 1′ Lecture First 3 Fundamental Units: Time, measured in seconds = 1/86 400 of m.s. day Length, measured in meters = c (1/299 792 458 sec) Mass, measured in kilograms = specimen Prefixes scale units to convenient size. Density is mass per unit volume. [kg/m3 ] Avogadro’s number is the number of atoms in a mole of an element, NAvogadro = 6.022x1023 Significant figures tell the tale. Scientific notation saves ink.

5. Physics 1710—Chapter 1 Measurement 0 Q&A: Q:Is this class mainly for engineers? I ask this because I am pre-med. Does this course apply to my field? A(s):No, it is for scientists as well. Yes, it does apply to your field. You will learn facts about how things move, e.g. consider muscles, joints, blood, air. You will grow an understanding of dynamics, e.g. energy, momentum and trauma. You will develop analytical and qualitative skills, e.g. think about diagnosis and drug dosing. This course is for all scientists and engineers.

6. Physics 1710—Chapter 1 Measurement 0 Laboratory Introduction Physics 1730 Dr. John Prince

7. Physics 1710—Chapter 1 Measurement 0 • Matteson’s Dicta Numbers 1 & 2: • 1. Physics is that branch of science concerned with the interaction of matter-energy in space-time. • 2. The physical universe consists of only matter and energy and the vacuum. • Late breaking news: what about “dark matter” and “dark energy?” They are 95% of universe and we don’t yet know what they are.

8. Physics 1710—Chapter 1 Measurement 0 Measurementis the quantitative comparison of a physical parameter to a standard unit. “Existential Physics” Activity: Measure the width of the top of your desk in “hands.”

9. Physics 1710—Chapter 1 Measurement 0 • Measurementis the quantitative comparison of a physical parameter to a standard unit. • ‽ A “hand” is not a standard unit. • Our measurement is subject to error. • Our measurement is coarse. Why did we observe a variety of values in our measurement?

10. Physics 1710—Chapter 1 Measurement 0 Measurementis the quantitative comparison of a physical parameter to a standard unit. Therefore we need standards. Accuracy is the difference of a measurement from the (unknown) true value. All measurement contain experimental error. Precision is the “fineness” of the division of the scale used to compare to the standard unit. Precision limits our knowledge.

11. Physics 1710—Chapter 1 Measurement 0 80/20Precisionis the fineness of a measurement. 80/20Accuracyis the correspondence of a measurement to an (unknown) true value. Measurement Less precise Standard Less accurate

12. Physics 1710—Chapter 1 Measurement 0 Significant figures: What numbers one writes down reveals one’s knowledge (and ignorance) of the actual true (but unknown) value. Example:2. 2.0 2.01 2.0085 2.00852 represent the values of a measurement at various levels of precision.

13. Physics 1710—Chapter 1 Measurement 0 Rules for Computing with Significant Figures: • When multiplying (or dividing) numbers, round result to same number of significant figures as the factor with least number of significant figures. • When adding (or subtracting), first round to same decimal place as contribution with the least precision, then compute.

14. Physics 1710—Chapter 1 Measurement 0 Rules for Rounding • If remainder is less than 5, truncate, i.e. round down. • Example: 3.1415927… ~ 3.14 • If remainder is larger than 5, round up. • Example: 3.1415927… ~3.1416 • If remainder is exactly 5, round up or down to leave last digit even. • Example: 31½ = 31.5000… ~32.

15. Physics 1710—Chapter 1 Measurement 0 Scientific Notation Number = Mantissa x 10 Exponent = _._____ E__ Big Numbers: 1.234567 x 10 3 = 1234.567 Small Numbers: 1.234567 x 10 –2 = 0.01234567

16. Physics 1710—Chapter 1 Measurement 0 Activity: Enter: “1.234567” ; “EXP” or “EE”; “03” Display should read: “1.234567 03” or “1.234567E03” Enter: “1.234567”; “EXP”; “03” ; “+/-” or “⇄” or “(-)” Display should read: “ “1.234567-03” or “1.234567E-03” Know Your Calculator

17. Physics 1710—Chapter 1 Measurement 1770 1780 1790 1800 1810 American Rev French Rev US Constitution Napoleon 0 Fundamental Units • Système International de Metrique (SI)— “Metric System” • First introduced in France in 1799—(on Napoleon’s coup) La $

18. Physics 1710—Chapter 1 Measurement 0 Time Standard: second [s] • (1/60)(1/60)(1/24) =1/86,400 mean solar day • 9,192,631,770 (exactly) times the period of vibration of a Cesium-133 atomic clock. • Time Demonstration

19. Physics 1710—Chapter 1 Measurement 0 Length standard: meter [m] • Meter defined in 1799, by Napoleon’s Republic. • 1/107 quadrant of Earth; C= 4.00x 107 m • Distance light travels in 1/299,792,458 sec • Meter Demonstration

20. Physics 1710—Chapter 1 Measurement 0 Derived Units of area and volume • Area: 10 m x 10 m = 100 m 2 = 1 are • 100 ares = 1 hectare = 1x104 m21 US acre = 0.4046 ha • Volume: m x m x m = m 3 = 1000 liter = 1000 l • e.g. 1000 cm 3 = 1 liter 1 US gallon = 3.7854118 liters ~ 3.8 l

21. Physics 1710—Chapter 1 Measurement 0 • Mass Standard : kilogram [kg] • kilo = 1000, 1 kg = 1000 gram • 1 kg is the mass of approximately 1/1000 m3 (=1 liter) of water • Mass is a fundamental property of all matter. • Each atom has a mass of ~1.66 x 10-27 kg times its “atomic mass number”

22. Physics 1710—Chapter 1 Measurement 0 • Mass Standard : kilogram [kg] • 1 kg weighs on earth about 2.2 pounds.

23. Physics 1710—Chapter 1 Measurement 0 • Amedo Avogadro • (1776-1856) • Italian Physicist • Proposed Avogadro’s Law (1811) 22.8 liters = 1 mole of gas = 6.022 x1023 molecules or atoms 12 g C = 1 mole

24. Physics 1710—Chapter 1 Measurement 0 Avogadro’s Number NA = 6.0221367(28) x 10 23 atoms/mole Atomic mass unit = u u = 1.660 540 2(10) x 10 –27kg (~ 1 2/3 yoctogram) NA‧ u = 1.00 x 10 –3 kg = 1.00 gram NA is the number of atoms in one “gram molecular weight” of an element.

25. Physics 1710—Chapter 1 Measurement 0 Practice: How much does a 5 US Gal can of water weigh? Density of water = 1.0 kg/l M = ρ V = (1.0 kg/l )(5 gal x 3.8 l/gal) = 19. kg W = 2.2 lbs/kg x 19. kg = 42. lbs

26. Physics 1710—Chapter 1 Measurement 0 • Summary Fundamental Dimensions and Units Time, measured in seconds; Length, measured inmeters; Mass, measured in kilograms. Prefixes scale units to convenient size. k =1000, M = 1 000 000 c = 1/100, m = 1/1000, μ =1/1 000 000 Density is mass per unit volume.ρ = m/V [kg/m3 ] Avogadro’s number is the number of atoms in a mole of an element. 6.022 x1023 atom/mole

27. Physics 1710—Chapter 1 Measurement 0 1′ Essay What was that about? An “Aha!” A Question Turn in Foolscap. Come to Recitation in Room 102 1:00 p.m. Today!