3. Essential idea: Since 1948, the Système International d’Unités (SI) has been used as the preferred language of science and technology across the globe and reflects current best measurement practice. Nature of science: (1)Common terminology: Since the 18th century, scientists have sought to establish common systems of measurements to facilitate international collaboration across science disciplines and ensure replication and comparability of experiments. (2)Improvement in instrumentation: Improvement in instrumentation, such as using the transition of cesium-133 atoms for atomic clocks, has led to more refined definitions of standard units. unavoidable (3)Certainty: Although scientists are perceived as working towards finding “exact” answers, there is unavoidable uncertainty in any measurement.

4. Understandings: ▪ Fundamental and derived SI units ▪ Scientific notation and metric multipliers ▪ Significant figures ▪ Orders of magnitude ▪ Estimation Applications and skills: ▪ Using SI units in the correct format for all required measurements, final answers to calculations and presentation of raw and processed data ▪ Using scientific notation and metric multipliers ▪ Quoting and comparing ratios, values and approximations to the nearest order of magnitude ▪ Estimating quantities to an appropriate number of significant figures Guidance: ▪ SI unit usage and information can be found at the website of Bureau International des Poids et Mesures ▪ Students will not need to know the definition of SI units except where explicitly stated in the relevant topics ▪ Candela is not a required SI unit for this course ▪ Guidance on any use of non-SI units such as eV, MeV c -2, Ly and pc will be provided in the relevant topics

5. International-mindedness: ▪ Scientific collaboration is able to be truly global without the restrictions of national borders or language due to the agreed standards for data representation Theory of knowledge: ▪ What has influenced the common language used in science? To what extent does having a common standard approach to measurement facilitate the sharing of knowledge in physics? Utilization: ▪ This topic is able to be integrated into any topic taught at the start of the course and is important to all topics ▪ Students studying more than one group 4 subject will be able to use these skills across all subjects Aims: ▪ Aim 2 and 3: this is an essential area of knowledge that allows scientists to collaborate across the globe ▪ Aim 4 and 5: a common approach to expressing results of analysis, evaluation and synthesis of scientific information enables greater sharing and collaboration

6. Physics has some of the most famous names in science. ▪ If a poll were to be taken on who is the most famous scientist, many people would choose… Albert Einstein A PHYSICIST ▪ other people might choose… A PHYSICIST Isaac Newton

7. The physics we will study was pioneered by the following four individuals: ▪ Other greats will be introduced when the time comes. Galileo Newton Maxwell Einstein Kinematics Dynamics Classical Physics Calculus Electrodynamics Relativity Quantum physics

8. Physics is the study of forces, and matter’s reaction to them. ▪ All of the sciences have examples of force: ▪ In biology, we have the bighorn sheep: F 12 F 21 W2W2 W1W1 f1f1 f2f2 F n2 F n1 Kilo Newtons ▪ In chemistry, we have the popping balloon

9. Dakota H-Bomb – 1 million tons of TNT List of nuclear weapons tests of the United States In physics, we have the biggest forces of all:

10. Meteor Crater - Arizona 100 Dakota H-Bombs

11. Physics is the study of the very small. ▪ And the very large. ▪ And everything in between. Barred Spiral Galaxy NGC 1300 About 2  10 21 meters in diameter The little spring is meant to indicate that the quarks inside a nucleon are held together by a force we call gluon exchange.

12. WHAT is PHYSICS? The study of matter, energy, and the interactions between them … in other words, everything! “Physics investigates the essential nature of the world, and biology describes a local bump. Psychology … describes a bump on a bump.” Willard Van Orman Quine, American philosopher (1908 – 2000) Remarkably, we have found that these laws can be expressed in terms of mathematical equations. Physics is the study of the fundamental laws of nature.

13. Side Note Theory of Classical Mechanics (Newton) worked perfectly for more than 100 years – and still works in nearly all everyday situations. But failed to successfully describe fast moving small particles. Tools developed and data didn’t fit with established theories Leaders of Modern physics (Einstein, Planck, Heisenberg, Bohr, etc.) had to be open-minded when data didn’t fit with established theories “No amount of experimentation can ever prove me right; a single experiment can prove me wrong” -- Albert Einstein No theory is here to stay forever.

14. Side Note In nearly all everyday situations, Einstein’s theory gives predictions almost the same as Newton’s. Main distinction is in extreme case of very high speed (close to the speed of light) Science of very fast: ● Special theory of relativity – Albert Einstein. The new theory gave us much more: Our view of the world is affected with that theory. – Our concepts of space and time underwent a huge change – mass and energy as a single entity ( E = mc 2 ). Quantum mechanics is the science of the very small: on the scale of atoms and subatomic particles.

15. Stands for Système international d'unités. It is standard body of measurements, the modern form of the metric system adopted in 1960. ▪The SI system is pretty much the world standard in units. Why use SI units? ▪ universal ▪ easy (metric system) SI Units ▪ The fundamental units in the SI system are… Lengthmeter (m) Masskilogram (kg) Timesecond (s) Electric Current (I)ampere (A) Temperaturekelvin (K) Amount of mattermole Intensity of light/Luminositycandela (cd) ▪ You will also use the gram. In Chemistry. In physics we use the kilogram (SI unit).

16. Length – 1 meter (1m) is the distance traveled by the light in a vacuum during a time of 1/299,792,458 second. Mass – 1 kilogram (1 kg) is defined as a mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sevres, France SI Units Time – 1 second (1s) is defined as 9,192,631,770 times the period of one oscillation of radiation from the cesium atom. ▪ The International Prototype of the Kilogram was sanctioned in 1889. Its form is a cylinder with diameter and height of about 39 mm. It is made of an alloy of 90 % platinum and 10 % iridium. The IPK has been conserved at the BIPM since 1889, initially with two official copies. Over the years, one official copy was replaced and four have been added. ▪ One meter is about a yard or three feet. ▪ One kilogram of mass has weight of 9.8 N on earth or about 2.2 pounds in USA -.

17. EX: Which one of the following is fundamental unit? A. CoulombB. Ohm C. Volt D. Ampere ▪ The body that has designed the IB course is called the IBO, short for International Baccalaureate Organization, headquartered in Geneva, Switzerland and Wales, England. ▪ The IBO expects you to memorize the fundamental units. equivalent The ampere is equivalent to one coulomb (roughly 6.241×10 18 electrons) per second One Ampere is defined as that current flowing in each of two infinitely ‑ long parallel wires of negligible cross ‑ sectional area separated by a distance of one metre in a vacuum that results in a force of exactly 2 x 10 ‑ 7 N per metre of length of each wire.

18. Learning Intentions You have already learned about… – What is physics – The 7 fundamental units What you will learn about… – Derived units – Converting between units

19. Fundamental and derived SI units ▪ In the sciences, you must be able to convert from one set of units (and prefixes) to another. EX: Suppose the rate of a car is 36 kmh -1, and it travels for 4 seconds. What is the distance traveled in that time by the car? ▪ distance: s = vt. s = 0.04 km = 211.2 ft FORBIDEN

20. Dimensional analysis ▪ You can use units to prove that equations are invalid. EX: Decide if the formulas are dimensionally consistent. The information you need is that v is measured in m/s, a is in m/s 2, x is in m and t is in s. (a) v = at 2 (b) v 2 = 3ax(c) x = at 2 Inconsistent Consistent Consistent ▪ The process of substituting units into formulas to check for consistency is called dimensional analysis. ▪ DA can be used only to show the invalidity of a formula. Both (b) and (c) are consistent but neither is correct. They should be: v 2 = 2ax and x = (1/2)at 2. numbers don’t have units

21. Fundamental and derived SI units Unit for any quantity that is measured or calculated in physics (generally science) is combinations of seven basic /fundamental units. Derived units are combinations of 7 basic ones. ▪ Speed - measured in meters per second (m s -1 ). ▪ Acceleration - measured in meters per second per second (m s -2 ). ▪ Mass density - measured in kilograms per meter 3 (kg m -3 ).

22. Swine flu virus: diameter of 10 to 300 nanometers (nanometer is equal to one billionth of a meter) 0.0000000000001m becomes 1.0 x 10 -13 m Scientific notation and prefixes

23. Very large and very small numbers: either scientific notation or prefixes should be used Power of 10Prefix Name Symbol 10 -12 picop 10 -9 nanon 10 -6 microµ 10 -3 millim 10 -2 centic 10 3 kilok 10 6 megaM 10 9 gigaG 10 12 teraT 1.The best current estimate of the age of the universe is 13 700 000 000 = 1.37 × 10 10 years = 13.7 billion years EX: scientific notation prefix 2. electron mass = 0.000 000 000 000 000 000 000 000 000 000 91 kg = 9.1 × 10 -31 kilograms

24. -53 ks 9.72 Gs 7.51 ns 4.321768 ks 200 ms EXAMPLE: http://en.wikipedia.org/wiki/Scientific_notation#Normalized_notation 0.00354 m = 3.54 x 10 -3 m = 3.54 mm

25. Scientific notation and prefixes individually: 1)0.00003004 2)0.0456 3)1045004 4)9340 5)1.0053 X 10 -3 (standard notation!) 6)5.302 X 10 4 (standard notation!) = 3.004 X 10 -5 = 4.56 X 10 -2 = 1.045004 X 10 6 = 9.34 X 10 3 = 0.0010053 = 53020 more practice

26. Smaller units every step is 10 ± 1 power They are grouped into steps 10 ± 3 femto pico nano micro mili kilo mega giga tera f p n  m k M G T f p n  m k M G T base unit 1 Larger units 10 -15 10 -12 10 -9 10 -6 10 -3 10 0 10 3 10 6 10 9 10 12 centi (c) deci (d) 10 -2 10 -1 NEXT: Unit conversions involving SI unit prefixes

27. form smaller unit to larger unit → expect smaller number = 1 or Chemistry from larger unit to smaller unit → expect bigger number or Chemistry = 1 EX:

28. The wavelenagth of green light is 500 nm. How many meters is this? I have 906 gigabyte hard drive on my computer. How many bytes of data will it hold? 4.3 x 10 4 ns = ? µs 5.2 x 10 8 ms = ? ks 1 ms = 10 -6 ks EX:

29. A dime is 1.0 mm thick.A quarter is 2.5 cm in diameter. The average height of an adult man is 1.8 m. Diameter of a red blood cell ≈ 8 μm Diameter of atomic nucleus ≈ 5 fm Diameter of the atom ≈ 100 pm =100 000 fm If an atom were as big as a football field nucleus would be about the size of a pea in the centre. Conclusion: you and I and all matter consists of almost entirely empty space. Diameter of Earth ≈ 13 Mm Diameter of sun ≈ 1.4 Gm Diameter of Milky Way ≈ 9500 Tm visible universe is thought to be around 10 25 m Scale of the Universe http://htwins.net/

30. EX:

31. 7.2 m 3 → mm 3 75 g/cm 2 → kg/m 2 100 mm 3 → m 3 72 km/h → m/s 20 m/s → km/h EX:

32. Done with units (fundamental and derived) scientific notation prefixes Forward to …..

33. Accuracy Accuracy is the closeness of agreement between a measured value and a true or accepted value Precision Precision is the degree of exactness (or refinement) of a measurement (results from limitations of measuring device used). No measurement can be "exact". You can never, NEVER get exact value experimentally Uncertainty and error in measurement Error in measurement is expected because of the imperfect nature of our measuring devices. The inevitable uncertainty is inherent in all measurements. It is not to be confused with a mistake or blunder

34. What is the length of the line? Significant figures EX: ▪ A ruler is an analog measuring device. ▪ So is a voltmeter with a needle. 01 certain digit:1 2 uncertain digit:7 or 8 estimate SIGNIFICANT FIGURES SIGNIFICANT FIGURES are all certain (reliably known) digits + one uncertain (estimate) 1.28 units

35. tenths place 09.400.0 ▪ On the other hand, if measuring with digital measuring device, one doesn’t know if the last digit is the result of rounding up, or rounding down or it is the measured digit. SIGNIFICANT FIGURES SIGNIFICANT FIGURES are all certain (reliably known) digits + one uncertain (last one)

36. Estimating quantities to an appropriate number of sig. fig. How long is this line? It is 1.28 cm (or maybe 1.27 cm) long ▪ The 1 and the 2 are the certain digits. ▪ The 8 (or 7) is the uncertain digit What is the reading on each of the graduated cylinders? Which digits are uncertain. EX: (A)(B) Read to the bottom of the meniscus. (A) reads 52.8 mL. The 8 is uncertain. (B) Reads 6.62 mL. The 2 is uncertain.

37. SIGNIFICANT FIGURES are reliably known digits + one uncertain (estimate) (1) All non-zero digits are significant. (2) All zeros between non-zero digits are significant. (3) Filler zeros to the left of an understood decimal place are not significant. (4) Filler zeros to the right of a decimal place are not significant. (5) All non-filler zeros to the right of a decimal place are significant. 438 g 26.42 m 0.75 cm 3 4 2 12060 m 900.43 cm 4545 220 L 60 g 30. cm 212212 0.006 L 0.08 g 1111 8.0 L 60.40 g 2424

38. Significant figures in calculations  Multiplication and division – round your answer to the same number of significant digits as the quantity with the fewest number of significant digits.  Addition and subtraction – round your answer to the same number of decimal places as the quantity with the fewest number of decimal places. (1.2 cm)(2 cm) 2.4 cm 2 2 cm 2  (2.75 cm) 2 7.5625 cm 2 7.56 cm 2 5.350 m/2.752 s1.944040698 m/s 1.944 m/s (0.0075 N)(6 m)0.045 Nm0.04 Nm 0.00530 m – 2.10 m -2.0947 m-2.09 m 1.2 cm + 2 cm 3.2 cm 3 cm 2000 m+2.1 m 2002.1 m 2000 m Find: calculator result: proper result:

39. Mass of universe 10 50 kg Diameter of universe 10 25 m Diameter of galaxy 10 21 m Age of universe 10 18 s Speed of light 10 8 m s -1 Diameter of atom 10 -10 m Diameter of nucleus 10 -15 m Diameter of quark 10 -18 m Mass of proton 10 -27 kg Mass of quark 10 -30 kg Mass of electron 10 -31 kg Planck length 10 -35 m Orders of magnitude

40. Quoting and comparing ratios, values and approximations to the nearest order of magnitude EX: Given that the smallest length in the universe is the Planck length of 10 -35 meters and that the fastest speed in the universe is that of light at 10 8 meters per second, find the smallest time interval in the universe. ▪ speed = d / t ▪ t = 10 -35 / 10 8 = 10 -43 seconds Find the difference in order of magnitude of the mass of the universe ( 10 50 kilograms) to the mass of a quark ( 10 -30 kilograms ). ▪ Make a ratio (fraction) and simplify. ▪ 10 50 kilograms / 10 -30 kilograms = 10 80. ▪ Note that the kilograms cancels leaving a unitless power of ten. ▪ The answer is 80 orders of magnitude. EX:

41. Quoting and comparing ratios, values and approximations to the nearest order of magnitude ▪ Diameter of nucleus is 10 -15 m. ▪ Diameter of atom is 10 -10 m. ▪ 10 -15 m / 10 -10 m = 10 -15 – (-10) = 10 -5. EX:

42. Quoting and comparing ratios, values and approximations to the nearest order of magnitude ▪ The “92” in 92 Sr means 92 nucleons. ▪ The mass of nucleons (protons and neutrons) is of the order of 10 -27 kg. ▪ 92 is of the order of 10 2. ▪ Thus 10 2  10 -27 kg = 10 -25 kg. EX:

43. Quoting and comparing ratios, values and approximations to the nearest order of magnitude EX:  V Earth = 10 12 km 3 = 10 12  (10 3 ) 3 = 10 12 + 9 = 10 21 m 3.  V sand = 1 mm 3 = 10 0  (10 -3 ) 3 = 10 0 - 9 = 10 -9 m 3.  N sand = V Earth / V sand = 10 21 / 10 -9 = 10 21 – (-9) = 10 30

44. Quoting and comparing ratios, values and approximations to the nearest order of magnitude Estimation revisited  Another form of estimation is to solve complex problems with the simplest math possible and obtain a ballpark figure as an answer.  If at all possible, only powers of ten are used. EXAMPLE: NY and LA are separated by about 3000 mi and three time zones. What is the circumference of Earth?  Since 3000 mi = 3 TZ, 1000 mi = 1 TZ.  There are 24 h in a day.  Earth rotates once each day. Thus there are 24 TZ in one circumference, or 24  1000 mi = 24000 mi.

45. Quoting and comparing ratios, values and approximations to the nearest order of magnitude The human heart rate is about 75 beats per minute. This is between 10 1 (10) and 10 2 (100).  But 1 hour is 60 min, which is also between 10 1 (10) and 10 2 (100).  Then our answer is between 10 1  10 1 = 10 2 and 10 2  10 2 = 10 4.