Laying the Groundwork

1. Laying the Groundwork Observing, Estimating, Measuring, Recording, Graphing, Analyzing, Interpreting …and Units!

2. We Are Scientists, We Use Scientific Notation!

3. Scientific Notation, Specifically 10n means 10 x 10 x 10 … [n times] 10-n means 1/(10 x 10 x 10 ….) [n times] 10a •10b = 10 a + b 10a ÷10b = 10 a - b

4. We are Scientists, We use the Metric System! • Length • Mass • Time • Temperature • First, a little historical information on the system • Then, a review of the prefixes • Finally, specifics for:

5. History of the Metric System • Created at the end of the 18th Century to provide a consistent system of units amidst a wide variety of different standards. • Previously, each area had its own units inherited from earlier times. • Not reproducable, not standard • e.g., a "cubit" was the length from the elbow to the tip of the middle finger. • e.g., a rundlet was worth 16 gallons in a certain town and 18 gallons in another town

6. History, Part 2 • The metric system became compulsory in France on Dec.10, 1799 (Napoleon was First Consul) and, being practical, spread slowly across Europe. • Not without resistance : a few years later, even France came back to the old system for several years. • Japan made it official in 1868 and Russia in 1917. • England was the last European country to adopt it : the adaptation period began in 1965 and was to end officially in 1980.

7. History, Part 3 • In 1960, the SI (International System) was created • It fine tuned the system, introducing some new units and shedding others. • It replaces the old systems, named MKSA, MTS, and CGS (although some intrepid physicists still use CGS from time to time, which is considered OK since they do at least provide a consistent set of secondary units.)

8. History, Part 4 • The seven primary units are now : • * length : meter (m) • * mass : kilogram (kg) • * time : second (s) • * electric current : ampere (A) • * temperature : Kelvin or Celsius (K or °C) • * quantity of matter : mole • * light intensity : candela (cd)

9. Prefixes One of the clever ideas behind the system was to use only multiples of ten. Today mainly multiples of 1000 are in use. These are the only words to memorize (if you're not lucky enough to have enjoyed them since Grade 3) : * 1018 : exa- (E) * 1015 : peta- (P) * 1012 : tera- (T) * 109 : giga- (G) * 106 : mega- (M) * 103 : kilo- (k) * 10-3 : milli- (m) * 10-6 : micro- (µ) * 10-9 : nano- (n) * 10-12 : pico- (p) * 10-15 : femto- (f) * 10-18 : atto- (a)

10. Old, but not Forgotten Some prefixes by ten, around the main unit, are still in use : * 100 : hecto- (h) like in hectolitre (used by the breweries - God save the beer !) * 10 : deca- (da) like in decameter (sometimes written dekameter) * 0.1 : deci- (d) like in decibel * 0.01 : centi- (c) like in centipoise (same root as "cent", you may say centidollar !)

11. Length Unit of length: meter The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.

12. Meter • Originally defined as one ten-millionth of the distance between a Pole and the Equator as measured from 1792 along a meridian from Dunkirk to Barcelona across Paris • This measurement took several years through wars and civil unrest • Astronomers were arrested by revolutionaries because they had lots of paper and white was the “King's color” ! • If the Earth were a perfect sphere, its circumference would be 40,000 km, and the distance from a Pole to the Equator would be 10 000 km.

13. A Fly in the Ointment • It was already known that the Earth was flattened on the Poles. • Nevertheless, a meridian was chosen (in a typical French Revolution way) because it was valid "for all people around the Earth, whereas the Equator only covers a small fraction of humanity". • The meter was set for a long time by its physical model in platinum-iridium, in Paris. Hard to reproduce, and eventually scientists needed more precision • Physicists introduced it as a multiple of a wavelength (1, 650, 763.73) times the wavelength of the radiation associated with a certain atomic jump in Krypton 86.

14. Historical Detail Meter was first defined as the length of a pendulum which oscillated with a period of two seconds. This was dropped because of the difficulty in measuring the exact length of the string from the oscillation axis to the center of the ball - and also the gravity "g" is not constant all over the Earth.

15. Special Units • One millionth of a meter, or micrometer, is often called micron • The angstrom, not SI but still used in physics, is equal to 10-10 meter

16. Old Anglo Saxon Units Used today ONLY in USA • inch : 25.4 mm • foot = 12 inches = 0.3048 m • yard = 3 feet = 0.9144 m • mile = 1760 yards = 1609.344 m (derived from the Roman Mile : "mille passus" equal to 1000 paces or double steps, estimated at 1475 to 1522 m. This makes the step = 0.75 m (remember the Romans were not as tall as we are). • nautical mile = 6076.115 feet = 1852 m

17. USA and the Metric System • Thomas Jefferson considered a conversion to the metric system. In 1889, the US Congress adopted the meter as a standard and, thereafter, the inch, foot, yard, etc. were defined in relation to the meter. • The Metric Conversion Act of 1975 committed the US to the increasing use of, and voluntary conversion to, the metric system of measurement.

18. Mass Unit of mass: kilogram   The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

19. Kilogram • As the name implies, the original unit was the gram (weight of 1 cubic centimeter or 1 milliliter of water at 4 °C) but it soon became the kg (or 1000 grams or one cubic decimeter of water), and defined by its model in platinum-iridium kept in Paris. • One may also mention the carat used in jewelry (5 carats = 1 gram). But carat is not an SI unit!

20. Historical Detail • Before the computations of the Dunkirk-Barcelona meridian were completed, a first measure was introduced : the grave (same root as gravity) equal to the weight of one cubic decimeter of water. • Later, the (now well defined) milligrave - already dubbed the gravet - was renamed the gram.

21. Old Anglo-Saxon Units • pound : 0.45359237 kg in the Avoirdupois system (but 0.3732417 kg in the Troy and Apothecaries systems.) The smallest unit common to the different systems is the grain ( = 64.7989 milligrams) with 7000 grains making one (Avoirdupois) lb. and 5760 grains for one pound in the other systems. The abbreviation "lb" comes from the equivalent Roman weight "libra”. • ounce : In Avoirdupois : 437.5 grains ( = 28.3495 g -- 16 oz = 1 lb.). In the other systems : 480 grains ( = 31.10348 g -- 12 oz = 1 lb.) 12 Roman "unciae" made 1 "libra" - uncia simply means one twelfth in Latin.)

22. Time Unit of time: second The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

23. Nature Gives Us Natural Time Scales • Originally, the second was 1/86400 of the mean solar day. • But, the mean solar day changes slowly, so it was redefined on a steadier atomic level • Original Cesium clocks good to about 1 second every 3,000 years

24. Atomic Clock at NIST The uncertainty of NIST-F1 is less than 2 x 10-15, which means it would neither gain nor lose a second in 20 million years!

25. Seemed Like a Good Idea, but... There was a trial to "metricate" the time and the calendar during the French revolution. Months were to be made of three weeks, each ten days long. Each day had 10 hours. The system lasted only a few years. The clockmakers opposed violently the millihours ( = 8.64 sec), while the clergy resented the cancellation of the Sabbath. This last opposition is probably at the root of the long time dislike towards the metric system in the US.

26. Temperature Unit of thermodynamic temperature: Kelvin The Kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

27. History of Temperature Scales The first to seal mercury in a glass rod was Daniel Fahrenheit in Germany (1709). He had to build a scale from scrap : zero was allocated to the temperature of a salty mixture, assuming that nothing could ever be colder and 96 was his estimate of the human body. With such a scale, water would freeze at 32 and boil at 212. 1686 - 1736

28. History of Temperature Scales • In 1730, in France, Rene Antoine Ferchault de Reaumur built the first alcohol thermometer. He allocated 0 to freezing water and 80 to boiling water. • In 1742, in Sweden, the astronomer Anders Celsius used a scale allocating 100 to freezing water and 0 (!) to boiling water. His scale was later inverted (0 to freezing water and 100 for boiling) and long known as "centigrade". Celsius 1701 - 1744

29. Half a Dozen One, 6 to the Other • Comparing the scales, 9° Fahrenheit = 4° Reaumur = 5° Celsius * C = (F - 32) * 5/9 * F = 32 + C * 9/5 • The two scales meet at - 40 * - 40°F is the same as - 40°C

30. Absolute Temperature • Starting from the absolute zero (at -273.15 C or -459.67 F), it was tempting to follow the old idea of Fahrenheit and have only a positive scale. This was done by Sir William Thomson, Lord Kelvin, from the Celsius scale. • Water is freezing at 273.15 K, and boiling at 373.15 K • The SI uses the Kelvin scale, defined by the triple point of water (at 273.16 K or 0.01°C) and absolute zero. 1824 - 1907

31. Counting and Measuring Physics is the science of measurement. “When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind. It may be the beginning of knowledge, but you have scarcely Advanced to the state of Science.” Lord Kelvin (1824 - 1907)

32. Accuracy and Precision Limit of precision of a measuring divide is one-half the smallest division of measurement the device is able to display The accuracy of a measurement is the extent to which systematic errors make a measured value differ from its true value Accurate Precise Accurate & Precise

33. Errors Systematic Errors: errors due either to incorrect design or calibration of the measuring device, or to incorrect reading or interpretation of the device Statistical Errors: differences in individual measurements of a quantity which are greater than the precision of the measuring device, these differences arise from fluctuations in the quantity being measured.

34. What It Means

35. Significant Digits The digits in a measured or calculated quantity are those digits which are known with certainty Rules: 1. When adding or subtracting measured quantities, the precision of the answer can only be as great as the least precise term in the sum or difference. All digits up to this limit of precision are significant. 2. When multiplying or dividing measured quantities, the number of significant digits can be only as great as the least number of significant digits in any factor in the calculation.

36. Insights into Sig Figs Zeroes can be confusing. They often appear only to locate the decimal point…which means they are not significant. Using scientific notation will resolve this issue. Calculators cannot increase the number of sig figs in nor the precision of your measurements. You must round off the result to the correct number of digits.

37. Vectors and Scalars A scalar is a quantity that has a magnitude only A vector is a quantity that has both a direction and a magnitude There are specific rules for adding and subtracting vectors. We’ll learn more about this later.

38. Graphs Graphs display in a ready visualized form the relationship between pairs of independent quantities. Scientists tend to use the words “graphs” and “plots” interchangeably.

39. Scatter Plots • Data consists of pairs of numbers, e.g., intensity and time, height and distance, salary and age • Plot allows you to perform mathematical fits, looking for trends

40. Histogram A histogram is defined as a bar graph that shows frequency data. The first step in making a histogram is to collect data and sort it into categories. To continue, you must label the data as the independent set or the dependent set. The characteristic you grouped the data by would be the independent variable and the frequency of that set would be the dependent variable.

41. Histogram • Histograms are "sorting bins." You have one variable, and you sort data by this variable by placing them into "bins." Then you count how many pieces of data are in each bin. The height of the rectangle you draw on top of each bin is proportional to the number of pieces in that bin.

42. We Are Scientists, We Use the Scientific Method • It is important to be as objective as possible. • There is no right place to enter the cycle. • Experiments must be reproducible. • There is no end to the cycle. • The cycle is not rigid.