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P2 (H) Make measurements with accuracy and precision and record data using scientific notation and International System (SI) units. P2 (I) Identify and quantify causes and effects of uncertainties in measured data. P2 (J) Organize and evaluate data and make inferences from data, including the use of tables, charts, and graphs. P2 (K) Communicate valid conclusions supported by the data through various methods such as lab reports, labeled drawings, graphic organizers, journals, summaries, oral reports, and technology-based reports. P2 (L) Express and manipulate relationships among physical variables quantitatively, including the use of graphs, charts, and equations. After studying this unit, the students should be able to Give the basic quantities of physics and their units Convert quantities from one set of units to another Perform dimensional analysis (metric and english units) Use scientific notation Report answers with a reasonable amount of precision, given the measurements provided Use basic trigonometric functions (SOH CAH TOA) Identify and give the relationships between quantities using sentence, symbols, formula and graphs Contents •Base quantities and their units •Definition of SI base units •Prefixes used in SI system •Mass and weight •Density •Temperature •Uncertainty in measurements •Scientific notation Systems of Measurement 1. English System – FPS- foot, pound, second 2. Metric System a) MKS – meter, kilogram, second b) CGS – centimeter, gram, second Base physical quantity Symbol for quantity Name for SI unit Symbol for SI unit Length l Meter m Mass m Kilogram Kg Time t Second s Electric current I Ampere A Thermodynami c temperature T Kelvin K Amount of substance n Mole mol Luminous intensity I Candela cd DATA SCIENCE is… the search for relationships that explain and predict the behavior of the universe. PHYSICS is… the science concerned with relationships between matter, energy, and its transformations. There is no such thing as absolute certainty of a scientific claim. The validity of a scientific conclusion is always limited by: • the experiment design, equipment, etc... • the experimenter human error, interpretation, etc... • our limited knowledge ignorance, future discoveries, etc... Scientific Law a statement describing a natural event Scientific Theory an experimentally confirmed explanation for a natural event Scientific Hypothesis an educated guess (experimentally untested) developed in France in 1795 a.k.a. “SI” - International System of Units The U.S. was (and still is) reluctant to “go metric.” • very costly to change • perception of “Communist” system • natural resistance to change • American pride The SI unit of: • length is the meter, m • time is the second, s • mass is the kilogram, kg. • electric charge is the Coulomb, C • temperature is the degree Kelvin, K • an amount of a substance is the mole, mol • luminous intensity is the candle, cd • The second is defined in terms of atomic vibrations of Cesium-133 atoms. • The meter is defined in terms of the speed of light. • The kilogram is still defined by an official physical standard. “Derived units” are combinations of these “fundamental units” Examples include speed in m/s, area in m2, force in kg.m/s2, acceleration in m/s2, volume in m3, energy in kg.m2/s2 1018 1015 1012 109 106 103 102 101 exa peta tera giga mega kilo hecto deka E P T G M k h da 10-18 10-15 10-12 10-9 10-6 10-3 10-2 10-1 atto a femto f pico p nano n micro m milli m centi c deci d Explore the metric system at link1, link2, and link3. See definitions of metric units here. Click here to do conversions. All measurements have some degree of uncertainty. Precision single measurement - exactness, definiteness group of measurements - agreement, closeness together Accuracy closeness to the accepted value % error = accepted - observed x 100% accepted Example of the differences between precision and accuracy for a set of measurements: Four student lab groups performed data collection activities in order to determine the resistance of some unknown resistor (you will do this later in the course). Data from 5 trials are displayed below. Group Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 avg 1 34 612 78 126 413 132.6 2 126 127 126 128 125 126.4 3 20 500 62 980 938 500 4 502 501 503 498 499 500.6 Suppose the accepted value for the resistance is 500 Ω. Then we would classify each groups’ trials as: Group 1: neither precise nor accurate Group 2: precise, but not accurate Group 3: accurate, but not precise Group 4: both precise and accurate 1. All non-zero digits are significant. 2. Zeros between other significant digits are significant. 3. Leading zeros are not significant. 4. Final zeros before the decimal are not significant. Operations with Significant Digits Addition and Subtraction (link) round the sum or difference to the least precise decimal place Multiplication and Division (link) round so that the product or quotient has a total number of significant digits equal to the total number of significant digits of the least precise quantity Learn more about significant digits here and here. Check your understanding here and here. The “bottom line” is that the precision to which a measured or calculated amount is written provides valuable information as to the precision (certainty) of that value and the device used to measure it. Practice on significant figures, scientific notation, precision vs accuracy, metric system prefixes.