# PHYSICS UNIT 0: FOUNDATIONS. MEASUREMENT Units of Measure - Metric System (SI) Fundamental Units: defined by scientists DimensionUnit Symbol lengthmeterm.

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PHYSICS UNIT 0: FOUNDATIONS

MEASUREMENT Units of Measure - Metric System (SI) Fundamental Units: defined by scientists DimensionUnit Symbol lengthmeterm masskilogramkg timeseconds currentampere A temperatureKelvinK Derived Units: combinations of fundamental units ex: area measured in m 2, density measured in g/cm 3

Measurement Important Ranges of Magnitudes to remember Distances – size of a nucleus(10^-15 m) to size of the universe (10^25 m) Masses – mass of an electron(10^-30 kg) to mass of the universe (10^53 kg) Times – time for light to pass a nucleus (10^-23 s) to age of the universe (10^18 s) So what are the order of magnitude differences?

MEASUREMENT prefixes: for larger or smaller quantities Prefix Symbol Value Example Giga G10 9 30 Gb = 30,000,000,000 b mega M 10 6 2.1 Mm = 2,100,000 m kilo k 10 3 3.5 kg = 3500 g deci d 10 –1 8.7 dL = 0.87 L centi c 10 –2 5.9 cs = 0.059 s milli m 10 –3 7.2 mmol = 0.0072 mol micro  10 –6 4.4  m = 0.0000044 m nano n 10 –9 9.0 ng = 0.000000009 g

MEASUREMENT conversions from one prefix to another: mega kilo none deci centi milli micro nano 1000 1000101010 1000 1000 larger units smaller units  divide   multiply 

MEASUREMENT conversion factors - multipliers that change units without changing equation’s overall value (factors have a value of 1) ex: 1 in = 2.54 cm factors: set up so units cancel ex: find the kilometers in 1 mile

MATHEMATICS Scientific Notation: shorthand for large & small numbers form: 0.00 × 10 0 (number ≥ 1 & < 10 × power of 10) ex: 450,000,000 = 4.5 × 100,000,000 = 4.5 × 10 8 0.0000036 = 3.6 × 0.000001 = 3.6 × 10 –6

MATHEMATICS Scientific Calculators 4.5 × 10 8 is entered and may appear as or 3.6 × 10 –6 is entered and may appear as or some calculators use instead of 3. 6 EE +/- 6 4. 5 EE 8 4.5 08 3.6 -06 EXP EE

UNCERTAINTY Significant Figures shorthand way of showing precision & uncertainty number of sig. fig's = # of digits BUT don't count beginning zeroes AND don't count ending zeroes unless there is a decimal. 234.1514.080 560,000 0.00282 5.6 × 10 5

UNCERTAINTY Significant Figures calculations cannot be more exact than measurements: a. round off to least number of sig. fig's ex:(1.05)(39.04)(251,000)(0.0044)=45271.5 65 round off to 2 sig. fig's = 45,000 b. round off once, at the end of all calculations c. when in doubt, round to 3 sig. fig's

PHYSICS UNIT 0: FOUNDATIONS

The 2 Major Types of Error in Experimental Physics Systematic Error- Errors inherent in the system of data taking. (Can not be cancelled with lots of data) Example – using an uncalibrated scale. Random Error- are inherently unpredictable. (Can be cancelled out with lots of data) Example – stopping a stop watch too early sometimes and too late other times.

Systematic Error There are 3 major types of systematic error human error: mistakes in reading & recording make repeat measurements (Do not include in lab write up, instead fix human problem). method error: mistakes in measurement methods choose the best method & use it consistently. instrument error: mistakes due to damaged instruments check instrument calibration, use carefully.

UNCERTAINTY Accuracy- the degree of closeness of experimental result with theoretical result. (Low systematic error) Assessing accuracy: percent error (if you know what the measurement should have been by other methods)

UNCERTAINTY Precision: limitations of a measuring instrument (Sensitivity) the more digits you can read, the more precision (less uncertainty) A precise measuring device will take repeated measurements that are close to each other.

GRAPHING title graph dependent variable: y, independent variable:x Uncertainty in data should be included on graph Include the equation that best fits the data purpose: finding patterns & relationships drawing graphs: choose & show scale on each axis - fit all data label each axis: measured quantity & units

GRAPHING graph interpretation: linear relationship: as x increases, y increases (y  x) y = mx+b m: slope, b:y-intercept Said “The distance traveled by a car moving at constant speed is directly proportional to the time travelled.”.

GRAPHING graph interpretation: quadratic relationship: as x increases, y increases (y  x 2 ) y = kx 2 k: appropriate constant Said “The bacteria population grew exponentially with time.”

GRAPHING graph interpretation: inverse relationship: as x increases, y decreases (y  1/x) y = k/x k: appropriate constant Said “For any given constant force acting on an object there is an inverse relationship between and object’s mass and it’s acceleration”

UNIT 0 QUIZ PREVIEW Concepts Covered: metric system: units, prefixes & conversions accuracy, precision & significant figures math skills – algebra, scientific notation, estimation, types of graphs. What’s On The Quiz: __ multiple choice/matching __ problems

Equations for Propagating Error Sum Difference Product Quotient

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