Chapter 1 Measurement, Models and Analysis. Definition of Physics: –Physics is the study of matter...

Chapter 1Chapter 1Measurement Models Measurement Models

and Analysisand Analysis

Definition of PhysicsDefinition of Physicsndash Physics is the study of matter and energy and their Physics is the study of matter and energy and their

relationshipsrelationships

What is the difference between pure What is the difference between pure science and applied sciencescience and applied sciencendash Pure science isPure science is

Studying a topic to gain knowledge or understand Studying a topic to gain knowledge or understand how something workshow something works

Examples Electron flow sunrsquos composition Examples Electron flow sunrsquos composition structure of chromosomesstructure of chromosomes

ndash Applied science isApplied science isThe practical use of scientific informationThe practical use of scientific information

Applied science can also be called Applied science can also be called technologytechnology

Examples Electricity Solar Power Genetic Examples Electricity Solar Power Genetic EngineeringEngineering

Pure SciencePure Science Applied ScienceApplied Science

QuestionQuestionndash What do we want to learn What do we want to learn

or understandor understand

HypothesisHypothesisndash An educated guess to An educated guess to

answer the questionanswer the question

ExperimentExperimentndash Testing the hypothesisTesting the hypothesis

AnalysisAnalysisndash Studying results to find Studying results to find

patternspatterns

ConclusionConclusionndash Do our results support our Do our results support our

hypothesishypothesis

ProblemProblemndash What do we want to What do we want to

change or improvechange or improve

DesignDesignndash A solution that we think will A solution that we think will

workwork

TestTestndash Build the design and see if Build the design and see if

it worksit works

AnalysisAnalysisndash Evaluate the results of the Evaluate the results of the

testtest

ConclusionConclusionndash Did the design work or do Did the design work or do

we need changeswe need changes

(the scientific method) (the engineering process)

Metric System (def) Metric System (def) ndash A set of standards of measurement where A set of standards of measurement where

units of different sizes are related by powers units of different sizes are related by powers of 10of 10

SI (def)SI (def)ndash (Syst(Systegraveegraveme Internationale drsquoUnitme Internationale drsquoUniteacuteeacutes) s)

International standards of measurement International standards of measurement adapted from the metric systemadapted from the metric system

Base Units (def)Base Units (def)ndash The seven fundamental units of measureThe seven fundamental units of measure

SI Base UnitsSI Base Units

LengthLength MassMass TimeTime TemperatureTemperature Amount of a Amount of a

SubstanceSubstance Electric Electric

CurrentCurrent Luminous Luminous

IntensityIntensity

metermeter kilogramkilogram secondsecond kelvinkelvin molemole

ampereampere

candelacandela

Base QuantityBase Quantity Base Unit Base Unit Symbol Symbol

mm kgkg ss KK molmol

AA

cdcd

These units are the most commonly used These units are the most commonly used units in Physics They are in the MKS units in Physics They are in the MKS (meter-kilogram-second) system(meter-kilogram-second) systemndash Two other systems are the CGS (centimeter-Two other systems are the CGS (centimeter-

gram-second) system and the FPI (foot-gram-second) system and the FPI (foot-pound-inch) system pound-inch) system

We will be working mostly with the MKS We will be working mostly with the MKS systemsystemAlways remember to stick with the same Always remember to stick with the same measurement system through the whole measurement system through the whole problemproblem

Derived Units (def)Derived Units (def)ndash Unit of a quantity that is a combination of Unit of a quantity that is a combination of

base unitsbase unitsExamples msec (unit of speed) kgExamples msec (unit of speed) kgmm22secsec22 (joule (joule a unit of energy)a unit of energy)

Note that all base units are in the MKS systemNote that all base units are in the MKS system

Review of Scientific NotationReview of Scientific NotationFormat Format MM x x 1010nn where where 11 M M 1010 and n is an and n is an integerinteger

11 Move the decimal point until one digit remains on Move the decimal point until one digit remains on the leftthe left

22 The number of places you moved the decimal is |n|The number of places you moved the decimal is |n|

33 The direction that you moved the decimal The direction that you moved the decimal determines determines the sign of the exponent nthe sign of the exponent n

aa If you moved the decimal to the If you moved the decimal to the rightright (the number is (the number is smallsmall) )

n is n is negativenegative

0000000123 = 0000000123 = 123 x 10123 x 10-7-7

bb If you moved the decimal to the If you moved the decimal to the leftleft (the number is (the number is largelarge) ) n is n is positivepositive

300000000 = 300000000 = 30 x 1030 x 1088

AddingSubtractingAddingSubtractingScientific NotationScientific Notation

AddingSubtracting numbers in scientific AddingSubtracting numbers in scientific notationnotation

aa Make ldquonrdquo the same between the numbers Make ldquonrdquo the same between the numbers that you are adding or subtractingthat you are adding or subtracting

bb Add or subtract ldquoMrdquoAdd or subtract ldquoMrdquo

cc Put your result in proper scientific notation Put your result in proper scientific notation and check significant figuresand check significant figures

MultiplyingDividing MultiplyingDividing Scientific NotationScientific Notation

Multiplying or dividing numbers in Multiplying or dividing numbers in scientific notationscientific notation

aa Multiply or divide the ldquoMrdquoMultiply or divide the ldquoMrdquo

bb Add exponents if multiplyingAdd exponents if multiplying

cc Subtract exponents if dividingSubtract exponents if dividing

dd Put your result in proper scientific notation Put your result in proper scientific notation and check significant figuresand check significant figures

Prefixes Used with SI UnitsPrefixes Used with SI Units

teratera TT 1 000 000 000 0001 000 000 000 000 10101212 terameter (Tm)terameter (Tm)

MultiplierMultiplier ScientificScientificPrefixPrefix SymbolSymbol (decimal)(decimal) NotationNotation ExampleExample

gigagiga GG 1 000 000 0001 000 000 000 101099 gigameter (Gm)gigameter (Gm)

megamega MM 1 000 0001 000 000 101066 megagram(Mg)megagram(Mg)

kilokilo kk 10001000 101033 kilometer (km)kilometer (km)

centicenti cc 001001 1010-2-2 centimeter (cm)centimeter (cm)

decideci dd 0101 1010-1-1 deciliter (dL)deciliter (dL)

millimilli mm 00010001 1010-3-3 milligram (mg)milligram (mg)

nanonano nn 0000 000 0010000 000 001 1010-9-9 nanometer (nm)nanometer (nm)

micromicro μμ 0000 0010000 001 1010-6-6 microgram (microgram (μμgg))

picopico pp 0000 000 000 0010000 000 000 001 1010-12-12 picometer (pm)picometer (pm)

femtofemto ff 0000 000 000 000 0010000 000 000 000 001 1010-15-15 femtosecond femtosecond (fs)(fs)

Prefixes most commonly used in Physics Prefixes most commonly used in Physics arearendash k c mk c m

Converting SI UnitsConverting SI Units

move decimal move decimal rightright

rarrrarrK H D K H D base unitbase unit d c m d c m

larrlarrmove decimal move decimal leftleft

Factor Label MethodFactor Label Method

Conversion Factor (def)Conversion Factor (def)ndash A multiplier equal to 1 A multiplier equal to 1

ExampleExample 1 kg = 1000 g1 kg = 1000 gndash Therefore Therefore

1 kg

1000 g

1000 g

1 kg= 1 = 1

The value of a quantity does not change The value of a quantity does not change when it is multiplied or divided by onewhen it is multiplied or divided by one

OR

ExamplesExamplesaa 1 Mg = 1 Mg = g g

ldquoldquoMrdquo means megaMrdquo means megabull Therefore we can rewrite 1 Mg as 10Therefore we can rewrite 1 Mg as 1066 g g

bb 1376 1376 μμm m = = mm = 1376 x 10= 1376 x 10-6 -6 mm

1 Eliminating a Prefix1 Eliminating a Prefix

2 Adding a Prefix2 Adding a Prefix

Use prefix table to create conversion factorUse prefix table to create conversion factor

ExampleExampleaa 137 m = ______ nm137 m = ______ nm

ldquoldquonrdquo = nanonrdquo = nano

A conversion factor is a ratio that is equal to 1 A conversion factor is a ratio that is equal to 1 For ldquonmrdquo we have two possibilitiesFor ldquonmrdquo we have two possibilities

Use the conversion factor that will cancel the Use the conversion factor that will cancel the units you need to eliminateunits you need to eliminate

1 nm

10-9 m

10-9 m

1 nm= 1 = 1OR

137 m x 1 nm

10-9 m= 137 x 109 nm

= 137 x 1010 nm

3 If you have more than one conversion3 If you have more than one conversion in the problem use multiple in the problem use multiple

conversion factorsconversion factorsExampleExample

aa Convert 11 cm to Convert 11 cm to μμmm1 cm = 101 cm = 10-2-2 m 1 m 1 μμm = 10m = 10-6 -6 mm

Conversion factorsConversion factors

= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m

The equatorial rotation velocity of the earth The equatorial rotation velocity of the earth is 46511 ms (meters per second) This is is 46511 ms (meters per second) This is based on the sidereal rotation of earth based on the sidereal rotation of earth which is the reference rotation period used which is the reference rotation period used by scientists by scientists

Trigonometry ReviewTrigonometry Review

11 The interior angles of a triangle total 180ordmThe interior angles of a triangle total 180ordm

22 Pythagorean theoremPythagorean theorem

33 Trig functionsTrig functions

The measuring tools that we will use most The measuring tools that we will use most frequently are the meter stick balance and frequently are the meter stick balance and stopwatchstopwatch

The meter stick and balance should The meter stick and balance should always be read with your eye directly in always be read with your eye directly in line with the device to avoid inaccuracy line with the device to avoid inaccuracy that results from that results from parallaxparallax

Parallax (def)Parallax (def)ndash The apparent shift in the position of an object The apparent shift in the position of an object

when it is viewed from different angleswhen it is viewed from different angles

Measurement UncertaintiesMeasurement Uncertainties

In most cases you read a device to the value of In most cases you read a device to the value of its finest division then estimate its finest division then estimate one decimalone decimal beyond thatbeyond that

DeviceFinest

divisionMeasurement

Meter stick 1 mm xx mm

Balance 01 g xxx g

Reading a stopwatch For a stopwatch you read Reading a stopwatch For a stopwatch you read what is given No estimating is requiredwhat is given No estimating is required

Accuracy vs PrecisionAccuracy vs Precision

AccuracyAccuracyndash How well the results of an experiment agree How well the results of an experiment agree

with the measured and accepted valuewith the measured and accepted value

PrecisionPrecisionndash The degree of exactness with which a quantity The degree of exactness with which a quantity

is measured using a given instrumentis measured using a given instrumentSometimes indicated by the number of significant Sometimes indicated by the number of significant figures a measurement containsfigures a measurement containsAlso has to do with the ldquorepeatabilityrdquo of the Also has to do with the ldquorepeatabilityrdquo of the measurement datameasurement data


For example a 6-place table is more For example a 6-place table is more precise than a 4-place table However if precise than a 4-place table However if there are errors in the 6-place table it may there are errors in the 6-place table it may be more or less accurate than the 4-place be more or less accurate than the 4-place tabletable

In many cases when precision is high and In many cases when precision is high and accuracy is low the fault can lie with the accuracy is low the fault can lie with the instrumentinstrument

Significant Digits Significant Digits (or Significant Figures)(or Significant Figures)

Significant Digits (def)Significant Digits (def)ndash The valid digits in a measurementThe valid digits in a measurement

Your answer can only be as exact as your Your answer can only be as exact as your least precise measurementleast precise measurement

When taking the measurements the When taking the measurements the estimated digit estimated digit isis significant significant

Significant Digits (cont)Significant Digits (cont)

Zeroes ndash When are they significantZeroes ndash When are they significantndash Nonzero digits are always significantNonzero digits are always significantndash All final zeros after the decimal point are All final zeros after the decimal point are

significant eg 3540000 ( 7 sig figs)significant eg 3540000 ( 7 sig figs)ndash Zeros between two other significant digits are Zeros between two other significant digits are

always significant eg 300004 (6 sig figs) always significant eg 300004 (6 sig figs) ndash Zeros used solely as placeholders are not Zeros used solely as placeholders are not

significant eg 0000009 (1 sig fig)significant eg 0000009 (1 sig fig)


How many significant figures are in each of the How many significant figures are in each of the numbers belownumbers below245 m 245 m rarrrarr

3 sig figs3 sig figs Rule 1Rule 1

308 km 308 km rarrrarr3 sig figs3 sig figs Rule 3Rule 3

180 g 180 g rarrrarr3 sig figs3 sig figs Rule 2Rule 2

000623 m 000623 m rarrrarr3 sig figs3 sig figs Rule 4Rule 4

Graphing DataGraphing Data

Identify the independent and dependent Identify the independent and dependent variables in your data variables in your data

The independent variable is plotted on the The independent variable is plotted on the horizontal or x-axis the dependent horizontal or x-axis the dependent variable is plotted on the vertical axis or y-variable is plotted on the vertical axis or y-axisaxis

The title of your graph is written ldquoy vs xrdquoThe title of your graph is written ldquoy vs xrdquo

Determine the range of the independent Determine the range of the independent variable to be plottedvariable to be plotted

Decide whether the origin (00) is a valid Decide whether the origin (00) is a valid data pointdata point

Spread the data out as much as possible Spread the data out as much as possible Let each division on the graph paper stand Let each division on the graph paper stand for a convenient unitfor a convenient unit

Number and label the horizontal axisNumber and label the horizontal axisndash The label should include the value name (eg The label should include the value name (eg

time) time) andand value units (eg seconds) value units (eg seconds)



Repeat steps 2 ndash 5 for the dependent Repeat steps 2 ndash 5 for the dependent variablevariablePlot the data points on the graphPlot the data points on the graphDraw the ldquobest fitrdquo straight line or smooth Draw the ldquobest fitrdquo straight line or smooth curve that passes through as many data curve that passes through as many data points as possible Do not use a series of points as possible Do not use a series of straight line segments that ldquoconnect the straight line segments that ldquoconnect the dotsrdquodotsrdquoGive the graph a title that clearly tells what Give the graph a title that clearly tells what the graph representsthe graph represents

Definition of PhysicsDefinition of Physicsndash Physics is the study of matter and energy and their Physics is the study of matter and energy and their

relationshipsrelationships

What is the difference between pure What is the difference between pure science and applied sciencescience and applied sciencendash Pure science isPure science is

Studying a topic to gain knowledge or understand Studying a topic to gain knowledge or understand how something workshow something works

Examples Electron flow sunrsquos composition Examples Electron flow sunrsquos composition structure of chromosomesstructure of chromosomes











patternspatterns






workwork


it worksit works


testtest













IntensityIntensity


ampereampere

candelacandela



AA

cdcd













0000000123 = 0000000123 = 123 x 10123 x 10-7-7


300000000 = 300000000 = 30 x 1030 x 1088

































1 kg

1000 g

1000 g

1 kg= 1 = 1


OR



bb 1376 1376 μμm m = = mm = 1376 x 10= 1376 x 10-6 -6 mm








1 nm

10-9 m

10-9 m

1 nm= 1 = 1OR

137 m x 1 nm

10-9 m= 137 x 109 nm

= 137 x 1010 nm





= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m












DeviceFinest

divisionMeasurement


Balance 01 g xxx g















































patternspatterns






workwork


it worksit works


testtest













IntensityIntensity


ampereampere

candelacandela



AA

cdcd













0000000123 = 0000000123 = 123 x 10123 x 10-7-7


300000000 = 300000000 = 30 x 1030 x 1088

































1 kg

1000 g

1000 g

1 kg= 1 = 1


OR



bb 1376 1376 μμm m = = mm = 1376 x 10= 1376 x 10-6 -6 mm








1 nm

10-9 m

10-9 m

1 nm= 1 = 1OR

137 m x 1 nm

10-9 m= 137 x 109 nm

= 137 x 1010 nm





= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m












DeviceFinest

divisionMeasurement


Balance 01 g xxx g














































IntensityIntensity


ampereampere

candelacandela



AA

cdcd













0000000123 = 0000000123 = 123 x 10123 x 10-7-7


300000000 = 300000000 = 30 x 1030 x 1088

































1 kg

1000 g

1000 g

1 kg= 1 = 1


OR



bb 1376 1376 μμm m = = mm = 1376 x 10= 1376 x 10-6 -6 mm








1 nm

10-9 m

10-9 m

1 nm= 1 = 1OR

137 m x 1 nm

10-9 m= 137 x 109 nm

= 137 x 1010 nm





= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m












DeviceFinest

divisionMeasurement


Balance 01 g xxx g

















































0000000123 = 0000000123 = 123 x 10123 x 10-7-7


300000000 = 300000000 = 30 x 1030 x 1088

































1 kg

1000 g

1000 g

1 kg= 1 = 1


OR



bb 1376 1376 μμm m = = mm = 1376 x 10= 1376 x 10-6 -6 mm








1 nm

10-9 m

10-9 m

1 nm= 1 = 1OR

137 m x 1 nm

10-9 m= 137 x 109 nm

= 137 x 1010 nm





= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m












DeviceFinest

divisionMeasurement


Balance 01 g xxx g





































































1 kg

1000 g

1000 g

1 kg= 1 = 1


OR



bb 1376 1376 μμm m = = mm = 1376 x 10= 1376 x 10-6 -6 mm








1 nm

10-9 m

10-9 m

1 nm= 1 = 1OR

137 m x 1 nm

10-9 m= 137 x 109 nm

= 137 x 1010 nm





= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m












DeviceFinest

divisionMeasurement


Balance 01 g xxx g







































bb 1376 1376 μμm m = = mm = 1376 x 10= 1376 x 10-6 -6 mm








1 nm

10-9 m

10-9 m

1 nm= 1 = 1OR

137 m x 1 nm

10-9 m= 137 x 109 nm

= 137 x 1010 nm





= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m












DeviceFinest

divisionMeasurement


Balance 01 g xxx g











































1 nm

10-9 m

10-9 m

1 nm= 1 = 1OR

137 m x 1 nm

10-9 m= 137 x 109 nm

= 137 x 1010 nm





= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m












DeviceFinest

divisionMeasurement


Balance 01 g xxx g









































= 11 cm

10-2 m

10-2 m

1 cm= 1 OR = 1

1 μμmm

10-6 m

10-6 m

1 μμmm

= 1 OR

11 cm x 10-2 m

1 cm= 11 x 104 μmx

1 μμmm

10-6 m












DeviceFinest

divisionMeasurement


Balance 01 g xxx g
















































DeviceFinest

divisionMeasurement


Balance 01 g xxx g





































Chapter 1 Measurement, Models and Analysis. Definition of Physics: –Physics is the study of matter...

Documents

Transcript of Chapter 1 Measurement, Models and Analysis. Definition of Physics: –Physics is the study of matter...