2.5 Velocity and Acceleration

211 Pages·2012·7.52 MB·English

IB Physics 1st Semester
Derrick mcneill
James H Dann, Ph.D.
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AUTHORS
Derrickmcneill
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JamesHDann,Ph.D.
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CONTRIBUTORS
AntonioDeJesusLópez
CatherinePavlov
ChrisAddiego
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iii
Contents www.ck12.org
Contents
1 Introduction 1
1.1 MetricUnits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 UnitConversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 ScientificMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 DevelopmentofHypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.6 ObservationsandExperiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.7 DevelopmentofTheories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Kinematics 26
2.1 UsingtheKinematicEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 PositionandDisplacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 RelativeVelocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 AverageVelocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5 VelocityandAcceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6 GraphingMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3 Newton’sLawsofMotion 47
3.1 PressureandForce. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Newton’sFirstLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Newton’sSecondLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4 FreeBodyDiagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5 ProblemSolving1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.6 TypesofForces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.7 Newton’sThirdLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 Fields 75
4.1 UniversalLawofGravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 GravityandSpaceProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.4 Coulomb’sLaw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.5 ElectricFields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.6 Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.7 MagneticFields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.8 LorentzForce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5 WorkandEnergy 113
5.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2 MechanicalAdvantage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.3 PotentialEnergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.4 KineticEnergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
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5.5 ConservationofEnergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.6 EnergyProblemSolving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.7 PowerandEfficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6 Momentum 136
6.1 Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.2 Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.3 ElasticCollisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.4 InelasticCollisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.5 EnergyandMomentumProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7 PeriodicMotion 153
7.1 PeriodandFrequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
7.2 AngularSpeed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.3 CircularMotion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.4 CentripetalAcceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.5 CentripetalForceProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.6 Springs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.7 Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
8 Waves 175
8.1 TypesofWaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.2 WaveEquation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
8.3 StandingWaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.4 DopplerEffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.5 SpeedofLight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.6 ElectromagneticSpectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
8.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
9 Thermal 193
9.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
9.2 SpecificHeatandPhaseChange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
10 PrinciplesofSimpleHarmonicMotion 204
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www.ck12.org Chapter1. Introduction
C 1
HAPTER
Introduction
Chapter Outline
1.1 METRIC UNITS
1.2 UNIT CONVERSIONS
1.3 VECTORS
1.4 SCIENTIFIC METHOD
1.5 DEVELOPMENT OF HYPOTHESES
1.6 OBSERVATIONS AND EXPERIMENTS
1.7 DEVELOPMENT OF THEORIES
1.8 REFERENCES
1
1.1. MetricUnits www.ck12.org
1.1 Metric Units
Studentswilllearnaboutthemetricsystemandhowtoconvertbetweenmetricunits.
Studentswilllearnaboutthemetricsystemandhowtoconvertbetweenmetricunits.
FrequentlyUsedMeasurements,GreekLetters,andPrefixes
Measurements
TABLE 1.1: TypesofMeasurements
Typeofmeasurement Commonlyusedsymbols Fundamentalunits
lengthorposition d,x,L meters(m)
time t seconds(s)
velocityorspeed v,u meterspersecond(m/s)
mass m kilograms(kg)
force F Newtons(N)
energy E,K,U,Q Joules(J)
power P Watts(W)
electriccharge q,e Coulombs(C)
temperature T Kelvin(K)
electriccurrent I Amperes(A)
electricfield E NewtonsperCoulomb(N/C)
magneticfield B Tesla(T)
Prefixes
TABLE 1.2: PrefixTable
SIprefix InWords Factor
nano(n) billionth 1∗10−9
micro(µ) millionth 1∗10−6
milli(m) thousandth 1∗10−3
centi(c) hundreth 1∗10−2
deci(d) tenth 1∗10−1
deca(da) ten 1∗101
hecto(h) hundred 1∗102
kilo(k) thousand 1∗103
mega(M) million 1∗106
giga(G) billion 1∗109
GreekLetters
TABLE 1.3: FrequentlyusedGreekletters.
µ“mu” τ“tau” Φ“Phi”∗ ω“omega” ρ“rho”
θ“theta” π“pi” Ω“Omega”∗ λ“lambda” Σ“Sigma”∗
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www.ck12.org Chapter1. Introduction
TABLE 1.3: (continued)
µ“mu” τ“tau” Φ“Phi”∗ ω“omega” ρ“rho”
α“alpha” β“beta” γ“gamma” ∆“Delta”∗ ε“epsilon”
Two very common Greek letters are ∆ and Σ . ∆ is used to indicate that we should use the change or difference
betweenthefinalandinitialvaluesofthatspecificvariable. Σdenotesthesumornetvalueofavariable.
Guidance
• Everyanswertoaphysicsproblemmustincludeunits. Evenifaproblemexplicitlyasksforaspeedinmeters
persecond(m/s),theansweris5m/s,not5.
• Ifaunitisnamedafteraperson, itiscapitalized. Soyouwrite“10Newtons,”or“10N,”but“10meters,”or
“10m.”
• Metric units use a base numbering system of 10. Thus a centimeter is ten times larger than a millimeter. A
decimeteris10timeslargerthanacentimeterandameteris10timeslargerthanadecimeter. Thusameteris
100timeslargerthanacentimeterand1000timeslargerthanamillimeter. Goingtheotherway,onecansay
thatthereare100cmcontainedinameter.
Example1
Question: Convert2500m/sintokm/s
Solution: Akm(kilometer)is1000timesbiggerthanameter. Thus,onesimplydividesby1000andarrivesat2.5
km/s
Example2
Question: Thelengthsofthesidesofacubearedoublingeachsecond. Atwhatrateisthevolumeincreasing?
Solution:Thecubesidelength,x,isdoublingeverysecond. Thereforeafter1seconditbecomes2x. Thevolumeof
thefirstcubeofsidexisx×x×x=x3. Thevolumeofthesecondcubeofside2xis2x×2x×2x=8x3. Theratio
ofthesecondvolumetothefirstvolumeis8x3/x3=8. Thusthevolumeisincreasingbyafactorof8everysecond.
WatchthisExplanation
MEDIA
Clickimagetotheleftformorecontent.
TimeforPractice
1. A tortoise travels 15 meters (m) west, then another 13 centimeters (cm) west. How many meters total has
shewalked?
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1.1. MetricUnits www.ck12.org
2. Atortoise,Bernard,startingatpointAtravels12mwestandthen150millimeters (mm)east. Howfarwest
ofpointAisBernardaftercompletingthesetwomotions?
3. 80m+145cm+7850mm=X mm. WhatisX ?
4. Asquarehassidesoflength45mm. Whatistheareaofthesquarein mm2?
5. A square with area 49cm2 is stretched so that each side is now twice as long. What is the area of the square
now? Includeasketch.
6. Arectangularsolidhasasquarefacewithsides5cminlength,andalengthof10cm. Whatisthevolumeof
thesolidin cm3? Sketchtheobject,includingthedimensionsinyoursketch.
7. Asyouknow,acubewitheachside4minlengthhasavolumeof64m3. Eachsideofthecubeisnowdoubled
in length. What is the ratio of the new volume to the old volume? Why is this ratio not simply 2? Include a
sketchwithdimensions.
8. WhatistheratioofthemassoftheEarthtothemassofasingleproton? (Seeequationsheet.)
9. Aspacecraftcantravel20km/s. Howmanykmcanthisspacecrafttravelin1hour (h)?
Answers
1. 15.13m
2. 11.85m
3. 89,300mm
4. 2025mm2
5. 196cm2
6. 250cm3
7. 8:1,eachsidegoesupby2cm,soitwillchangeby23
8. 3.5×1051:1
9. 72,000km/h
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www.ck12.org Chapter1. Introduction
1.2 Unit Conversions
Studentswilllearnhowtoconvertunitsfrommetrictoenglishsystemandviceverseusingdimensionalanalysis.
Studentswilllearnhowtoconvertunitsfrommetrictoenglishsystemandviceverseusingdimensionalanalysis.
KeyEquations
1meter=3.28feet
1mile=1.61kilometers
1lb. (1pound)=4.45Newtons
Guidance
• Thekeytoconvertingunitsistomultiplybyacleverfactorofone. Youcanalwaysmultiplyby1,becauseit
doesnotchangethenumber. Since1in. isequalto2.54cm,then1= 2.54cm = 1in . Thus,onecanmultiply
1in 2.54cm
bythisformof1inordertocancelunits(seevideobelow).
• Writeouteverystepandshowallyourunitscancellingasyougo.
• When converting speeds from metric to American units, remember the following rule of thumb: a speed
measured in mi/hr is about double the value measured in m/s (i.e., 10m/s is equal to about 20 MPH).
Rememberthatthespeeditselfhasn’tchanged,justourrepresentationofthespeedinacertainsetofunits.
• When you’re not sure how to approach a problem, you can often get insight by considering how to obtain
the units of the desired result by combining the units of the given variables. For instance, if you are given a
distance(inmeters)andatime(inhours),theonlywaytoobtainunitsofspeed(meters/hour)istodividethe
distancebythetime. Thisisasimpleexampleofamethodcalleddimensionalanalysis,whichcanbeusedto
findequationsthatgovernvariousphysicalsituationswithoutanyknowledgeofthephenomenathemselves.
Example1
Question: 20m/s=? mi/hr
Solution:
20m/s(1mi/1600m)=.0125mi/s
.0125mi/s(60s/min)=.75mi/min
.75mi/min(60min/hr)=45mi/hr
WatchthisExplanation
5