B-2 Physics SR

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StudentResource

B-2:Physics

Copyright 2008 Aviation Australia

Allrightsreserved.Nopartofthisdocumentmaybereproduced,transferred,sold,orotherwisedisposedof,withoutthewrittenpermissionofAviationAustralia.


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B-2 Physics

CONTENTS

Definitions 5

StudentResources 6

Introduction 7

WhatisPhysics? 2.0-1

Matter 2.1-1

Statics 2.2.1-1

Kinetics 2.2.2-1

Dynamics 2.2.3-1

FluidDynamics 2.2.4-1

Thermodynamics 2.3-1

Optics(Light) 2.4-1

WaveMotionandSound 2.5-1


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DEFINITIONS

Define

Todescribethenatureorbasicqualitiesof.

Tostatetheprecisemeaningof(awordorsenseofaword).

State

Specifyinwordsorwriting.

Tosetforthinwords;declare.

Identify

Toestablishtheidentityof.

List

Itemise.

Describe

Representinwordsenablinghearerorreadertoformanideaofanobjectorprocess.

Totellthefacts,details,orparticularsofsomethingverballyorinwriting.

Explain

Makeknownindetail.

Offerreasonforcauseandeffect.


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STUDENTRESOURCES

JeppesenGeneral

StudentResourceB-2


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INTRODUCTION

Thepurposeofthissubjectistofamiliariseyouwithmathematicsandphysicsassociated

withaircraftdesign,manufactureandmaintenance.Oncompletionofthefollowingtopicsyouwillbeableto:

Topic 2.1 Matter

Definethenatureofmatterregarding:

Thechemicalelements

Structureofatoms

Molecules.

Definechemicalcompounds.

Definematterinsolid,liquid,andgaseousstates.Identifychangesbetweenstatesofmatteranddefinetheprocess.

Topic 2.2.1 Statics

Describeforces,momentsandcouplesandrepresenttheinteractionoftheseasavectordescribingsimplemachinesandmechanicaladvantage.

Describethecentre-of-gravityofamass.

Describetheelementsoftheoryofstress,strainandelasticitytothefollowing:

Tension

Compression

Shear

Torsion.

Describethenatureandpropertiesofsolids,fluids,andgases.

Describetheactionofpressureandbuoyancyinliquids(barometers).

Topic 2.2.2 Kinetics

Describethefollowingaspectsoflinearmovement:

Uniformmotioninastraightline

Motionunderconstantacceleration(motionundergravity).

Describetheuniformcircularmotion(centrifugal/centripetalforces)aspectofrotationalmovement

Describeperiodicmotionandpendularmovement.

Describesimpletheoryofthefollowing:

Vibration

Harmonics

Resonance.

Describevelocityratio,mechanicaladvantageandefficiency.


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Topic 2.2.3 Dynamics

Describethefollowingwithregardtomass:

Mass Force

Inertia

Work

Power

Energy(potential,kineticandtotal)

Resultantforceandequilibrium

Heat

Efficiency.

Describemomentumandconservationofmomentum.

Describeimpulse.

Describegyroscopicprinciples.

Describefriction,itsnatureandeffects,andthecoefficientoffriction(rollingresistance).

Topic 2.2.4.1 Fluid Dynamics SG)

Describespecificgravityanddensityinrelationshiptofluids.

Topic 2.2.4.2 Fluid Dynamics Viscosity)

Describethefollowinginrelationshiptofluids:

Viscosity-fluidresistance

Effectsofstreamlining

Effectsofcompressibility

Describethefollowingtypesofpressure:

Static

Dynamic

Total

StateBernoullisTheoremanddescribetheoperationofaventuri.


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Topic 2.3 Thermodynamics

Describetemperatureandtheoperationofthermometers.

Describethefollowingtemperaturescales: Celsius

Fahrenheit

Kelvin.

DefineHeat

Definespecificheatanddescribeheatcapacity

Describethefollowingmethodsofheattransfer:

Convection

Radiation

Conduction

Describevolumetricexpansion

Statethefirstandsecondlawsofthermodynamics

Describethefollowingregardinggases:

Idealgaslaws

Specificheatatconstantvolumeandconstantpressure

Workdonebyexpandinggas

Describethefollowing:

Isothermalexpansionandcompression Adiabaticexpansionandcompression

Enginecycles

Constantvolumeandconstantpressure

Refrigeratorsandheatpumps

Latentheatsoffusionandevaporation

Thermalenergy

Heatofcombustion

Topic 2.4 Optics Light)

Describethenatureoflightandstatethespeedoflight

Describethelawsofreflectionandrefraction:

Reflectionatplanesurfaces

Reflectionbysphericalsurfaces

Refractionoflightthroughvariousmedia

Theuseoflenses

Describethenatureanduseoffibreoptics.


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B:September2010 Re 3

Topic 2.5 Wave Motion And Sound

Describethenatureofwavemotion:

Mechanicalwaves Sinusoidalwavemotion

Interferencephenomena

Describethecharacteristicsofsound:

Production

Intensity

Pitch

Quality

Statethespeedofsoundanddescribefactorsthataffectit

DescribetheDopplerEffect.


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IssueB:January2008 Revision2 2.0-1

WHAT IS PHYSICS?

Ever since Humankinddeveloped theability toponder itsexistence, questions have been

askedconcerningthenatureofitsenvironment.Latin,thelanguageoftheRomanEmpire,containedthewordPhysicaforNature,henceouruseof Physicsastheoverallnameofthebodyofknowledgewhichattemptstodescribetheinanimateworld.

We have become adept at observing and measuring the phenomena that surround us.Certain individuals,e.g.ArchimedesandNewton, throughchanceandcircumstance,wereabletodeveloptherelationships,betweenelementsoftheseevents,whicharenowcalledtheLawsofPhysics.

In many cases, the absolute truths still elude us, and the scientific community has onlymodelstooffer.Forexample,theoriginoftheUniverse,ortheStructureoftheAtom.

Evenso, we have now gained enough knowledge tocreate and control the technologicalenvironmentinwhichwelive.

Thiscourse attemptstoaddress the basics which serveto underpinmostof the technicalknowledge that an Aircraft Maintenance Engineer needs. For organisational purposes,Physicsisdividedupintoanumberoftopics,howeveritisimportanttorememberthatnatureworksitsvariousstrandsofmagicsimultaneously.

Therestofthisintroductionendeavourstoprovidethereaderwiththeabsoluteminimumofknowledgewithwhichtoattacktheseseparatetopics.


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Origins of the Universe

RecentobservationshavegivenustheBigBangTheory,whichinitsmostbasicform,tellsusthatthespaceinwhichyouandI,andtherestofthe10 50kgofmatterexist,beganasapointsource,andhasexpandedintowhatwecalltheUniverse.

TheuniversehasclumpedtogetherintoGalaxies,andwithinthesearePlanetarySystemsassociatedwithStars.

Themostfrequentlyaskedquestionwhenfacedwiththisconceptis:

OK,whatwastherebeforetheBigBang?Well,thesimplestanswerisnothingbecausetimeitselfcameintoexistenceandthereiscanbenoconceptofbefore.SeeFig1.Therearenotimevaluesforanyuniversesizelessthanzero.

Forallintentsandpurposes,ourconceptoftimeasameansbywhichwecanmeasuretherateatwhicheventsoccurwillsuffice,andourstudieswillconcentrateonthosetopicswhichexplainoureverydaylives.



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Nature of the Universe


Apart from its size, whatare the other characteristicsorproperties of theUniverse as weperceiveittoday?Whatdoesitcontain?

Wehavealreadymentionedone-the1050

kgofmatter.Theotherisenergy.

What is energy?

TheGreek word, energos-means thatbywhich activity ispossible, so innon-physicsterms,itcouldbethoughtofasthatwhichcauseschange.However,thatisnotmeasurableenoughforphysicists.

Wesaythatenergyprovidesthecapabilitytochangethestateofmotion,ormatterofsomeobjectorother,andexistsinmanyformsinafixedamount.Forexample, kineticenergyistheenergypossessedbyamovingmasscapableofcausingchange,while potentialenergyistheenergywithinacompressedspringwhichcouldcausechange.

Energyusedisalwaysfullyaccountedforintermsoftheactivityproduced.

What is matter?

The states ofmatter canbe solid, liquid orgaseous, and each of these is related to theamountofinternalenergypossessedbythematterbeingunderconsideration.

Wecandetectthisinternalenergy,andcallitheat.Itwasoriginallythoughttobeaninvisiblefluidcalledcaloric;however,wenowknowitisboundupinthevibratorymotionofthebasicparticleswhichmakeupmatter,calledatomsandmolecules.

Theamountofheatpresentdependsonthequantityofmatter,buthowhotitisdoesnt.Weexpresshotnessastemperatureanditismeasuredindegrees.

Ourstar,calledtheSun,hasradiatedenergyontothisplanetallthroughitsexistence,and

all changes of state or motion we experience today, are only possible because of thisradiation,pastandpresent.

AnexceptiontothisisthedevelopmentanduseofAtomicorNuclearEnergy,whichinvolvestheconversionofmatterintoenergy,inasimilarwaytothatprocessusedbystars.

Properties of Matter

Amountsofmatteraremeasuredinunitsofmassofwhichthestandardisthekilogram,andthepresenceofamassaffectsspaceintwoways.

Firstly,thereistheamountofspaceoccupiedbyacertainmass.Thisisrepresentedbyitssize in three dimensions. The product of an objects length, width, and height is calledvolume,andwhenallthreedimensionsaremeasuredinmetres,wegetcubicmetres.

Secondly,allmassesinspaceattracteachothertoacertaindegree,dependingontheirsizeanddistanceapart.ItisthispropertyofmassthatgivesallobjectsonthegiantmasswecallPlanetEarth,(includingus), weight.TheLatinwordmeaningheavywas,gravitas,-hencethepropertyisnowcalled,Gravity.Becausetheeffectsofgravityextendoutwardsfromamass,themassissaidtohaveaGravitationalFieldsurroundingit.


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Density

Tocompare different typesofmatter, let ussee how much ofeach occupieseachcubicmetreofspace,i.e.thenumberofkilogramsofthesubstancepercubicmetre.Thisderivedpropertythusmeasuresthedensityofaparticularsubstance,andwegetthefirstrelationshipbetweenproperties,i.e.ourfirstLawofPhysics:

metreubiceramsogig

Volume

mass

)rdensity

3

Asmentioned,theunitskilogramandmetre,arestandardised,andmost countriesmaintainanorganisationtoensurethattheyrepresentthesamemeasurementatalltimes.

InAustralia,thisistheNationalMeasurementLaboratory,locatedwithintheCSIRODivisionofAppliedPhysicsinSydney.

Theunitkg/m3isaderivedunit.

Time

Themeasurementofspaceoccupiesthreedimensionsof theUniverse,butisnotsufficientforustoincludetheprogressofaneventinthatmeasurement.

For this we have the concept of time, often called the Fourth Dimension. Our ancestorsobservedthecyclesofnature,thepassageofthesunetc.whichgavethemtheinitialunitsofdaysandyears.

Thebasicunitoftime,thesecond,sisnowfundamentalandstandardised.

Motion

Withtheconceptoftime,wecanmeasurehowamassmaychangeitspositioninspace,inotherwords,theideaofmotion.

Anobject,(amass),canbeinparticularstateofmotion:

Atrest(notmoving),zerometrespersecond,(0m/s)

Changingitspositionataconstantrate,(i.e.acertainnumberofm/s)

Or,thatratecoulditselfbechangingwithtime,givingusm/spersecond,(m/s2)

A constant rate of m/s is called speed or velocity

A constant rate of m/s per s is called acceleration

WhatisrequiredtobeabletochangethisStateofmotion?



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Toquantifythispushorpull,Newtontooktheproductofthemassandaccelerationrequired,andcalleditforce,-thatwhichisrequiredtochangemotionstate.

Energy and Force

Englishscientist,IsaacNewton(16421727),observedthatifyougaveamassapushorapull,itsstateofmotionchanged.

Forexample,justgoingfromatrest,to,movingmeantanaccelerationmusthavetakenplace.

Energyhasbeenusedinthisprocess,butnotusedup.Theenergyusedtopropeltheobjectstillexistsastheobjectsmotion,(andinotherformsthatwillbediscussedlater.)

Theenergyrequiredtoprovidethepushtochangethisstateofmotionwasfoundtodependonthemasscontainedintheobjectandtheamountofacceleration.

Moremassand/ormoreaccelerationrequiredmorepush.

ionAcceleratassorce

This will give us another derived unit for force, the kg.m/s per s. Far too unwieldy, soappropriatelyenough1kg.m/spers,isactuallycalled1Newton.

Forcesarenotalwaysappliedbydirectcontactwithanobject.Letusrevisitgravity.

Should you beunluckyenough tobeunsupported by the ground ora floor in the Earthsgravitationfield,youwillexperienceachangeinmotionstate.(Fall!)

Ignoringforthemomentthatwehaveanatmospherewhichactuallyslowsthingupabit,itcan be shown that we fall with an acceleration of 9.8 m/s per s. This is called theaccelerationduetogravityforEarth,andhasitsownsymbol-g.

Fromabove, Force= Massx Acceleration,and when thatacceleration isg, that force is

calledyourweight.


s!

To all intents andpurposes,gisconstant

forallusEarthboundsurfacedwellers,sointerchangingthewordsmassandweightdoesnotleadtoshortmeasure

Newtons)inasseight

Pressure

Pushingonasurface(orjustallowingweighttoactonthesurface)createspressure.

ItisdefinedasForceperunitareaor:

Pa)ascalsr

2

AfterBlaisePascal(1623-1662)


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Work and Power

Energywasusedduringourapplicationofforce,andtohelpquantifywhathappenstothisenergy,wetaketheproductof theappliedforceandthedistancemovedduringthechangeofposition,andcallitwork.

movedeanisorceork

The work done equals the energy used, including the energy used to overcome anyresistance,e.g.frictionandairresistance.

Another derived unit appears, the Newton Metre, better known as the Joule after JamesJoule(1818-1889),andcannowbeusedasthestandardunitforenergyofanyform.

Powerissimplyameasurementoftherateatwhichworkisdoneorenergyisused.

J/s

Time

Usednergy

r

Time

doneork

Power

JoulespersecondarecalledWatts,afterJamesWatt(17361819),whoexperimentedwiththeworkdonebyhorsesastheypulledbargesaroundthecanalsofEngland.

W46orsepower

Initial Conclusions

So, what is physics? The study of matter and the activity it gets up to with the energyavailable?

Initssimplestform,theUniversecanbesaidtobeacollectionofMatterandEnergy,sothatmaybeasgoodananswerasany,buttobesurewemustnowstartinvestigatingthings

furtherbyinthemoretraditionalmannertopicbytopic.

Initially,wewilltakeacloserlookatthestructureofmatter,bothinitseverydayandsmallestform.Thentherewillbemoreonhowforcecanbeputtogooduseandhowdifferenttypesofmotioncanbeanalysed.

Differentformsofenergyarediscussed,includingHeat,Light,andSound,toseehowtheycreatethevariousphenomenathatoccur.TherelationshipsbetweentheMatterandEnergycouldjustaseasilybecalledtheLawsofNature.AddChance tothemixandmaybe, justmaybe,thepictureiscomplete.

PS What about Electricity?

Trytoimagineaworldwithoutelectricity!Noteasy,howevertherehasbeennomentionofitsofarinthisintroductiontoPhysics.

TheuseofelectricityissoimportantthatithasitsownModule,(B1-3).However,ittoohasitsoriginsinnature,andwillbebrieflyintroducedwhenwelookatthestructureofmatterinitssmallestforms.(Atomsandmolecules)



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Fundamental Units

TheSystemInternationale,(SIorMetricSystem)hasbeeninternationallyagreed,buttherearemanyexamplesoftheBritishSystemstillused.Forexample,psiforpressure.

Property Metric SI) British Conversion

Mass Kilogramkg Slug 1Slug=14.59KG

Length metreM FootFT 1FT=0.305M

Time Second Second N/A

Force NewtonN PoundLB 1LB=4.45N

Pressure Pascalpa LB/SQIN(PSI) 1PA=0.00015PSI

Work/energy Joule FootPound 1J=0.738FT.LB

Accelerationduetogravity

9.81m/sperS 32.2FT/SPERS N/A

Order of Magnitude

Inthemetricsystem,manyprefixesareusedtodenotehowmanyofanyparticularunitarebeingused.Thefollowingtablewillbeuseful.



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B:January2008 Re 2

Ambient Conditions

Atmospheric Pressure

Weliveatthebottomofanatmospherecomprisingofamixtureofgaseouselementsand

compoundscalledair.Theweightofairactsoverthesurfaceoftheplanetcausingittobeunderatmosphericpressure,accordingtotheruleP=F/A.

Extendingto160,000km,withavaryingdensitydependingonheight,oneatmosphereexertsanaveragepressure,atsealevelof101,320N/m2

i.e.101,320Pa,whichismorecommonlywrittenas

als)hectopascPa013.2

Alternatively,1bar=100,000Pa,soIatmosphereis1.0132baror1013.2mb

InBritishunits,1atmosphereis14.7lb/in2

Onepracticalmethodofdeterminingatmosphericpressureistomeasurehowhighacolumn

ofliquidcanbesupportedbythispressure.(Abarometer.)

Itturnsouttobe29.92inchesor760mmofmercury.

We feel no ill effect from this pressure because we are permeable enough to allow thepressureinsideustoequalisetothis.Rapidascentsordescentsthroughtheatmosphereareadifferentstory,andaircraftareengineeredtocopewiththis.

Ambient Temperature

Thesunradiatesitsenergycontinuouslyontheplanetanditsatmosphere.Overtime,thisoceanofairhassettledintoacomplexseriesofweatherpatterns,oneelementofwhichis

thetemperatureatanygivenlocation.Thischangesfromplacetoplace,andwithyourheightabovesealevel.

Thetemperatureismeasuringtherelativedegreeofhotnessofoneareaoveranotherandisconstantly changing as the day proceeds and the weather patterns shift.Atsealevel,thetemperaturerangesfromabout-30degreesCelsiustoabout+50C.Atthetypicalcruisingheightofapassengerjet,thetemperatureisjustabove-60C.MoreinTopic3.

International Standard A tmosphere

The performanceofany aircraftdependsheavily on air density,and weve just seen that

densityvariesfromlocationtolocationandwithheight,astheatmosphericpressurechangeswiththetimeofdayandweatherexperienced.

Tocreateabenchmarkagainstwhichaircraftperformancecanbemeasured,anInternationalStandard Atmosphere was defined. The essential features of the ISA are a sea leveltemperatureof15C,andpressureequalto1013.2hPa.

Should the conditions be different from these at a particular location, then importantperformancefactorsliketake-offandlandingdistancescanbeeasilycalculated.

Issue vision 2.0-8


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B-2.1MatterIssueB:January2008 Revision1 Page1of8

TOPIC2.1:MATTERMatterreferstoeverythingwhichoccupiesspace,andhasmasswhichexistsinoneofthreephysicalstates,solid liquid andgaseous. ThetotalmassoftheUniverseisconserved,thismeaningitcannotbecreatedordestroyed,onlychangedfromoneformtoanother.Ifyouburn1kgofwood,youfinishwith1kgofash,smoke,andothergases.

Beforewecandiscussthedifferentpropertiesofeachstate,letuslookathowallformsofmatterareputtogether.

Matteritselfismadeupofsmallparticles.Thesimplestformsofmatteraretheelements whoseconstituentparticlesarecalledatoms,asmodeledbelow.

Atomsarelargelyspacewitharelativelydensenucleusmadeupofelementaryparticles,protonsandneutrons andoneormoreshellsofelectrons atcertainfixeddistances. Eachshellrepresentsanenergylevelwithintheatom.

Itrequiressometwohundredmillionofthemsidebysidetoformalineacentimeterlong.

Imaginethefullstopattheendofthissentence.Itisprobablyabout0.5mmindiameter.

Ifthatrepresentsthenucleus,thentheelectronsinthefirstshellwouldbeabout50metersaway.

Withintheatom,therearefourFundamentalInteractionswhichgiverisetoallotherphysical

processesintheUniverse.Simplydescribed,andinorderofincreasingstrength,theyare:

1. Gravity;thisisthesameasalreadydiscussed,butveryinsignificantontheatomicscale.

2.

TheWeakNuclearInteraction,whichcontributestoradioactivity.

3.

TheElectromagneticInteraction;actsbetweenthenucleusandelectronsandisthesourceofelectricalandmagneticenergy.

4.

TheStrongNuclearInteraction;holdsthenucleitogether.

Tohelpanalyseinteraction3,wesaytheprotonhasapositiveelectriccharge,andtheelectron,anegativeelectriccharge,wherechargeisafundamentalpropertyofmatteratthislevel,(inasimilarwaytomassatalllevels.)

(ThewordselectronandelectricitycomefromtheGreekwordforamber,thefirstsubstanceinvestigatedwithsomeofthepropertieswenowcontrolsoconfidentlytoday.)


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ElementsaredetailedinthePeriodic Table. Forexample,purecopperisanelementbecauseitiscomprisedonlyofcopperatoms(Cu).Anatomisthesmallestpartofanelementthatretainsthepropertiesofthatelement.

Electronssurroundthenucleusinsuccessivegroupsorshellslikesphereswithinspheres

ACopperatomhas2electronsinitsfirstorKshell,8inthesecondorLshell,and18inthethirdorMshell,andoneelectroninitsfourth(N)andfinal,outershell.

Whethertheoutershellisrelativelyempty,halffull,ornearlyfulldeterminessomeoftheelectricalpropertiesoftheelement.

Allatomsfollowthisrule:

Maximumnumberofelectronspossibleineachshell=2n2wherenistheshellnumber.


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The Periodic Table of Elements

Eachatomhasanidentifiablenumberofprotons,neutrons,andelectrons.Inaddition,everyatomhasitsownatomic number,aswellasitsownatomic mass (asdepictedintheperiodic

tablebelow).

CopperhasanAtomicNumberof29,becauseithas29protons.ItsAtomicMassis63.55amu,amorecomplexcalculationinvolvingaveragingthemassofthetotalnumberofprotonsandneutronstogether.(Electronmassis0.0005timeslessthaneitheraprotonoraneutron,andconsideredinsignificant.)

kg0.6mu

27

amu00000 000 00000 00025 000 00kgr

Ions

Atomswhichhavelostorgainedanelectronduringaprocess.Anatomlosinganelectronwillbecomepositive,whilstanatomgaininganelectronwillbecomenegative.

Isotopes

Atomsofthesameelementwithdifferentnumbersofneutrons.TheAtomicNumberremainsthesame,buttheAtomicMasschanges.


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Compounds

Thereare109knownelementscurrently,howevermostofthematteraroundushasbeenformed by one or more elements combining in such a way to form completely new

substancescalledcompounds.

This is called chemical bonding and generally when atomsbond together, they shareortransferelectronsandformmolecules.

Waterisacompoundbecauseitismadeupofhydrogenandoxygenatoms(H2O).Thesameistrueofcarbon dioxide(CO2)andcommon salt,sodiumchloride(NaCl).

In theexampleofH2O(water), the oxygen atomhas six electrons in its outer, orvalenceshell.Becausethereisroomforeightelectronsinthevalenceshell,oneoxygenatomcancombinewithtwohydrogenatomsbysharingthesingleelectronfromeachhydrogenatom.

Figure 1 Water Molecule

A compound is matter in which all the molecules are identical, but the molecules arecomprisedofdifferentatomsinexactproportions.Thetwoormoreindividualelementsarechemicallycombinedtoformaseparatesubstancewhosecharacteristicsmaybecompletelydifferentfromtheoriginalelementcharacteristics.


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Amoleculecanhave:

Justoneatom(helium)

Twoatomsofthesameelement(oxygenO2) Atomsofseveraldifferentelements(waterH

2

O)

SubscriptsindicatenumberofparticularatomsinthemoleculeAl2

O3

meanstwoatomsofaluminiumandthreeatomsofoxygenineachmoleculeofalumina

Mixtures

Amixtureisamingledmassoftwoormoresubstanceswhereeachsubstanceretainsitownindividual characteristics.Forexample,thefigurebelowisarepresentationofNaClinH 2O(saltywater).

Mixtureshavevaryingratiosofingredientsthatdo not combine chemicallyastheydoinacompound.

Otherexamplesofmixturesare,air(amixtureofoxygen,nitrogen,carbondioxideandothergases)andmetal alloys.

Metalalloyssometimeschangecharacteristicswhenthemetalsaremerged.Forexample,aluminiumbecomesstrongerandharderwhenalloyedwithcertainothermetals.


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Thisisaphysicalratherthanachemical combination,occurringatamicroscopicscale.

Thefigureisamicroscopiccross-sectionofametal alloyshowingcrystallinestructure.

Mixturesmaybeseparatedintotheoriginalsubstances

States of Matter

Allatomsandmoleculesinmatterareconstantlyinvibratorymotion.Thedegreeofmotioni.e.theinternalkineticenergypossessedbythematter,determinesitsphysicalstate.ThisinternalKEiswhatweknowasheat.Whatwecalltemperatureis,infact,onlyameasureofthismolecularactivity.

So,attheeverydayscaleofthings,theseelements,compoundsandmixturesexistassolidsliquidsorgases,dependingontheirinternalenergyorheatcontent.

Figure 2

Thephysicalstateofacompoundhasnoaffectonacompoundschemicalstructure.Ice,water,andsteamareallH2O.


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Solids

Asolidhasadefinitevolumeandshape,andisindependentofitscontainer.Forexample,arockthatisputintoajardoesnotreshapeitselftoformtothejar.Inasolidthereisverylittleheatenergyand,therefore,themoleculesoratomscannotmoveveryfarfromtheirrelativeposition.Forthisreasonasolidisincompressible,thatis,hasconstantdensity.

Liquids

Whenheatenergyisaddedtosolidmatter,itsmolecularmovementincreases.Thiscausesthemoleculestoovercometheirrigidshape.Whenamaterialchangesfromasolidtoaliquid,thematerialsvolumedoesnotsignificantlychange.

However,thematerialconformstotheshapeofthecontaineritsheldin.Liquidshavedefinitevolumebutnotshape.

Anexampleofthisismoltensteel.Althoughthemoleculesofaliquidarefartherapartthanthoseofasolid,theyarestillnotfarenoughaparttomakecompressingpossibleandliquidsarealsoconsideredincompressible.

Inaliquid,themoleculesstillpartiallybondtogether.Thisbondingforceisknownassurfacetensionandpreventsliquidsfromexpandingandspreadingoutinalldirections.Surfacetensionisevidentwhenacontainerisfilled.

Gas

Asheatenergyiscontinuallyaddedtoamaterial,themolecularmovementincreasesfurtheruntiltheliquidreachesapointwheresurfacetensioncannolongerholdthemoleculesdown.Atthispointthemoleculesescape,becominggasorvapour.Theamountofheatrequiredtochangealiquidtoagasvarieswithdifferentliquids.

Gasesdifferfromsolidsandliquidsinthefactthattheyhaveneitheradefiniteshapenorvolume.Chemically,themoleculesinagasareexactlythesameastheywereintheirsolidorliquidstate.However,becausethemoleculesinagasarespreadout,gassesarecompressible.

Flow

Thesamepropertythatallowsliquidsandgasestoadopttheshapeoftheircontainers,alsoallowsthemtoflow,andtheycanbothbecalledfluids.


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B-2.2.1StaticsIssueB:January2008 Revision3 Page1of22

TOPIC2.2.1:STATICS

Forces

Aforcecanbedescribedasthatwhichcanproduceachangeinabodysstateofmotion.Anapplicationofforcewill:

start

stop

accelerate,or

decelerate,amass

Ifenergyisavailable,thenforcescanbeusedtodowork.

ForceisanexampleofaVECTORquantitythatneedmagnitude(size)anddirectiontobefullydefined.

MostquantitiesareSCALARSandaredefinedwithsizeonly.

Forexample,temperature,length,andtime.

Scaledrawingsareaconvenientwaytorepresentvectors.

Vector Addition

ActivityResolveasingleforceintohorizontalandverticalcomponents


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Sometimes,forcesactatdifferentdirectionsonabody.Incasessuchasthese,forcesmustberesolvedtocalculatearesultant net force.

Whenanobjectdoesnotchangeitsstateofmotionorrest,the resultant of all the forcesacting on it is zero,anditissaidtobeinastateofequilibrium.

Forexample,ifacarisbeingpushedatoneendbyapersonandopposedattheotherendbyasimilarforce,thecardoesnotmove.The sum of the positive and negative forces arezero.

Activity.Whyarethescalesintheslidenotinequilibrium?

Moments and Levers

Eithersideoftheleverbelow,hasamomentwhichistheforcemultipliedbythedistance,fromthefulcrum,orpivot,(calledthearm)

Thesystemisbalancedwhentheloadmomentandtheeffortmomentareequal.Iftheeffortforceisincreased,theloadwillberaised.

Thesmallereffortforcemovesthroughalargerarctoraisetheheavierloadasmalldistance.Thisistheprinciplebehindleverage


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AleverisanexampleofaSimple Machine,whichisadeviceusedtogainaMechanicalAdvantage,MA,

Effort

Load

Ahere

Inotherwords,themultiplicationofaforcebytheuseofleverage.

Themechanicaladvantageofafirst-class leverdependsonthedistancemovedbyeffortcomparedtoload.

Thepurposeofaleveristoperformwork,foraload(L)tobeliftedbyaneffort(E),pivotingaroundafulcrum(F).

Iftheloadmovedisgreaterthantheeffortused,themachinehasapositiveMA.

Anexampleofafirst-class leverisaCROWBAR

L

F

E

Thefulcrumissituatedbetweentheloadandtheeffort,andtheloadisgreaterthantheeffort.

ThelidonlyneedstoberaisedashortdistancebutyourhandtravelsalargerdistanceHenceleverage


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Examplesofasecond-class leverincludecockpitcontrollevers,suchasathrottleorthrustlever,andasimplewheelbarrow.

L

Theloadissituatedbetweenthefulcrumandtheeffort.Theloadisgreaterthantheeffort.PositiveMA.

Anexampleofathird-class leveristheretractionmechanismonanaircraftlandinggear

L

E

Theeffortisbetweenthefulcrumandtheload.Theeffortisgreaterthantheload,andmovesthroughasmallerdistanceMAislessthan1


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Velocity Ratio

AVelocity Ratioisthedirectratiooftwospeedsthatmaybepresentinthesamesystem.

Forexample,considerapulleysystemthatusesanMAof4.

Theoperatorwillpullthroughametreofropetoraisetheloadby0.25m.

Therefore,theropemoves4timesasfastastheloadisbeingraised.

Thevelocityratiois4:1

So,MA=DistanceRatio=VR


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Couples

Acoupleis atypeofmomentwhich isderivedfrom two equal forces acting in parallel butopposite directions on two different points of a body.

Toexplainthisconcept,consideranaircraftflyingstraightandlevel.Ifacontrolinputismadetoturntheaircrafttotheleft,aforceisgeneratedatboththeleftwingtipandtherightwingtipthroughtheailerons.

Theforcesareequal,butactinoppositedirection.

Theforcesproduceatorqueortwistingforcetotheaircraft,causingittoturn.

Ifthewingspanoftheaircraftisbmetres,thenthetorqueproducedbythiscoupleisgivenby:

Nm

Otherexamplesincludetapsandsteeringwheels.

Activity

Usingtheprincipleofmoments,provethatT=Fxbforanaeroplaneofwingspanb.


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Centre of Gravity (CG)

TheCentreofGravity(CGorCofG)ofabodyisthepointfromwheretheweightappearstoact,irrespectiveofthebodysposition.

Thecgofregularlyshapedbodiesofuniformdensityiseasytofind.Itissimplythegeometriccentreofthebodies

Ifanirregularlyshapedsolidishungfirstfromonepoint,andthenfromanotherpoint,itsCGistheintersectionoftheverticalspassingthroughthesepoints.

TheentireweightofabodyisconsideredtoactdownthroughtheverticalpassingthroughitsCG.

Thebodycanberaisedwithouttopplingbyanupward-actingforceappliedtotheunderside

ofthebodywheretheverticalexactlyleavesit.

Applicationoftheupwardforceatanyotherpointwouldtendtotiltthebody.


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ThereforeslingorliftloadsasneartotheCGaspossible.

Thecgofanaircraftshiftsifpassengers,baggage,orequipmentinthecabinmove,orifunequalamountsoffuelareusedfromtanksinoppositewings.

ThereisarangeofacceptableCGpositionsbetweenaforwardlimitandanaftlimit.

Thiswillensuretheaircraftremainscontrollablewithoutbecomingtailheavyornoseheavy.

Consideraperfectlycirculardiscofconstantthicknessanddensitywithanaxlethroughitscentre.

Thediscwillbebalancedatallpositionstowhichitmayberotatedarounditscgatthecentreoftheaxle.

Butfurthertothis,balancewillberetainedregardlessofthenumberofweightsthatareaddedtothedisc,providingtheyarepairedoffdiametricallywithequalandoppositemoments.


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Balance of Rotating Components

Evenwithanobjectofregularshapeadiscorwheelforinstancethethicknessorotherdimensionsmayvaryslightlybecauseofmanufacturingtolerances,orbecauseofwearor

damageduringuse.

Alsothedensitymaynotbeperfectlyuniformthroughoutthematerial.Thesefactorsmaymeanthecgdoesnotcoincidewiththegeometriccentreoraxisofrotation.

Theunbalancedconditionwillcausevibrationduringrotation.Torectifythisproblemthecgmustbeshiftedtomakeitthesamepointasthecentreofrotation.

Thiscanbedonebyaddingsmallmassesofmaterialtothelightsideofthecomponent,orbyremovingsmallmassesofmaterialfromitsheavysideuntilitbalances.

Figureaboveshowsapropellerinastaticbalancingrig.


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Thepropellerssupportingmandrelorspindlerollsfreelyonapairofhorizontalknifeedgeswithverylittlefriction.Thiskindofbalancingisalsocalledmassbalancing.

Theheaviestblademovesdownward.Whenperfectlybalancedthepropellerwillremain

stationaryinanypositiontowhichitisturned.

Caremustbetakenthatevenslightairmovementsdonotcausewrongindicationofbalanceorimbalance.

Manyotherrotatingcomponentsarebalancedduringmanufacture.

Examplesincludelanding-gearwheelassemblies,helicopterrotors,compressors,turbines,fans,andtherotorsingenerators,magnetos,andgyroscopes.

Someofthesemayrequirere-balancingduringreconditioningproceduresfollowingwear,damage,orreplacementofparts.

Foracomponentspinningatveryhighspeedevenatinyamountofunbalancemayproduceexcessivevibration.


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Stress, Strain and Elasticity

Stressistheforceactingthroughasectionofsolidmaterialanddefinedasforceperunitarea.

Area

ForceStress

Strainisthedeformationofthematerialasaresultofthestress.

Ifthestrainislessthanthematerialselastic limit,theelasticityofthematerialwillallowittoreturntoitsnaturallength.

Strainbelowtheelasticlimitisdirectlyproportionaltotheappliedstress(HookesLaw).

Doublingstresswilldoublethestrain,(belowtheelasticlimit)

Ifthecrosssectionalareaofthebaris2sqm,thenthestresswillbe

2

2

9.81000 N/m4900Stress

Ifitwas0.5mlongandextendsby2mm,whatisthestrain?

%0.4100%500

2Strain

Tensiondescribesforcesthattendtopullanobjectapart.

Flexiblesteelcableusedinaircraftcontrolsystemsisanexampleofacomponentdesignedtowithstandtensionloads.


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Compression istheresistancetoanexternalforcethattriestopushanobjecttogether.

Theweightofanaircraftcausescompressivestresstotherunway.

Aircraftrivetingisperformedusingcompressive forces.

Whencompressionloadsareappliedtotherivethead,therivetshankwillexpanduntilitfills

theholeandformsabutttoholdthematerialstogether


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Shear Stress

Shear stressesoccurwhenexternalforcesdistortabodysothatadjacentlayersofmaterialtendtoslide overoneanother.Shearstresstriestosliceabodyapart.

Shearstressmayalsooccurinfluids,forexamplealayerofoilorgreasebetweentwoslidingmetalsurfaces.

Somemoleculesoflubricantclingtoeachslidingsurface.Thesubsequentlayersoflubricanttendtoslideovereachothertoreducefrictionbetweenthemetalsurfaces.

Anaeroplanewingorahelicopterrotorbladeisverysimilartoaplankorboard.Aerodynamic and gravitational forcestrytobendthewingorbladeupwardsandonwards.

Consequently,thetopandbottomsurfacesofthewingareunderalternating compressionand tensile stressesandmustbeconstructedtowithstandthefatiguethatcoulddevelopfromthissituation.

Duringoperation,movingpartsexperienceavarietyofloadings,causedbyvibration,changesofload,andtemperaturechanges.

Repeatedapplicationsofsmallloadsmayeventuallyresultinfatiguefailure.

Fatiguefailuresarequitecommoninaircraftandmotorcars,andareatleastascommonasoverloadfailures.


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Torsional Stress

Torsion or torqueisaformofshearstress.Ifatwistingforceisappliedtoarodthatisfixedatoneend,thetwistwilltryandslidesectionsofmaterialovereachother.

Theresultisthat,in the direction of the twist,thereiscompressionstressandinthedirectionopposite to the twist,tensionstressdevelops.

Acrackcanoriginateatthepointofhighesttensilestressinapart.

Suchacrackcangrowprogressivelyandthepartsstrengthisreducedsomuchthatitsuddenlybreaks.

Residual Stress (Locked In Stress)

Abruptoruneventemperaturechangestendtocauseinternalstress.

Thisoftenoccurswhenheat-treatingmetals.

Thiseffectoftenexplainswhyacomponentfailsinserviceeventhoughitsexternallyappliedstresslevelsarelow.

ResidualStresscanbebeneficial.Thecontrolledcrazingofsomecarwindscreensinacrashorwhenhitbyastone,isachievedbybuildingresidualstressintotheglasswhenthewindscreenismade.


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Pressure

Both liquids and gases are fluids,thereforethetheorybehindbuoyancyandpressureinliquids,suchaswater,andgases,suchasair,issimilar.

Animportantdifferencetoremember,though,isthatliquids are considered incompressible,that is, have a constant density, while gases are compressible.

Pressure Between Solid Surfaces

Pressureisdefinedas:

Forceperunitarea

2

N/m

Area

Force

ssurer

Usingg=10m/spers

2

N/m50

4

1000

lock

2

N/m000

1

1000

,lock

Thisexplainswhyhighheelshoesdomoredamagetowoodenfloors,andwidewheelsdistributeacarsweightoverthetarmac.


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Pressure in Fluids

PressureisstilldefinedasForceperunitarea,butinafluiditiscausedbythecontinualbombardmentofthemoleculesagainsttheinsideofthecontainer

Thepressureexertedbyacolumnofliquidisdeterminedbytheverticalheight of the column,gravity, and the density of the fluid.

The pressure isnotaffectedbythevolumeorshapeoftheliquid.

gh

where p=densitykg/m3

m=masskg h=depthm


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Density and Specific Gravity

Densityisdefinedasthemass per unit volumeofasubstance.

Agivenvolumeofleadhasmanytimesthemassofthesamevolumeofwater.Whenthedensityofotherliquidsarecomparedtowater,atableofcomparative densities orspecific gravitiescanbedetermined.(JeppGenp.2-5)

Gasolinehasaspecificgravityof0.72,whichmeansitsweightis72 of the same amount ofwater.

GasesarecomparedtoairtoobtainanSG.

NoteThetermRelativeDensityisusedtocomparethedensityofairatdifferentaltitudestosealevel

TheSGofaviationfuelvariesduetoavarietyoffactorssuchas:

refiningprocess;

storagefacilities;

ambientconditions.

Activity Fuelling Exercise 1

TherefuellerorengineermustchecktheSGofthefuelsupply,tocalculatehowmanylitreswillprovidetheweightoffuelrequested.

SGlitres)Volumeuelfeight


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Buoyancy

Archimedes principle statesthatanitemplacedinfluidwilldisplaceavolumeoffluidequaltoitsownvolume.

Furthermore,theobjectsubmergedinthefluidissupportedbyaforceequaltotheweightofthefluiddisplaced.Thisisthebuoyancy force.Thereforeifabodydisplacesmorefluidthanitsownweightitwillfloat.

ThreebodiesofthesamevolumebutofdifferentSGsareshowneitherfloatingorsubmergedinwater:

BodyAwithSGof0.25onlysubmerged

BodyBwithSGof0.5onlysubmerged

BodyCwithSGof2willnotfloatinwaterweightisdthough

IftankwerefilledwithfluidwithSGgreaterthan2BodyA&Bwouldfloathigher,&bodyCwouldalsofloatshipsfloathigherinsaltwaterthaninfresh.

Lowerdensitymaterialsfloatonhigherdensitymaterials.


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Forexample,

gasolineoroilwillfloatonwater;Watersinkstothebottomofapetroltank.

icewillfloatonwater;

leadwillfloatonmercurybutsinkinwater.

Use of Pressure for MA

Pascalslawstates,changesinpressureundiminishedtoallpartsofthefluidanditscontainer.

PascalsLawcanbeusedtoprovideMechanicalAdvantage,e.g.AHydraulicJack.Thesamevolumeoffluidisdisplacedateachendofthesystem

Thesamevolumeoffluidisdisplacedateachendofthesystem,1psispreadover10squareinchescansupport10lbso,MA=10.

Notethatthelargepistonwillonlymoveup1/10ofthedistancethesmallpistonmovesin.


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Ifapistonsuchastheaboveisusedtodriveinbothdirectionsaninterestingsituationoccurs.

Thesamepressureprovidesdifferentforcesaccordingtodirectionoftravelduetothedifferingareaavailable.

Thiswillalsoaffectthespeedatwhichtheoperationwilloccur

Measurement of Pressure

Atmosphericpressureatalocationthendependsontheweight of the column of airabovethatlocation.Typically14.7psiatsealevelupto4.4.psiat29,000ft.

Gaugepressurereadspressureabove(orbelow)atmosphericsoAbsolutePressureisGaugePressureplusAtmosphericPressure.

TyrepressuregaugesreadGaugePressure.

Forpassengercomfort,modernaircraftretainacabinaltitudeequivalentto8000or11psi.Cruisingat29,000ft,theoutsidepressureis4.4psi.

Therefore,thestructureoftheaircraftisexperiencingadifferential pressureof

psi.6.41

Thisisasignificantcomponentofthetotalstressontheairframe


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Properties of Solids, Liquids and Gases

Solidshaveadefiniteshapeandadefinitevolumewhichisindependentofitscontainer.

Inasolidtheforces(bonds)thatkeeptheatomsormoleculestogetherarestrong.Therefore,asoliddoesnotrequireoutsidesupporttomaintainitsshape.

Mostmetalsaresolidsandassuchareusuallyhardandstrongandcapableofbeingshapedmechanically,(malleableandductile).

Bothliquidsandgasesareclassifiedas fluids.Atanypointonthesurfaceofasubmergedobject,theforceexertedbyafluidisperpendiculartothesurfaceoftheobject.

Theforceexertedbythefluidonthewallsofthecontainerisperpendiculartothewallsatallpoints.

Althoughliquidsandgasesbothsharethecommoncharacteristicsoffluids,theyhavedistinctivequalitiesoftheirown.

Aliquidisregardedasincompressible,(fixeddensity)whereasagasiscomparativelyeasytocompress.

Achangeinvolumeofagascaneasilybeachievedbychangesoftemperatureand/orpressure.

Agivenmassofgashasnofixedvolumeandwillexpandcontinuouslyunlessrestrainedbyacontainingvessel.


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B-2.2.1StaticsIssue on Page22of22

B:January2008 Revisi 3

PageIntentionallyLeftBank


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B-2.2.2KineticsIssueB:January2008 Revision1 Page1of10

TOPIC2.2:KINETICS

Kineticsisallaboutstatesofmotion.Wewilllookathowobjectscantransferfromplacetoplace,andinsomecaseshaveamotionwhilstnotactuallygettinganywhere!

Displacement and Distance

Theaircraftmaytravelatotaldistanceof2kmasitveersleftandright,butitsdisplacement,measuredonlyasthedifferencebetweenthestartpointandfinishpoint,willbeless.

Thedisplacementoftheaircraftinaneasterlydirectiononlyislessagain

Displacementreferstothepositionofanobjectrelativetoitspointoforigin.Thisisdifferenttodistance whichisthetotallengthtravelledbyanobjectfromitspointoforigin.

Displacementtakesdirectionintoconsideration,butdistancedoesnotcareaboutdirection.


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Speed and Velocity

Asimilardistinctioncanbemadebetweenspeedandvelocity.

Theybothrefertothedistance travelled per unit of time,forexample,milesperhour,metrespersecondetc.However,velocityisavectorquantity,sodirectionisimportant.

Speedisascalarquantity,sodirectionisirrelevant.

Averagespeedisdistancetravelleddividedbytimetaken.

Averagevelocityisthefinaldisplacementdividedbythetotaltime.

Acceleration

Whenanobjecthasaninitialvelocitythen,afteraperiodoftime,thatvelocityhaschanged(increasedordecreased),theobjectissaidtohaveaccelerated.

Accelerationcanbepositiveornegative.Negativeaccelerationiscalleddeceleration.

Accelerationistherate of change in velocity.Averageaccelerationisfoundbydividingthechangeinvelocitybythetotaltimetakenforthischangetooccur.

Aformulacanbeusedtorepresentthis:

t

v

(accelerationequalschangeinvelocitydividedbychangeintime)

or,

t

)

a

wherev=finalvelocity,u=initialvelocityandt=time.

Accelerationisavector,soachangeindirectionevenwhenundertakenatconstantspeed,isanacceleration.


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Youwillrememberthatforceisdefinedasthatwhichusesenergytoproduceachangeinmotionstate.NEWTONexploredthisandformulatedhisthreefamousLaws.

1.

A body will remain at rest or continue its uniform motion in a straight line until acted upon

by an external net force

ThislawisastatementaboutINERTIAwhichisthepropertyofmassthatresists changes inmotion.

2.

The acceleration of a body is directly proportional to the force applied to it and is inversely

proportional to the mass of the body.

Thislawisrepresentedbytheformula:

F = ma (forceequalsmassmultipliedbyacceleration).

Imagineanobjectatrestonatable.Itwillstaythatwayunlesspushed.(Newton1).

Itispushedforwardbyanexternalforceandaccelerates.(Newton2)Stoptheforceandiftherewasnofurtherresistanceitwouldcontinueforeveratitsnewspeed.

Infact,thereisfriction,whichprovidesanotherexternalforceandtheobjectdeceleratesandstops.(AlsoNewton2)

Nowimagineaspacecraftoutsideouratmosphere.Asinglepushwillaccelerateittoanewvelocitywhichitwillmaintainforever,(oruntilithitssomething!)

Alternatively,ifthesamecraftwasgivenacontinuouspushbyamotor,itwouldcontinuetoacceleratereachingenormousvelocities.

AspecialcaseofF=maisW=mg,wheregistheaccelerationcausedbythegravitationalattractionbetweenthemassmandtheEarth,equalling9.8m/spersec,andproducestheforcewecallweightW.

3. For every action, there is an equal and opposite reaction.

Theupwardthrustofarocketisthereactiontotheforcepropellingthemassofhotgasdownward.

Standonaskateboardandthrowalargemassawayfromyourself,andyouwillrollintheoppositedirection.

Linear Motion

Motionissaidtobeuniformifequaldisplacementsoccurinequalperiodsoftime.Inotherwordsconstantvelocity.


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Considerabodymovinginastraightline.Wehaveseveralrelationshipswecanuse.

time

ntisplaceme

velocityverage

and

time

distance

speedverage

and

t

u

wherev=finalvelocity,u=initialvelocityandt=time.

Howeverforlinearmotion,distanceanddisplacementwillbethesame,andwecanextendtheabovetoincludethefollowing,wheres=distance

2

2

1

atut 2

2

1

att

at t

2

v

s

as

2

Circular Motion

InaccordancewithNewtonsFirstLaw,theobjectwouldshootoffonastraightpathunlessaCentripetalForceiscontinually appliedtokeepitturningalongthecurve.

Newtons3rdLawdemandsthatthereisareactionthethisforcekeepingthestringintension,theCentrifugalForce.

Theobjectisacceleratedtowardsthecentreoftheorbit.

Anobjecttravellingalongacurvedpathtends,atallinstants,toflyoffonthestraightlinethat

formsatangenttothecurveofitspath(ifthestringbreaks,forexample).


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Tangential

direction

CentripetalforceisgivenbyNewtons2ndLaw

ma

rmr

r

mv

2

w

wheremismass,visvelocity,wisangularvelocity(rpm)andristheradius.

Thereforedoublingtherpm,quadruplesthecentrifugalforce,whichinagrindingwheel,forexample,istryingtopullitapart!ObserveRPMlimits!

Thisisalsooneofthereasonsaturbinebladecreepsorelongatesduringoperation.

Otheraircraftcomponentssusceptibletocentrifugalstressesare:

PropellerandHelicopterrotorblades

Wheelsandtyres


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Orbits

TheEarthorbitstheSunandtheMoonorbitstheEarth.Inbothcasestheorbitingbodyusesthecentrifugalforcecreatedbytheirmotiontobalancetheattractionofgravity.

TheSpaceShuttleandothersatellitesdoexactlythesame.ThefurtherfromtheEarththecraftis,theslowertheorbitalrpmneedstobe,howeverthelinearvelocityisgreater.

Eventuallyataheightofabout22,300miles,wehaveaGeosynchronousorbit,thatis,anorbitwherethesatellitespeedmatchestherotationoftheEarth,anditstaysoverthesamespot.

Theweightlessnessexperiencedbyanastronautisaresultofthesameequilibrium.

Hisorherweight,isbalancedbycentrifugalforce.

Activity:

Addtheforcestothediagram.


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Periodic Motion

Periodic motionorsimpleharmonicmotionreferstorepeatedmotion,i.e.thatwhichrepeatsovertime.Forexample,themassonaspring(below)orapendulum.

Thesimplependulumconsistsofaweighthangingfromapointbyastring.Iftheweightissetswinging,theoscillationsaretermedperiodicmotion,andtheoscillationsarepredictable.

TheenergycontainedinabodymovingwithSHMiscalledwave energy.

SHMoccursaroundanequilibriumpositionwhenamassissubjecttoalinearrestoringforce.


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Alinearrestoringforceisonethatgetsproportionallylargerwithdisplacementfromtheequilibriumposition.

Elasticityisthepropertyofanobjectormaterialwhichcausesittoberestoredtoitsoriginalshapeafterdistortion.

ItissaidtobemoreelasticifitrestoresitselfmorepreciselytoitsoriginalconfigurationapianowireisMOREelasticthanarubberband.

Amassonaspringisagoodexamplewhenstretched,itexertsarestoringforcewhich

tendstobringitbacktoitsoriginallength.Belowtheelasticlimit,therestoringforceisproportionaltotheamountofstretch.(Hooke'sLaw.)

Themotionissinusoidalanddemonstratesasinglenaturalorresonantfrequency.

Theamplitudeisthemaximumdistancethemassmovesfromitsequilibriumposition.Itmovesasfarononesideasitdoesontheother.

Thetimethatittakestomakeonecompleterepetitionorcycleiscalledtheperiodofthemotion.Wewillusuallymeasuretheperiodinseconds.

Frequencyisthenumberofcyclespersecondthatanoscillatorgoesthrough.Frequencyismeasuredin"hertz"whichmeanscyclespersecond.

Periodandfrequencyarecloselyconnected;theycontainthesameinformation:

1/Tfr/f

ThekeyfeatureofSHMisthattheperiodorfrequencyofthemotiondoesnotdependontheamplitudeoftheoscillation

Fromapracticalviewpoint,thiseffectwasusedtomakethefirstaccurateclocksapendulumtakesthesametimetomakeoneoscillation,eventhoughtheamplitudeoftheoscillationsdampswithtimetheperioddoesnotchange.

ApendulumsperiodTisgivenby:

[L/g] whereLislength

Inreality,oscillationsdonotcontinueforevertheygraduallydecreasetheirmotionasenergyislosttofriction.Youmaywantthesoundcausedbyapianooraguitartocontinueinthisway.

Butyouwanttheoscillationofyourcartostopimmediatelyaftergoingoverabump.Hencethedampers,(shockabsorbers.)


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Vibrationisatermnormallyreservedforhighfrequencyperiodicmotion

Inanaircraft,rotatingorreciprocalcomponentssuchasenginesandpropellersproducevibrationwhichcanbeannoyinganddestructive.

Vibrationexperiencedinanaircraftmayoriginatefromtheengines, turbulence, or from flightcontrol flutterduetowornhingesorlinkagebearings.

Theconstant vibration is annoyingtoflightcrewandpassengers.

Also,thestructureoftheaircraftandothercomponentscanvibrateinsympathyandstructural damage and component wear can occur.

Metal fatigueisanexampleofsuchstructuraldamage.

Resonance

Thenaturalorresonantfrequencyofanobjectisthefrequencywherethatobjectvibratesnaturally,orwithoutanexternalforce.

Iftwoobjectshavethesamenaturalfrequencyandarejoinedtoeachother,whenoneofthemvibrates,itcantransfer its wave energy to the other objectmakingitvibrate.

Thistransferofenergyisknownasresonance

Becauseresonancecaninducevibrationitcanexertdestructiveforcesonanaircraft.For

example,itispossibletohaveportionsofanaircraft,suchasthepropeller,vibrateinresonanceatcertainenginespeeds.


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B-2.2.2KineticsIssue on Page10of10


Harmonics

Harmonicsexistasmultiples ofanoriginal,naturalfrequency.

Thatis;

ifthenaturalfrequencyis100 Hz

the1stharmonicisat200 Hz

andthe2ndharmonicisat300 Hzetc

Harmonicscanresonateaswellasnaturalfrequencies


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B-2.2.3DynamicsIssueB:January2008 Revision1 Page1of12

TOPIC2.2.3DYNAMICS

OneofthefundamentalpropertiesoftheUniverseisthatitcontainsenergy,whichinturncanbeusedtoeffectchange.Whenthatchangeisthestateofmotionofamass,thenaforce

hasbeencreated.

Dynamicsisthestudyofforcesatworkinmotion,andtheuseofenergy.

The Difference between Mass and Weight

TheEarthisalargemassinspaceandthereisamutualattractionbetweenitandeverythingonitssurface.BecausetheEarthissomuchbiggerthaneverythingelse,itseemsliketheattractionisonlyoneway.

NewtonsLawstellusthat mg

sowhenthatforceistheresultoftheaccelerationduetogravity,g,were-writethisas:

mg

ser/sgeight

So,whydowesayourweightis70kgandnot70x9.8700N?

Well,weshouldnt!

Ithasonlybecomeacceptablebecause,ifweallstayontheEarth,theerrorbecomesconstant.

Gotothemoon,whosemassI/6thatoftheEarth,andyourweightwillnotbethesame.

Youwillstillhave70kgofmass,buttheweightreducesto

Newtons14

6

9.80

Ourearthlymuscles,usedtosupporting700N,canmakeour114Nbodyjumpmuchhigher.

TraveltoJupiter,(mass2timesEarth)andyouwillweigh70x9.8x2.51715N

Thesamemuscleswillcollapseunderthestressoftryingtosupportthisforce.


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Inertia

Inertiaisthepropertyofamasswhichcausesittoresist any change in its state of motion

Newtonsfirstlawofmotionstates:

Abodywillremainatrestorcontinueitsuniformmotioninastraightlineuntilacteduponbyanexternalnetforce.

Thelargerthemass,thegreatertheinertia.

Work

Whenaforceactsonanobject,overcomesinertia,andsetsitinmotion,work isdone.Unlesstheobjectmovesthroughadistancetheworkdoneissaidtobezero.

Workdoneisfoundbytheformula

Fs

WhereF=force,s=distanceTheunitofworkintheSIsystemisthejoule, whichequals1 Newton metre (Nm)

Example:

Ifanobjectismoved10metresbyaforceof100newtons,theworkiscalculatedas:

Fs

(Nm)000

W =1 000 joules.

IntheImperialsystemofmeasurement,ameasureofworkisthefoot-pound,theeffortof

raisingonepoundofmassbyonefoot.


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Power

Poweristherateofdoingwork.Whendeterminingtheamountofworkdone,thetimerequiredtodotheworkisnotconsidered.Powerontheotherhandtakestimeinto

consideration.

Forexample,ifapersonclimbsaflightofstairs,theyperformthesameamountofworkwhethertheywalkuporrunup.However,whenthepersonrunsuptheyareworkingatafaster rateandthereforeusingmore power.

t

TheunitSIunitofpoweristhewatt.Onewattisthepowergeneratedwhenonejouleofworkisdoneinonesecond.

Intheimperialsystemofmeasurement,powerisexpressedinfoot/pounds per second andonehorsepowerisequivalentto550foot/poundspersecondand746Watts

Becausedistanceorceork

Poweracbewrittenastime

distanceorce

Butdistancedividedbytimeisvelocity

so Velocityorceower

Watts)/sNv

ActivityThedrag(airresistance)ofanaircraftis1500N.Whatpowerisrequiredtoflyat360km/hr(AnsinkW)

Whatisimpliedifyouhavea230kWmotor?

Energy

Energyprovidesthecapacityforworktobedoneandeffectchange.TheSIunitofenergyisthejoule.

Onejouleofenergycandoonejouleofworkassumingtherehavebeennolosseslike

friction.Animportantconceptwhenthinkingaboutenergyisthelawoftheconservationofenergywhichstates:

Energycanneitherbecreatednordestroyed.Itcanonlybechangedfromoneformtoanother.

Forexample,acarturnsthechemicalenergyfoundinpetrolintomechanicalenergy,heatandsound.


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Thepotentialenergyinabodyorofabodymeansstored energy, storedinthebodybecauseofitsposition, conditionorchemical nature.

Potential Energy

Eventhoughanobjectisnotdoingwork,itcanstillbecapableofdoingwork.Forexample,amassheldabovetheground.

Whileitisbeingheldithasnomotion,soitisnotdoingwork.Ifitisthenreleased,itwillfallimmediately,thusdoingwork.

)ghE

height(m)(9.8m/sravityoueccnass(kg)

Hydroelectricpowerusestheenergystoredbyamassofwaterflowingdownhill.

Adrumofgasoline,astickofexplosive,orachocolatebarallcontainpotentialenergy,

becauseoftheirchemicalcomposition.

Kinetic Energy

Kineticenergyisenergyabodyhasbecause of its motion.Ifabodyisheldaloftandthenreleased,asitstartstofalltogroundthepotential energy is converted to kinetic energy.

Theformulaforcalculatingkineticenergyis:

Joulesmv

2

1KE

,

wherem=mass(kg)andvvelocityinm/s


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Total Energy

Inaccordancewiththelawofconservationofenergy,thetotal energydoesnotchange,butpotentialenergycanbetransformedintokineticenergyandvice-versa.

Afallingmasshasmaximumpotentialenergyathighestelevation(PE = mgh). Kineticenergyiszerobecausethebodyhasnomotion(KE = mv2).

Oncethemassisreleasedandstartsfalling,thepotentialenergystartstobeconvertedtokineticenergy.

Halfwaythroughitsfall,thepotentialenergyexactlyequalsthekineticenergy.

Then,attheinstantthebodystrikesthefloor,thekineticenergyismaximum.

Ithasnodistancelefttofallsopotentialenergyiszero.

Friction

Whenobjectsmovetheyusuallyrollorslideincontactwithotherobjectsorsubstances.

Suchslidingorrollingcontactshaveresistancetotheforcethatcausesthemotion.Thisresistanceiscalledfriction.

Inmostindustrialapplicationstheminimisation of friction is sought,withlubricant,yetfrictionbetweenourshoesandthegroundisnecessarytobeabletowalkandrun.

Likewise,itisthefrictionbetweentyresandtheroadandbetweenbrakerotorsanddiscsthathelpsslowdownavehicle.

Thecoefficient of friction referstothedifferences in friction between various materials.

Thehigherthecoefficientoffriction(),thegreatertheresistancebetweentwosurfaces.

Lubrication reducesfriction.

Therearethreetypesoffriction

1. StartingorStatic-Overcominginitialresistanceuntilbreakawayoccurs.

2.

Sliding-Resistanceduringsteadymotion.

3.

Rolling-Singlepointcontactresistanceislessthansliding.

Stillneedsomefrictionotherwisethewheelwillnotgrip.

Theamountofslidingfrictioncanbecalculatedfromtherelationship

N

whereNisthereactiontotheweightoftheobjectfromthesurfaceonwhichitissliding.


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Fromaboveitcanbeseenwhypullingaboxwithaslightupwardangleiseasierthatpushingwhenyourforcemaybeslightlydownonthebox.

Consideranaircraftlanding.Justaftertouchdownthewingsarestillsupportingsomeoftheweight,andthefrictionbetweenthewheelsandthesurfacewillbesmallandbrakingwillbeinefficient.

L

W

N

butN L

)

Thegreaterthelift,thesmallerthefriction.

Airflowspoilersareusedtodumpthisliftandallowthepilottobeginbrakingearlier

Someexampleofare:

Steelonsteel 0.09

Rubbertyreonairportrunway 0.7(dry)and0.5(wet)

Teflononteflon 0.04


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Coefficients of rolling resistanceareverysmall.

Forexample:

Rubbertyresonconcrete 0.02

Rollerbearings 0.001

Rollingonesurfaceoveranothercreateslessfrictionthanslidingonesurfaceoveranother.

Heat

Heatisoneofthemostusefulformsofenergybecauseofitsdirectrelationshipwithwork,andwiththeuseofengines.Othertypesofenergycanbetransformed,inaccordancewiththelawofconservationofenergy,intoheat.

Heatisalsofoundasaconsequenceoffriction.Theheatproducedbyfrictionisusuallyunwanted.


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Efficiency

Withanymachinery,theefficiency is the ratio of work output to workor energy input.If100joulesofworkisputintoageartrainandtheoutputis90joules,theefficiencyissaidtobe:

100

(in)

(out)

Efficiency

90fficiency00

100

90

Itisfrictionthatprimarilydeterminestheefficiencyofamachine,becausethefrictionbetweenmovingpartscreatesheat,soundandsometimeslight.

Alloftheseareclassifiedasenergylosses.

Reducingfrictionisusuallyaccomplishedbylubricationorstreamlining.


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Momentum

Inertiahasbeendefinedasthetendencyofamasstoresistchangesinitsstateofmotion.Momentumhoweveristheproductofthisinertiaandthemotionitalreadyhas.

Therearetwotypesofmomentum,linearandangular.

Linear momentumisameasureofthetendencyofamovingbodytocontinueinmotionalongastraightline.Momentumisdefinedastheproductofthemassandvelocityofabody.

M = mv.

Momentumisconserved,soiftwomassesm1andm2travellingatv1andv2collide,stickingtogether,andcontinueasasinglemasswithnewvelocityv,then:

v

2

(V is a vector, so direction is important)

Angular momentumisameasureofthetendencyofarotatingbodytocontinuetospinaboutanaxis.

M = m

wwherewistherpmorangularvelocity.AspinningskatercanvaryherRPMbymovingherarmsinandout,changingtheresistancetoherrotation

Extendingherarmsplacestheirmassfurtherfromtheaxisofrotationandtheresistancetospinincreases,reducingtherpm.Bringingtheminbringstheirmassclosertotheaxisandtherpmincreases.Thatshesomehowspeedsup,seeminglygainingenergyfromsomewhere,isanillusion.


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ItisactuallyduetotheConservationofAngularMomentum.

Impulse

Ifaforceisappliedtoamovingbody,thatbodysstateofmotionisaltered.ThemomentumofthebodyischangedbyanamountcalledtheImpulse.

(Impulse)I=Ft(Forcemultipliedbytime)

Aspacecraftsburni.e.applyingthrustforanumberofsecondsisanexampleofan

Impulse

Activity

ConsideramassmactedonbyaforceFfortseconds.Itchangesvelocityfromutov.

ShowthattheImpulse=Ftisequivalenttoachangeinmomentummutomv.


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A Simple Gyroscope

Agyroscopeisanyrotating mass. Ausefulexampleisthetypeconsistingofarotormountedongimbals,sothatitssupportingplatformorcasecanbeturnedinoneormoreplanes

aroundtherotorwithoutchangingtherotorsplaneofrotation.Likeallrotatingmasses,thegyroscopehastwofundamentalcharacteristics.Thesearegyroscopic inertia (rigidity in space)andprecession.

Gyroscopic rigidity

Thisisthenaturalpropertyofanyrotatingmasstoresistchangestoitsplaneofrotationunlessanexternalforcecausesachange.

Thisisthereasonaspinningtoporcoinremainsuprightuntilitrunsdown.

Iftherotorisinacasesecurelyfittedtotheairframe,itwillshowchangesofaircraftattitude.

ThisisthebasisfortheinstrumentcalledtheArtificialHorizonorAttitudeIndicator.Precession

Thisthechange of the plane of rotationcausedbyanexternalforce.

Ifa forceis appliedtothe rotatingmass, overcoming the natural rigidity, then its planeofrotationwilldeflect900inthedirectionofrotation.

Pushingthenoseofthisaircraftdowncausestheproptoswingthewholeairframeleft.

Iftherotorisalignednosetotailitwilldeflectwhentheaircraftisturned,andmeasureRate

ofTurnTrythesewiththebikewheel!!


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B-2.2.3DynamicsIssue on Page12of12




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TOPIC 2.2.4: FLUID DYNAMICS

PHYSICAL NATURE OF MATTER

Matteriscomposedofseveralmolecules.Themoleculeisthesmallestunitofasubstancethatexhibitsthephysicalandchemicalpropertiesofthesubstance.Furthermore,allmoleculesofaparticularsubstanceareexactlyalikeanduniquetothatsubstance.

Mattermayexistinoneofthreephysicalstates,solid,liquid,andgaseous.Allmatterexistsinoneofthesestates.Aphysicalstatereferstothephysicalconditionofacompoundandhasnoaffectonacompoundschemicalstructure.Inotherwords,ice,water,andsteamareallH2Oandthesametypeofmatterappearsinallofthesestates.

Sol id Liquid Gas

Definite Shape- Independent of the container

Indefinite Shape- takes the shape of the container

Indefinite Shape- takes the shape of the container

Define Volume Define Volume Indefinite Volume

Not easily compressible

- littl e free space between particles

Not easily compr essible

- litt le free space between particles

Compressible

- lots o f free space between particles

Does not f low easily

- particles cannot move past one

another

Flows easily

- particles can move past one another

Flows easily

- particles can move past one another

Characteristics of Matter

Allatomsandmoleculesinmatterareconstantlyinmotion.Thismotioniscausedbytheheatenergyinthematerial.Thedegreeofmotiondeterminesthephysicalstateofmatter.

DENSITY

Thedensityofasubstanceisitsweightperunitvolume.

Thedensityofsolidsandliquidsvarieswithtemperature.However,thedensityofagasvarieswithtemperatureandpressure.Tofindthedensityofasubstance,dividetheweightofthesubstancebyitsvolume.Thisresultsinaweightperunitvolume.

Density=Weight/Volume

Forexample,theliquidwhichfillsacertaincontainerweighs1,497.6pounds.Thecontaineris4

feetlong,3feetwideand2feetdeep.Therefore,itsvolumeis24cubicfeet(4ft.x3ft.x2ft.).Basedonthis,theliquidsdensityis62.4lbs/ft.

62.4poundspercubicfoot=1,497.6/24ft

TrainingMaterialOnly B-2.2.4FluidDynamics

IssueB:January2008 Revision3 Page1of12


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Becausethedensityofsolidsandliquidsvarywithtemperature,astandardtemperatureof4Cisusedwhenmeasuringthedensityofeach.Althoughtemperaturechangesdonotchangetheweightofasubstance,theydochangethevolumeofasubstancethroughthermalexpansionor

contraction.Thischangesasubstancesweightperunitvolume.Whenmeasuringthedensityofagas,temperatureandpressuremustbeconsidered.Pressureismorecriticalwhenmeasuringthedensityofgasesthanitisforothersubstances.Thedensityofagasincreasesindirectproportiontothepressureexertedonit.

Standardconditionsforthemeasurementofthedensitiesofgaseshavebeenestablishedat0Cfortemperatureandapressureof76cmofmercury(Hg)(Thisistheaveragepressureoftheatmosphereatsealevel).Densityiscomputedbasedontheseconditionsforallgases.

SPECIFIC GRAVITY S.G.)

Itisoftennecessarytocomparethedensityofonesubstancewiththatofanother.Forthisreason,astandardisneededfromwhichallothermaterialscanbecompared.Thestandardwhencomparingthedensitiesofallliquidsandsolidsiswaterat4C.Thestandardforgasesisair.

Inphysicsthewordspecificreferstoaratio.Therefore,specificgravityiscalculatedbycomparingtheweightofadefinitevolumeofsubstancewiththeweightofanequalvolumeofwater.The

followingformulasareusedtofindspecificgravity(sp.gr.)ofliquidsandsolids:

sp.gr.=weightofasubstance/weightofequalvolumeofwater.

sp.gr.=Densityofasubstance/densityofwater.

Thesameformulasareusedtofindthedensityofgasesbysubstitutingairforwater.

Specificgravityisnotexpressedinunits,butasapurenumber.Forexample,ifacertainhydraulicliquidhasaspecificgravityof0.8,1cubicfootoftheliquidweighs0.8timesasmuchas1cubicfootofwater.

Specificgravityisindependentofthesizeofthesampleunderconsiderationandvariesonlywiththesubstancethesampleismadeof.

Adevicecalledahydrometerisusedtomeasurethespecificgravityofliquids.Thisdevicehasatubular-shapedglassfloatcontainedinalargerglasstube.Thefloatisweightedandhasaverticallygraduatedscale.




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Thescaleisreadatthesurfaceoftheliquidinwhichthefloatisimmersed.Whenfilledwithaliquidhavingadensitygreaterthanpurewater,thefloatrisesandindicatesagreaterspecificgravity.Forliquidsoflesserdensity,thefloatsinks.

VISCOSITY IN LIQUIDS

Viscosityisoneofthemostimportantpropertiesofhydraulicfluids.Itisameasureofafluidsresistancetoflow.Aliquid,suchasgasoline,whichflowseasilyhasalowviscosity;andaliquid,suchastar,whichflowsslowlyhasahighviscosity.

Theviscosityofaliquidisaffectedbychangesintemperatureandpressure.Asthetemperatureofaliquidincreases,itsviscositydecreases.Thatis,aliquidflowsmoreeasilywhenitishotthanwhenitiscold.Theviscosityofaliquidincreasesasthepressureontheliquidincreases.Asatisfactoryliquidforahydraulicsystemmustbethickenoughtogiveagoodsealatpumps,

motors,valves,andsoon.Thesecomponentsdependonclosefitsforcreatingandmaintainingpressure.Anyinternalleakagethroughtheseclearancesresultsinlossofpressure,instantaneouscontrol,andpumpefficiency.


http://www.brbbv.com/media/Image/VI%20Improver.jpg


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earancesofcloselyfittedparts,lines,andinternalpassages.Thisresultsinpressuredropsthroughoutthesystem,sluggishoperationoftheequipmentandanincreaseinpowerconsumpti

allyoils,butitalsoappliestogases.

peratureofagasrises,itbecomesmoreviscous.Inotherwords,theviscosityof

gasesvariesdirectlywithtemperature,andtheviscosityofliquidsvariesinverselywith

oilbecomesextremelythinathightemperaturesandextremelyty

re nd,consequently,

promotesrapidstartingandpromptcirculation;itresistsexcessivethinningwhenthemotorishotandthusprovidesfulllubricationandpreventsexcessiveoilconsumption.

Leakagelossesaregreaterwiththinnerliquids(lowviscosity).Aliquidthatistoothinwillalsoallowrapidwearingofmovingparts,orofpartsthatoperateunderheavyloads.Ontheotherhand,iftheliquidistoothick(viscositytoohigh),theinternalfrictionoftheliquidwillcauseanincreaseinthe

liquidsflowresistancethroughcl

on.

VISCOSITY IN GASES

ThetermViscosityisusedmostlyinregardtoliquids,especi

Theviscosityofairisaconsiderationinaerodynamics.

Whenthetem

temperature.

VISCOSITY INDEX

Theviscosityindex(V.I.)ofanoilisanumberthatindicatestheeffectoftemperaturechangesontheviscosityoftheoil.AlowV.I.signifiesarelativelylargechangeofviscositywithchangesoftemperature.Inotherwords,thethickatlowtemperatures.Ontheotherhand,ahighV.I.signifiesrelativelylittlechangeinviscosioverawidetemperaturerange.

Anidealoilformostpurposesisonethatmaintainsaconstantviscositythroughouttemperatuchanges.TheimportanceoftheV.I.canbeshowneasilybyconsideringautomotivelubricants.AnoilhavingahighV.I.resistsexcessivethickeningwhentheengineiscolda


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AnotherexampleoftheimportanceoftheV.I.istheneedforahighV.I.hydraulicoilforaircraft,sincehydrauliccontrolsystemsmaybeexposedtotemperaturesrangingfrombelow65Fathighaltitudestoover100Fontheground.

Fortheproperoperationofthehydrauliccontrolsystem,thehydraulicfluidmusthaveasufficientlyhighV.I.toperformitsfunctionsattheextremesoftheexpectedtemperaturerange.

STREAMLINING

Allthreeobjectshavethesamecross-sectionalarea.

Aflatshapefightsairflowandcausesmoredragorresistance.

Acurvedshapeallowsairtoflowsmoothlyaroundit.

Streamliningistheshapingofanobject,suchasanaircraftbodyorwing,toreducetheamountof

dragorresistanceair,duetoviscosity,tomotionthroughastreamofair.

Streamliningreducestheamountofresistanceandincreaseslift.

Toproducelessresistanceforsubsonicstreamlining:

Thefrontoftheobjectshouldbewellrounded

Thebodyshouldgraduallycurvebackfromthemidsectiontoataperedrearsection

COMPRESSIBILITY

Thetermscompressibilityandincompressibilitydescribetheabilityofmoleculesinafluidtobe

compactedorcompressed(mademoredense)andtheirabilitytobouncebacktotheiroriginaldensity,inotherwords,their"springiness."

Anincompressiblefluidcannotbecompressedandhasrelativelyconstantdensitythroughout.Liquidisanincompressiblefluid.




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Atloweraltitudes,airhasahigherdensityandisconsideredincompressiblefortheoreticalandexperimentalpurposes.

Agaseousfluidsuchasair,ontheotherhand,canbeeithercompressibleorincompressible.



EFFECTS OF COMPRESSIBILITY

Generally,fortheoreticalandexperimentalpurposes,gasesareassumedtobeincompressiblewhentheyaremovingatlowspeeds--underapproximately220milesperhour.Themotionoftheobjecttravellingthroughtheairatsuchspeeddoesnotaffectthedensityoftheair.Thisassumptionhasbeenusefulinaerodynamicswhenstudyingthebehaviourofairinrelationtoairfoilsandotherobjectsmovingthroughtheairatslowerspeeds.

However,whenaircraftbegantravellingfasterthan220milesperhour,assumptionsregardingtheairthroughwhichtheyflewthatweretrueatslowerspeedswerenolongervalid.Athighspeedssomeoftheenergyofthequicklymovingaircraftgoesintocompressingthefluid(theair)and

changingitsdensity.TheairathigheraltitudeswheretheseaircraftflyalsohaslowerdensitythanairnearertotheEarth'ssurface.Theairflowisnowcompressible,andaerodynamictheorieshavehadtoreflectthis.Aerodynamictheoriesrelatingtocompressibleairflowcharacteristicsandbehaviourareconsiderablymorecomplexthantheoriesrelatingtoincompressibleairflow.


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STATIC, DYNAMIC AND TOTAL PRESSURE

Whenanaircraftflies,ittravelsthroughafluid(air)whichhasacertainatmosphericpressureduetotheweightoftheatmosphere(staticpressure).

Theaircraftalsohasforward,dynamic,motionwhichmeansthatitisstrikingairmoleculesatarateproportionaltoitsspeed(dynamicpressure).

Thesumofthestaticanddynamicpressureisthetotalpressure(PtorP0),alsoknownasthetotalpitotpressure,stagnationpressureofthefluid.

Aircraftusepitottubestomeasureairspeed.

Staticpressureistheactualpressureofthefluid,whichisassociatednotwithitsmotionbutwithitsstate.Inaircraft,staticpressureisopentotheatmosphereandismeasuredperpendiculartotheairflowthroughaholeinthewall.

DynamicPressureisparalleltotheflowofairandcanbeexpressedas:q = rV, whereristhefluiddensityandVisthefluidvelocity.


http://upload.wikimedia.org/wikipedia/commons/4/47/Airspeed_p1230157.jpghttp://upload.wikimedia.org/wikipedia/commons/4/47/Airspeed_p1230157.jpg


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Staticpressureisusedtocalculateaircraftaltitude.

MEASURING DYNAMIC PRESSURE

Totalpressureisfedtotheinsideofthesealedcapsule.Asthestaticpressurevariesinthecase,thesealedcapsuleexpandsorcontracts.Thisisequivalentto:pV2 = Total Pressure P

Asuitablelinkcanmovesanindicatorasrequired.

q=rVisthenusedtocalculateairspeedinflight:




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BERNOULLIS PRINCIPLE

TheSwissmathematicianandphysicistDanielBernoullidevelopedaprinciplethatexplainstherelationshipbetweenpotentialandkineticenergyinafluid.

Allmattercontainspotentialenergyand/orkineticenergy.Inafluid,thepotentialenergyisthatcausedbythepressureofthefluid,whilethekineticenergyisthatcausedbythefluidsmovement.Althoughtheenergycannotbecreatedordestroyed,itispossibletoexchangepotentialenergyforkineticenergyorviceversa.

InFigureatubeisshowninwhichthecross-sectionalareagraduallydecreasestoaminimumdiameterinitscentersection.Atubeconstructedinthismanneriscalledaventuri,orventuritube.Wherethecross-sectionalareaisdecreasing,thepassagewayisreferredtoasaconverging

duct.Asthepassagewaystartstospreadout,itisreferredtoasadivergingduct.TheventuriisusedtoillustrateBernoullisprinciple,whichstatesthat:thestaticpressureofafluid(liquidorgas)decreasesatpointswherethevelocityofthefluidincreases,providednoenergyisaddedtonortakenawayfromthefluid.

Asaliquid(fluid)flowsthroughtheventuritube,thegaugesatpointsA,B,andCarepositionedtoregisterthevelocityandthestaticpressureoftheliquid.

Inthewidesectionoftheventuri(pointsAandCinFigure),theliquidmovesatlowvelocity,producingahighstaticpressure,asindicatedbythepressuregauge.Asthetubenarrowsinthecenter,itmustcontainthesamevolumeoffluidasthetwoendareas.

Inthenarrowsection(pointsB),theliquidmovesatahighervelocity,producingalowerpressure

thanthatatpointsAandC,indicatedbythevelocitygaugereadinghighandthepressuregaugereadinglow.

BERNOU LLI S THEOREM EQU ATION

Bernoulli'sprinciplecanbeappliedtovarioustypesoffluidflow,resultinginwhatislooselydenotedasBernoulli'sequation.Infact,therearedifferentformsoftheBernoulliequationfordifferenttypesofflow.ThesimpleformofBernoulli'sprincipleisvalidforincompressibleflows(e.g.mostliquidflows)andalsoforcompressibleflows(e.g.gases)movingatlowMachnumbers.MoreadvancedformsmayinsomecasesbeappliedtocompressibleflowsathigherMachnumbers

TheslideshowsoneofmanyformsofBernoulli'sequationwhichappearsinmanyphysics,fluidmechanics,andairplanetextbooks:

StaticPressure+DynamicPressure=TotalPressure=ConstantBernoulli'sprinciplecanbederivedfromtheprincipleofconservationofenergy.Thisstatesthatinasteadyflowthesumofallformsofmechanicalenergyinafluidalongastreamlineisthesameat




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allpointsonthatstreamline.Thisrequiresthatthesumofkineticenergyandpotentialenergyremainconstant.

VENTURI EFFECT

TheVenturieffectisthereductioninfluidpressurethatresultswhenafluidflowsthroughaconstrictedsectionofpipe.Thefluidvelocitymustincreasethroughtheconstrictiontosatisfythe

equationofcontinuity,whileitspressuremustdecreaseduetoconservationofenergy:thegaininkineticenergyisbalancedbyadropinpressure.

AnequationforthedropinpressureduetotheVenturieffectmaybederivedfromacombinationofBernoulli'sprincipleandtheequationofcontinuity.

Thelimitingcaseoftheventurieffectischokedflow,inwhichaconstrictioninapipeorchannellimitsthetotalflowratethroughthechannel,becausethepressurecannotdropbelowzerointheconstriction.

Referringtothediagramshown,usingBernoulli'sequationinthecaseofincompressibleflows(suchastheflowofwaterorotherliquid,orlowspeedflowofgas),therelationshipofthepressureP

ofafluidtoitsvelocityV

wouldbegivenby:




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whereisthedensityofthefluid,v1isthe(slower)fluidvelocitywherethepipeiswider(point1),v2isthe(faster)fluidvelocitywherethepipeisnarrower(point2).Thisassumestheflowingfluid(orothersubstance)isnotsignificantlycompressible-eventhoughpressurevaries,thedensityis

assumedtoremainapproximatelyconstant.TheVenturieffectisnamedafterGiovanniBattistaVenturi,(17461822),anItalianphysicist.

Venturisarefoundinmanyapplications.

Thepistonforcesairthroughtheventuriinfiguresothepressureatthethroatdrops.Atmosphericpressureintheroundcontainer(reservoir)isnowgreater,andtheliquid(red)travelsupthetube,joinstheairstream,andissprayed.

AnextensionofBernoullisTheoremisthebasisofhowsomeoftheliftisgeneratedbyaircraftwings,propellersandhelicopterrotorblades.

Thetopofthewingroughlyapproximatestohalfofaventuri.Theairpassingoverthetopsurfaceofthewingmovesatahighervelocity.Thehighervelocitycausesadecreasedpressurethere,andapressuredifferencebetweenupperandlowerwingsurfacescontributestotheforceknownaslift.

Note:Leadingedgesexperiencetotalpressure,notdynamicpressureonly.




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B-2.3ThermodynamicsIssue on Page1of22


TOPIC2.3:THERMODYNAMICS

EarlierenergywasdescribedasthatpropertyoftheUniversewhichcancausechange.

Throughtheapplicationofforce,workisdone.

Everystarradiatestheenergyitdevelopsinternally,andanyassociatedplanetsattheappropriatedistancecanabsorbandusethisenergytoevolveaccordingly.

Heatisoneformofenergy,andinmanycasestheproductionofheatanditssubsequentreleasecandousefulwork.

TheConservation of Energystatesthatenergycannotbecreatedordestroyed,onlyconvertedfromoneformtoanother.

Energyconcerningtheapplication,lossortransferofheatistermedthermal energy.

Accordingtothelawofconservationofenergy,thermal energy cannot be created or

destroyed, but it is converted from, and to, other forms of energy.Forexample,thermalenergymaybecreatedfromelectrical, chemical, mechanicalornuclearenergy.

Itcanbeconvertedtomechanical orkinetic energy.Theheatinathermalprocesscanalsoaddenergytochemical reactions.

Althoughallsubstancescanabsorbandradiateheatenergy,itisthegasesthatcanmosteasilyturnthisintousefulwork.Theworkdonebyanexpandinggasisoneofthebasicprinciplesbehindpropulsion.


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Heat Transfer

Conduction

Conductionrequiresphysical contactbetweenabodyhavingahighlevelofheatenergyandabodyhavingalowerlevelofheatenergy.

Whenacoldobjectcomesintocontactwithahotterobject,theactionofthemoleculesinthehotmaterialtransfers some of their energytothemoleculesinthecoldermaterial.

Similarly,ifonepartofabodyisheatedthentheenergywillbetransferredinternallymoleculetomoleculeastheybecomemoreagitated.

Eventuallytheactivityofthemoleculesinthetwomaterialsbecomesequalisedandthusthetemperatures also equalise, beforefallingasheatislosttothesurroundings.

Anexampleofheattransferbyconductionistheremovalofheatfromanenginecylinderbycooling fins.

Thecombustionofgasolineinthecylinderreleasesheatwhichisconductedtothecylinderheadandcoolingfins.

Theheatisthenconductedtothecoolerairandcarriedaway.


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Convection

Convection istheprocessbywhichheatistransferredbybulkmovementofafluid.

Asfluidisheatedbyaheatsource,it becomes less dense and rises,beingreplacedbycoolerfluid.

Heating water in a kettle, heating air in a houseandthecirculation of atmospheric heataree

B-2 Physics SR

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