Physics Sept 12th

8/4/2019 Physics Sept 12th

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KEYCONCEPTSAfter ompletinghischapterouwillbeableo

. explainow istance,osition,and isplacementre ifferent

. explainow peed,elocity,ndaccelerationre ifferent

. explainow ectorsnd calarsare ifferento add nd ubtractectorssingscale iagramsnd lgebraicmethodsr obtain otionnformationromposition-time,elocity-time,ndacceleration-timeraphs

',e solv niformelocitynd,' , uniformccelerationroblems,,,0sing lgebraicethodsar "describeowheaccelerationdUeogravityffectshemotionofobjeclsloseo hesurJaceof Earth. assesS,ltg,]imnactnsocietyandheenvironmentfatechnologyhat ppliesonceptsrelatedokinematics

WhatEffectsDo MovingObjects HaveonSocietyand the Environment?Automobiles havebeen made in North America for over 100years.As technology has advanced, automobile designs have changed substantially. Foexample, a 1909 Ford Model T could travel at a maximum speed of approximately 70 km/h. This was considered a frightening speed at the time. Ovetime, vehicleshavebecome aster.Today,manycars can reachspeedsof 200 km/hor more, much higher than the speed imits on any Canadianroads.Scientistsand engineerscontinue to develop a deeper understanding omotion and the factors that affect it. This knowledge, coupled with technological advances, has enabled them to produce extremely fast experimentaland vehicles.The ThrustSSC SuperSonicCar) reachedan astounding speeof 1228 km/h. This extraordinary British-built vehicle was driven by a RoyaAir Force pilot and powered by two jet engines. The team that built theThrustSSC and other competing groups are now attempting to build evefaster vehicles.

Although we benefit greatly from motor vehicles that transport hugeamounts of goods daily and make travel much easier, we now realize thaburning largeamounts of fossil fuels has a negative mpact on our environmentFuel consumption for the ThrustSSCwas a mind-boggling 55 L of gasolineperkilometre. In comparison, the passenger ehiclesyou seeon the street consumeabout 0.07 L/km. Many researchershave turned their attention to producingpractical vehicles with a lower environmental impact.

Studentsat the University of Waterloo are moving the technology of passengevehicles away from fossil fuels altogether. They have designed and constructeda series of solar vehicles called Midnight Sun, which have reached speedsof117 km/h. The team capturedthe world record for the longest ourneyby asolar-poweredcar.

Faster,more efficient vehicles are an important part of the future of trans-portation in Canada. Today'sstudents are tomorrow's scientists and engineersWith a sound understanding of the physicsof motion, we can improve today'stransportation and environmental technologies to help protect our planet.

,:Answerhe ollowinguestionssingour urrentnowledge.3. How avehemotionapabilitiesfautomobilesYou il lhavechanceo evisitheseuestionsater,pplying changedverhepast entury?conceptsnd killsromhe hapter. 4. How avehangesn echnologieshat pply1. Givehreexamplesfscientificanguagehat an e conceptsbout otionffectedocietyndheused0describehemotionfobjects. environment?2. Explainow raphsan rovidenformationbouthemotionfanobject.


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TheEffectof Gravityon the Motionof ObjectsSkills:redicting,erforming,bserving,nalyzingIn his ctivity,ouwill nvestigateowmassnd hapechangeheeffect fgravityn hemotionfobjectsallingthroughheair.EquipmentndMaterials;sphericalbjectsfdifferentmass;sheetfpaper1. Pick p hewo pheresnddentifyhichsheavier.2. Predicthichphereilt eachhe loorirstfyoureleaseoth f hem imultaneouslyromhe ameheight.ecordour redictionnd xplainoureasoning.3. Holdhe wo pherestarm'sengthrom our ody tthe ameeight.eleasehe wo pheres.ecoroourobservations.@

Use autionhenroppinghe pheres.o ot ropthemnear oureet0r near ther tudents,ickup hespheresromheloormmediatelv.

*dbb'oi A2.'l4. Repeattep with ne pherend lat heetfpaperRecordour bservatrons.5. Crumplehe iecefpapersednStep nto ball fapproximatelyhe ameize sone f he pheres.6. Repeattep withhe rumptedaperalt ndhesphere.ecordour bservations.A. Did our bservationsnStep supporthepredictionyoumadenStep ? f not, rovideeasonshyhepredictionas ot upported.:rir:'B. DidhemassfeachpherenStep affecthe imettookhe pheresoreachhe loor?:,:rr:C. Comparend ontrastour bservationsorStep withthoseorSteo . :::,;,D. Comparend ontrastour bservationsorStep withthoseorStep . r''r.,


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SlMetric nitsThe lsystemleSystdmeinternational'unit6s)rovidesaseunitsormeasuringundamentalphysicaluantities.xamplesfbaseunits remetresm)ordistanceand isplacementnd econdss)for ime. omehysicaluantitiesuse erivednitshat re efinedin erms fa combinationfbaseunits.nexamolefa derivednitismetreser econdm/s),hichstheSlunitor peednd elocity.

kinematics hestudy f motionmotiona changen anobject'socationasmeasuredya particularbserverdistanced) the otal ength f hepathtravelledyanobjectn motiondirectionhe ine nobjectmoves longfrom particulartartingoint

Distance, ositiofl,andDisplacementYou seeand nteractwith movingobjectseveryday.Whether you are racing downski hill or running for a schoolbus, motion is part of your everydayife. Long umpathletesare rrery awareof distance,position, and displacement. ong jumpersrundown a stretchof track to a foul line and then ump as ar aspossiblento a sandpi(Figure ). Theirgoal s to increasehe distance f their umps.Todo this, hey ocuon their speed, trength,and technique.Successfulong umpersmaster his goal bapplying he physicsof motion.

Figure Longumpersttempto maximizehehorizontalistancef heirumps.

Describing he Motion of ObiectsTo understand he motion of objects,we must first be able to describemotionPhysicists seanumber of specific erms andunits to describemotion. You are ikelyfamiliar with many of these ermsand units.Kinematicss the term usedby physicistsand engineerso describe he studyohow objectsmove. \4rat exactly s motion?Motions a changen the locationof anobject,asmeasured y an observer.Distance,n physicserms,means he total lengthof the path travelledby an object n motion. The SI metric baseunit for distancesthe metre(m). To helpyou understand he terms hat describemotion, imagine hayou are at your home n Figure 2.You are at the locationmarked"0 m'" If you walkdirectly rom home o your school n a straight ine,you will travela distance f 500mIf you walk from your school o the library and then return home,you will travelanadditional istance f 700m f 1200m : 1900 . (FIf your friend wantsto know how to get to the library from your horne, ellinghim to walk for 1200m is not very helpful Youalsoneed o tell your friend whichdirectionto go.Directions the line an objectmovesalong rom a particularstartingpoint,expressedn degreesn a compass r in termsof the compass oints(northwest,east,and south).Directionscan alsobe expressed s up, down, eft, right, for-ward,and backwards.Directionsareoftenexpressedn brackets fter he distance orother value).For example,500 m [E] indicates hat the object s 500m to the eas

Many ranchesf engineeringuse rinciplesf kinematics.olearnmore bout ecomingnengrneer,

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Direction s mportantwhendescribingmotion. f theschooln Figure2 syourstartingpoint, the ibrary is in a differentdireciion rom your school hariyour home s. f thelibrary syour startingpoint, thenyour schoolandhomeare n the samedirection.

W+-r E

Scalarand Vectoreuantities-{ scalar uantity s a quantity hat hasmagnitude size)only.Distances an exampleof a scalarquantity.since.directions so lportant in describingmotion, physicistsfiequentlyuse erms hat includedirection n their definitions. i vectors a quantitythathasmagnitude size)andalsodirection.An arrow s praced bovehesymbor oravariablewhen t represents vectorquantity. $Positionand Displacement

Figure Distancend irectionlostraightine

scalara quantityhathasonlymagnitudesize)vectora quantityhathasmagnitud(size)nddirection

Positions the distanceand directionof an object rgy u particularreference oint.Positionsa vectorquantity epresentedythesy,mbol . Noii., ,fr" *.,o, arrowabovethesymbold' Thisarrow-ndicateshat position savector: t hasadirectionaswellasamagnitude.For exampre,f home s your reference oint, the positionof the schoolin Figure2 is 500m [E].Note hat he magnitude ithe poritio' i, tte sameas hestraightJinedistance 500m) from home o"school, ut thi p"ritlr;""rr" includeshedirection(dueeast E]). Thepositionof the school rom point o ;;* be describedbv theequation4cnoor500m[E]Now assumehat theribrary syour reference oint, or the point 0m. Thepositionofthe school rom thereferenceoint (library)ca1be describJ bv theequationTscnoor700mfW]once thepositionof an objecthasbeendescribed, ou candescribewhathap_p,enso the objectwhen it moves rom that position.This is dispracement_the

-cfangen an object'sposirion.Displacements represented y,il;;; ai\otice thevectorarrow ndicatingthatdisplacements a vecto-lquant ity. he r!symbolA is the Greek etteiderta.Delta s always"ua urltiunge in,,,soAdas thange n position."As with anychange, isplacementanbe calculated-subtractinghe initial positionvector rom the finai positionvector:

r\d : dp1- dnitiarl.vhenan objectchangests position more than once (experienceswo or morehe otaldispracement/1 of theobject;;";;;;lated by addingdisplacementssing he followingequation:

positiond) thedistancenddirectioanobjectrom referenceoint

displacementA7) thechangenpositionf anobiect

To eviewcalar nd ector

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ndr: nd, td,


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when ouwalkrom ne laceoanother,our ositionhanges.his hangenyourpositionsdisplacement.he isplacementan ecalculatedsingour ositiont hebeginningndheendofyourourney ith heequationd : i1inu1- nitiar.ememberthat ositionsa vectoruantity,oyou aveo ake irectionnto ccount.n hefollowingampleroblems,ewill alculateisplacementssingrangef echniques.ReferoFigure or he irsthree ampleroblems.InSampleroblem,wewill alculatehedisplacementfanobject ith n nitialpositionf0 m. W----+ E,,.;,oqE;,.

library

lmaginehat ouwalkrom omeoschoolna straighHineroute. hatsyour isplacement?SolutionFigureshowshat omes he tartingointoryourourney.Whenouareat home,our ositionasnotchanged.herefore,yournitial ositions zero. ourchool as positionf 500m[E]relativeoyour ome.Given:rrnoo,500m E];?n,*. 0 m

Given: @ 1200 wl;l?, : 1000m W] from igure)Required:A7,Analysis:n his roblem,eare ot implyalculatingchangenposition,eare indinghe um f wodifferentdisplacements.he isplacementsre ivennFigure.To alculatehe otal isplacement,ewillneedouse ectoraddition.hisssimplefboth ectorsavehe ameirection.

FigureSampleroblem:CalculatingisplacementromaZero tartingointyVectorubtraction

RequiredldAnalysis: d : dr*oo, ?no.n,Solution: Z : 7,*o' - 7n0,.:500mlEl-0m

A7:500mlElStatemenLourisplacementhen alkingrom our omeoschools500m E].

Sampleroblem:CalculatingisplacementyVectorubtractionWhatsyour isplacementfyouwalkrom ourchoolo he Statementourisplacementhen alkingrom choolo helibrary?otehat llpositionsremeasuredelativeoyour ome. librarys700m E].Given:,noo, 500m E];7,,*u* 1200m E]Required:7Analysis:d: 7,,"u" dscnoorSofution:d:d6,u, - ?,.noor: 1200 El- 500m Ejl7 :zoomir lSample roblem: CalculatingotalDisplacementyVectordditionOne ight fterworkingt he ibrary,oudecideogo o hemall.Whatsyourotaldisplacementhenwalkingromhelibraryo hemall?

Defininghe nitialtartingositionfyourmotions0 mwioften akeisplacementroblemsimpler.nSampleroblem,ifwehad efined masbeinghe ocationf heschool,t woulhaveeenbviousromhe iagramhathe isplacementromthe choolo he ibrarys700m E].

lf he isplacementromhe ibrary0your omesrepresentedyA@and hedisplacementrom our ometo hemalls representedyL^dr,henhe otal isplacemeAdr,sgivenyvectordditionf hesewodisplacementtdr: ti , + ti,Sofution:d-,: ti , + ti ,: 1200 w] + 1000 wll7r:zzoom5w1Statement hen alklngromhe ibraryo hemall,ouexperiencedisplacementf2200m Vtt].


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Sampleroblem:Calculatingotal isplacementyAdding isplacementsn0ppositeirectionsA dogspractisingorher gilityompetition.heeaveser At his oint,t appearshatwehave problem.e eedoadtrarnernd uns 0mduewestopick pa ball. hehencarriesheball 7m due ast nd ropst nto bucket.Whats he og'sotal isplacement?Solution

avector ith directionWJoa vector ith directionE].Wecanransformhis roblemo hat oth ectorsointn he amdirection.o oso, onsiderhedirectionE]obe he ame s"negative"WJ.he ector7m E]s he ames 27 m W].

a7r:sgm[w]Statementhe og'sotal isplacements53m WJ.

ln his roblem,he ivenaluesre isplacements.o alculate wecanhereforeewriteheequations ollows'tre otal isplacement,ewill ddhesewo isplacementectors. : B0m W]- 27m W]Given:@ 8om wl;a?, 27mlElRequired:?,Analysis:l, : n^d, tl,Solution:dr: l^1,+ ti ,:Bomlwl+27mlElPractice1. Agolferits ballrom golfee tapositionf16.4m fi relativeo he lubhouse.

The all omes0 est tapositionf64.9m fi relativeo he lubhouse.eterminethedisplacementf hegolf all. * [ans:4s.5,Ml]2. A rabbituns .8m N] nd tops0nibblensomerass.he abbitthen ops .3m N] oscratchgainstsmallree.Whats he abbit'sotaldisplacement?#[ans:r0.1N]l3. A skateboarderlides.2m uparamp,tops,ndhen lides.7mdownhe ampbeforeumpingff.Whatshis otal isplacementp he amp? ai"Eans:.5m up]lVectorScaleDiagramsIn Tutorial 1, you used algebra o determine the displacement of an object in a straightiine. However, there is another method you can use to solve displacement problems:r-ector scale diagrams. Vectorscale diagramsshow the vectors associatedwith a dis-placement drawn to a particular scale. A vector can be representedby a directed inesegment,which is a straight line between two points with a specific direction. Line seg-ments have magnitude only (Figure a(a)). A directed line segment is a line segmqntrr-ithan arrowhead pointing in aparticular direction (Figure a(b)). For example, AB isa line segment n the direction from point A to point B. Line segmentBA is the sameline segmentbut in the direction from point B to point A (Figure a(c)). A directed inesegment that representsa vector always has two ends.The end with the arrowhead isreferred to as the tip. The other end is the tail. A vector scale diagram is a representa-tion of motion using directed line segments drawn to scale with arrowheads to showtheir specific directions. Vector scale diagrams are very useful in measuring the totaldisplacement of an object from its original position. {$

I t iprp-f

(b)

B,': tatt

vector cale iagrama vector iagradrawn sing specificcaledirectedinesegment straightinebetweenwopoints itha specificdirection

Geomaticsechniciansollectatausing PS,urveying,nd emotesensing.heylsoecordata singgeographicnformationystems(GlS).IS nalystsapturendmanagepatialnformationoruseingovernmentnd ndustry.o earnmoreboutecominggeomaticstechnicianrGISnalyst,nitt''A (c)a)

(a)A ine egmentb)Directedine egmentE(c)Directedine egment7


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. Consider two displacements,L,i, = zoo m [W] and Lir= 500 m [W]. We cdetermine the total displacement hat results rorn adding tiiesevectors togetherdrawing avector scalediagram. In general,when drawing"avecto, s.alediagram,yshould choosescales hat produce-diagramsapproximatelyone-half to one full pain size'The arger the diagram, the more preciseyour resultswin be.Figure 5 shows a vector diagram d.awn to a scalewhere 1 cm in the diagram reresents100m in the real worrd. Note that eachvector in Figure 5 has a tip (the ewith an arrowhead)and a tail (the other end). vecto^ cun b-eaddedby joining thetip to tail. This is similar to,using a-number rine in mathematics.Thus,after appryour.clrsen scale'l ig.ure5 showsAT, drawn asa vector7. 0 cmin rengthpointingdwest'Th e ti p of L,d, is o.ined o rh e airof Lir.In other words, n" airpr"."-. :r^7is drawn as a directed Itlry"gT"Athat is S.Ocm long pointing due west, startiwhere the displacementA7, ends.The total displacemlni, Adr, i, the displacemefrom the tail, or start, of the first vector to the tip, or end,of the secondvector. n thcase'Adt pointsdue westand hasa lengthof r2 cm. convert ing his measuremby applying our scalegivesa total displa-ementof 1200m twl.For straight-linemotion, vector scalediagramsarenot very complex.we will looat more advancedvector scalediagrams n chapter 2 when we considermotion itwo dimensions.

scalecm 100mNttAdr: .1200m W]

Adr:569t* tip 44:700mftV1r*1fi*:: :i*fii.i:!'xii

In heollowingampleroblem,wewill etermineisplacementyusingectorcalediagrams.onsidernexamplenwhich otionccursn wooppositeirections.Sample roblem:Using Vector caleDiagram0DetermineheTotalDisplacementorTwoMotionsnOppositeirections

tai

hat ou re oingovisit ourriend.eforeou etou ecideostop t hevarietytore.f youwalk 00m N]our omeo he tore,ndhenravel00m S] oyourouse,hatsyourotal isplacement?t ournitial isplacementrom our omeo he tore erydyour isplacementromhe toreoyourriend'souseLdr.

@= 200m1ltl; 7,= 600m S]d,

dr: td, + Ld,igureshowshegivenectors,ithhe ipofAd,o heai lof ldr.fne esultantector?, sdrawnn ed,he ait fA@ o he ipoI Ldr.Theirectiont ?, is1S1.d,measurescm n engthnFigure,sousinghe calefcm 100m, heactual agnitudef17, s400m.elativeoyour taftingoint tyour ome,ourisplacements400m S].

scalecm:100NttTOTC

ad,:ZOOmJwIhome

friend'shouse

Adr: 699 tt,Ld,

Figure Solutioncale iagramoraddingectorsith changeindirection


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Practice1. Acardrives3m w] oastop ign.tthen ontinuesn ora displacementf46m fi.Use vectorcale iagramodeterminehecar'sotal isplacement.6GH ans:20m fy]l2. Arobinlies 2m s] ocatchworm ndhenties 9m N]backo tsnest. sevectorcaleiagramodeterminehe obin'sotal isplacement.# a*ans:27N]I

SummaryMotion involves a change n the position of an object.Motion can be describedusing mathematicalrelationships.A scalar is a quantity that has magnitude (size) only.A vector is a quantity that hasmagnitude (size)and direction.You can determine the displacementof an object by subtracting he startposition from the end position.You can determine total displacement by adding two or more displacementstogether algebraically or by using a vector scalediagramVectorscan be addedby joining them tip to tail.

Questions1. Whichf he ollowinguantitiesre ectors,ndwhichare calars?e ureoexplainhe easoningoryouranswer.: ' :(a)Abirdiies distancef20m.(b)A rains ravellingt 00km/h ue orth.(c) t akesnathlete0.37 o un100m.2. Explainhe ollowingnyour wnwords:(a) hedifferenceetweenositionnd isplacement(b) hedifferenceetweenistancend isplacement3. Whats hedisplacementfa ocomotivehat hangestspositionrom 5mffi to76mM? ca+4. Acar hangestspositionrom 2km trVJto39 m E].Whats he ar's isplacement?trt

5. Determinehe otal isptacementoreach f he ollowinmotionsyalgebraicethodsnd yusingcalediagrams.*e(a)A7. 1om wl;ld, 3.0m wl0) Aa : iom wl;l?, 3.0m El(c)A7' 2Bm : 7.0m sl(0 Aa : 7.0mwl;a7, 12 mE];ld, : s.o mw]Apersonalks 0pacesorwardollowedy3pacesforward,nd inally pacesackwards.ii +iB(a)Draw vectorcaleiagramepresentinghis ersonmotion.se scalef 1cm i purr. -(b)Checkour nswerypacingut hismotionourselfHow losesyour xperimentalesulto hat redictedbyyour ectorcale iagram?

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