CBSE-iCLASSXIUNIT-3CENTRAL BOARD OF SECONDARY EDUCATIONShiksha Kendra, 2, Community Centre, Preet Vihar, Delhi-110 092 IndiaPHYSICSLAWS OF MOTIONCONTENTSPrefacevAcknowledgementviiiTEACHERSMANUALLearningoutcomesixTeachingNotesxiLessonPlanMatrixxvWeblinks/vediolinks/otherreferencesxviiiSTUDENTSMANUALIntroduction3NewtonsFirstLawofMotion5NewtonsSecondLawofMotion6Studentactivity16Studentactivity29Studentactivity315NewtonsThirdLawofMotion17Studentactivity417ConservationofLinearMomentum21ApplyingNewtonsLaw23EquilibriumforTranslatoryMotion30Friction33Studentactivity534DynamicsofCircularMotion40Studentactivity640 NewtonsLawsinNon-InertialFramesofReference47Postcontentstudentworksheet157Postcontentstudentworksheet260Postcontentstudentworksheet362Postcontentstudentworksheet465PREFACEThe Curriculum initiated by Central Board of Secondary Education -International (CBSE-i) is a progressive step in making the educational content and methodology moresensitiveandresponsivetoglobalneeds.Itsignifestheemergenceof afreshthoughtprocessinimpartingacurriculumwhichwouldrestorethe independenceofthelearnertopursuethelearningprocessinharmonywith theexistingpersonal,socialandculturalethos.TheCentralBoardofSecondaryEducationhasbeenprovidingsupporttothe academicneedsofthelearnersworldwide.Ithasabout11500schoolsaffliated toitandover158schoolssituatedinmorethan23countries.TheBoardhas always been conscious of the varying needs of the learners and has been working towards contextualizing certain elements of the learning process to the physical, geographical,socialandculturalenvironmentinwhichtheyareengaged.The CBSE-ihasbeenvisualizedanddevelopedwiththeserequirementsinview.Thenucleusoftheentireprocessofconstructingthecurricularstructureisthe learner.Theobjectiveofthecurriculumistonurturetheindependenceofthe learner, given the fact that every learner is unique. The learner has to understand, appreciate,protectandbuildonknowledge,values,beliefsandtraditional wisdom. Teachers need to facilitate the leaner to make the necessary modifcations, improvisationsandadditionswhereverandwhenevernecessary.The recent scientifc and technological advances have thrown open the gateways ofknowledgeatanastonishingpace.Thespeedandmethodsofassimilating knowledgehaveputforthmanychallengestotheeducators,forcingthemto rethinktheirapproachesforknowledgeprocessingbytheirlearners.Inthis context,ithasbecomeimperativeforthemtoincorporatethoseskillswhich willenabletheyounglearnerstobecomelifelonglearners.Theabilitytostay current, to upgrade skills with emerging technologies, to understand the nuances involvedinchangemanagementandtherelevantlifeskillshavetobeapartof thelearningdomainsofthegloballearners.TheCBSE-icurriculumhastaken cognizanceoftheserequirements.TheCBSE-iaimstocarryforwardthebasicstrengthoftheIndiansystem ofeducationwhilepromotingcriticalandcreativethinkingskills,effective communication skills, interpersonal and collaborative skills along with information andmediaskills.Thereisaninbuiltfexibilityinthecurriculum,asitprovides afoundationandanextensioncurriculum,inallsubjectareastocatertothe differentpaceoflearners.TheCBSEintroducedtheCBSE-icurriculuminschoolsaffliatedtoCBSEat theinternationallevelin2010atprimaryandsecondarylevelinclassesIand IXandsubsequentlyinthesession2011-12initiatedthecurriculumatClassII, VIandclassX.Thecurrentsessionwilltakethecurriculumforwardtoclasses III,VIIandXI.AnimportantfeatureoftheSeniorSecondaryCurriculumisitsemphasison thespecialisationindifferentfeldsofstudyandpreparingastudentforhigher professionallifeandcareerattheworkplace.TheCBSE-i,keepinginmind, thedemandsofthepresentGlobalopportunitiesandchallenges,isofferingthe newcurriculuminthesubjectofEnglish,Physics,Chemistry,Biology,Geography, Accountancy,BusinessStudies,InformationandCommunicationTechnology,and Mathematicsattwolevels,Mathematics-Iforthestudentsofpuresciencesand Mathematics-IIforthestudentsofCommerceandothersubjects.Therearesomenon-evaluativecomponentsinthecurriculumwhichwouldbe commenteduponbytheteachersandtheschool.Theobjectiveofthispartor thecoreofthecurriculumistoscaffoldthelearningexperiencesandtorelate tacitknowledgewithformalknowledge.Thiswouldinvolvetrans-disciplinary linkagesthatwouldformthecoreofthelearningprocess.Perspectives,SEWA (SocialEmpowermentthroughWorkandAction),LifeSkillsandResearchwouldbe theconstituentsofthisCore.TheCoreskillsarethemostsignifcantaspects ofalearner'sholisticgrowthandlearningcurve.The International Curriculum has been designed keeping in view the foundations oftheNationalCurricularFramework(NCF2005)NCERTandtheexperience gathered by the Board over the last seven decades in imparting effective learning tomillionsoflearners,manyofwhomarenowglobalcitizens.The Board does not interpret this development as an alternative to other curricula existingattheinternationallevel,butasanexerciseinprovidingthemuch needed Indian leadership for global education at the school level. The Curriculum envisagespedagogywhichwouldinvolvebuildingonlearningexperiences insidetheclassroomoveraperiodoftime.TheBoardwhileaddressingthe issues of empowerment and capacity building of teachers believes that all school mustbudgetforandensureteachersinvolvedwithCBSE-iarecontinuously updated.I appreciate the sincere effort put in by Dr. Sadhana Parashar, Director (Training) CBSE, Dr. Srijata Das, Education Offcer, CBSE and the team of Offcers involved inthedevelopmentandimplementationofthismaterial.TheCBSE-iwebsiteenablesallstakeholderstoparticipateinthisinitiative throughthediscussionforumsprovidedontheportal.Anyfurthersuggestions arewelcome.VineetJoshi Chairman,CBSEACKNOWLEDGEMENTSAcknowledgements Advisory Shri Vineet Joshi, Chairman, CBSE Dr. Sadhana Parashar,Director (Training), CBSE Conceptual Framework Shri G. Balasubramanian, Former Director (Acad), CBSE Ms. Abha Adams, Consultant, Step-by-Step School, NoidaDr. Sadhana Parashar, Director (Training), CBSE Ideators Prof. A K Bakshi Ms. P RajeshwariDr. Niti Nandini ChatnaniMs. Neeta Rastogi Dr. N K SehgalMs. Urmil GulianiDr. Anil K BaliDr. Anshu Prof. Kapil KapoorMs. Anita MakkarDr. Preeti TewariDr Rajesh Hassija Ms. Renu AnandProf. Biswajit NagDr. Deeksha BajpaiMr. Mukesh Kumar Dr. Barkatullah Khan Ms. Avnita Bir Dr. Jacqueline Symss Ms. Usha Sharma Mr. S K AgarwalaDr. Om Vikas

Material Developers English: Ms Gayatri Khanna Ms Renu Anand Ms. P Rajeshwary Ms. Sandhya Awasthi Ms. Manna Barua Ms. Veena Bhasin Ms. Urmil Guliani Ms. Sudha Ravi Mr. Anil Kumar Ms. Vijaylaxmi Raman Ms. Neerada Suresh Ms. Himaal Handoo Chemistry: Dr. G S Sodhi Dr. Vimal Rarh Dr. Shalini Baxi Dr. Vinita Arora Dr. Vandana Soni Ms. Charu Maini Ms. Rashmi Sharma Ms. Kavita Kapoor Biology: Dr. Ranjana Saxena Dr. Neeraja Sood Dr. P Chitralekha Ms. Mridula Arora Ms. Lucy Jad Ms. Priyanka Choudhury Ms. Prerna Gosain Ms. Malini Sridhar Physics: Dr. B. Biswal Ms. Namarata Alwadhi Mr. Dhirender Sharma Ms. Vandana Banga Mr. Vivek Mathematics: Dr. Sushil Kumar Mrs. Monica Talwar Mrs. Charu Dureja Mrs. Seema Juneja Dr. H K Bhatia Geography: Ms. K Jaya Dr. Preeti Tewari Ms. Rupa Das Ms. S Fazal Daoud Firdausi Ms. Neena Phogat Ms. Sujata Sharma Ms. Deepa Kapoor Ms. Bharti Malhotra Ms. Isha Kaushik Mr. Riyaz Khan Economics: Mr. S K Agarwala Ms. Ambika Gulati Ms. Nidhi Singh Ms. Malti Modi Ms. Sapna Das Ms. Ingur Agarwal Mr. Shankar Kulkarni Mr. Sandeep Sethi Accountancy: Mr. S S Sehrawat Dr. K Mohna Dr. Balbir Singh Mr. Bhupendra Kriplani Ms. Komal Bhatia Mr. Sandeep Sethi Business Studies: Dr. S K Bhatia Ms. Meenu Ranjan Arora Mrs. Shegorika Mr. Sandeep Sethi Ms. Usha Sharma Mr. Bhupendra Kriplani Ms. Komal Bhatia Ms. Ravisha Aggarwal ICT: Mr. Mukesh Kumar Ms. Nancy Sehgal Ms. Purvi Srivastava Ms. Gurpreet Kaur Coordinators: Ms. Sugandh Sharma, E O Dr. Srijata Das, E O Dr Rashmi Sethi, E O Ms.S. Radha Mahalakshmi,E O Mr. Navin Maini, R O (Tech) Ms. Madhu Chanda, R O (Inn) Shri R. P. Sharma, Consultant (Science) Shri Al Hilal Ahmed, AEOSh R.P Singh,AEOMs. Anjali Chhabra, AEOMs. Neelima Sharma, Consultant (English) Mr. Sanjay Sachdeva, S O CONTENT LEARNINGOUTCOMESForce and Inertiaintuitive concept of forcedefnition of force inertiaStudents would be able to: appreciate the intuitive concept of force.understand thatforce can be defned as an external agency thatis needed to change the state of rest or of uniform motion of a body.recognize that external agencies can exert forces on a body even from a distanceappreciate that a bodycancontinue in its state of rest ,or of uniform motion in a straight line, only when no external force acts on it. comprehend the meaning of the term inertiaunderstand that the massof a body can be regarded as ameasure ofits inertia.Newtons laws of motionThe frst law of motionConcept of momentumSecond law of motionImpulseThird law of motion state Newtons frst law ofmotion. cite examples illustrating the frst law of motiondefne the term momentum andwriteitsmathematical form.understandthat the force, acting on a body , is related to its rate of change of momentum.state Newtons second law of motion and write its mathematical form.obtain the usual form(F=ma) ,of the second law, and know its limitation.solve problems based on the second law of motion.use the second law of motion for writing the dynamical equation of motion of a given body.use the second law of motion to defne the unit of force.defne the term impulse and write its mathematical form.state the relation between impulse and change in momentum.state Newtons third law ofmotion.Understand that, in nature, forces always occur in pairs.Appreciatethat forces of action and reaction act on different bodies and hence cannot cancel each other. cite examples of Newtons third law of motion in everyday life situations.understand that the internal forces in a body, ora system of particles, always add up to give a null force.identify different kinds of forces like normal reaction, tension and weightSYLLABUSLEARNINGOUTCOMESTEACHERS'MANUALCONTENT LEARNINGOUTCOMESLaw of conservation of linear momentum and its applicationsstate the law of conservation of linear momentum.understand that this law is a consequence of the third law of motion.use the law of conservation of linear momentumin different situations.Equilibrium of concurrent forcesunderstand the meaning of the term equilibrium and know its difference from the state of rest.analyse the details of the equilibrium ofa body.know the necessary and suffcient conditions for the equilibrium of a body acted upon by concurrent forces.Frictionstatic and kinetic frictionLaws of frictionRolling frictionLubricationrecall the concept of the force of friction.differentiate between static and kinetic friction defne the term coeffcient of friction and write the mathematical expression for it.state the laws of friction and appreciatetheir empirical nature.comprehend the meaning ofthe term rolling frictionknow about practical situations in daily lifewhere friction is undesirable and where it is usefulunderstand the role of lubricants in reducing frictionDynamics of uniform circular motioncentripetal force example of circular motion (vehicle on level circular road, vehicle on banked road)recall the concept of uniform circular motiondefne the term centripetal force and write its mathematical expression.show an understanding of the application of centripetal force to explain motion of a body moving along a curved path.analyse the motion of a vehicle on a level circular road in terms ofthe different forces acting on it.appreciate the need for banking of curved roads.explain the motion of a vehicle on a banked road and appreciate how the banking of roads can help to reduce the wear & tear of vehicle tyres.Dynamics for non inertial observerpseudo forcecentrifugal forceDifferentiate between inertial and non inertial observersunderstand the need for pseudo forceUnderstand the role of the centrifugal forceCite examples from daily life involving centrifugal forcesApplyNewtons Laws for non inertial observerTEACHINGNOTESNewtonslawsofmotionareoneofthestrikingandlandmarkdiscoveries inthestudyofPhysics.Theselawsformthebasisofstudyofmechanicsand areextremelyusefulinotherbranchesofPhysics.Theteachermayconveythe signifcance of these laws by making the students understand how these help us to understand the concept of force,to defne a unit of force and prove useful not only in understanding the cause of motion but also to calculate the subsequent detailsofmotionofanobjectonthebasisoftheavailableinformationaboutits initialstateofmotionandtheforcesactingonit.Suitableexamplesfromday-to-daylifesituationsmaybecitedtoclarifyandre-inforcethebasicconcepts andtoinitiatethestudentstothechallengingtaskofunderstandingbasicsof dynamicsofmotion.The concept of momentum is a very basic and fundamental concept. The teacher mayuseexamplesfromday-to-daylifetoemphasizewhymomentum-often referred to as the quantity of motion possessed by an object- needs to be defned astheproductofthemassoftheobjectanditsvelocity.Thelinkbetween Newtonsthirdlawofmotionandthelawofconservationofmomentumneeds tobeclearlybroughtout.Itwouldbesignifcanttoensurethatthestudents clearlyunderstandthedifferencebetweensystemandsurroundingsina givenphysicalsituationandusethisunderstandingtodifferentiatebetween theinternalandexternalforcesforagivensystem-surroundingsetup.The signifcance of the absence of external forces as being a critical and fundamental criterion for the validity of the law of conservation of momentum may be clearly broughtout.Suitableexamples-likethatofaprojectileinmotionbreakingup intofragmentsorofanobjectbreakingupduetointernalcausesorthesystem oftwoobjectsundergoingacollisionetc.canbeandshouldbeusedtoclarify thisconcept.Havingclarifedtheconceptofmomentum,itmaybeworthwhiletopoint outthedifferencebetweenthetwoapparentlyequivalentformsofNewtons secondlawofmotion(Force=rateofchangeofmomentumandForce=mass Xacceleration).Itneedstobemadecleartothestudentsthatsecondofthese twoformsisvalidonlywhenthemassoftheobjectremainsconstant.Itis thefrstform(Force=rateofchangeofmomentum-thatisthebasicformof thesecondlawofmotionandthesecond(butmoreoftenused)form(Force =massacceleration)isaspecialcaseofthebasicformthatisvalidonlyfor systemswhosemassdoesnotchangewithtime.Infamiliarsituationswecan sometimehavesystemswhosemasschangeswithtime.Themotionoarocket (continuouslyburningitsfuel,aleakingwatertankermovingontheroad,or aconveyorbeltcarryingStone-dustetc.aresomeexamplesofsystemswhose masskeepsonchangingwithtime.Theneedforuseofthemathematicsof calculus- for analyzing the details of motion of such systems- may be clarifed andexplained.Theconceptofequilibriumanditsdifferencefromthestateofrestneedsto clearlybroughtout.Itmaybeemphasizedthatwhenasystem/objectisunder theactionofanumberofconcurrentforceswhoseresultantequalszero,it wouldbeinequilibriumbecause,undersuchacondition,therewouldbeno changeinthestateofmotionofthesystem/object.Thiswouldbeasuitable situationtoclarifythatanobject,initiallyatrest,ormovingwithaconstant velocity is regarded as undergoing no change in its state of motion if it continues tobeatrest,or,continuesmovingwithitsconstantvelocity.Thestudents would thus be enabledto differentiate between static and dynamic equilibrium. Itmaybeusefultopointoutthesignifcanceofthewordconcurrentsothat thestudentsrealizethatforsystemonnon-concurrentforces,asystemneed notbeinequilibriumevenwhentheresultantofalltheforcesactingonthe system is zero. They would then be in a better position to understand the general completesetofconditionsofequilibrium(resultantofallforcestobezeroas wellasthesumofmomentsofalltheforcesaboutagivenpointtobezero) whentheystudythedetailsofrotationalmotion.The concept of friction and the nature offrictional forces and their signifcance canbeintroducedthroughfamiliarday-to-daylifesituations.Itwouldbe worthwhile to point out the role of the force of friction in walking and cycling. Inboththesecases(unliketheusualsituations),theforceoffrictionactsalong the direction of walking and cycling but only on the rear-wheel of the cycle that isconnectedtothepedals)andthereasonforthesameshouldbeexplained through Newtons thirdlaw of motion. The difference between static, kinetic and rolling friction needs to be clearly explained. The study of friction and frictional forcesshouldalsobeusedasasuitablepointforintroducingthestudentsto theconceptoffree-bodydiagramsandtheirroleandusefulnessinsolvinga varietyofproblemsonthebasisofthesecondlawofmotion.Thestudentscan alsobemadefamiliarwithdifferenttermsliketension,thrust,normalreaction etc.usedtodescribedifferenttypesofforcesindifferentsituations.Ithardly needstobeemphasizedthatthestudentsmaybegivensuffcientpracticein solvingvarietyofproblemsthroughfreebodydiagramssothattheybecome confdentinusingsecondlawofmotionandappreciatingitsroleinanalyzing thedetailsofmotionofobjectsindifferentsituations.Thestudyofdynamicsofuniformcircularmotionisagoodsituationto explainhowthespeedofanobjectcanremainconstantevenwhenitisbeing constantlyacteduponbyaforce.Theconceptofcentripetalforceanditsrole andsignifcanceinensuringthataparticlekeepsonmovinginitscircularpath hastobeclearlybroughtout.Examplesofplanetsorbitingtheearthorthe electronsorbitingthenuclearsalongwiththefamiliarexampleofaballbeing swung in a circular path by a string can be used to explain different sources of centripetal force in differentsituations. It may be explained as to why there is a need for a tangential force along with the radial centripetal force to being about achangeinthespeedofmotionofaparticlemovinginacircularpath. The concept of centripetal force along withthe associated concept of centrifugal forcecanbeusedtoexplainwhytheequalandoppositeforcesofactionand reactiondonotcanceleachother.Thestudentsmaybehelpedtounderstand thattheforcesofactionandreactiondonotcanceleachotherbecausethey actondifferentobjects.Theywouldthenbeabletoappreciatethatthereisno built-inconfictbetweenthethirdlawofmotionandthefrstlawofmotion.Theunitalsointendstointroducestudentstothedifferencebetweeninertial observersandinertialframesofreferenceandnon-inertialframesof reference.Thisintroductionwillalsoenablethestudentstoappreciatehowachangein theframeofreferencecanaltertheperspectiveofobservingandanalyzingthe detailsofmotionofagivensystem.Theconceptofcentrifugalforcecoupled withthatoftheframeofreferencewillhelpthestudentstogetabasicfeel about the difference between real forces and pseudo or fctitious forces. It may beworthwhiletojustintroducethestudentstothefactthattheconceptof pseudoorfctitiousforcescanproveusefulandhelpfulinunderstandingthe details of motion on the basis of Newtons laws of motion in apparently diffcult situations.The concepts studied in this unit are to be used in almost every successive unit. Henceunderstandingoftheirminutedetailsneedstobestrengthenedbyciting numberofdailylifeexamplesandbyprovidinghands-on-experienceswith activitiesgiveninthestudentsmannual.Theactivitiesshouldbeaccompanied withappropriatequestions.Whiledealingwithproblems;thestudentsmaybe askedtoprepareachecklistof (a)Thesystem(b) Theappropriateobserver(c)Theappropriateaxissystemand(d)Thefreebodydiagramrelatedtothegivensystem/problemThestudentsalsoneedtobemadeawareofthecommonmisconceptions,some ofwhichhavebeenpointedoutinthestudymaterial.Finally,thestudentshavetobeencouragedtoattemptasmanyunsolved problemsaspossible.Oneneedstorememberthataclearunderstanding ofthelawsofmotionisthefoundationonwhichthestudentssubsequent understandingoftheconceptsofPhysicsreststoalargeextent.Oneneeds togivemaximumattentiontomakethisfoundationassoildandstrongas possible.CONTENT SKILLS LEARNINGOUTCOMESForce ObservationsUnderstanding the conceptUnderstand the meaning of forceRealize that unless there is a net force acting on the body, a change in the state of its motion is not possibleRecognize that external agencies can exert force on a body even from a distanceDefne the SI unit of forceInertia Analytical reasoning abilityClassifcation of inertia.Observations with respect to daily life situation.Defne the termDifferentiate between inertia of rest and inertia of uniform motionUnderstand that mass is a measure of the inertia of a bodyNewtons frst law of motionApplication of acquired knowledgeState the frst lawCite examples of frst law of motionMomentum Assimilate the concept Defne the termKnow theSI unit of momentumNewtons second lawDeductive reasoningComprehend the concepts State the second law of motionObtain the usual equation of force (F = ma)from the concept of rate of change of momentumUnderstand that for a constant force, acceleration of a body is inversely proportional to its mass.Solve numerical problems based on Newtons laws of motionImpulse Higher order thinking based learningUnderstand the relation between force, time and the change of momentum (impulse) of an objectKnow theSI unit of impulseLESSONPLANMATRIXCONTENT SKILLS LEARNINGOUTCOMESNewtons third lawAnalytical thinking State Newtons third law of motionAppreciate that forces always occur in pairsComprehend that forces of action and reaction act on different bodies.Equilibrium of concurrent forcesUnderstanding the signifcance of the term concurrent forces.Understand the signifcance of the term equilibriumFinding the relations between the different forces acting on a body is equilibriumFrictionStatic frictionKinetic frictionRolling frictionAnalytical thinkingExplorationDifferentiate between static and kinetic force of frictionUnderstand the concept and cause of frictionDifferentiate between static and kinetic frictionKnow the laws of frictionUnderstand the terms: Coeffcients of static and kinetic frictionRealize that kinetic friction is less than static frictionInvestigate methods to reduce the force of frictionUnderstand the use of lubricantsAppreciate that friction is a necessary evilMeaning of rolling frictionDifferentiate between sliding friction and rolling frictionDynamics of uniform circular motionRecallCo-relating the conceptsRecall the basic concepts of circular motionCentripetal forceIdentify the agency/cause providing the centripetal force in different situationsDefne the term and obtain the expression for the centripetal forceFind the applications of centripetal force.Vehicle on level circular roadScrutiny of daily life situationsUnderstand the role of static frictionDraw free body diagramWrite the equations and solve the problems.CONTENT SKILLS LEARNINGOUTCOMESVehicle on banked roadCorrelate thetheoretical concept with practical situationsAppreciate the role of banking of roadsDraw free body diagramsWrite the equations and solve the problemsNon inertial frame of referenceComprehend the conceptsAnalytical thinkingDifferentiate betweeninertial and non inertial observers.Draw appropriate free body diagram according to different observersAppreciate the signifcance of pseudo forcesFind the magnitude and direction of pseudo force in some simple situations.Understand when the centrifugal force can be regarded as a pseudo force.WEB-LINKS/VEDIOS/OTHERREFERENCEShtp://www.hazelwood.K12.mo.us/~grichert/sciweb/applets.htmlhtp://www.clickandlearn.org/Physics/sph3u/fricton_force.htmlhtp://www.tribology-abc.com/abc/fricton.htmlhtp://www.hazelwood.k12.mo.us/~grichert/sciweb/applets.htmlTEACHERSTUDENTSUPPORT MATERIALCBSE-i CBSE-i Unit 3 : Laws of Motion3INTRODUCTION Weknowthatweneedthreebasicconceptsdisplacement,velocityand accelerationtodescribethedetailsofmotionofagivenobject.Thistype ofdescriptivestudyofmotionwherewelearnaboutthewaysandmeans ofdescribingmotionisknownaskinematics.Thekinematicalequationsof motionhavedifferentformsfordifferenttypesofmotionbutalongwiththe appropriateuseofmathematicsofdifferentialandintegralcalculus,theyform theframeworkthroughwhichonecandescribeandknowthedetailsofany typeofmotion.A little refection, however, shows that our study of motion needs to go beyond a mere description of the same. We also need to know the basic cause of motion andthecause/sthatbringaboutchangesinthemotionofagivenobject.Our simple observations on different objects immediately reveal the following simple fact:Anychangeinthemotionofanobjectis,invariably,theresultofsome interaction(directorindirect)betweentheobjectandsomethingelseinits surroundings.WeusethetermForceforanysuchinteraction.Wecan,therefore,saythat forceisthecauseofmotionaswellasthecauseofanychangeinitsstateof motion.Thestudyofmotion,throughconsiderationsoftheforcesinvolved,is knownasdynamics.Ourbasicconceptsconcerningthedynamicalstudyofmotionhavestemmed fromtheworksofGalileo(1564-1642)andNewton(1642-1727).Thesetwo scientistsareuniversallyregardedasthefoundersofthesubjectofdynamics. NewtonsbookthePrincipiaisregardedasthebasicpillarofthestudyof mechanics.CBSE-i Unit 3 : Laws of Motion4SIRISAACNEWTON(1642-1727)Sir Isaac Newton was a great scientstwhose many discoveries greatly infuencedourlives.Thesestllformthebasisfordescribingand understandingtheobservatonsinoursurroundings.Hisdiscoveryof the well known three laws of moton form the basis of our qualitatve andquanttatvedefnitonofforce.PrincipiaMathematcaabookwritenbyNewtonisconsideredas bibleforClassicalPhysics.HewasborninWoolstrope,England,on Christmas day in 1642, and died on leaving behind a legacy of the use of scientfc method inourlife.Hiswords,saidtobequotedbyhimtowardstheendofhislife:Ifeellikeachildplayingontheseashoreandfndingapretypebbleoraniceshellhere andtherewhilethevastoceanoftruthstllliesunexploredbeforemeareasourceofinspiratonforallofustocontnueourunendingsearchforthesecrets andmysteriesofnature.3.1.1FirstlawofmotionAblockkeptonthefoordoesntmoveonitsown.Ifthesameblockispushed withsomeforcealongthefoor,itslowsdownasitmovesforward.Isthere anythingcommoninthesetwosituations?Galileotriedtoanalyzeandcomparethestateofmotionandrestwiththehelp ofsomethoughtexperiments.Inoneofsuchexperiments,aballisconsideredtoberollingbackandforth betweentwoidenticalsmoothinclines.(a)Galileo suggested that if a ball is dropped along the left Incline from some point A it will eventually reach a point B at same height on the right incline.(b)Iftherightinclineismadeless steeper,theballwouldreachthe same height but would have to cover agreaterdistance.(c)If the right incline is made horizontal, the ball will continue to move forever toattainasitseeksthesameheight.Hence thevelocityoftheball,movingonthefat horizontaltrack,willnotchange.Figure1A ABBFigure2CBSE-i Unit 3 : Laws of Motion5Galileoconcludedthatitisnotinthenatureofanobjecttostoponcesetin motion;rather,itopposesanychangesinitsmotion.Thistendencyofanobject toresistoropposeanychangeinitsstateofmotioniscalledinertia.Physical quantities,contributingtothistendency,arenotknownfully.Ourdailylife experiencessuggestthatinertiaofmassiveobjectsismore,becausewefnd greater diffculty in changing the state of motion of heavier objects. For example, withthesamemusculareffort,onecanthrowabasketballwithgreatervelocity thanashotput. Masscanbeameasureofinertiaasitisobservedtocontroltheinertiaof objectsevenwhentheyareindifferentstatesofmotion.(a)Stateofrestofanobjectcanbeassociatedwithinertiaofresti.e.objects, at rest, remain at rest unless an external force acts on them. When a vehicle startsmovingsuddenly,passengerssittinginthevehiclefallbackwards, aspassengerstendstoremainatrestduetoinertia.(b)Stateofmotion(speed)leadstoinertiaofmotioni.e.objectsinmotion keep moving unless an external force acts on them. When a moving vehicle stopssuddenly,passengerssittinginittendtofallforwardastheupper partsoftheirbodiescontinuetomoveduetoinertiaofmotion.(c)Wecanalsospeakoftheinertiaof directioni.e.objectsinmotiontryto maintaintheirdirectionofmotion unless an external force acts on them. Whenavehicletakesasuddenturn, objectsinittendtofalloutwards astheytendtocontinuetomovein straightlineduetotheirinertiaof direction.Onecanthussaythatanexternaleffortis needed to change the state of rest, direction ofmotionorthespeedofabody;this externaleffortiscalledforce.InNewtonsownwordseverybodypersistsinitsstateofbeingatrestor ofmovinguniformlystraightforwardexceptinsofarasitiscompelledto changeitsstatebytheforceimpressedonit.Figure3CBSE-i Unit 3 : Laws of Motion6Itimpliesthat:(a)Anobjectatrestwillcontinuetoremainatrestunlessanexternalforce actsonit.(b)Anobjectinmotionwillcontinuetohaveauniformvelocityi.e.keepon movingwiththesamespeedandinthesamedirection,unlessanexternal forceactsonit.Many scientists and philosophers before Newton like Galileo and Descartes, had hinteduponthepropertyofinertia.Newtoninfactgavethecreditoffrstlaw of his above conclusion, which we now call as his frst law of motion to Galileo (1564-1642).ThefrstlawofmotionisalsoknownasLawofinertia.CONCEPT PROBECanyoufndtheacceleratonoftheearth,duetoitsrotatonalorrevolutonalmoton,at apointonitsequator?Read more.htp://www.hazelwood.K12.mo.us/~grichert/sciweb/applets.html3.2.1SecondlawofmotionAbasketballandashotput,botharetobegiventhesamespeedortobethrowntothe samedistance.Inwhichcaseitwillbeeasier?Theanswerwouldbe:basketball.Doyouknow?Why?Becauseithaslowermass.Nowthrowabasketballtowardsanotherpersonwithdiferentspeeds.Askthepersonto stopthem.Inwhichcasewasiteasiertostop?SUGGESTED ACTIVITY 1Ourexperiencesindailylife,liketheaboveactivity,suggestthatbothmass andvelocityareimportantfordecidingthemagnitudeofforceneededina given situation. Different forces are needed to give the same speed to basketball andshotput,alsodifferentforcesareneededtostopabasketballmovingwith differentspeeds.CBSE-i Unit 3 : Laws of Motion7Onclubbingthetwoquantities,massandvelocity,anewquantityiscoined calledmomentum.Itisdefnedastheproductofmass(m)andvelocity(v)of givenobjectandwrittenas p=mvMomentumisavectorquantitywhosedirectionissameasthatofthevelocity. ItsSIunitsarekgm/s.Itcanbeunderstoodasmeasureofquantityofmotion,asindailylifeanything having strong momentum is considered to carry that state for long. Force acting onanobjectdependsonthechangeinmomentuminagivenintervaloftime.Accordingly, net force on an object is directly proportional to the rate of change ofmomentumofthatobject.Henceinstantaneousforceisgivenby:F d pdtF=kd pdtF= d pdtThevalueoftheconstantofproportionality,k,dependsonthewaywedefne theunitofforce.InSIunits,wetakek=1.HenceTheaboveexpressiongivesaquantitativewaytodefneandmeasureforce. Werealizethatforcedependsnotonlyonthechangeinmomentumbutalso theintervalinwhichthischangetakesplace.Forceisavectorquantityandits directionissameasthatofthechangeofmomentum.Wehave: avF= 2 1( )f ip ppt t t = NowF= ( ) d p d m p d v dmdt dt dt dtm v = = +CBSE-i Unit 3 : Laws of Motion8Ifmassofanobjectdoesnotchangewithtime,wehave dmdt=0.Henceforce canbewrittenasF= d vdtm ma=(where d vdta| | |= | |\ .istheaccelerationofthegivenobject)Thedirectionofforceis,therefore,thesameasthatofaccelerationofthe givenobject.Inrectangularcoordinateform,forceandaccelerationcanbewrittenasF= x y zF i F j F k + +a= x y za i a j a k + + x y zF i F j F k + + = ( )x y zm a i a j a k + +ThisimpliesthatFx=ma xFy=mayFz=mazHencetheforcesalongthex,yandzaxescanbeexpressedas:Fx=maxFy=mayFz=mazUnitsofforceSIunitsofforceisthenewton,(symbolN)inthehonourofNewtonwho discoveredthelawsofmotion.InCGSunits,theabsoluteunitofforceisdyne (symboldyn).CBSE-i Unit 3 : Laws of Motion9OneNewtoncanbedefnedastheforcethatwouldcauseanaccelerationof 1ms2inamassof1kg.Onedyne,similarly,equalstheforcethatwouldproduceanaccelerationof 1cms2inamassof1g.Itfollowsthat1N=105dyne.Sometimesgravitationalunitsareusedtomeasureforce.InSIunitsthe gravitationalunitofforceisthekilogramweight(kgwt).Itisalsoknownas kilogramforce(kgf).Onekilogramweightorkilogramforceisthatforcewhichcancausean accelerationof9.8ms2inabodyofmass1kg.1kgwt=9.8NIn the CGS system, the gravitational unit is gram weight (g wt).It is also known as gram force (gf). One gram weight or gram force is that force which can cause anaccelerationof980cms2inabodyofmass1g.1gwt=980dynUsingadigitalweighingbalance,getanestmateofaforceof1Nbypressingitwiththe helpofyourfnger.1Ncanalsoberegardedasnearlyequaltotheforceexperiencedby our(stretched)palmwhenamassof100gisputonit.SUGGESTED ACTIVITY 2Weighing machines actually tell the weight (force on a body due to earth) in terms of kgwt. Trytofndoutyourweightintermsofnewton.Did You Know??AnInterestingQuery:ForceappliedandtheResultingDirectionofmotion.Supposeweaskourselvesthisquestion:Aforce,sayF,isappliedonanobject.Wouldthedirectionofdisplacementof theobjectbealongthatofF?CBSE-i Unit 3 : Laws of Motion10ItisusualtoexpectalaymantosayYestothisquestion.However,aclose lookatthebasicterms(usedfordescriptionofmotion)andNewtonssecond lawrevealsthat,ingeneral,thisisnotso.Weknowthat d svdt= .Henced s v dt = ,whichimpliesthattheinstantaneous directionofdisplacementofanobjectisalongthedirectionofitsinstantaneous velocity.Further,asperNewtonssecondlaw,F m a = .Thisimpliesthatitis theaccelerationoftheobject(andnotitsvelocity)whichhasthesamedirection asthatoftheforceapplied.Fromkinematicalequationsofmotion,weknowthatv=u a t +Hencethedirectionofv(and,therefore,ofdisplacement)canbethesameas thatofa(and,therefore,oftheforceapplied)onlyifEither(i) | | u=0Or(ii)ahasthesamedirectionasthatofuThus,anobjectwouldgetdisplaced,alongthedirectionoftheforceapplied onit,onlywhenEither(i)theobjectisinitiallyatrestOr (ii) the force applied is along the same direction as that of the initial velocity oftheobject.Ingeneral,however,thedisplacementoftheobjectwouldbeinadirection differentfromthatoftheappliedforce.AcloserlookatthetwoformsofNewtonssecondlawofmotion:Newtonssecondlawofmotion,hasthemathematicalform:F= d pdtCBSE-i Unit 3 : Laws of Motion11Sincep mv = ,thisimpliesthatF=( )d d v dmdt dt dtmv m v + =In most of the ordinary situations, we can regard M to be a constant and therefore dmdt| | |\ .equalszero.However,(i)For objects moving at speeds close to that of light, we have, from Einsteins theoryofrelativity m = 0221mvc, which indicates that m keeps on changing with changes in v.(ii)Forobjectslikearocketburningoutitsfueloraleakingwatertanker, theoverallmassoftheobjectkeepsonchangingwithtime.Wecannot,therefore,regardthemassoftheobjecttobeaconstantinall situations.Theoftenusedformofthesecondlaw,namely,F=m ais,therefore,aspecialformofthislawthatcanbeusedonlyforobjectswhose massdoesnotchangewithtime.ItistheformF= d pdtofthesecondlawthatmustthereforeberegardedasthefundamentaland generalmathematicalrepresentationofNewtonssecondlawofmotion.ILLUSTRATION1.Aballofmass1kgisdroppedfromapoint20mabovethe ground which after hitting the ground rises to a same height. Findthechangeinmomentumofballduetocollisionwith theground.SOLUTION.massm=1kgspeedwithwhichballstrikesthegroundv2u2=2asCBSE-i Unit 3 : Laws of Motion12v20=2(10)(20)v=400 =20m/sdownwardsVelocitybeforecollidingwithground fv= 20j Speed after colliding with ground will be same as it eventually attains same height.Velocityofballaftercollision fv= 20jChangeinmomentumduringcollisionp =( )f i f ip p m v v = ILLUSTRATION2.Inthepreviousproblemfndtheforceexertedbygroundon theballifinteractiontimebetweenballandgroundis0.1 second?SOLUTION.Averageforceontheballduetoground avF= 2 1f ip ppt t t = p = 40j avF= 400.1400Njj =ILLUSTRATION3.A1000kgcardevelopedasnagandisstandinginthemiddleofa road.Thedriverandahelppulleditwithtworopesrespectively withforces200 2 N45eastofsouthand400N30northofeast. Assumingnegligiblefriction,fndtheaccelerationofcar.Figure4xy20 mvfviFigure5pfpiyxCBSE-i Unit 3 : Laws of Motion13SOLUTION.Figure6SENW200 N200 24530x200 N200 2 SENW4530y200 2 cos 45200 cos 30200 sin 30200 2 sin 45yxChooseacoordinatesystemasshowninfgureNetforcealongx-axisFx=200 2 cos45+400cos30Fx=2001 32 22 400 +Fx=200+4000.86Fx=544NSimilarlynetforcealongy-axisFy=400sin30200 2 cos45Fy=400 12200122 Fy=200200Fy=0NUsingNewtonssecondlawF= x yF i F j +F= 544i m a=a= 2544100 5.44 m/s i i =Thereforeaccelerationisalong+x-axisi.e.dueeast.CBSE-i Unit 3 : Laws of Motion143.2.2MassThefrstlawhelpsustodefnemassasmeasureofinertia.Itisacharacteristic propertyofabodywhich,inaway,canberegardedasrelatedtoitsexistence. Literally, mass can be regarded as the matter content of a body. Hence it depends onthenumberofatomsormoleculesithasgot. Thesecondlawofmotionprovidesuswithaquantitativewaytodefnemass. Asperthislaw,masscanbedefnedasratioofnetforceactingonthebodyto itsresultingacceleration.m= Fa(1)ConsidertwoblocksAandBundertheinfuenceofsamenetforce.Letthe accelerationofblockBbemorethanthatofblockA(i.e.,aB>aA)Fromtheaboveequation,weget ABmm= BAaa>1Hencewecanconcludethatthemoremassiveanobjectis,thesmallerisits acceleration for a given force. We also realize that by comparing the acceleration ofagivenobject,withthatofastandardmassof1kg,wecanfndthemass ofthatobject.Themassofabodyisascalarquantity.3.2.3WeightofabodyThe concept of weight is often used in daily life as an indicator of its heaviness orlightness.Inphysics,itistheforceexperiencedbyabodyduetothe gravitationalpulloftheearththatiscalledasitsweight.Weareawarethatthe acceleration due to earths gravitational force, for bodies near the earths surface, is9.8ms2.ByNewtonssecondlaw,weightofabodyisgivenbyF=mgHere g isaccelerationduetogravity.Itsvaluecanvarywiththelocationof placeontheearth.Thedirectionofweightissameasthatofaccelerationdue togravityi.e.towardsthecentreofearth,orverticallydownwards.CBSE-i Unit 3 : Laws of Motion15Figure7hmgmgReCONCEPT PROBE1. Howcanonemeasuremassinaspacestaton?2. Howcanonechangetheweightofanobject? 3.2.4ImpulseLetdiferentstudentsbeaskedtocatchwaterballoonsofdiferentsizesthathavebeen throwntodiferentheights.Theycandiscussthebeststrategytocatchtheballoonsafely. Changeinspeed,forballoonsofapartcularmassthrowntoapartcularheightissame buttheduratonoverwhichthecatchisspreadisimportant.Why? SUGGESTED ACTIVITY 3Theaboveactivitycanhelpustounderstandthatforagivenchangein momentumbuttakingplaceoverdifferenttimeintervalsresultsindifferent forces. Greater the interval of impact, lesser the force experienced by the person catchingtheballoon,(forthesamechangeinmomentum).Itfollowsthatwhile catchingtheballoon,oneshouldtakethehandsback,andtherebyincreasethe intervalofimpact. Weknowthattheforceactingonabodycancauseittoaccelerateandthereby, changesitsmomentum.Sometimestheforceactingonthebodyis(i)notconstantduringtheimpact(ii)actsforaverysmalldurationAtennisballhitbyaracket,collisionoftwobilliardsball,canbeviewedas examplesofsuchsituations.Insuchcases,itisverydiffculttomeasurethe CBSE-i Unit 3 : Laws of Motion16durationofimpactorvariationof forceduringtheimpact.Insuch situations,theimpactoreffectofa forcecanbemeasuredthroughthe changeinmomentumofthebody. Thechangeinmomentum,caused byaforceiscalledtheimpulseof force.Theexpressionfortheimpulseofforceistherefore,ButI= f iP P P = But d Pdt=FI= 21ttF dtWecanalsowrite: Pt= avFWhere fPisthefnalmomentumand iPistheinitialmomentumofthebody onwhichthegivenforceacts.OnecanwritetheimpulseexpressionalsoasI= avFtavPtF| || | |\ .= Theimpulseofforcecanthereforebealsodefnedastheproductoftheforce andthedurationforwhichitactsonagivenbody.Incaseofvaryingforces,wecanwriteI= 21ttF dtFigure8CBSE-i Unit 3 : Laws of Motion17The SI units of impulse are Ns or kg m/s. It is a vector quantity whose direction isthesameasthatofforceorthatofthechangeinmomentum.3.3NEWTONSTHIRDLAWOFMOTIONMaterialsrequired:balloons(oneforeachteam)plastcstraws(oneforeachteam)cellotape plastcstring,8-10metersinlengthastopwatchameasuringtapeProcedure:1.Dividestudentsintogroupsoffourorfve. 2. Atachoneendofthestringtotheblackboardwithtape.Askonememberofthe teamtoholdtheotherendofthestringsothatitistautandroughlyhorizontal. 3. Ask one member to blow up a balloon and hold it, at its opening, in his or her fngers. Now ask another member of the team to tape the straw along the side of the balloon. Threadthestringthroughthestrawandholdtheballoonatthefarendoftheline.4. Assignonemembertotmetheracetllitreachestheblackboardorwhenitstops moving. 5. Measure the exact distance the rocket travelled. Calculate the average speed at which theballoontravelled.Distance(cm) Time(s) Speed(cm/s)Team1Team2Team3Team4Thewinnerofthisraceistheteamwiththefastestaverageballoonspeed.SUGGESTED ACTIVITY 4StrawBalloonCBSE-i Unit 3 : Laws of Motion18Whatmakestheballoonrocketmove?Whatexertsforceontheballoon?What makestheairrushoutoftheballoon?Onecanexplainitlikethis:theair, gushingoutofballoon,exertsaforceontheballoonwhiletheballoonexerts forceontheairintheoppositedirection.Inasimilarway,abilliardball,whenitstrikesanotherballatrest,causesthe changeinvelocityofboth.Thisalsosuggeststhatthetwoballsexertforces oneachotherinoppositedirections,resultinginthechangeinmomentumof both. TheresultsofsuchobservationsledNewtontosuggestthatforeveryaction betweentwobodies,thereisalwaysanequalandoppositereaction.Onecan, thereforesaythatthemutualforcesbetweentwobodiesarealways(i)equalinmagnitude(ii)oppositeindirection(iii)collinear(iv)actondifferentbodiesThese results were formalized by Newton in the form ofastatementthatisnowknownasthirdlaw.AccordingtoNewtonsthirdlaw:ForasystemoftwobodiesAandB,theforceonAduetoB,isequaland oppositetotheforceonBduetoA.ForceonAduetoB AB( ) F= BA( ) FForceonBduetoANewtonsthirdlawimpliesthat,inthisuniverse,no forceisisolatedandeveryforcehasitscounterpart whichisequalandoppositetoiti.e.forcesoccursin pairs.In the light of this law, it would be amusing to realize that a man of 70 kg standing on the surfaces of force, experiencingaforce(equaltohisweight)of686N duetoearthmustbepullingtheearthwiththesame force.Figure9B AFABFBAFigure10mgmgmanEarthCBSE-i Unit 3 : Laws of Motion19Ifonecalculatestheaccelerationofthemanduetothisforce,itcomesoutto be9.8ms-2.Whatwillbetheearthsacceleration?Massofearthisverylarge (Me=61024kg)ascomparedtomassofman(m=70kg).Therefore,forthe sameforce,theratiooftheaccelerationoftheearthandthemanis earthmanaa= 2324706 1010mMe=Henceaccelerationofearthisinsignifcantascomparedtoman.Communicationisheavilydependentonsatellitesthesedays,whichareput inspace,withthehelpofrockets.Whatcausestheserocketstogoup,even thoughtheearthispullingthemdowncontinuously?Weallknowthatincase ofrocketsgasesareproducedbyburningoftheirfuel.Asthesegasesoozeout in the downward direction, the rocket moves in the upward direction. The third lawthushelpsustounderstandhowsatellitesgoupinspace.EquationofMotionofaRocketWecanobtainanequationforthemotionofarocketwhichisburningitsfuel gasesataconstantrate.LetM0betheinitial(total)massofarocketandletitbeburningitsfuelgases ataconstantrateofmassunitsperunittime.Letusalsoassumethatthe exhaustgasesescapeoutoftherocketwithaconstantspeed,say,u.LetMbethemassoftherocketataninstanttandletvbeitsspeedatthat instant.Wehave=M ddtdM=dtThisdecreasedMinthemassoftherocketcomesaboutbecauseoftheburning of its fuel. Since the escape gases go out with a speed u, the rocket speed must goupbyanamountdvsuchthat(dM)u=(M)dvorudt=Mdvdv= Mu dt CBSE-i Unit 3 : Laws of Motion20ButM=M0t.Hencedv= 0(M )u dttByintegrationweget 0vdv=u00(M )tdtt orv= 00( )log (M )teutorv=u[logeM0loge(M0t]=uloge 011Mt ( ( ( (| | ( | (\ . =uloge 10M1t| | |\ .uloge 0M1t | | |\ .+forthosevaluesofandtforwhichwecanassumet