DynamicsKinematics

–describesmotiononlyDynamics

explainsmotionbyfindingthelawsthatgovernitFreebodydiagramNewton’s3lawsanalyzingforcesnormalforceforcestensionfrictiondragforcestaticfrictiondynamicfrictionNewton’s3lawsofmotion(1)

lawofinertia(2)

F=ma(3)

action=reactionInertiaAbodyatrestremainsatrest,or,ifinmotionremainsinmotionataconstantvelocityunlessactedonbyanetexternalforceForexample,“friction”isanexternalforceNofriction-thebodydoesnotchangeitsstateofmotionexamples:iceskatesWhatis“mass”?Mass=quantityofmatterItdependsonbothvolumeanddensityoftheobjectExamples:

plastic,water,metalandair-havedifferentdensitiesWeightisNOTmass.Weightisgravitationalforce(net)Force=Mass*accelerationForceisavector,likeaccelerationUnitofforce:Newton(N)=kgm/s2Weight=gravitationalforce

Newton’s3rdlaw

ACTION=REACTIONButondifferentobjectsmamaequalforce!ma=maAction–onthegas,fromtherocketReaction–ontherocket,fromthegasupwardforcecomesfromthetableThisiscalled:thenormalforcethebagisnotmoving:noaccelerationThe“Normalforce”Normalforce–alwaysperpendiculartothecontactingsurfaceFreeBodyDiagramW1orm1gWeight(mg)

–Alwaysdrawnfromthecenter,straightdownNormalForce(FN)

–Asurfaceforcealwaysdrawnperpendiculartoasurface.Tension(TorFT)

–forceinropesandalwaysdrawnAWAYfromobject.Friction(Ff)-

Alwaysdrawnopposingthemotion.m2gTTFNFfsystemmgFNFfInclineproblemsWhatistheacceleration:iffrictionisnegligibleiffrictionis45Nm=60kgTheinclineproblem–askier2,Resolvingweightintocomponents1,EstablishingthecoordinatesystemForceparalleltotheslope:Thenetforce,withoutfriction,is:Theaccelerationis:Withoutfriction“Tension”isaforceThetensionisthesameeverywherealongaropenomass,non-stretchablemMMg-FT

=Ma

PulleyproblemFT

FT

MgWhatistheacceleration?MgFT

MFreebodydiagram1mΝmgFT

=ma

Freebodydiagram2Whatisthetension?m=70kgnoacceleration:netforce=0Horizontalforces:Verticalforces:Symmetry!Weightnotinthemiddle:whatarethetensions?Mass=15kgm=15kg

VerticalforcesFrictionFrictionisaforcethatopposesrelativemotionbetweensystemsincontactIftwosystemsareincontactandmovingrelativetoeachother,thenthefrictionbetweenthemiscalledkineticfrictionkineticfrictionKineticfrictionisproportionaltothenormalforcebetweenthetwosystems,andalsodependsonthepropertiesofbothsurfaces.Staticfriction:whenthereisnomotion,butthereisattemptmotion

TheforceofstaticfrictionincreasesasonepushesontheobjectμsisthecoefficientofstaticfrictionNisthenormalforce(forceperpendiculartothesurface)Dynamicfriction/Kineticfriction

:whenthereisrelative

motionμkisthecoefficientofdynamicfrictionBut,ithasanupperlimitThecoefficientofdynamicfrictionisalwayssmallerthanthecoefficientofstaticfrictionAskierwithamassof62kgisslidingdownasnowyslopeFindthecoefficientofkineticfrictionfortheskieriffrictionisknowntobe45.0NNormalforce:Frictionforce:29MechanicalforcesbetweentwoobjectsAtthecontactingpoint–Normalforce&Friction30FNfDragForcesOntheobjectmovinginaliquidorinairOpposesmotionProportionaltothesquareofthespeedAisthecrosssection

areaCisthedragcoefficientρisthedensityofthegasvisthespeedSkydiverinfreefallWhenFD=mg,theaccelerationiszeroDensityofairDragcoefficientv=98m/s=350km/hv=49m/s=175km/hA=0.7m2“terminalvelocity”HeadfirstSpreadeagleAnotherdragforce:Stokes'

lawTheforceofviscosityonasmallspheremovingthroughaviscousfluidisgivenbyFd

isthefrictionalforce–knownas

Stokes'dragμ

isthe

dynamicviscosity

(thetextbookusesthesymbol

η)R

istheradiusofthesphericalobjectv

isthe

flowvelocity

relativetotheobjectmMPulleyproblemFT

FT

MgWhatshouldbethemassMtomakethesystemmoveif:Atwhatangledoesanobjectstarttomove?Whatwillbeitsaccelerationthen?Kineticfriction:Staticfriction:Thenormalforceis:Thestaticfrictionsforceis:Theobjectstartstomovewhen:Moving:always!critical

conditionIftheforceistoosmall,theblockoficedoesnotmoveTomaketheblockmove,weneed:iceonice:Whatistheaccelerationonceitstartsmoving?Thenormalforceissmaller!Iftheforceistoosmall,theblockoficedoesnotmoveTomaketheblockmove,weneed:m1m2Inthegym,therockclimber(ofmassm1)isprotectedbyanotherperson(ofmassm2).Dowerequirethepersononthegroundtobeheavier?Ifnot,theoneonthegroundshouldnotbetoolight.Canyoufindtheminimumrequirementforthemassesandotherparameters?T=m1gm2gθNfs

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