Work,EnergyandMomentumNotes

3–MomentumandCollisions

Momentumisaquantityofmotionthatdependsonboththemassandvelocityoftheobjectinquestion.

Theunitsofmomentumare:

Remember:Momentumisa_________quantity,withthesamesignasitsvelocity.Aswithanyvectoryoucanassignanydirectionaspositiveandtheoppositeasnegative,butasconventionwewillrefertouportotherightaspositiveanddownortotheleftasnegative.

Example:Abaseballpitcherhurlsaballat32m/s.Thebattercrushesitandtheballleavesthebatat48m/s.Whatwastheball’schangeinmomentum?

RememberthatmomentumisaVECTORwhichmeans:

Impulse:

Recallthatmomentumistheproductof_________and___________.Sincewewillnotbedealingwithchangingmasses,wecandefineanobject’schangeinmomentumas:

Wheneveranetforceactsonabody,anaccelerationresultsandsoitsmomentummustchange.

Derivation:

Let’strytounderstandhowforcesrelatetochangesinmomentumwithafewexamples. Astudentjumpsoffadesk.Whentheylandtheybendtheirkneesonimpact.Whydoesthishelppreventsomeseriousdamagetotheirknees?

Coachesformanysportssuchasbaseball,tennisandgolfcanoftenbeheardtellingtheirathletesto“followthrough”withtheirswing.Whyisthissoimportant?

Conventionalwisdomsuggeststhatcarsshouldbemadetoughandrigidtopreventinjuryduringacollision,howevernewervehiclesareallbuiltwithlargecrumplezones.Why?

Abeanbagandahighbounceballofequalmassesaredroppedfromthesameheight.Thebeanbagisbroughttoastopinthesametimethattheballisincontactwiththefloor.Whichoneexertsagreateraverageforceonthefloor?

TheLawofConservationofMomentumMomentumisausefulquantitybecauseinaclosedsystemitisalwaysconserved.Thismeansthatinanycollision,thetotalmomentumbeforethecollisionmustequalthetotalmomentumafterthecollision.

Therearetwowaysofthinkingabouttheconservationofmomentum:

(1)

(2)

ExampleA115kgfullbackrunningat4.0m/sEastisstoppedin0.75sbyahead-ontackle.Calculate

a) theimpulsefeltbythefullback.b) theimpulsefeltbythetackler.c) theaveragenetforceexertedonthetackler.

ExampleA1250kgcartravelingeastat25m/sturnsduenorthandcontinuesonat15m/s.Whatwastheimpulseofthecarexertedwhileturningthecorner?

Collisionscanbegroupedintotwocategories,

ElasticCollisions:

InelasticCollisions:

Inrealitycollisionsaregenerallysomewhereinbetweenperfectlyelasticandperfectlyinelastic.Asamatteroffact,itisimpossibleforamacroscopiccollisiontoeverbeperfectlyelastic.Perfectlyelasticcollisionscanonlyoccurattheatomicorsubatomiclevel.Whycan’tmacroscopiccollisioneverbetrulyelastic?

Inelastic

Elastic

Explosions

A9500kgcabooseisatrestonsometracks.An11000kgenginemovingeastat12.0m/scollideswithitandtheysticktogether.Whatisthevelocityofthetraincarsafterthecollision?

Afirecrackerisplacedinapumpkinwhichexplodesinintoexactlytwopieces.Thefirstpiecehasamassof2.2kgandfliesdueeastat26m/s.Thesecondchunkheadsduewestat34m/s.Whatwastheinitialmassofthepumpkin?

Tworugbyplayersofequalmasscollideheadonwhiletravelingatthesamespeed.Whatistheirfinalspeed?Ismomentumconserved?Isenergyconserved?Iskineticenergyconserved?

Aprotontravelingat2x103m/scollideswithastationaryprotonandcomestorest.Whatisthefinalspeedoftheotherproton?Iskineticenergyconserved?

Analphaparticlehasamassapproximately4timeslargerthanaproton.Aprotontravelingtotherightat3200m/sstrikesastationaryalphaparticleitreboundsat1920m/s.Whatisthefinalspeedofthealphaparticle?

Work,EnergyandMomentumNotes

4–Collisionsin2-D

Whendealingwithcollisionsin2-dimensionsitisimportanttorememberthatmomentumisavectorwithmagnitudeanddirection.Whenfindingthetotalmomentumwehavetodo:

Collisionsnotat90o(becauselifeisneverthateasy…):

A4.0kgbowlingballismovingeastatanunknownvelocitywhenitcollideswitha6.1kgfrozencantaloupeatrest.Afterthecollision,thebowlingballistravelingatavelocityof2.8m/s32oNofEandthecantaloupeistravelingatavelocityof1.5m/s41oSofE.Whatwastheinitialvelocityofthebowlingball?

ComponentMethodWeneedtobreakthefinalmomentaofthetwoobjectsintoxandycomponents:

Before After

Collisions at 90o: A 750 kg Peugeot travelling at 21 m/s West collides with a 680 kg Fiat travelling at 18 m/s South. If the two cars become entwined what is their total final velocity?

Remember that it is momentum that is conserved, so we need to add the ______________ NOT _____________