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General Physics

by: Nichole Keebler

General Physics PHYSICS 103

Nichole Keebler
GPA 3.95

Nitin Rai

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Nitin Rai
Class Notes
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This 5 page Class Notes was uploaded by Nichole Keebler on Thursday September 17, 2015. The Class Notes belongs to PHYSICS 103 at University of Wisconsin - Madison taught by Nitin Rai in Fall. Since its upload, it has received 43 views. For similar materials see /class/205219/physics-103-university-of-wisconsin-madison in Physics 2 at University of Wisconsin - Madison.


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Date Created: 09/17/15
Physics 103 Lecture 11 Collisions and Explosions Today s lecture covers applications of concepts from lecture 10 02232005 Pnysics i03 Spiing 2005 U Wisconsin 1 Impulse and MomentumReprise o MomentumImpulse Theorem tFmAtEI ppiAp o For single object O lfF 0 then momentum conserved Ap 0 For system of objects o Pmi 2 Sp 0 Internal forces forces between objects in system 0 External forces all other forces 0 FmAt AP u ai o ime 0 then total momentum conserved APMai 0 0 Applications Collisions amp Explosions 02232005 Pnysics i03 Spiing 2005 U Wisconsin Collisions I now after quot 1 39quot2 Explosions M quotbeforequot 3 E quotafterquot 02232005 Pnysics i03 Spiing 2005 U isconsin 3 Proced ur39e Draw quotbeforequot quotafterquot Define system so that Fax 0 Set up axes Compute Pmmi quotbeforequot Compute Pmmi quotafterquot Set them equal to each other Some Terminology Elastic Collisions collisions that conserve kinetic energy Inelastic Collisions collisions that do not conserve kinetic energy Completely Inelastic Collisons objects stick together 02232005 Pnysics i03 Spiing 2005 U Wisconsin Explosions l M V2 quotafterquot v ix E Example m1 M3 m2 2M3 Which block has larger momentum quot Each has same momentum Which block has larger velocity quot mv same for each Which block has larger kinetic energy quot KE mv22 m2v22m pZZm smaller mass has larger KE Is kinetic energy conserved 02232005 Pnysics i03 Spiing 2005 U Wisconsin 5 smaller mass has larger velocity quotbeforequot 02232005 Collisions or Explosions in Two Dimensions O O O Q before offer Pmdllx and Pmdlly Independently conserved P P Ptotulxbefore 39 Ptotalxufter Physics i03 sonng 20050 Wisconsin totalxbefore totalxufter REID 5 Explosions M quotbeforequot h A B D b Which of These is possible Explosions M quotbeforequot h Us ak Which of These is possible A lt A B B lt bofh neiTher39 02232005 Physics i03 Spying 2005 U WlSCOHSlH 7 02232005 Physics i03 Spying 2005 U WlSCOHSlH s A railroad car is coasTing along a horizonTal Track wiTh speed V when iT 0 In tWO39dlmenSIOHal elaStIC C0ll30nsi the conseNatlon laWS runs inTo and connecTs wiTh a second idenTical railroad car iniTially aT resT Assuming There is no fricTion beTween The cars and The rails whaT 1 allow US to detelm39ne the nal mOtlon is The speed of The Two coupled cars after The collision 2 place restrictions on possible final motions 3 do not allow us to say anything about the final motion 1 V 2 VZ CORRECT l l 3 W4 4 O u m m EM anyr m W m m Demo M h g Iders 02232005 Physics i03 Spying 2005 U WlSCOHSlH 9 02232005 Physics i03 Spying 2005 U WlSCOHSlH i0 Preflight 4 amp 5 WhaT physical quanTiTies are conserved in The above collision 1 Only momenTum is conserved CORRECT 2 Only ToTal mechanical energy is conserved 3 BoTh are conserved 4 NeiTher are conserved 02232005 menTum is conserved because The neT energy is noT conserved Energy is always conserved There are no exTernal forces acTing on The so boTh momenTum and mechanical Physics i03 Spying 2005 U Wisconsin sysTem energy are conserved coupled The collision is inelasTic and kineTic MomenTum is noT conserved bc The Train has To slow down when H hiTs The nexT one Preflight 6 amp 7 Suppose rain falls vertically into an open cart rolling with k As a negligible friction along a straight honzo ntal trac sult of the accumulating water the speed of the cart 1 increases 2 does not change 3 decreases o Mass Is Increaslng verTical impulse by Track inelasTic collision Mass is increasin and The harizanTal momenTum is fixed 02232005 So The velaciTy musT decrease Physics i03 Spying 2005 U Wisconsin i2 Preflight 8 amp 9 0 Suppose rain falls vertically into an open cart rolling along a straight horizontal track with negligible friction As a result of the accumulating water the kinetic energy of the can 1 increases Momentum is constant Mass increases velocity decreases and so does kinetic energy p22M n 10 20 IWI WWI mlin moms Maggi 1 1 2 KE mv2 m2V2 2 2 m 2m 02232005 Physics i03 soiing 2005 U Wisconsin i3 02232005 Physics i03 soiing 2005 U Wisconsin i4 Ballistic Pendulum Its easier to measure dthan to measure H so after a small bit of geometry we get m 0L A projectile of mass m moving horizontally with speed v strikes a stationary mass M suspended by strings of length L Subsequently m M rise to a height of H Given H what is the initial speed vof the projectile 02232005 Physics 103 soiing 2005 U Wisconsin Ballistic Pendulum II 0 Two stage process 1 m collides with M inelastically Both M and m then move to ether with a velocity V before having risen significantly 2 M and m rise a height H conserving energy E no nonconservative forces acting after collision 02232005 Pnysics 103 Spiing 2005 U Wisconsin Ballistic Pendulum Ill 0 Stage 1 Momentum is conserved nergy is not conserve mv mMV in xdirection 0 Stage 2 Energyis conserved 12 mMV2 mMgH gt v 29H 5 Eliminating V gives v 1 Mm 29H 5 02232005 Pnysics 103 Spiing 2005 U Wisconsin Shooting Pool 0 Assuming t Collision is elas ic KE is conserved O No spin is imparted O Balls have the same mass 0 One ball starts out at rest 0 Then the angle between the balls a er the collision is 90 I Pr pi gt 39 Xh 39 xquot ch Pf before a er 02232005 Pnysics 103 Spiing 2005 U Wisconsin Shooting Pool 0 Eiastic rneans conservation or kinetic energv p azizwi v Choose axessuch lh llhz inili l lquot momentum is in x direction then P Wu 5 Imlml X Q x py 0 P2 aims m Spring 2005 u wismnsin Shooting Pool Smoe p pfcosz5plcos pzoos ploos pzcos picoszo 7 e pfcos 5 pcose x 7 axis in pcosspzcos yraxls censinmpzsmo Let39s see if the solution suggested is comment a i 90quot en case Sm pond ease sin a tram coso mm cose pzsintoos pzzoosit sm sm wees i39 Conservation of energvii ozizaizoos Physcs m Spring zoos u Wenomin Pythagorus to the Rescue Vector sum of final momenta vector sum of initial momenta But from elastic collision we have conservation of kinetic energy and thus pnz p2 P22 This is The Pythagorean formula for a right Triangle 02232005 Wm 03 swingzoos u wismin scratcning i ozizaizoos Shooting Pool 0 Tip irvou snoot a ban spotted on tne oot x vou nave a good cnance or Physcs m Spring zoos u Wenomin Rocket Propulsion o Tne operation or a rocket depends on tne lavv or conservation or its eiecteo me o Tnis is oirrerenttnan propulsion on tne eartn Wheretvvo ooiects exert orces on eacn otner gtgt road on car gtgt train on track 0 The rocket is acceierateo as a result or tne thrust or tne exhaust gases 0 Tnis represents tne inverse or an ineiastic coiiision M mum is conserved o iltinetic Energv is increased at tne expense or tne stored energv or tne rocket mei 02232005 Wm 03 swingzoos u wismin ozizaizoos Rocket Propul v M Am p M Amv 0 The initial mass ofthe rocket is M Am O M is the mass ofthe rocket O m is the mass ofthe fuel 0 The initial velocity ofthe rocket is v Physcs m Spring zoos u Wenomin Rocket Propulsion 1W Am m E E E 3 gt vAv I The rocket s mass is M I The mass ofthe fuel Am has been ejected I The rocket s speed has increased to v Av 02232005 Phrer mar Sprth 2005 u Wtsmnsm 25 Rocket Propulsion nal I The basic equation for rocket propulsion is O M is the initial mass ofthe rocket plus fuel O M is the nal mass ofthe rocket plus any remaining fuel O The screed ofthe rocket is proportional to the exhaust spee 02232005 thscs m Sphrg 2005 u Weeumh Thrust of a Rocket o The thrust rs the torce exerted Oh the rocket by the erected exhaust ases o The rhstahtaheous thrust rs gwen by o The thrust rhcreases as the exhaust speed rhcreases and as the burn rate AMAt rhcreases 02232005 Phrer mar Sprth 2005 u Wtsmnsm 27


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