Phys Scientists & Engineers II
Phys Scientists & Engineers II PHY 184
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This 7 page Class Notes was uploaded by Quinn Larkin on Saturday September 19, 2015. The Class Notes belongs to PHY 184 at Michigan State University taught by Gary Westfall in Fall. Since its upload, it has received 6 views. For similar materials see /class/207616/phy-184-michigan-state-university in Physics 2 at Michigan State University.
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Date Created: 09/19/15
Physics for Soiem leta amp Beginners 2 Spring Semester 2005 Lecture 49 upper39 signs for moving away from each other lower39 for39 Towards each other April 26 2005 Physics forScbntistsampEngineers 2 1 April 26 2005 Physics for Sci39entistsampEngineers 2 new 2 y y 39 Note X 1 gtI evem Lorentz transformation I contains both time l39 f x39 dilation and length a contraction 4 q Galilei x x vt y y z z 1 th Small v Galilei special case of Lorentz I Relativistic momentum April 26 2005 Physics forScbntistsampEngineers 2 3 April 26 2005 Physics for Sci39entistsampEngineers 2 I NonrelaTivisTic I RelaTivisTic need To consider The conTribuTion of The mass Kinetic Enemy 2 K mv To The energy I Energy conTained in The mass of a parTicle I This is The energy ThaT a arTicle has when iT is aT resT someTimes also called resT energyquot I When a parTicle is in moTion Then iTs energy increases jusT like The Time becomes dilaTed Kinetic Energy 2 by subTracTion of The resT energy I NonrelaTivisTic limiT vltltc y1 2 122c2 April 202005 Physics fur ScienlislsampErigirieers 2 I From The energy we can obTain The kineTic energ 1 38 2 1x2 x4 sq uare Miemermtum and Eer I STarT wiTh The resulTs for momenTum and energy and 3 7 m17gt p2 jzmzv2 E y me2 gt E2 y2m204 I Square of The gammafacTor K y 1mc2 1v2 c2 1mc2 mv2 5 April 262005 Physics fur ScienlislsampEngineers 2 6 Momentum and Energy 2 I Finally we Take square rooT 72 1 1 02 I NegaTive rooT39 anTimaTTer Dirac 1 2 l vzc2 02 122 3 I Case of zero mass phoTons I Express E2 as a funcTion of pl 2 2 2 2 2 C 2 4 C V 1 2 4 2 4 v 2 4 m C m C m C m C C2 V2 C2 V2 C2 V2 2 leC4 2 2 quot12sz2 leC4 y2m2V2C2 C V mzc4 7262 April 202005 Physics fur ScienlislsampErigirieers 2 7 April 202005 Physics fur ScienlislsampErigirieers 2 Eneth amp Mewme Divide momentum by energy p y mv v 262 v E ymc2 c This gives us an additional energymomentum relationship April 20 2005 Physics fur ScientislsampEngineers 2 9 Enemywmgm m Question If an electron has a speed of 99 of that of light what is its total energy what is its kinetic energy and what is its momentum Answer Rest energy of electron E51110S eV0511MeV Rest mass m0511 MeVc2 remember 1 eV 16091019 J Gamma for 99 of c 1 1 7 09 41 132 Jl 0992 39 Total energy E y E0 709 0511 MeV362 MeV April 26 2005 Physics f0rScienlislsampEngmeers 2 10 Energywwemtm 2 Answer cont Kinetic energy of electron in this case K 7 1E0 609 0511 MeV311 MeV E 099362 M V Momentum p e358 MeVC C C An accelerator to achieve this is quite small and inexpensive but in the last 1 is where it gets big and expensive At SLAC the speed reached by electrons is 999999999 of the speed of light and it takes an accelerator of length 3 km to accomplish this April 26 2005 Physics fur ScientislsampEngineers 2 ll April 26 2005 Physics f0rSclerillslsampErigmeers 2 12 Mae and Kirava Newtonian theory of gravity GmM z mack Mass m appears on both sides of this equation Right side source of the interaction gravitational mass Left side mass undergoing acceleration inertial mass Experimental finding gravitational mass inertial mass Newtonian gravity works extremely well except near very large masses Example Small deviations from observed orbit of Mercur Equipelm Principle Einstein 1907 If a person falls freely he will not feel 39 ight Consequence you cannot distinguish if you are in an accelerating reference frame or if you are subject to the gravitational force Equivalence Principle All local freely falling non rotating laboratories are fully equivalent for the performance of all physical experiments Space and time are locally curved due to the presence of masses Auniza 2on5 Auniza 2on5 N curved sw Twodimensional example Imagine a flat rubber sheet suspended at the edges Put a bowling ball on it local deformation a9 calmed Spac 2 Now put two objects on the rubber sheet Objects are attracted to each other and move towards each other gt Gravitational interaction My Auniza 2on5 Aunt more to Physics for Seimtists a Engineers 2 Spring SemesTer 2005 LecTure 35 Energy Transport The raTe of energy TransporTed by an elecTromagneTic wave is given by The PoynTing vecTor The insTanTaneous power per uniT area of The wave is given by March 25 ZEIEIS Physics forScieniisisampEngineers 2 Review l2 The energy in The elecTric and magneTic fields of The elecTromagneT wave are equal 1 1 The radiaTion pressure due To a ToTally absorbed elecTromagneTic wave is H l P The radiaTion pressure due To a reflecTed elecTromagneTic wave is jusT Twice The absorbed value March 25 was Physics forSCienlislsampEngineers 2 Polarization Consider The elecTromagneTic wave shown The elecTric field for This elecTromagneTic wave always poinTs along The y axis Taking The XCleS as The direcTion ThaT The wave is Traveling we can define a plane of oscillaTion for The elecTric field of The elecTromagneTic wave as shown This Type of wave is called a plane polarized wave in The y direcTion We can represenT The polarizaTion of an elecTromagneTic wave by looking aT The elecTric field vecTor of The wave in The XZ plane which is perpendicular To The direcTion The wave is Traveling The elecTric field oscillaTes in The y plane March 25 ZEIEIS Physics forScieniisisampEngineers 2 March 25 was Physics forSCienlislsampEngineers 2 maximum 323 Polarization 3 The elecTromagneTic waves making up The ighT emiTTed by mosT T We can represenT ighT wiTh many common ighT sources such as an incandescenT ighT bulb have random polarizaTions by summing The y componenTs polarizaTions and summing The z componenTs To produce Each wave has iTs eecTric field vecTor osciaTing in a differenT plane The heT Y and Z comPOhehTS This ighT is called unpolarized ighT We can represenT The polarizaTion of The ighT from an unpolarized 39 For UhPOlahlzed 9th we ObTalh equal comPOhehTS TT T source by drawing many waves like The one shown on The previous page in The Yquot and Z39dlheCTthS buT wiTh random orienTaTions If There is less neT polarizaTion in The y direcTion Than in The z direcTion Then we say ThaT The ighT is parTially polarized in The z direcTion March 25 Zuni Physics forScieniisisampEngineers Z i March 25 Zuni Physics forScieniisisampEngineers Z n Polla iza mi 64 We can change unpolarized ighT To polarized ighT by passing The I The componenTs of The unpolarized ighT Polarization unpolarized ighT Through a polarizer ThaT have same polarizaTion as The A polarizer allows only one componenT of The polarizaTion of The ighT To P lahlzeh are TransmiTTed bUT The i pass Through componenTs of The ighT ThaT are One way To make a polarizer is To produce a maTerial The consisTs of Perpendlwlar To The POlarlzer are absorbed long parallel chains of molecules ThaT effecTively leT componenTs of The ighT pass wiTh one polarizaTion and block ighT wiTh componenTs If polarized ighT wiTh polarizaTion parallel l 39 perpendicular To ThaT direcTion To The polarizing angle is incidenT on The quot We will discuss polarizers wiThouT Taking inTo accounT The deTails of The P lahlzehl all The ll9hT Passes Thhough l molecular sTrucTure InsTead we will characTerize each polarizer wiTh a polarizing direcTion If polarized ighT wiTh polarizaTion Unpolarized ighT passing Through a polarizer will emerge polarized in PehPehdlCUlah T0 The P lahl2lh9 angle is A The Polarizing direcTion incidenT on The polarizer none of The 39 ighT is TransmiTTed T March 25 Zuni Physics forScieniisisampEngineers Z 7 March 25 Zuni Physics forScieniisisampEngineers Z n P a Z ampMmm Now eT39s consider The inTensiTy of The ighT ThaT passes Through a polarizer We begin wiTh unpolarized ighT wiTh inTensiTy I0 Unpolarized ighT has equal componenTs of polarizaTion in The yand z direcTions AfTer passing Through a verTica polarizer only The ycomponenT of The polarizaTion remains The inTensiTy Iof The ighT passing Through The polarizer is given by 1 1 1 2 0 because The unpolarized ighT had equal conTribuTion from The yand z componenTs and only The ycomponenTs are TransmiTTed by The verTica polarizer This facTor of one half only applies To The case of unpolarized ighT passing Through a polarizer minimum in Now eT39s assume ThaT polarized ighT passes Through a polarizer and ThaT This ighT has a polarizaTion ThaT is noT parallel or perpendicular To The polarizing direcTion of The polarizer The angle beTween The incidenT polarizaTion is 6 The componenT of The elecTric field Eof The ighT ThaT is TransmiTTed is given by E E0 cosQ where E0 is The elecTric field of The incidenT polarized ighT The inTensiTy of The ighT I0 before The polarizer is given by I0 LE3 1 E Clue ZCIU O March 25 Zuni Physics fDrSCienlislsampEngineers Z a March 25 Zuni Physics fDrSCienlislsampEngineers Z in Polla izatimi in AfTer The ighT passes Through The polarizer The inTensiTy I is given by 1 1 E2 20110 The TransmiTTed inTensiTy in Terms of The iniTiaI inTensiTy is 1 1 I E2 E0 cos 92 I0 cos2 9 Zone 20110 This resulT is called The Law of Malus This equaTion only applies To The case of polarized ighT incidenT on a polarizer Now we will do a specific example of The inTensiTy of ighT passing Through polarizers Example 1th P amen 7 I Consider The case of unpolarized ighT wiTh inTensiTy IO incidenT on Three 2 polarizers I The firsT polarizer has a polarizing direcTion ThaT is verTical I The second polarizer has a polarizing angle of 45 wiTh respecT To The verTical I The Third polarizer has a polarizing angle of 90 wiTh respecT To The verTical I WhaT is The inTensiTy of The ighT passing Through all The polarizers in Terms of The iniTial inTensiTy March 25 Zuni Physics fDrSCienlislsampEngineers 2 ii March 25 Zuni Physics fDrSCienlislsampEngineers Z i Z
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