ENGINEERING PHYSICS I
ENGINEERING PHYSICS I PHY 303K
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This 4 page Class Notes was uploaded by Malvina Orn on Monday September 7, 2015. The Class Notes belongs to PHY 303K at University of Texas at Austin taught by Jack Turner in Fall. Since its upload, it has received 61 views. For similar materials see /class/181824/phy-303k-university-of-texas-at-austin in Physics 2 at University of Texas at Austin.
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Date Created: 09/07/15
Summary on unit 1 update 91110 Constants c3 X103ms1u mp mn R17 gtlt 10 27kg G 67 X 10 11Nm2k92 Sec 1119 Coord vector r lt zy2 gt Ti 7 W f lt 0039 cost9ycost92 gt For 2D case 7 W f lt 0089 sim gtlt caseboos y gt Vectors Sec 15 Addition substraction magnitude of a vector unit vector Displacement Ar rf 7 ri Average velocity Total distance traveledtravel time or vavg ArAtv1At1 VQAtQ At1 At Position up date rf ri Vangt lnstantaneous velocity V LimAL w ArAt lnstantaneous acceleration a dvdt For constant acceleration Vavg gr Otherwise for suf ciently small At use eg Vavg N Vf Momentum p 7mm 7 NW 5 lVlC O Nonrelativistic approximationNR 7 7gt 1 p mv 6 Identity BeyW Where y pcm vc AscAt As cAt The extended Newton s law of motion F ApAt 0 If F 0 p p15 constant Which is Newton s rst law 0 If F f 0 for NR case it leads to F ApAt ma Where a AVAt is acceleration This is Newton s second law For the R case F ApAt AVAt mv yma With a AVAt Sec 2128 also read 29 Momentum principle Ap pf 7 pl FAt Momentum Principle is given by a vector equation The equation is valid for each Cartesian component A special case 1d NR and Fconstant or a Fm constant 0 From momentum principle Ap FnetAt With a Fm it leads to vf vi at O For a constant acceleration case vavg vi vf2 Why 0 Position update As vangt vi vf2At This leads to As viAt 12aAt2 Derive Sec 3135 Four kinds of forcesor 39 t quot n quot quot t quot strong and weak Gravitational force F 7 Cgmi Near surface of earth With radius R F mg m 15162 m m 1terative procedure3d 0 Begin With the object s momentum and position P1312 and the force at t ti 0 IL lterative Loop Take time step tf ti At Apply Momentum principle to update pi to pf 0 Position update moves the object from ri to rf 0 Set present pfrf Frj tf to next step plxi Fri ti Go to IL Principle of reciprocity Newton s third law Force on 2 due to 1 and force on 1 due to 2 satis es the relationship Flong 7F2 m1 Spring force1d Magnitude satis es the relationship lFl klsl With sign F 7kg 8 L 7 L0 The stretched case has 8 gt 0 leading to attraction The compressed case has 8 lt 0 leading to repulsion Summary 0n unit 3 update 5712 Chapter 6 68617 Pair interactions and potential energy of multiparticles Eggs EimiczKiEiltJUij Potential energy due to interaction between one pair A and B 0 AU 7W is the work done by the force exerted on B by A B moves from initial to final position 0 How is the force related to U 39 1 variable cases FT 7dUr dr and Fm 7dUdz c U r 7 0 r 7 oo increases r 7 0 Attractive U lt 0 repulsive U gt 0 Gravity Ur 7072M F 702M Electricity Ur F 4760 Satellite circular orbit Centripetal force mvzr GmMrz K 2 Chapter 7 Internal Energy Ideal spring U 12m2 Fsprmg 71 K U mvfmmQ kA22 z Acoswt w 1 km Morse potential Ummse EM 1 7 6 T TW2 7 EM U r is a function of position coordinate only It is independent of the paths taken to reach 7 Einte39rnal E Ethe39rmal Erotatitmal Evib39ratitmal Echemical not Kmmsl Energy principle AEsys W Q other Ethem CmT where C is specific heat in units of Jg Dissipation Teri ninal velocity at Fm mg Fm 712 CpAiZ Friction MSFN FM MFN Chapter 8 Energy Quantization When W97m is negligible we describe the system by its energy state E K U where E takes on all values The E states in sun comet macro system compared to those in H atom i nicro systei n 72 mMr KU 712GmMr o Similarities U 7 cc 71 7 For E lt 0 bound states For E Z 0 continuum and unbound 0 Differences in E lt 0 region Macro system can have bound states at any E lt 0 no well defined i ninii nui n Micro systei n has discrete bound states and has a ground state which defines rmm Frank Hertz experii nente H g 7 e H 9 It illustrates the discreteness of the 2nd level of Hg atom Photons Light is made of wave energy packets called photons symbol y Its size is w A wavelength E7 m hcA 12406Vnm with h h27T Planck s constant h 66 gtlt 10 34J s 0 Atomic excitations X atom 7 X at0m Energetic X particle may kick ground state to an excited level 0 Emission Decay from 2th level leads to emission of y with energy E7 E 7 E where 1 lt j lt 239 7 1 0 Absorption Electron at ground level excited to 2th level leads to absorption dark line at E7 El 7E1 Boltzman factor ezp7E7kBT kBT ltlt E1 gt no excitations kBT gtgt E1 gt excitations ii nportant For BF 16V at T 300K BF w 3 gtlt 10 At T 5000K BF N 01 Vibration Harmonic oscillators levels with equal spacing EN N me E0 N 1 2 we i m Photon spectra y ray 106eV X ray 104eV visible 18 31 eV i nicrowaves 10 4eV radio 10 6eV Chapter 9 Multiparticle Systems CoM Point Particle systei n Moi nentui n 13525 MBCM where 15525 tot M Ellmi PP moves with velocity 170M Moi nentui n principle applied to the PP systei n dist Fnet m Real system AE AKWW AK Nzl AU Kmms Mv M 23 Km Km Km U9 M gym Km inf where w 27rT with I Examples Tinghoop MR2 Lil5k MRZ Imth MI27 sphere Summary on unit 2 update 10710 Sec 36313 Electric force F kg 23 Where 168 1 9 X lOgNmQCQ 47m Reciprocity Applicable for 712 forces eg grav and elec forces Here each object may have a nite size But it must be uniformly spherically symmetric r is the distance from center to center Momentum principle implies conservation of momentum ie Apsys Apem 0 Many body system 0 Psys mlpl mgpg and Fuel F1 F2 If the internal forces satisfy the principle of reciprocity then F1 F2 Will only include external forces 0 Center of mass an effective one body system For NR Pam Mcmvcm Where Mam m1 7212 9 Or ch PomMom m1V2 m1V2 and ram m1T2 m2r2 Sec 41417 Ballspring model 1 mole NA 6 X 1023 atoms M molar mass V molar volume 0 Mass density p MV mdg Where d3 is the atomic volume and m the atomic mass 6 One interatomic bound F kls One cable L nd A md2 F kmnAL Solve knm k1 o Young s modulus FAALL FAL gtlt LA kmn gtlt ndmdQ Isld Derivative form of MomPrinciple dpdt Fnet Conventional equation of motion NR case F ma Frequency of oscillations and speed of sound 6 Equation of motion dmvdt mdvdt mdQIdt 7km 0 Analytic solution I Acoswt w 0 Speed of sound 1 We W Md 0 Chemical bounds of a nucleus With length and stiffness d k and of its isotope with d k are essentially the same ie d m d and k m 16 since both have practically the same charge content Sec 51 to 57 Rate of change of momentum o Statics equilibrium dpdt 0 Fm EiFi 0 Motion along a curved path p pp dpdt F FH dpdtp F1pdpdt pvR ym UQR 6 Local circle de nes R v and Fig 526 537 9 lletR or lAplAt vR Sec 6167 Introduction to Energy Principle 0 Energy of a single particle E 772152 E 72102 K NR case K m 12mv2 1722721 in Joules R case E2 pc2 7213 16V 16 X 10 19J 1MeV 1066V 0 Energy principle AEsymm W QM o WF Az FAI FATCOSOE ATFATH 0 Near earth surface F 7mg W ining For rdependent force W EF Ar if F dr 0 Example Spring force F 7km Work by spring in slowing the ball W 7161 7 Summary on Ch 1012 update 42912 Ch 10 Collisions Interaction over a short time A1592S netAt 6 AE AK Em W Q s 0 3 types Elastic AK 0 Inelastic AK lt 0 Maximally inelastic stuck together or K751 0 Change of internal energy E K Em AE 0 implies AEW 7AK 7AK751 Changing reference frames Notations 1 172 153 154 where 173 lf and 174 Elf 0 1 Bowling ball BB hits ping pong ball PB at rest In lab frame M111 mfg M113 I 771114 BB frame is where BB is at rest so meme 111 Velocities in different frames related by V V 7 meme PB in BB frame 12 112 7 111 711 After elastic bounce PB velocity in BB frame is 111 712 111 Back to lab frame In general V V mem PB in lab frame 114 111 01 2111 What is the sign of 03 in elastic collisions where 02 0 in 3 cases m1 lt 7712 m1 m2 m1 gt 771239 Elastic head on collisions for arbitrary m1 m2 111 112 Ug 211m 7 111 and 114 211m 7 02 Derive Ballistic Pendulum 1d collision 3 phases 1 initial i nomentarily after collision m M stuck together 3 block reaches final height I 7 2 psys mill psysf m MV 2 7 3 AE AK AU 0 AEW 0 why39 Beyond 1d Impact l b b durca e tattuing angle increases Rutherford scattering a on Au large angles proved atomic nuclei hypothesis Ch 11 Angular 7 t39 Translational orbital Angular EVIomentumEMMA FA gtlt 17 l tmm l rp sin 9 71p Angular i nomentum principle about A dEAdt FA FA FA gtlt E IFAI rF sin 71F Planetary Motion dEAdt F gtlt 13 0 implies EA const r 3 VVM 7i M7M7L Ixepler s 2nd law At 7 const AA 7 iiAt At 7 2 m 7 Rotational spin Angular quot I Lmt FLOM gtlt 17 13 Angular i noi nentui n principle about CoM A dL39rotdt TnetCM Angular IVIomentum of i nultiparticle system Ltot mes Lmt Example A spinning dumbbell with masses m1 m2 m separated by d also orbits some point at a distance To M Rotational angular velocity is wspm Translational angular velocity is wtmm so 110M TCthmm Two angular i noi nenta are Lmt 2m g2 wspm mes 2mrngtmm Example Boy merry go round Torque negligible so AL At 0 L1 71mm Lf mszf Iggy7 Example Meteorite hits satellite A1552S 0 AE Use AE 0 to find AEW Angular kinematics Replace linear variables with angular ones i Z7 7 w 37 p mi 7 L Iw F 7 739 Rigid body rotation AL TAt implies wf M At Angular acceleration is a T I For constant torque angular position update 6f 9 wavAt way wf w 2 Bohr Atom Angular i nomentum is quantized litmmpl rp N h Bohr radius r N 2 Bohr 7147r50254mg 7 7136 eV 2N27L2 N2 energy levels E Chapter 1 Entropy Limits on the Possible Einstein Model for 3d lattice Nosciuam 3Nat0m ksymmmm 4ksatom Microstates Formula 9 liailvl zh Entropy S kB In 9 Equilibrium for two blocks Stat S1S2 is i naximized 2nd Law of Thermodynamics A closed system will tend toward i naximum entropy Temper ature IT E dSdEW Specific heat capacity C AEatomAT Boltzmann Distribution QEe EkBT 32 gt W267 Mv2kBT Boltzmann factor e EkBT MaxwellBoltzmann speed distribution 131 47139 Mi113T Average Kmms for an ideal Kmms MiIZ ngT Specific Heat of a diatomic CV ngT 3 vib ngT gt
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