Capítulo. of Particles: Energy and Momentum Methods
|
|
- Caroline French
- 6 years ago
- Views:
Transcription
1 Capíulo 5 Kieics of Paicles: Eegy ad Momeum Mehods
2 Mecáica II Coes Ioducio Wok of a Foce Piciple of Wok & Eegy pplicaios of he Piciple of Wok & Eegy Powe ad Efficiecy Sample Poblem 3. Sample Poblem 3. Sample Poblem 3.3 Sample Poblem 3.4 Sample Poblem 3.5 Poeial Eegy Cosevaive Foces Cosevaio of Eegy Moio Ude a Cosevaive Ceal Foce Escuela Técica Supeio de Igeieos Idusiales Sample Poblem 3.6 Sample Poblem 3.7 Sample Poblem 3.9 Piciple of Impulse ad Momeum Impulsive Moio Sample Poblem 3.0 Sample Poblem 3. Sample Poblem 3. Impac Diec Ceal Impac Oblique Ceal Impac Poblems Ivolvig Eegy ad Momeum Sample Poblem 3.4 Sample Poblem 3.5 Sample Poblems 3.6 Sample Poblem!
3 Mecáica II Piciple of Impulse ad Momeum Dimesios of he impulse of a foce ae foce*ime. Uis fo he impulse of a foce ae ( kg m s ) s kg m s N s Fom Newo s secod law, d F ( mv ) mv liea momeum d Fd d mv Fd Imp Fd mv ( ) mv + Imp mv impulse of mv he foce F The fial momeum of he paicle ca be obaied by addig vecoially is iiial momeum ad he impulse of he foce duig he ime ieval. Escuela Técica Supeio de Igeieos Idusiales 5-3
4 Mecáica II Impulsive Moio Foce acig o a paicle duig a vey sho ime ieval ha is lage eough o cause a sigifica chage i momeum is called a impulsive foce. Whe impulsive foces ac o a paicle, mv F m + v Whe a baseball is suck by a ba, coac occus ove a sho ime ieval bu foce is lage eough o chage sese of ball moio. Noimpulsive foces ae foces fo which F is small ad heefoe, may be egleced. Escuela Técica Supeio de Igeieos Idusiales 5-4
5 Mecáica II Sample Poblem 3.0 SOLUTION: pply he piciple of impulse ad momeum. The impulse is equal o he poduc of he cosa foces ad he ime ieval. auomobile weighig 4000 lb is dive dow a 5 o iclie a a speed of 60 mi/h whe he bakes ae applied, causig a cosa oal bakig foce of 500 lb. Deemie he ime equied fo he auomobile o come o a sop. Escuela Técica Supeio de Igeieos Idusiales 5-5
6 Mecáica II Sample Poblem 3.0 SOLUTION: pply he piciple of impulse ad momeum. mv Imp m + v Takig compoes paallel o he iclie, mv ( W si 5 ) F 0 ( 88f s) + ( 4000si 5 ) s Escuela Técica Supeio de Igeieos Idusiales 5-6
7 Mecáica II Sample Poblem 3. SOLUTION: pply he piciple of impulse ad momeum i ems of hoizoal ad veical compoe equaios. 4 oz baseball is piched wih a velociy of 80 f/s. fe he ball is hi by he ba, i has a velociy of 0 f/s i he diecio show. If he ba ad ball ae i coac fo 0.05 s, deemie he aveage impulsive foce exeed o he ball duig he impac. Escuela Técica Supeio de Igeieos Idusiales 5-7
8 Mecáica II Sample Poblem 3. y x SOLUTION: pply he piciple of impulse ad momeum i ems of hoizoal ad veical compoe equaios. mv Imp m + v x compoe equaio: mv + F F 89lb x x mv cos ( 80) + F ( 0.5) ( 0cos 40 ) y compoe equaio: 0 + F mv si 40 F F y y y x lb F 89 lb i lb j, F 97.5 ( 0.5) ( 0cos 40 ) ( ) ( ) lb Escuela Técica Supeio de Igeieos Idusiales 5-8
9 Mecáica II Sample Poblem 3. 0 kg package dops fom a chue io a 4 kg ca wih a velociy of 3 m/s. Kowig ha he ca is iiially a es ad ca oll feely, deemie (a) he fial velociy of he ca, (b) he impulse exeed by he ca o he package, ad (c) he facio of he iiial eegy los i he impac. SOLUTION: pply he piciple of impulse ad momeum o he package-ca sysem o deemie he fial velociy. pply he same piciple o he package aloe o deemie he impulse exeed o i fom he chage i is momeum. Escuela Técica Supeio de Igeieos Idusiales 5-9
10 Mecáica II Sample Poblem 3. SOLUTION: pply he piciple of impulse ad momeum o he package-ca sysem o deemie he fial velociy. y x m p v + ( mp + mc ) Imp v x compoes: m v cos ( m + m ) p ( 0 kg)( 3 m/s) cos30 ( 0 kg + 5 kg) v p c v v 0.74 m/s Escuela Técica Supeio de Igeieos Idusiales 5-0
11 Mecáica II Sample Poblem 3. pply he same piciple o he package aloe o deemie he impulse exeed o i fom he chage i is momeum. y x m p v + Imp mpv x compoes: m p v cos30 + F x m ( 0 kg)( 3 m/s) cos30 + Fx ( 0 kg) v p v F x 8.56 N s y compoes: m p v si30 + F 0 ( 0 kg)( 3 m/s) si30 + F 0 y y F y 5N s ( 8.56 N s) i + ( 5 N s) j F 3.9 N s Imp F Escuela Técica Supeio de Igeieos Idusiales 5 -
12 Mecáica II Sample Poblem 3. To deemie he facio of eegy los, T T m p v ( 0 kg)( 3m s) 45 J ( m + m ) v ( 0 kg + 5 kg)( 0.74m s) 9.63 J p c T T 45 J 9.63 J 45 J T Escuela Técica Supeio de Igeieos Idusiales 5 -
13 Mecáica II Impac Impac: Collisio bewee wo bodies which occus duig a small ime ieval ad duig which he bodies exe lage foces o each ohe. Lie of Impac: Commo omal o he sufaces i coac duig impac. Diec Ceal Impac Ceal Impac: Impac fo which he mass cees of he wo bodies lie o he lie of impac; ohewise, i is a ecceic impac.. Diec Impac: Impac fo which he velociies of he wo bodies ae dieced alog he lie of impac. Oblique Ceal Impac Oblique Impac: Impac fo which oe o boh of he bodies move alog a lie ohe ha he lie of impac. Escuela Técica Supeio de Igeieos Idusiales 5-3
14 Mecáica II Diec Ceal Impac Escuela Técica Supeio de Igeieos Idusiales odies movig i he same saigh lie, v > v. Upo impac he bodies udego a peiod of defomaio, a he ed of which, hey ae i coac ad movig a a commo velociy. peiod of esiuio follows duig which he bodies eihe egai hei oigial shape o emai pemaely defomed. Wish o deemie he fial velociies of he wo bodies. The oal momeum of he wo body sysem is peseved, m v + m v m v + m v secod elaio bewee he fial velociies is equied. 5-4
15 Mecáica II Diec Ceal Impac Peiod of defomaio: Peiod of esiuio: m v Pd m m u Rd m v simila aalysis of paicle yields Combiig he elaios leads o he desied secod elaio bewee he fial velociies. u e coefficie of Rd Pd 0 e v u e u v v v u v v u e ( v v ) esiuio Pefecly plasic impac, e 0: Pefecly elasic impac, e : Toal eegy ad oal momeum coseved. v v v m v + mv ( m + m )v v v v v Escuela Técica Supeio de Igeieos Idusiales 5-5
16 Mecáica II Oblique Ceal Impac Fial velociies ae ukow i magiude ad diecio. Fou equaios ae equied. No ageial impulse compoe; ageial compoe of momeum fo each paicle is coseved. Nomal compoe of oal momeum of he wo paicles is coseved. Nomal compoes of elaive velociies befoe ad afe impac ae elaed by he coefficie of esiuio. Escuela Técica Supeio de Igeieos Idusiales ( v ) ( v ) ( v ) ( v ) ( v ) + m ( v ) m( v ) + m ( v ) m [ ] ( v ) ( v ) e ( v ) ( v ) 5-6
17 Mecáica II Oblique Ceal Impac lock cosaied o move alog hoizoal suface. Impulses fom ieal foces F ad F alog he axis ad fom exeal foce F ex exeed by hoizoal suface ad dieced alog he veical o he suface. Fial velociy of ball ukow i diecio ad magiude ad ukow fial block velociy magiude. Thee equaios equied. Escuela Técica Supeio de Igeieos Idusiales 5-7
18 Mecáica II Oblique Ceal Impac Tageial momeum of ball is coseved. Toal hoizoal momeum of block ad ball is coseved. Nomal compoe of elaive velociies of block ad ball ae elaed by coefficie of esiuio. ( v ) ( v ) ( v ) + m ( v ) x m( v ) + m ( v ) x m [ ] ( v ) ( v ) e ( v ) ( v ) Noe: Validiy of las expessio does o follow fom pevious elaio fo he coefficie of esiuio. simila bu sepaae deivaio is equied. Escuela Técica Supeio de Igeieos Idusiales 5-8
19 Mecáica II Poblems Ivolvig Eegy ad Momeum Thee mehods fo he aalysis of kieics poblems: - Diec applicaio of Newo s secod law - Mehod of wok ad eegy - Mehod of impulse ad momeum Selec he mehod bes suied fo he poblem o pa of a poblem ude cosideaio. Escuela Técica Supeio de Igeieos Idusiales 5-9
20 Mecáica II Sample Poblem 3.4 SOLUTION: Resolve ball velociy io compoes omal ad ageial o wall. Impulse exeed by he wall is omal o he wall. Compoe of ball momeum ageial o wall is coseved. ball is how agais a ficioless, veical wall. Immediaely befoe he ball sikes he wall, is velociy has a magiude v ad foms agle of 30 o wih he hoizoal. Kowig ha e 0.90, deemie he magiude ad diecio of he velociy of he ball as i ebouds fom he wall. ssume ha he wall has ifiie mass so ha wall velociy befoe ad afe impac is zeo. pply coefficie of esiuio elaio o fid chage i omal elaive velociy bewee wall ad ball, i.e., he omal ball velociy. Escuela Técica Supeio de Igeieos Idusiales 5-0
21 Mecáica II Sample Poblem 3.4 SOLUTION: Resolve ball velociy io compoes paallel ad pepedicula o wall. v vcos v v vsi v Compoe of ball momeum ageial o wall is coseved. v v v pply coefficie of esiuio elaio wih zeo wall velociy. 0 v v e 0.9 ( v 0) ( 0.866v) 0.779v v 0.779vλ vλ v 0.96v a Escuela Técica Supeio de Igeieos Idusiales 5 -
22 Mecáica II Sample Poblem 3.5 SOLUTION: Resolve he ball velociies io compoes omal ad ageial o he coac plae. Tageial compoe of momeum fo each ball is coseved. The magiude ad diecio of he velociies of wo ideical ficioless balls befoe hey sike each ohe ae as show. ssumig e 0.9, deemie he magiude ad diecio of he velociy of each ball afe he impac. Toal omal compoe of he momeum of he wo ball sysem is coseved. The omal elaive velociies of he balls ae elaed by he coefficie of esiuio. Solve he las wo equaios simulaeously fo he omal velociies of he balls afe he impac. Escuela Técica Supeio de Igeieos Idusiales 5 -
23 Mecáica II Sample Poblem 3.5 SOLUTION: Resolve he ball velociies io compoes omal ad ageial o he coac plae. ( v ) v cos f s ( v ) v si f s ( v ) v cos60 0.0f s ( v ) v si f s Tageial compoe of momeum fo each ball is coseved. ( v ) ( v ) 5.0f s ( v ) ( v ) 34.6f s Toal omal compoe of he momeum of he wo ball sysem is coseved. m( v) ( ) ( ) ( + m v m v + m v ) m( 6.0) + m( 0.0) m( v ) + ( m v ) ( v ) + ( v ) 6. 0 Escuela Técica Supeio de Igeieos Idusiales 5-3
24 Mecáica II Sample Poblem 3.5 The omal elaive velociies of he balls ae elaed by he coefficie of esiuio. v v e v v [ ] ( ) ( ) ( ) ( ) 0.90[ 6.0 ( 0.0) ] 4. 4 Solve he las wo equaios simulaeously fo he omal velociies of he balls afe he impac. ( v ) 7.7f s ( ) 3.7f s v v v v v 7.7λ + 5.0λ f s a λ λ 4.9f s a Escuela Técica Supeio de Igeieos Idusiales 5-4
25 Mecáica II Sample Poblem 3.6 SOLUTION: Deemie oieaio of impac lie of acio. The momeum compoe of ball ageial o he coac plae is coseved. all is hagig fom a iexesible cod. ideical ball is eleased fom es whe i is jus ouchig he cod ad acquies a velociy v 0 befoe sikig ball. ssumig pefecly elasic impac (e ) ad o ficio, deemie he velociy of each ball immediaely afe impac. Escuela Técica Supeio de Igeieos Idusiales The oal hoizoal momeum of he wo ball sysem is coseved. The elaive velociies alog he lie of acio befoe ad afe he impac ae elaed by he coefficie of esiuio. Solve he las wo expessios fo he velociy of ball alog he lie of acio ad he velociy of ball which is hoizoal. 5-5
26 Mecáica II Sample Poblem 3.6 siθ 0.5 θ 30 SOLUTION: Deemie oieaio of impac lie of acio. The momeum compoe of ball ageial o he coac plae is coseved. mv + F mv mv 0 ( v ) 0.5v0 ( ) si m v The oal hoizoal (x compoe) momeum of he wo ball sysem is coseved. mv + T mv + mv m( v ) cos30 m( v ) ( 0.5v0 ) cos30 ( v ) ( v ) + v 0.433v0 si30 mv si 30 v Escuela Técica Supeio de Igeieos Idusiales 5-6
27 Mecáica II Sample Poblem 3.6 The elaive velociies alog he lie of acio befoe ad afe he impac ae elaed by he coefficie of esiuio. [ ] ( v ) ( v ) e ( v) ( v ) v si 30 ( v ) v0 cos30 0.5v ( v ) 0.866v0 0 Solve he las wo expessios fo he velociy of ball alog he lie of acio ad he velociy of ball which is hoizoal. ( v ) 0.50v0 v v0 v v v 0 0.7v α v λ 0.50v λ 0.693v β a Escuela Técica Supeio de Igeieos Idusiales 5-7
28 Mecáica II Sample Poblem kg block is dopped fom a heigh of m oo he he 0 kg pa of a spig scale. ssumig he impac o be pefecly plasic, deemie he maximum deflecio of he pa. The cosa of he spig is k 0 kn/m. SOLUTION: pply he piciple of cosevaio of eegy o deemie he velociy of he block a he isa of impac. Sice he impac is pefecly plasic, he block ad pa move ogehe a he same velociy afe impac. Deemie ha velociy fom he equieme ha he oal momeum of he block ad pa is coseved. pply he piciple of cosevaio of eegy o deemie he maximum deflecio of he spig. Escuela Técica Supeio de Igeieos Idusiales 5-8
29 Mecáica II Sample Poblem 3.7 SOLUTION: pply piciple of cosevaio of eegy o deemie velociy of he block a isa of impac. T T T 0 + V m T J V ( v ) ( 30)( v ) W + V y ( 30)( 9.8)( ) 588 J 0 ( 30)( v ) + 0 ( v ) 6.6m s V Deemie velociy afe impac fom equieme ha oal momeum of he block ad pa is coseved. m( v) + m( v ) ( m + m ) v3 ( )( 6.6) + 0 ( ) v v 4.70m s Escuela Técica Supeio de Igeieos Idusiales 5-9
30 Mecáica II Sample Poblem 3.7 x Iiial spig deflecio due o pa weigh: 3 W k ( )( 9.8) m pply he piciple of cosevaio of eegy o deemie he maximum deflecio of he spig. T V T V T V V ( m + m ) v ( )( 4.7) g g + V + V e kx e m ( 0 0 )( ) ( W + W )( h) 3 ( x ) 4 x3 + ( 0 0 ) x ( x ) ( 0 0 ) x x 4 + V 3 T 4 + V 4 + kx 4 44 J 0.4 J 3 3 ( x ) + ( 0 0 ) 4 x 4 h x x m m h 0.5 m Escuela Técica Supeio de Igeieos Idusiales 5-30
PHYS PRACTICE EXAM 2
PHYS 1800 PRACTICE EXAM Pa I Muliple Choice Quesions [ ps each] Diecions: Cicle he one alenaive ha bes complees he saemen o answes he quesion. Unless ohewise saed, assume ideal condiions (no ai esisance,
More informationSupplementary Information
Supplemeay Ifomaio No-ivasive, asie deemiaio of he coe empeaue of a hea-geeaig solid body Dea Ahoy, Daipaya Saka, Aku Jai * Mechaical ad Aeospace Egieeig Depame Uivesiy of Texas a Aligo, Aligo, TX, USA.
More informationOne of the common descriptions of curvilinear motion uses path variables, which are measurements made along the tangent t and normal n to the path of
Oe of he commo descipios of cuilie moio uses ph ibles, which e mesuemes mde log he ge d oml o he ph of he picles. d e wo ohogol xes cosideed sepely fo eey is of moio. These coodies poide ul descipio fo
More informationApplications of force vibration. Rotating unbalance Base excitation Vibration measurement devices
Applicaios of foce viaio Roaig ualace Base exciaio Viaio easuee devices Roaig ualace 1 Roaig ualace: Viaio caused y iegulaiies i he disiuio of he ass i he oaig copoe. Roaig ualace 0 FBD 1 FBD x x 0 e 0
More informationComparing Different Estimators for Parameters of Kumaraswamy Distribution
Compaig Diffee Esimaos fo Paamees of Kumaaswamy Disibuio ا.م.د نذير عباس ابراهيم الشمري جامعة النهرين/بغداد-العراق أ.م.د نشات جاسم محمد الجامعة التقنية الوسطى/بغداد- العراق Absac: This pape deals wih compaig
More informationÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s
MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN
More informationCircular Motion. Radians. One revolution is equivalent to which is also equivalent to 2π radians. Therefore we can.
1 Cicula Moion Radians One evoluion is equivalen o 360 0 which is also equivalen o 2π adians. Theefoe we can say ha 360 = 2π adians, 180 = π adians, 90 = π 2 adians. Hence 1 adian = 360 2π Convesions Rule
More informationWORK POWER AND ENERGY Consevaive foce a) A foce is said o be consevaive if he wok done by i is independen of pah followed by he body b) Wok done by a consevaive foce fo a closed pah is zeo c) Wok done
More information( ) ( ) ( ) ( ) (b) (a) sin. (c) sin sin 0. 2 π = + (d) k l k l (e) if x = 3 is a solution of the equation x 5x+ 12=
Eesio Mahemaics Soluios HSC Quesio Oe (a) d 6 si 4 6 si si (b) (c) 7 4 ( si ).si +. ( si ) si + 56 (d) k + l ky + ly P is, k l k l + + + 5 + 7, + + 5 9, ( 5,9) if is a soluio of he equaio 5+ Therefore
More informationProblems and Solutions for Section 3.2 (3.15 through 3.25)
3-7 Problems ad Soluios for Secio 3 35 hrough 35 35 Calculae he respose of a overdamped sigle-degree-of-freedom sysem o a arbirary o-periodic exciaio Soluio: From Equaio 3: x = # F! h "! d! For a overdamped
More informationTransistor configurations: There are three main ways to place a FET/BJT in an architecture:
F3 Mo 0. Amplifie Achiecues Whe a asiso is used i a amplifie, oscillao, file, seso, ec. i will also be a eed fo passive elemes like esisos, capacios ad coils o povide biasig so ha he asiso has he coec
More informationC(p, ) 13 N. Nuclear reactions generate energy create new isotopes and elements. Notation for stellar rates: p 12
Iroducio o sellar reacio raes Nuclear reacios geerae eergy creae ew isoopes ad elemes Noaio for sellar raes: p C 3 N C(p,) 3 N The heavier arge ucleus (Lab: arge) he ligher icomig projecile (Lab: beam)
More informationHarmonic excitation (damped)
Harmoic eciaio damped k m cos EOM: m&& c& k cos c && ζ & f cos The respose soluio ca be separaed io par;. Homogeeous soluio h. Paricular soluio p h p & ζ & && ζ & f cos Homogeeous soluio Homogeeous soluio
More informationINF 5460 Electronic noise Estimates and countermeasures. Lecture 13 (Mot 10) Amplifier Architectures
NF 5460 lecoic oise simaes ad couemeasues Lecue 3 (Mo 0) Amplifie Achiecues Whe a asiso is used i a amplifie, oscillao, file, seso, ec. i will also be a eed fo passive elemes like esisos, capacios ad coils
More informationBy the end of this section you will be able to prove the Chinese Remainder Theorem apply this theorem to solve simultaneous linear congruences
Chapte : Theoy of Modula Aithmetic 8 Sectio D Chiese Remaide Theoem By the ed of this sectio you will be able to pove the Chiese Remaide Theoem apply this theoem to solve simultaeous liea cogueces The
More informationENGINEERING MECHANICS
Egieerig Mechaics CHAPTER ENGINEERING MECHANICS. INTRODUCTION Egieerig mechaics is he sciece ha cosiders he moio of bodies uder he acio of forces ad he effecs of forces o ha moio. Mechaics icludes saics
More informationPhysics 111 Lecture 5 Circular Motion
Physics 111 Lectue 5 Cicula Motion D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Multiple Objects q A block of mass m1 on a ough, hoizontal suface is connected to a ball of mass m by a lightweight
More informationChapter 6 - Work and Energy
Caper 6 - Work ad Eergy Rosedo Pysics 1-B Eploraory Aciviy Usig your book or e iere aswer e ollowig quesios: How is work doe? Deie work, joule, eergy, poeial ad kieic eergy. How does e work doe o a objec
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES In igid body kinemaics, we use he elaionships govening he displacemen, velociy and acceleaion, bu mus also accoun fo he oaional moion of he body. Descipion of he moion of igid
More informationTDCDFT: Nonlinear regime
Lecue 3 TDCDFT: Noliea egime Case A. Ullich Uivesiy of Missoui Beasque Sepembe 2008 Oveview Lecue I: Basic fomalism of TDCDFT Lecue II: Applicaios of TDCDFT i liea espose Lecue III: TDCDFT i he oliea egime
More informationto point uphill and to be equal to its maximum value, in which case f s, max = μsfn
Chapte 6 16. (a) In this situation, we take f s to point uphill and to be equal to its maximum value, in which case f s, max = μsf applies, whee μ s = 0.5. pplying ewton s second law to the block of mass
More informationPHYS Summer Professor Caillault Homework Solutions. Chapter 5
PHYS 1111 - Summe 2007 - Pofesso Caillault Homewok Solutions Chapte 5 7. Pictue the Poblem: The ball is acceleated hoizontally fom est to 98 mi/h ove a distance of 1.7 m. Stategy: Use equation 2-12 to
More informationENGI 4430 Advanced Calculus for Engineering Faculty of Engineering and Applied Science Problem Set 9 Solutions [Theorems of Gauss and Stokes]
ENGI 44 Avance alculus fo Engineeing Faculy of Engineeing an Applie cience Poblem e 9 oluions [Theoems of Gauss an okes]. A fla aea A is boune by he iangle whose veices ae he poins P(,, ), Q(,, ) an R(,,
More information1 Notes on Little s Law (l = λw)
Copyrigh c 26 by Karl Sigma Noes o Lile s Law (l λw) We cosider here a famous ad very useful law i queueig heory called Lile s Law, also kow as l λw, which assers ha he ime average umber of cusomers i
More informationDYNAMIC OCEANOGRAPHY
DYNAMIC OCEANOGRAPY JAN ERIK WEER Depame of Geoscieces ecio fo Meeoolog ad Oceaogaph Uivesi of Oslo 9..4 CONTENT. ALLOW-WATER TEORY, QUAI-OMOGENEOU OCEAN. Iviscid moio, poeial voici.3. Liea waves i he
More informationCalculus BC 2015 Scoring Guidelines
AP Calculus BC 5 Scorig Guidelies 5 The College Board. College Board, Advaced Placeme Program, AP, AP Ceral, ad he acor logo are regisered rademarks of he College Board. AP Ceral is he official olie home
More informationOn imploding cylindrical and spherical shock waves in a perfect gas
J. Fluid Mech. (2006), vol. 560, pp. 103 122. c 2006 Cambidge Uivesiy Pess doi:10.1017/s0022112006000590 Pied i he Uied Kigdom 103 O implodig cylidical ad spheical shock waves i a pefec gas By N. F. PONCHAUT,
More informationME 321 Kinematics and Dynamics of Machines S. Lambert Winter 2002
ME 31 Kiemaic ad Dyamic o Machie S. Lamber Wier 6.. Forced Vibraio wih Dampig Coider ow he cae o orced vibraio wih dampig. Recall ha he goverig diereial equaio i: m && c& k F() ad ha we will aume ha he
More informationGEF DYNAMIC OCEANOGRAPHY: Waves and wave-induced mass transport in the ocean
GEF46 - DYNAMIC OCEANOGRAPHY: Waves ad wave-iduced mass aspo i he ocea JAN ERIK H. WEBER Depame of Geoscieces ecio fo Meeoolog ad Oceaogaph Uivesi of Oslo E-mail: j.e.webe@geo.uio.o Auum 3 CONTENT I. GOVERNING
More informationS, we call the base curve and the director curve. The straight lines
Developable Ruled Sufaces wih Daboux Fame i iowsi -Space Sezai KIZILTUĞ, Ali ÇAKAK ahemaics Depame, Faculy of As ad Sciece, Ezica Uivesiy, Ezica, Tuey ahemaics Depame, Faculy of Sciece, Aau Uivesiy, Ezuum,
More informationF D D D D F. smoothed value of the data including Y t the most recent data.
Module 2 Forecasig 1. Wha is forecasig? Forecasig is defied as esimaig he fuure value ha a parameer will ake. Mos scieific forecasig mehods forecas he fuure value usig pas daa. I Operaios Maageme forecasig
More informationLet s express the absorption of radiation by dipoles as a dipole correlation function.
MIT Deparme of Chemisry 5.74, Sprig 004: Iroducory Quaum Mechaics II Isrucor: Prof. Adrei Tokmakoff p. 81 Time-Correlaio Fucio Descripio of Absorpio Lieshape Le s express he absorpio of radiaio by dipoles
More information5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( )
5-1. We apply Newon s second law (specfcally, Eq. 5-). (a) We fnd he componen of he foce s ( ) ( ) F = ma = ma cos 0.0 = 1.00kg.00m/s cos 0.0 = 1.88N. (b) The y componen of he foce s ( ) ( ) F = ma = ma
More informationCameras and World Geometry
Caeas ad Wold Geoe How all is his woa? How high is he caea? Wha is he caea oaio w. wold? Which ball is close? Jaes Has Thigs o eebe Has Pihole caea odel ad caea (pojecio) ai Hoogeeous coodiaes allow pojecio
More informationECSE Partial fraction expansion (m<n) 3 types of poles Simple Real poles Real Equal poles
ECSE- Lecue. Paial facio expasio (m
More information2 f(x) dx = 1, 0. 2f(x 1) dx d) 1 4t t6 t. t 2 dt i)
Mah PracTes Be sure o review Lab (ad all labs) There are los of good quesios o i a) Sae he Mea Value Theorem ad draw a graph ha illusraes b) Name a impora heorem where he Mea Value Theorem was used i he
More informationComputer Propagation Analysis Tools
Compue Popagaion Analysis Tools. Compue Popagaion Analysis Tools Inoducion By now you ae pobably geing he idea ha pedicing eceived signal sengh is a eally impoan as in he design of a wieless communicaion
More informationS n. = n. Sum of first n terms of an A. P is
PROGREION I his secio we discuss hree impora series amely ) Arihmeic Progressio (A.P), ) Geomeric Progressio (G.P), ad 3) Harmoic Progressio (H.P) Which are very widely used i biological scieces ad humaiies.
More informationMomentum and Collisions
SOLUTIONS TO PROBLES Section 8. P8. m 3.00 kg, (a) omentum and Collisions Linea omentum and Its Consevation v ( 3.00î 4.00ĵ ) m s p mv ( 9.00î.0ĵ ) kg m s Thus, p x 9.00 kg m s and p y.0 kg m s. p p x
More informationOutline. Review Homework Problem. Review Homework Problem II. Review Dimensionless Problem. Review Convection Problem
adial diffsio eqaio Febay 4 9 Diffsio Eqaios i ylidical oodiaes ay aeo Mechaical Egieeig 5B Seia i Egieeig Aalysis Febay 4, 9 Olie eview las class Gadie ad covecio boday codiio Diffsio eqaio i adial coodiaes
More informationToday - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations
Today - Lecue 13 Today s lecue coninue wih oaions, oque, Noe ha chapes 11, 1, 13 all inole oaions slide 1 eiew Roaions Chapes 11 & 1 Viewed fom aboe (+z) Roaional, o angula elociy, gies angenial elociy
More informationLecture 2: Stress. 1. Forces Surface Forces and Body Forces
Lectue : Stess Geophysicists study pheomea such as seismicity, plate tectoics, ad the slow flow of ocks ad mieals called ceep. Oe way they study these pheomea is by ivestigatig the defomatio ad flow of
More information= 4 3 π( m) 3 (5480 kg m 3 ) = kg.
CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential
More informationSuppose we have observed values t 1, t 2, t n of a random variable T.
Sppose we have obseved vales, 2, of a adom vaable T. The dsbo of T s ow o belog o a cea ype (e.g., expoeal, omal, ec.) b he veco θ ( θ, θ2, θp ) of ow paamees assocaed wh s ow (whee p s he mbe of ow paamees).
More informationNeutron Slowing Down Distances and Times in Hydrogenous Materials. Erin Boyd May 10, 2005
Neu Slwig Dw Disaces ad Times i Hydgeus Maeials i Byd May 0 005 Oulie Backgud / Lecue Maeial Neu Slwig Dw quai Flux behavi i hydgeus medium Femi eame f calculaig slwig dw disaces ad imes. Bief deivai f
More informationFresnel Dragging Explained
Fresel Draggig Explaied 07/05/008 Decla Traill Decla@espace.e.au The Fresel Draggig Coefficie required o explai he resul of he Fizeau experime ca be easily explaied by usig he priciples of Eergy Field
More informationRoot Finding. x 1. The solution of nonlinear equations and systems. The Newton-Raphson iteration for locating zeros. Vageli Coutsias, UNM, Fall 02
Roo idig The solio of oliea eqaios ad sysems Vageli Cosias, UNM, all The Newo-Raphso ieaio fo locaig zeos f ( )/ f ( ) ' f '( ) f ( ) Eample: fidig he sqae oo f f ( ) '( ) a a a Deails: iiial ieae ms be
More informationCHAPTER 25 ELECTRIC POTENTIAL
CHPTE 5 ELECTIC POTENTIL Potential Diffeence and Electic Potential Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic foce on the paticle given by F=E. When
More informationChemical Engineering 374
Chemical Egieerig 374 Fluid Mechaics NoNeoia Fluids Oulie 2 Types ad properies of o-neoia Fluids Pipe flos for o-neoia fluids Velociy profile / flo rae Pressure op Fricio facor Pump poer Rheological Parameers
More informationMovie Review Part One due Tuesday (in class) please print
Movie Review Pat One due Tuesday (in class) please pint Test in class on Fiday. You may stat at 8:30 if you want. (The topic of powe is not on test.) Chaptes 4-6 Main Ideas in Class Today Afte class, you
More informationPROBLEM Copyright McGraw-Hill Education. Permission required for reproduction or display. SOLUTION. v 1 = 4 km/hr = 1.
PROLEM 13.119 35,000 Mg ocea lier has a iitial velocity of 4 km/h. Neglectig the frictioal resistace of the water, determie the time required to brig the lier to rest by usig a sigle tugboat which exerts
More informationTHE SOIL STRUCTURE INTERACTION ANALYSIS BASED ON SUBSTRUCTURE METHOD IN TIME DOMAIN
THE SOIL STRUCTURE INTERACTION ANALYSIS BASED ON SUBSTRUCTURE METHOD IN TIME DOMAIN Musafa KUTANIS Ad Muzaffe ELMAS 2 SUMMARY I is pape, a vaiaio of e FEM wic is so-called geeal subsucue meod is caied
More informationBINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =
wwwskshieduciocom BINOMIAL HEOREM OBJEIVE PROBLEMS he coefficies of, i e esio of k e equl he k /7 If e coefficie of, d ems i e i AP, e e vlue of is he coefficies i e,, 7 ems i e esio of e i AP he 7 7 em
More informationPhysics 101 Lecture 6 Circular Motion
Physics 101 Lectue 6 Cicula Motion Assist. Pof. D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Equilibium, Example 1 q What is the smallest value of the foce F such that the.0-kg block will not slide
More informationphysicsandmathstutor.com
physicsadmathstuto.com physicsadmathstuto.com Jue 005. A cuve has equatio blak x + xy 3y + 16 = 0. dy Fid the coodiates of the poits o the cuve whee 0. dx = (7) Q (Total 7 maks) *N03B034* 3 Tu ove physicsadmathstuto.com
More information20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241
Chapte 0 Electicity 41 0-9 ELECTRIC IELD LINES Goals Illustate the concept of electic field lines. Content The electic field can be symbolized by lines of foce thoughout space. The electic field is stonge
More informationc) (6) Assuming the tires do not skid, what coefficient of static friction between tires and pavement is needed?
Geneal Physics I Exam 2 - Chs. 4,5,6 - Foces, Cicula Motion, Enegy Oct. 10, 2012 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults with
More informationBINOMIAL THEOREM An expression consisting of two terms, connected by + or sign is called a
BINOMIAL THEOREM hapte 8 8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4 5y, etc., ae all biomial epessios. 8.. Biomial theoem If
More informationCOMBUSTION. TA : Donggi Lee ROOM: Building N7-2 #3315 TELEPHONE : 3754 Cellphone : PROF.
COMBUSIO ROF. SEUG WOOK BAEK DEARME OF AEROSACE EGIEERIG, KAIS, I KOREA ROOM: Buldng 7- #334 ELEHOE : 3714 Cellphone : 1-53 - 5934 swbaek@kast.a.kr http://proom.kast.a.kr A : Dongg Lee ROOM: Buldng 7-
More informationKEY. Math 334 Midterm II Fall 2007 section 004 Instructor: Scott Glasgow
KEY Math 334 Midtem II Fall 7 sectio 4 Istucto: Scott Glasgow Please do NOT wite o this exam. No cedit will be give fo such wok. Rathe wite i a blue book, o o you ow pape, pefeably egieeig pape. Wite you
More informationMATH Midterm Solutions
MATH 2113 - Midtem Solutios Febuay 18 1. A bag of mables cotais 4 which ae ed, 4 which ae blue ad 4 which ae gee. a How may mables must be chose fom the bag to guaatee that thee ae the same colou? We ca
More informationEasy. r p 2 f : r p 2i. r p 1i. r p 1 f. m blood g kg. P8.2 (a) The momentum is p = mv, so v = p/m and the kinetic energy is
Chapte 8 Homewok Solutions Easy P8. Assume the velocity of the blood is constant ove the 0.60 s. Then the patient s body and pallet will have a constant velocity of 6 0 5 m 3.75 0 4 m/ s 0.60 s in the
More informationGround Rules. PC1221 Fundamentals of Physics I. Uniform Circular Motion, cont. Uniform Circular Motion (on Horizon Plane) Lectures 11 and 12
PC11 Fudametals of Physics I Lectues 11 ad 1 Cicula Motio ad Othe Applicatios of Newto s Laws D Tay Seg Chua 1 Goud Rules Switch off you hadphoe ad page Switch off you laptop compute ad keep it No talkig
More informationEMA5001 Lecture 3 Steady State & Nonsteady State Diffusion - Fick s 2 nd Law & Solutions
EMA5 Lecue 3 Seady Sae & Noseady Sae ffuso - Fck s d Law & Soluos EMA 5 Physcal Popees of Maeals Zhe heg (6) 3 Noseady Sae ff Fck s d Law Seady-Sae ffuso Seady Sae Seady Sae = Equlbum? No! Smlay: Sae fuco
More informationBINOMIAL THEOREM NCERT An expression consisting of two terms, connected by + or sign is called a
8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4, etc., ae all biomial 5y epessios. 8.. Biomial theoem BINOMIAL THEOREM If a ad b ae
More informationEGN 3321 Final Exam Review Spring 2017
EN 33 l Em Reew Spg 7 *T fshg ech poblem 5 mues o less o pcce es-lke me coss. The opcs o he pcce em e wh feel he bee sessed clss, bu hee m be poblems o he es o lke oes hs pcce es. Use ohe esouces lke he
More informationCONTROL OF TANDEM-TYPE TWO-WHEEL VEHICLE AT VARIOUS NOTION MODES ALONG SPATIAL CURVED LAY OF LINE
COTROL O TADEM-TYPE TWO-WHEEL EHICLE AT ARIOUS OTIO MODES ALOG SPATIAL CURED LAY O LIE АS Besha Kaves КМ Bass Т Kaves LА Toka Wheeled vehicle is cosideed as a maeial poi ude he codiios of o-uifom moveme
More informationPS113 Chapter 5 Dynamics of Uniform Circular Motion
PS113 Chapte 5 Dynamics of Unifom Cicula Motion 1 Unifom cicula motion Unifom cicula motion is the motion of an object taveling at a constant (unifom) speed on a cicula path. The peiod T is the time equied
More informationPHYS 1114, Lecture 21, March 6 Contents:
PHYS 1114, Lectue 21, Mach 6 Contents: 1 This class is o cially cancelled, being eplaced by the common exam Tuesday, Mach 7, 5:30 PM. A eview and Q&A session is scheduled instead duing class time. 2 Exam
More information6.2 Improving Our 3-D Graphics Pipeline
6.2. IMPROVING OUR 3-D GRAPHICS PIPELINE 8 6.2 Impovig Ou 3-D Gaphics Pipelie We iish ou basic 3D gaphics pipelie wih he implemeaio o pespecive. beoe we do his, we eview homogeeous coodiaes. 6.2. Homogeeous
More informationVECTOR MECHANICS FOR ENGINEERS: Vector Mechanics for Engineers: Dynamics. In the current chapter, you will study the motion of systems of particles.
Seeth Edto CHPTER 4 VECTOR MECHNICS FOR ENINEERS: DYNMICS Fedad P. ee E. Russell Johsto, J. Systems of Patcles Lectue Notes: J. Walt Ole Texas Tech Uesty 003 The Mcaw-Hll Compaes, Ic. ll ghts eseed. Seeth
More informationANSWERS, HINTS & SOLUTIONS HALF COURSE TEST VII (Main)
AIITS-HT-VII-PM-JEE(Mai)-Sol./7 I JEE Advaced 06, FIITJEE Studets bag 6 i Top 00 AIR, 7 i Top 00 AIR, 8 i Top 00 AIR. Studets fom Log Tem lassoom/ Itegated School Pogam & Studets fom All Pogams have qualified
More informationLagrangian & Hamiltonian Mechanics:
XII AGRANGIAN & HAMITONIAN DYNAMICS Iouco Hamlo aaoal Pcple Geealze Cooaes Geealze Foces agaga s Euao Geealze Momea Foces of Cosa, agage Mulples Hamloa Fucos, Cosevao aws Hamloa Dyamcs: Hamlo s Euaos agaga
More informationIdeal Amplifier/Attenuator. Memoryless. where k is some real constant. Integrator. System with memory
Liear Time-Ivaria Sysems (LTI Sysems) Oulie Basic Sysem Properies Memoryless ad sysems wih memory (saic or dyamic) Causal ad o-causal sysems (Causaliy) Liear ad o-liear sysems (Lieariy) Sable ad o-sable
More informationROTATIONAL MOTION PR 1
Eistei Classes, Uit No.,, Vadhma Rig Road Plaza, Vikas Pui Ext., Oute Rig Road New Delhi 8, Ph. : 969, 87 PR ROTATIONAL MOTION Syllabus : Cete of mass of a two-paticles system, Cete of mass of a igid body;
More information= 5! 3! 2! = 5! 3! (5 3)!. In general, the number of different groups of r items out of n items (when the order is ignored) is given by n!
0 Combiatoial Aalysis Copyight by Deiz Kalı 4 Combiatios Questio 4 What is the diffeece betwee the followig questio i How may 3-lette wods ca you wite usig the lettes A, B, C, D, E ii How may 3-elemet
More informationPhysics 30: Chapter 2 Exam Momentum & Impulse
Physics 30: Chaper 2 Exam Momenum & Impulse Name: Dae: Mark: /29 Numeric Response. Place your answers o he numeric response quesions, wih unis, in he blanks a he side of he page. (1 mark each) 1. A golfer
More informationMechanics and Special Relativity (MAPH10030) Assignment 3
(MAPH0030) Assignment 3 Issue Date: 03 Mach 00 Due Date: 4 Mach 00 In question 4 a numeical answe is equied with pecision to thee significant figues Maks will be deducted fo moe o less pecision You may
More informationExam 3: Equation Summary
MAACHUETT INTITUTE OF TECHNOLOGY Depatment of Physics Physics 8. TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t = Exam 3: Equation ummay = Impulse: I F( t ) = p Toque: τ =,P dp F P τ =,P
More informationElectrical Engineering Department Network Lab.
Par:- Elecrical Egieerig Deparme Nework Lab. Deermiaio of differe parameers of -por eworks ad verificaio of heir ierrelaio ships. Objecive: - To deermie Y, ad ABD parameers of sigle ad cascaded wo Por
More informationEDEXCEL NATIONAL CERTIFICATE UNIT 28 FURTHER MATHEMATICS FOR TECHNICIANS OUTCOME 2- ALGEBRAIC TECHNIQUES TUTORIAL 1 - PROGRESSIONS
EDEXCEL NATIONAL CERTIFICATE UNIT 8 FURTHER MATHEMATICS FOR TECHNICIANS OUTCOME - ALGEBRAIC TECHNIQUES TUTORIAL - PROGRESSIONS CONTENTS Be able to apply algebaic techiques Aithmetic pogessio (AP): fist
More informationDiscussion 02 Solutions
STAT 400 Discussio 0 Solutios Spig 08. ~.5 ~.6 At the begiig of a cetai study of a goup of pesos, 5% wee classified as heavy smoes, 30% as light smoes, ad 55% as osmoes. I the fiveyea study, it was detemied
More informationPure Math 30: Explained!
ure Mah : Explaied! www.puremah.com 6 Logarihms Lesso ar Basic Expoeial Applicaios Expoeial Growh & Decay: Siuaios followig his ype of chage ca be modeled usig he formula: (b) A = Fuure Amou A o = iial
More informationCOST OPTIMIZATION OF SLAB MILLING OPERATION USING GENETIC ALGORITHMS
COST OPTIMIZATIO OF SLAB MILLIG OPERATIO USIG GEETIC ALGORITHMS Bhavsa, S.. ad Saghvi, R.C. G H Pael College of Egieeig ad Techology, Vallah Vidyaaga 388 20, Aad, Gujaa E-mail:sake976@yahoo.co.i; ajeshsaghvi@gce.ac.i
More informationPhysics 1A (a) Fall 2010: FINAL Version A 1. Comments:
Physics A (a) Fall 00: FINAL Vesion A Name o Initials: Couse 3-digit Code Comments: Closed book. No wok needs to be shown fo multiple-choice questions.. A helicopte is taveling at 60 m/s at a constant
More informationChapter 5. really hard to start the object moving and then, once it starts moving, you don t have to push as hard to keep it moving.
Chapte 5 Fiction When an object is in motion it is usually in contact with a viscous mateial (wate o ai) o some othe suface. So fa, we have assumed that moving objects don t inteact with thei suoundings
More informationODEs II, Supplement to Lectures 6 & 7: The Jordan Normal Form: Solving Autonomous, Homogeneous Linear Systems. April 2, 2003
ODEs II, Suppleme o Lecures 6 & 7: The Jorda Normal Form: Solvig Auoomous, Homogeeous Liear Sysems April 2, 23 I his oe, we describe he Jorda ormal form of a marix ad use i o solve a geeral homogeeous
More informationDynamics of Rotational Motion
Dynamics of Rotational Motion Toque: the otational analogue of foce Toque = foce x moment am τ = l moment am = pependicula distance though which the foce acts a.k.a. leve am l l l l τ = l = sin φ = tan
More informationSpectrum of The Direct Sum of Operators. 1. Introduction
Specu of The Diec Su of Opeaos by E.OTKUN ÇEVİK ad Z.I.ISMILOV Kaadeiz Techical Uivesiy, Faculy of Scieces, Depae of Maheaics 6080 Tabzo, TURKEY e-ail adess : zaeddi@yahoo.co bsac: I his wok, a coecio
More informationCalculus Limits. Limit of a function.. 1. One-Sided Limits...1. Infinite limits 2. Vertical Asymptotes...3. Calculating Limits Using the Limit Laws.
Limi of a fucio.. Oe-Sided..... Ifiie limis Verical Asympoes... Calculaig Usig he Limi Laws.5 The Squeeze Theorem.6 The Precise Defiiio of a Limi......7 Coiuiy.8 Iermediae Value Theorem..9 Refereces..
More informationChapter 5. Applying Newton s Laws. Newton s Laws. r r. 1 st Law: An object at rest or traveling in uniform. 2 nd Law:
Chapte 5 Applying Newton s Laws Newton s Laws st Law: An object at est o taveling in unifom motion will emain at est o taveling in unifom motion unless and until an extenal foce is applied net ma nd Law:
More informationThe Eigen Function of Linear Systems
1/25/211 The Eige Fucio of Liear Sysems.doc 1/7 The Eige Fucio of Liear Sysems Recall ha ha we ca express (expad) a ime-limied sigal wih a weighed summaio of basis fucios: v ( ) a ψ ( ) = where v ( ) =
More informationQuiz 6--Work, Gravitation, Circular Motion, Torque. (60 pts available, 50 points possible)
Name: Class: Date: ID: A Quiz 6--Wok, Gavitation, Cicula Motion, Toque. (60 pts available, 50 points possible) Multiple Choice, 2 point each Identify the choice that best completes the statement o answes
More informationME 141. Engineering Mechanics
ME 141 Engineeing Mechnics Lecue 13: Kinemics of igid bodies hmd Shhedi Shkil Lecue, ep. of Mechnicl Engg, UET E-mil: sshkil@me.bue.c.bd, shkil6791@gmil.com Websie: eche.bue.c.bd/sshkil Couesy: Veco Mechnics
More informationThe Non-Truncated Bulk Arrival Queue M x /M/1 with Reneging, Balking, State-Dependent and an Additional Server for Longer Queues
Alied Maheaical Sciece Vol. 8 o. 5 747-75 The No-Tucaed Bul Aival Queue M x /M/ wih Reei Bali Sae-Deede ad a Addiioal Seve fo Loe Queue A. A. EL Shebiy aculy of Sciece Meofia Uiveiy Ey elhebiy@yahoo.co
More informationSpring 2001 Physics 2048 Test 3 solutions
Sping 001 Physics 048 Test 3 solutions Poblem 1. (Shot Answe: 15 points) a. 1 b. 3 c. 4* d. 9 e. 8 f. 9 *emembe that since KE = ½ mv, KE must be positive Poblem (Estimation Poblem: 15 points) Use momentum-impulse
More informationReal-time TDDFT simulations within SIESTA. Daniel Sánchez-Portal, Rafi Ullah, Fabiano Corsetti, Miguel Pruneda and Emilio Artacho
Real-ime TDDFT simulaios wihi SIESTA Daiel Sáchez-Poal, Rafi Ullah, Fabiao Cosei, Miguel Pueda ad Emilio Aacho Mai objecive Apply eal-ime simulaios wihi ime-depede desiy fucioal heoy TDDFT o sudy eleco
More informationExistence and Smoothness of Solution of Navier-Stokes Equation on R 3
Ieaioal Joual of Mode Noliea Theoy ad Applicaio, 5, 4, 7-6 Published Olie Jue 5 i SciRes. hp://www.scip.og/joual/ijma hp://dx.doi.og/.436/ijma.5.48 Exisece ad Smoohess of Soluio of Navie-Sokes Equaio o
More informationb) (5) What average force magnitude was applied by the students working together?
Geneal Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibium Nov. 3, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults
More informationCircular-Rotational Motion Mock Exam. Instructions: (92 points) Answer the following questions. SHOW ALL OF YOUR WORK.
AP Physics C Sping, 2017 Cicula-Rotational Motion Mock Exam Name: Answe Key M. Leonad Instuctions: (92 points) Answe the following questions. SHOW ALL OF YOUR WORK. ( ) 1. A stuntman dives a motocycle
More information