ANALYSIS OF KINEMATICS AND KINETOSTATICS OF FOUR-BAR LINKAGE MECHANISM BASED ON GIVEN PROGRAM

Size: px
Start display at page:

Download "ANALYSIS OF KINEMATICS AND KINETOSTATICS OF FOUR-BAR LINKAGE MECHANISM BASED ON GIVEN PROGRAM"

Transcription

1 SINTII POINGS IV INTNTIONL ONGSS "MINS. TNOLОGIS. MTILS." 7 - SUMM SSSION NLSIS O KINMTIS N KINTOSTTIS O OU- LINKG MNISM S ON GIVN POGM W ISSN - PINT ISSN - Pof.soc.. Shl Pof.soc.. Likj. * Pof.ss.. ji. MSc. Qelj M. cul of Mechnicl ngineeing Uniesi of Pishin sn Pishin Kosoo *coesponing uho bsc: In his ppe is pesene Snhesis of fo-b linkge echnis of he lif c eusion. In his echnis e inouce een highe kineic pis. The oeen of he echnis is epee peioicll n i is sufficien o o is kineic su fo n ngle 7 [eg]. The escipion of he echnis oeen cn be pefoe in he gfonlicl o nlicl ph b cenes of spee oens which belong o now link n loop of he cene echnis n he insn cenes belonging o he wo ele oeens. In he kineic nlsis of he fow echniss e use gphicl ehos. These e siple n uniesl king i possible o eeine he posiions eloci n cceleion of he links of n sucue. Wih he pplicion of conepo clculing echnolog he gphicl ehos in he nlsis of echniss ke he igh plce. The eloci of ech link of he echnis linkge h pefos he oeen of he plne cn be shown s e geoeic of he insn cene spee n he spee of oion oun he cene of he insnneous. The nlsis will be pefoe b Mh sofwe while kineosic nlsis will be cie ou using onou Meho coping esuls of wo iffeen sofwe s Mh n Woking Moel. The siulion pees will be copue fo ll poins of he conous of echnis. o he siulions esuls we he use Mh n Woking Moel sofwe s. Kewos: MNISM; OLLOW; TTO; SIGN; VLOIT; LTION; POGM. Inoucion Kineics n nic su of echniss using plns n gphic ehos is known h peissie eo. To e his eo is equie use of nlic ehos especill fo nic su of s echniss whee eo is no llowe. In espie of h wok uing clculions which e equie fo nlic su fo s echniss his eho is equie This ppe hs been elise wih wo pplicion sofwe s: Mh n Woking Moel. In his ppe is pesene fie-b linkge n siple cnk echnis G s shown in he figue below. In his echnis fisl is eeine n. The sses e ope since he oens of inei nee o clcule. The kineic p of he ppe will be coplee b fining he elociies n cceleions of ech poin n G. In his w e eeine he ngul cceleions n elociies of he linkges n. Whees fo he kineosic p will be eeine he ecion foces of he poins: N 6 n which e cing on he leing link. In he picue e shown boies: igh ingle o slie b. ig. : Linkge n cnk echnis w n p n n p p W W 7 n p.8[eg] p cos γ p cos T T 7[eg] G cos sin n cos p sin sin β n cos cos γ 9 eg β sin... sin I VOLUM V P.P

2 .8[eg] cos 9 eg cos cos sin sin n γ β γ β ig. igs fo posiions elociies... eg zih in Soluion Gien cos sin n G Poin sin.8. ig. Velociies n cceleion of poin Poin.. sin cos 78 SINTII POINGS IV INTNTIONL ONGSS "MINS. TNOLОGIS. MTILS." 7 - SUMM SSSION W ISSN - PINT ISSN - I VOLUM V P.P

3 ig. Velociies n cceleion of poin Poin sin cos ig. Velociies n cceleion of poin Poin sin ig. Velociies n cceleion of poin. Kineosic nlsis of he linkge echnis Gien : G eg.eg...7eg sin cos sin cos g Linkge I The equilibiu coniions fo he poin e equl o zeo. Si linkges e use fo he kineosic nlsis. o he fis linkge e gien he following equilibiu coniions n fo he ile poins of he linkge poin n fo he bo ss M. 79 SINTII POINGS IV INTNTIONL ONGSS "MINS. TNOLОGIS. MTILS." 7 - SUMM SSSION W ISSN - PINT ISSN - I VOLUM V P.P

4 ig. Linkge I quilibiu coniions fo he poin nic equions of oion fo link : sin cos cos sin cos Linkge II lso fo he linkge II e wien he equilibiu coniions which e cene bo ss n oen of inei fo he poin. ig. 6. Linkge I quilibiu coniions fo he poin nic equions of oion fo link : cos cos sin Linkge III lso fo he linkge III e wien he equilibiu coniions which e cene M bo ss n oen of inei fo he poin. ig. 7. Linkge I quilibiu coniions fo he poin nic equions of oion fo link : coseg coseg cos g In peious equions e 9 unknown foces-oens: in Whee: i n i e coponens of join foces 8 SINTII POINGS IV INTNTIONL ONGSS "MINS. TNOLОGIS. MTILS." 7 - SUMM SSSION W ISSN - PINT ISSN - I VOLUM V P.P

5 esuls fo posiions: esuls fo ech poin e gien below whee sep ies b. 8 SINTII POINGS IV INTNTIONL ONGSS "MINS. TNOLОGIS. MTILS." 7 - SUMM SSSION W ISSN - PINT ISSN - I VOLUM V P.P

6 SINTII POINGS IV INTNTIONL ONGSS "MINS. TNOLОGIS. MTILS." 7 - SUMM SSSION W ISSN - PINT ISSN - onclusions n ecoenions In his ppe e e he clculions of ll posiions isplceen fo he whole echnis n lso e eeine he plns fo elociies n cceleions fo ech poin. owee in his ppe e shown he ouline plnes of he echnis se s he igs fo ech linkge hough Mh sofwe Si-b linkge echnis igs which e eie b Woking Moel e los siil o he igs eie b Mh Though Woking Moel sofwe e eie he esuls of ecions fo he equilibiu coniions of si b linkge echnis ngul elociies n cceleions fo he poins n fo he ngles n in ie oin hough he con un s he genel conclusion; he esuls eie b boh sofwe se s fo hei igs fo ll poins of he si b linkge echnis e wihin he esonble bounies.. efeences Shl : 8 isenjii i Meknize e Kopjue Ushie esh kulei i Inhinieisë Meknike Pishinë. ehwl W. Luck K.7 esech of ouple ues of Geoeicl Poles of fis Oe ounl of Mechniss n Mnipulos ol. 6 n. pp. -6. Shl he ë Likj n Milin uqi. "Snhesis of echnis bse on gien pog." I Poceeings Volues 6.8 : Siulion fo echnis b Woking Moel sofwe In he secon p of his ppe is cie ou he siulion fo ll poins n G ie epenen of linkge echnis b Woking Moel which is shown in he following. Poiis hisophe G. " noel echnis o pouce figue-eigh-shpe close cues in he hee-iensionl spce." Poceeings of Thi Inenionl onfeence on peiens/pocess/sse Moeling/Siulion & Opiizion hens. 9. Uesh hn. ll. Snhesis of couple cues wih cobine pln c followe echniss b geneic lgoih. Poeeing of n Inenionl onfeence on opue ngineeing n Technolog heng hin. U.S. hn S.V. oshi.. Snhesis n nlsis of couple cues wih cobine pln c followe echniss Inenionl ounl of ngineeing Science n echnolog Vol. No. 6 pp. - ig. 8: igs in Woking Moel fo ngul eloci n cceleion n 8 I VOLUM V P.P

COMPUTER AIDED ANALYSIS OF KINEMATICS AND KINETOSTATICS OF SIX-BAR LINKAGE MECHANISM THROUGH THE CONTOUR METHOD

COMPUTER AIDED ANALYSIS OF KINEMATICS AND KINETOSTATICS OF SIX-BAR LINKAGE MECHANISM THROUGH THE CONTOUR METHOD SINTIFI PROINGS XIV INTRNTIONL ONGRSS "MHINS. THNOLОGIS. MTRILS." 17 - SUMMR SSSION W ISSN 55-X PRINT ISSN 55-1 OMPUTR I NLYSIS OF KINMTIS N KINTOSTTIS OF SIX-R LINKG MHNISM THROUGH TH ONTOUR MTHO Pof.so..

More information

ME 141. Engineering Mechanics

ME 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 information

Technical Vibration - text 2 - forced vibration, rotational vibration

Technical Vibration - text 2 - forced vibration, rotational vibration Technicl Viion - e - foced viion, oionl viion 4. oced viion, viion unde he consn eenl foce The viion unde he eenl foce. eenl The quesion is if he eenl foce e is consn o vying. If vying, wh is he foce funcion.

More information

Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis 2/3/2007 Physics 253

Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis   2/3/2007 Physics 253 Science Adeisemen Inegoenmenl Pnel on Clime Chnge: The Phsicl Science Bsis hp://www.ipcc.ch/spmfeb7.pdf /3/7 Phsics 53 hp://www.fonews.com/pojecs/pdf/spmfeb7.pdf /3/7 Phsics 53 3 Sus: Uni, Chpe 3 Vecos

More information

Derivation of the differential equation of motion

Derivation of the differential equation of motion Divion of h iffnil quion of oion Fis h noions fin h will us fo h ivion of h iffnil quion of oion. Rollo is hough o -insionl isk. xnl ius of h ll isnc cn of ll (O) - IDU s cn of gviy (M) θ ngl of inclinion

More information

Physics 201, Lecture 5

Physics 201, Lecture 5 Phsics 1 Lecue 5 Tod s Topics n Moion in D (Chp 4.1-4.3): n D Kinemicl Quniies (sec. 4.1) n D Kinemics wih Consn Acceleion (sec. 4.) n D Pojecile (Sec 4.3) n Epeced fom Peiew: n Displcemen eloci cceleion

More information

Axis. Axis. Axis. Solid cylinder (or disk) about. Hoop about. Annular cylinder (or ring) about central axis. central axis.

Axis. Axis. Axis. Solid cylinder (or disk) about. Hoop about. Annular cylinder (or ring) about central axis. central axis. Insucos: Fiel/che/Deweile PYSICS DEPATENT PY 48 Em ch 5, 5 Nme pin, ls fis: Signue: On m hono, I he neihe gien no eceie unuhoie i on his eminion. YOU TEST NUBE IS TE 5-DIGIT NUBE AT TE TOP OF EAC PAGE.

More information

when t = 2 s. Sketch the path for the first 2 seconds of motion and show the velocity and acceleration vectors for t = 2 s.(2/63)

when t = 2 s. Sketch the path for the first 2 seconds of motion and show the velocity and acceleration vectors for t = 2 s.(2/63) . The -coordine of pricle in curiliner oion i gien b where i in eer nd i in econd. The -coponen of ccelerion in eer per econd ured i gien b =. If he pricle h -coponen = nd when = find he gniude of he eloci

More information

Ch.4 Motion in 2D. Ch.4 Motion in 2D

Ch.4 Motion in 2D. Ch.4 Motion in 2D Moion in plne, such s in he sceen, is clled 2-dimensionl (2D) moion. 1. Posiion, displcemen nd eloci ecos If he picle s posiion is ( 1, 1 ) 1, nd ( 2, 2 ) 2, he posiions ecos e 1 = 1 1 2 = 2 2 Aege eloci

More information

1. Kinematics of Particles

1. Kinematics of Particles 1. Kinemics o Picles 1.1 Inoducion o Dnmics Dnmics - Kinemics: he sud o he geome o moion; ele displcemen, eloci, cceleion, nd ime, wihou eeence o he cuse o he moion. - Kineics: he sud o he elion eising

More information

() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration

() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration Secion 1.4 Moion in Spce: Velociy nd Acceleion We e going o dive lile deepe ino somehing we ve ledy inoduced, nmely () nd (). Discuss wih you neighbo he elionships beween posiion, velociy nd cceleion you

More information

Classification of Equations Characteristics

Classification of Equations Characteristics Clssiiion o Eqions Cheisis Consie n elemen o li moing in wo imensionl spe enoe s poin P elow. The ph o P is inie he line. The posiion ile is s so h n inemenl isne long is s. Le he goening eqions e epesene

More information

Physics 232 Exam I Feb. 13, 2006

Physics 232 Exam I Feb. 13, 2006 Phsics I Fe. 6 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio. The oio hs peiod o.59 secods. iiil ie i is oud o e 8.66 c o he igh o he equiliiu posiio d oig o he le wih eloci o sec.

More information

LECTURE 5. is defined by the position vectors r, 1. and. The displacement vector (from P 1 to P 2 ) is defined through r and 1.

LECTURE 5. is defined by the position vectors r, 1. and. The displacement vector (from P 1 to P 2 ) is defined through r and 1. LECTURE 5 ] DESCRIPTION OF PARTICLE MOTION IN SPACE -The displcemen, veloci nd cceleion in -D moion evel hei veco nue (diecion) houh he cuion h one mus p o hei sin. Thei full veco menin ppes when he picle

More information

An object moving with speed v around a point at distance r, has an angular velocity. m/s m

An object moving with speed v around a point at distance r, has an angular velocity. m/s m Roion The mosphere roes wih he erh n moions wihin he mosphere clerly follow cure phs (cyclones, nicyclones, hurricnes, ornoes ec.) We nee o epress roion quniiely. For soli objec or ny mss h oes no isor

More information

(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.

(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1. Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)

More information

Control Volume Derivation

Control Volume Derivation School of eospace Engineeing Conol Volume -1 Copyigh 1 by Jey M. Seizman. ll ighs esee. Conol Volume Deiaion How o cone ou elaionships fo a close sysem (conol mass) o an open sysem (conol olume) Fo mass

More information

Motion on a Curve and Curvature

Motion on a Curve and Curvature Moion on Cue nd Cuue his uni is bsed on Secions 9. & 9.3, Chpe 9. All ssigned edings nd execises e fom he exbook Objecies: Mke cein h you cn define, nd use in conex, he ems, conceps nd fomuls lised below:

More information

Faraday s Law. To be able to find. motional emf transformer and motional emf. Motional emf

Faraday s Law. To be able to find. motional emf transformer and motional emf. Motional emf Objecie F s w Tnsfome Moionl To be ble o fin nsfome. moionl nsfome n moionl. 331 1 331 Mwell s quion: ic Fiel D: Guss lw :KV : Guss lw H: Ampee s w Poin Fom Inegl Fom D D Q sufce loop H sufce H I enclose

More information

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s

ÖRNEK 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 information

Today - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations

Today - 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 information

Ans: In the rectangular loop with the assigned direction for i2: di L dt , (1) where (2) a) At t = 0, i1(t) = I1U(t) is applied and (1) becomes

Ans: In the rectangular loop with the assigned direction for i2: di L dt , (1) where (2) a) At t = 0, i1(t) = I1U(t) is applied and (1) becomes omewok # P7-3 ecngul loop of widh w nd heigh h is siued ne ve long wie cing cuen i s in Fig 7- ssume i o e ecngul pulse s shown in Fig 7- Find he induced cuen i in he ecngul loop whose self-inducnce is

More information

Motion. ( (3 dim) ( (1 dim) dt. Equations of Motion (Constant Acceleration) Newton s Law and Weight. Magnitude of the Frictional Force

Motion. ( (3 dim) ( (1 dim) dt. Equations of Motion (Constant Acceleration) Newton s Law and Weight. Magnitude of the Frictional Force Insucos: ield/mche PHYSICS DEPARTMENT PHY 48 Em Sepeme 6, 4 Nme pin, ls fis: Signue: On m hono, I he neihe gien no eceied unuhoied id on his eminion. YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP O

More information

Sharif University of Technology - CEDRA By: Professor Ali Meghdari

Sharif University of Technology - CEDRA By: Professor Ali Meghdari Shaif Univesiy of echnology - CEDRA By: Pofesso Ali Meghai Pupose: o exen he Enegy appoach in eiving euaions of oion i.e. Lagange s Meho fo Mechanical Syses. opics: Genealize Cooinaes Lagangian Euaion

More information

PHYSICS 1210 Exam 1 University of Wyoming 14 February points

PHYSICS 1210 Exam 1 University of Wyoming 14 February points PHYSICS 1210 Em 1 Uniersiy of Wyoming 14 Februry 2013 150 poins This es is open-noe nd closed-book. Clculors re permied bu compuers re no. No collborion, consulion, or communicion wih oher people (oher

More information

USING LOWER CLASS WEIGHTS TO CORRECT AND CHECK THE NONLINEARITY OF BALANCES

USING LOWER CLASS WEIGHTS TO CORRECT AND CHECK THE NONLINEARITY OF BALANCES USING OWER CSS WEIGHTS TO CORRECT ND CHECK THE NONINERITY OF BNCES Tiohy Chnglin Wng, Qiho Yun, hu Reichuh Mele-Toledo Insuens Shnghi Co. d, Shnghi, P R Chin Mele-Toledo GH, Geifensee, Swizelnd BSTRCT

More information

Computer Aided Geometric Design

Computer Aided Geometric Design Copue Aided Geoei Design Geshon Ele, Tehnion sed on ook Cohen, Riesenfeld, & Ele Geshon Ele, Tehnion Definiion 3. The Cile Given poin C in plne nd nue R 0, he ile ih ene C nd dius R is defined s he se

More information

2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.

2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information. Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl

More information

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3 DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl

More information

Forms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics:

Forms of Energy. Mass = Energy. Page 1. SPH4U: Introduction to Work. Work & Energy. Particle Physics: SPH4U: Inroducion o ork ork & Energy ork & Energy Discussion Definiion Do Produc ork of consn force ork/kineic energy heore ork of uliple consn forces Coens One of he os iporn conceps in physics Alernive

More information

ENGI 4430 Advanced Calculus for Engineering Faculty of Engineering and Applied Science Problem Set 9 Solutions [Theorems of Gauss and Stokes]

ENGI 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 information

f(x) dx with An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples dx x x 2

f(x) dx with An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples dx x x 2 Impope Inegls To his poin we hve only consideed inegls f() wih he is of inegion nd b finie nd he inegnd f() bounded (nd in fc coninuous ecep possibly fo finiely mny jump disconinuiies) An inegl hving eihe

More information

Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =

Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = = Mi i fd l Phsic 3 Lecure 4 Min poins of od s lecure: Emple: ddiion of elociies Trjecories of objecs in dimensions: dimensions: g 9.8m/s downwrds ( ) g o g g Emple: A foobll pler runs he pern gien in he

More information

Physics Worksheet Lesson 4: Linear Motion Section: Name:

Physics Worksheet Lesson 4: Linear Motion Section: Name: Physics Workshee Lesson 4: Liner Moion Secion: Nme: 1. Relie Moion:. All moion is. b. is n rbirry coorine sysem wih reference o which he posiion or moion of somehing is escribe or physicl lws re formule.

More information

A 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m

A 1.3 m 2.5 m 2.8 m. x = m m = 8400 m. y = 4900 m 3200 m = 1700 m PHYS : Soluions o Chper 3 Home Work. SSM REASONING The displcemen is ecor drwn from he iniil posiion o he finl posiion. The mgniude of he displcemen is he shores disnce beween he posiions. Noe h i is onl

More information

Chapter 10. Simple Harmonic Motion and Elasticity. Goals for Chapter 10

Chapter 10. Simple Harmonic Motion and Elasticity. Goals for Chapter 10 Chper 0 Siple Hronic Moion nd Elsiciy Gols or Chper 0 o ollow periodic oion o sudy o siple hronic oion. o sole equions o siple hronic oion. o use he pendulu s prooypicl syse undergoing siple hronic oion.

More information

Average & instantaneous velocity and acceleration Motion with constant acceleration

Average & instantaneous velocity and acceleration Motion with constant acceleration Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission

More information

Motion in a Straight Line

Motion in a Straight Line Moion in Srigh Line. Preei reched he mero sion nd found h he esclor ws no working. She wlked up he sionry esclor in ime. On oher dys, if she remins sionry on he moing esclor, hen he esclor kes her up in

More information

One 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

One 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 information

Physics 101 Lecture 4 Motion in 2D and 3D

Physics 101 Lecture 4 Motion in 2D and 3D Phsics 11 Lecure 4 Moion in D nd 3D Dr. Ali ÖVGÜN EMU Phsics Deprmen www.ogun.com Vecor nd is componens The componens re he legs of he righ ringle whose hpoenuse is A A A A A n ( θ ) A Acos( θ) A A A nd

More information

An Exploration of Dynamics of the Moving Mechanism of the Growth Cone

An Exploration of Dynamics of the Moving Mechanism of the Growth Cone Molecules 3 8 7-38 olecules ISSN 4-349 hp://www.pi.o Invie Lecue An Eploion of Dnics of he Movin Mechnis of he owh Cone Ruin Wn Hsuo Hshi 3 Zhin Zhn 4 n un-bo Dun 5 School of Science Donhu Univesi 88 Wes

More information

A GENERAL METHOD TO STUDY THE MOTION IN A NON-INERTIAL REFERENCE FRAME

A GENERAL METHOD TO STUDY THE MOTION IN A NON-INERTIAL REFERENCE FRAME The Inenaional onfeence on opuaional Mechanics an Viual Engineeing OME 9 9 OTOBER 9, Basov, Roania A GENERAL METHOD TO STUDY THE MOTION IN A NON-INERTIAL REFERENE FRAME Daniel onuache, Vlaii Mainusi Technical

More information

Chapter 4 Circular and Curvilinear Motions

Chapter 4 Circular and Curvilinear Motions Chp 4 Cicul n Cuilin Moions H w consi picls moing no long sigh lin h cuilin moion. W fis su h cicul moion, spcil cs of cuilin moion. Anoh mpl w h l sui li is h pojcil..1 Cicul Moion Unifom Cicul Moion

More information

THE DESIGN METHOD OF ROBUST CONTROL BY FLEXIBLE SPACECRAFT. V.Yu. Rutkovsky, S.D. Zemlyakov, V.M. Sukhanov, V.M. Glumov

THE DESIGN METHOD OF ROBUST CONTROL BY FLEXIBLE SPACECRAFT. V.Yu. Rutkovsky, S.D. Zemlyakov, V.M. Sukhanov, V.M. Glumov THE DESIGN METHOD OF ROBUST CONTROL BY FLEXIBLE SPACECRAFT V.Yu. Rukosky, S.D. Zelyko, V.M. Sukhno, V.M. Gluo Insiue of Conol Sciences, Russin Acey of Sciences, Pofsoyuzny 65, 7997, Moscow, Russi Tel:+7(95)334

More information

Equations from The Four Principal Kinetic States of Material Bodies. Copyright 2005 Joseph A. Rybczyk

Equations from The Four Principal Kinetic States of Material Bodies. Copyright 2005 Joseph A. Rybczyk Equions fom he Fou Pinipl Kinei Ses of Meil Bodies Copyigh 005 Joseph A. Rybzyk Following is omplee lis of ll of he equions used in o deied in he Fou Pinipl Kinei Ses of Meil Bodies. Eh equion is idenified

More information

X-Ray Notes, Part III

X-Ray Notes, Part III oll 6 X-y oe 3: Pe X-Ry oe, P III oe Deeo Coe oupu o x-y ye h look lke h: We efe ue of que lhly ffee efo h ue y ovk: Co: C ΔS S Sl o oe Ro: SR S Co o oe Ro: CR ΔS C SR Pevouly, we ee he SR fo ye hv pxel

More information

Homework 5 for BST 631: Statistical Theory I Solutions, 09/21/2006

Homework 5 for BST 631: Statistical Theory I Solutions, 09/21/2006 Homewok 5 fo BST 63: Sisicl Theoy I Soluions, 9//6 Due Time: 5:PM Thusy, on 9/8/6. Polem ( oins). Book olem.8. Soluion: E = x f ( x) = ( x) f ( x) + ( x ) f ( x) = xf ( x) + xf ( x) + f ( x) f ( x) Accoing

More information

Circuits 24/08/2010. Question. Question. Practice Questions QV CV. Review Formula s RC R R R V IR ... Charging P IV I R ... E Pt.

Circuits 24/08/2010. Question. Question. Practice Questions QV CV. Review Formula s RC R R R V IR ... Charging P IV I R ... E Pt. 4/08/00 eview Fomul s icuis cice s BL B A B I I I I E...... s n n hging Q Q 0 e... n... Q Q n 0 e Q I I0e Dischging Q U Q A wie mde of bss nd nohe wie mde of silve hve he sme lengh, bu he dimee of he bss

More information

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration

Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse

More information

WORK 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

Time-Space Model of Business Fluctuations

Time-Space Model of Business Fluctuations Time-Sace Moel of Business Flucuaions Aleei Kouglov*, Mahemaical Cene 9 Cown Hill Place, Suie 3, Eobicoke, Onaio M8Y 4C5, Canaa Email: Aleei.Kouglov@SiconVieo.com * This aicle eesens he esonal view of

More information

Addition & Subtraction of Polynomials

Addition & Subtraction of Polynomials Addiion & Sucion of Polynomil Addiion of Polynomil: Adding wo o moe olynomil i imly me of dding like em. The following ocedue hould e ued o dd olynomil 1. Remove enhee if hee e enhee. Add imil em. Wie

More information

Physics 232 Exam I Feb. 14, 2005

Physics 232 Exam I Feb. 14, 2005 Phsics I Fe., 5 oc. ec # Ne..5 g ss is ched o hoizol spig d is eecuig siple hoic oio wih gul eloci o dissec. gie is i ie i is oud o e 8 c o he igh o he equiliiu posiio d oig o he le wih eloci o.5 sec..

More information

Homework 2 Solutions

Homework 2 Solutions Mah 308 Differenial Equaions Fall 2002 & 2. See he las page. Hoework 2 Soluions 3a). Newon s secon law of oion says ha a = F, an we know a =, so we have = F. One par of he force is graviy, g. However,

More information

D zone schemes

D zone schemes Ch. 5. Enegy Bnds in Cysls 5.. -D zone schemes Fee elecons E k m h Fee elecons in cysl sinα P + cosα cosk α cos α cos k cos( k + π n α k + πn mv ob P 0 h cos α cos k n α k + π m h k E Enegy is peiodic

More information

Available online Journal of Scientific and Engineering Research, 2018, 5(10): Research Article

Available online   Journal of Scientific and Engineering Research, 2018, 5(10): Research Article vilble online www.jse.com Jounl of Scienific n Engineeing Resech, 8, 5():5-58 Resech icle ISSN: 94-6 CODEN(US): JSERBR Soluion of he Poblem of Sess-Sin Se of Physiclly Non-Line Heeiily Plsic Infinie Ple

More information

Axis Thin spherical shell about any diameter

Axis Thin spherical shell about any diameter Insucos: Fiel/che/Deweile PYSICS DEPATET PY 48 Finl Em Apil 5, 5 me pin, ls fis: Signue: On m hono, I he neihe gien no eceie unuhoie i on his eminion. YOU TEST UBE IS TE 5-DIGIT UBE AT TE TOP OF EAC PAGE.

More information

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218

Chapter 2. Motion along a straight line. 9/9/2015 Physics 218 Chper Moion long srigh line 9/9/05 Physics 8 Gols for Chper How o describe srigh line moion in erms of displcemen nd erge elociy. The mening of insnneous elociy nd speed. Aerge elociy/insnneous elociy

More information

Relative and Circular Motion

Relative and Circular Motion Relaie and Cicula Moion a) Relaie moion b) Cenipeal acceleaion Mechanics Lecue 3 Slide 1 Mechanics Lecue 3 Slide 2 Time on Video Pelecue Looks like mosly eeyone hee has iewed enie pelecue GOOD! Thank you

More information

Physics 232 Exam II Mar. 28, 2005

Physics 232 Exam II Mar. 28, 2005 Phi 3 M. 8, 5 So. Se # Ne. A piee o gl, ide o eio.5, h hi oig o oil o i. The oil h ide o eio.4.d hike o. Fo wh welegh, i he iile egio, do ou ge o eleio? The ol phe dieee i gie δ Tol δ PhDieee δ i,il δ

More information

PHYS PRACTICE EXAM 2

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 information

FM Applications of Integration 1.Centroid of Area

FM Applications of Integration 1.Centroid of Area FM Applicions of Inegrion.Cenroid of Are The cenroid of ody is is geomeric cenre. For n ojec mde of uniform meril, he cenroid coincides wih he poin which he ody cn e suppored in perfecly lnced se ie, is

More information

3.1 Velocity: m s. x t. dx dt. x t (1) 3.2 Acceleration: v t. v t. dv dt. (2) s. 3.3 Impulse: (3) s. lim. lim

3.1 Velocity: m s. x t. dx dt. x t (1) 3.2 Acceleration: v t. v t. dv dt. (2) s. 3.3 Impulse: (3) s. lim. lim . unen n eie quniie n uni unen Phi quniie e hoe h n e ie efine, n fo whih he uni e hoen ii, inepenen of ohe phi quniie. o. unen uni Uni So Dienion engh Mee Tie Seon T M Kiog g M uen ineni Apee A igh ineni

More information

Rotations.

Rotations. oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse

More information

The energetic balance of the friction clutches used in automotive

The energetic balance of the friction clutches used in automotive Recen Reseches in Auoic Conol The enegeic blnce of he ficion cluches use in uooive BOROZAN ION SILVIU, MANIU INOCENTIU, ARGESANU VERONICA, KULCSAR RAUL MIKLOS Mechonics Depen Poliehnic Univesiy fo Tiiso,

More information

Computer Propagation Analysis Tools

Computer 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 information

September 20 Homework Solutions

September 20 Homework Solutions College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum

More information

3 Motion with constant acceleration: Linear and projectile motion

3 Motion with constant acceleration: Linear and projectile motion 3 Moion wih consn ccelerion: Liner nd projecile moion cons, In he precedin Lecure we he considered moion wih consn ccelerion lon he is: Noe h,, cn be posiie nd neie h leds o rie of behiors. Clerl similr

More information

Physics Mechanics. Rule #2: LABEL/LIST YOUR KNOWN VALUES AND THOSE DESIRED (Include units!!)

Physics Mechanics. Rule #2: LABEL/LIST YOUR KNOWN VALUES AND THOSE DESIRED (Include units!!) Phic Mechnic Rule #1: DRAW A PICTURE (Picoil Repeenion, Moion Dim, ee-bod Dim) Dw picue o wh he queion i decibin. Ue moion dim nd ee-bod dim o i ou in eein wh i oin on in he queion. Moion Dim: + ee-bod

More information

PHYSICS 102. Intro PHYSICS-ELECTROMAGNETISM

PHYSICS 102. Intro PHYSICS-ELECTROMAGNETISM PHYS 0 Suen Nme: Suen Numbe: FAUTY OF SIENE Viul Miem EXAMINATION PHYSIS 0 Ino PHYSIS-EETROMAGNETISM Emines: D. Yoichi Miyh INSTRUTIONS: Aemp ll 4 quesions. All quesions hve equl weighs 0 poins ech. Answes

More information

e t dt e t dt = lim e t dt T (1 e T ) = 1

e t dt e t dt = lim e t dt T (1 e T ) = 1 Improper Inegrls There re wo ypes of improper inegrls - hose wih infinie limis of inegrion, nd hose wih inegrnds h pproch some poin wihin he limis of inegrion. Firs we will consider inegrls wih infinie

More information

P441 Analytical Mechanics - I. Coupled Oscillators. c Alex R. Dzierba

P441 Analytical Mechanics - I. Coupled Oscillators. c Alex R. Dzierba Lecure 3 Mondy - Deceber 5, 005 Wrien or ls upded: Deceber 3, 005 P44 Anlyicl Mechnics - I oupled Oscillors c Alex R. Dzierb oupled oscillors - rix echnique In Figure we show n exple of wo coupled oscillors,

More information

t v a t area Dynamic Physics for Simulation and Game Programming F a m v v a t x x v t Discrete Dynamics

t v a t area Dynamic Physics for Simulation and Game Programming F a m v v a t x x v t Discrete Dynamics Dynic Physics for Siulion n Ge Progring F Discree Dynics. Force equls ss ies ccelerion (F=) v v v v Mike Biley This work is license uner Creive Coons Aribuion-NonCoercil- NoDerivives.0 Inernionl License

More information

How to Solve System Dynamic s Problems

How to Solve System Dynamic s Problems How o Solve Sye Dynaic Proble A ye dynaic proble involve wo or ore bodie (objec) under he influence of everal exernal force. The objec ay uliaely re, ove wih conan velociy, conan acceleraion or oe cobinaion

More information

Homework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is:

Homework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is: . Homewok 3 MAE 8C Poblems, 5, 7, 0, 4, 5, 8, 3, 30, 3 fom Chpte 5, msh & Btt Point souces emit nuetons/sec t points,,, n 3 fin the flux cuent hlf wy between one sie of the tingle (blck ot). The flux fo

More information

Practice Problems - Week #4 Higher-Order DEs, Applications Solutions

Practice Problems - Week #4 Higher-Order DEs, Applications Solutions Pracice Probles - Wee #4 Higher-Orer DEs, Applicaions Soluions 1. Solve he iniial value proble where y y = 0, y0 = 0, y 0 = 1, an y 0 =. r r = rr 1 = rr 1r + 1, so he general soluion is C 1 + C e x + C

More information

Chapter Direct Method of Interpolation

Chapter Direct Method of Interpolation Chper 5. Direc Mehod of Inerpolion Afer reding his chper, you should be ble o:. pply he direc mehod of inerpolion,. sole problems using he direc mehod of inerpolion, nd. use he direc mehod inerpolns o

More information

Energy Problems 9/3/2009. W F d mgh m s 196J 200J. Understanding. Understanding. Understanding. W F d. sin 30

Energy Problems 9/3/2009. W F d mgh m s 196J 200J. Understanding. Understanding. Understanding. W F d. sin 30 9/3/009 nderanding Energy Proble Copare he work done on an objec o a.0 kg a) In liing an objec 0.0 b) Puhing i up a rap inclined a 30 0 o he ae inal heigh 30 0 puhing 0.0 liing nderanding Copare he work

More information

PHY2053 Summer C 2013 Exam 1 Solutions

PHY2053 Summer C 2013 Exam 1 Solutions PHY053 Sue C 03 E Soluon. The foce G on o G G The onl cobnon h e '/ = doubln.. The peed of lh le 8fulon c 86,8 le 60 n 60n h 4h d 4d fonh.80 fulon/ fonh 3. The dnce eled fo he ene p,, 36 (75n h 45 The

More information

SOME USEFUL MATHEMATICS

SOME USEFUL MATHEMATICS SOME USEFU MAHEMAICS SOME USEFU MAHEMAICS I is esy o mesure n preic he behvior of n elecricl circui h conins only c volges n currens. However, mos useful elecricl signls h crry informion vry wih ime. Since

More information

Introduction to Numerical Analysis. In this lesson you will be taken through a pair of techniques that will be used to solve the equations of.

Introduction to Numerical Analysis. In this lesson you will be taken through a pair of techniques that will be used to solve the equations of. Inroducion o Nuerical Analysis oion In his lesson you will be aen hrough a pair of echniques ha will be used o solve he equaions of and v dx d a F d for siuaions in which F is well nown, and he iniial

More information

Invert and multiply. Fractions express a ratio of two quantities. For example, the fraction

Invert and multiply. Fractions express a ratio of two quantities. For example, the fraction Appendi E: Mnipuling Fions Te ules fo mnipuling fions involve lgei epessions e el e sme s e ules fo mnipuling fions involve numes Te fundmenl ules fo omining nd mnipuling fions e lised elow Te uses of

More information

Circular Motion. Radians. One revolution is equivalent to which is also equivalent to 2π radians. Therefore we can.

Circular 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 information

Reinforcement learning

Reinforcement learning CS 75 Mchine Lening Lecue b einfocemen lening Milos Huskech milos@cs.pi.edu 539 Senno Sque einfocemen lening We wn o len conol policy: : X A We see emples of bu oupus e no given Insed of we ge feedbck

More information

5.1-The Initial-Value Problems For Ordinary Differential Equations

5.1-The Initial-Value Problems For Ordinary Differential Equations 5.-The Iniil-Vlue Problems For Ordinry Differenil Equions Consider solving iniil-vlue problems for ordinry differenil equions: (*) y f, y, b, y. If we know he generl soluion y of he ordinry differenil

More information

CHAPTER 29 ELECTRIC FIELD AND POTENTIAL EXERCISES

CHAPTER 29 ELECTRIC FIELD AND POTENTIAL EXERCISES HPTER ELETRI FIELD ND POTENTIL EXERISES. oulob Newton l M L T 4 k F.. istnce between k so, foce k ( F ( The weight of boy 4 N 4 N wt of boy So,. foce between chges 4 So, foce between chges.6 weight of

More information

BINOMIAL THEOREM OBJECTIVE PROBLEMS in the expansion of ( 3 +kx ) are equal. Then k =

BINOMIAL 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 information

Rotational Motion and the Law of Gravity

Rotational Motion and the Law of Gravity Chape 7 7 Roaional Moion and he Law of Gaiy PROBLEM SOLUTIONS 7.1 (a) Eah oaes adians (360 ) on is axis in 1 day. Thus, ad 1 day 5 7.7 10 ad s 4 1 day 8.64 10 s Because of is oaion abou is axis, Eah bulges

More information

Solutions to Problems : Chapter 19 Problems appeared on the end of chapter 19 of the Textbook

Solutions to Problems : Chapter 19 Problems appeared on the end of chapter 19 of the Textbook Solutions to Poblems Chapte 9 Poblems appeae on the en of chapte 9 of the Textbook 8. Pictue the Poblem Two point chages exet an electostatic foce on each othe. Stategy Solve Coulomb s law (equation 9-5)

More information

Physics 2A HW #3 Solutions

Physics 2A HW #3 Solutions Chper 3 Focus on Conceps: 3, 4, 6, 9 Problems: 9, 9, 3, 41, 66, 7, 75, 77 Phsics A HW #3 Soluions Focus On Conceps 3-3 (c) The ccelerion due o grvi is he sme for boh blls, despie he fc h he hve differen

More information

Primal and Weakly Primal Sub Semi Modules

Primal and Weakly Primal Sub Semi Modules Aein Inenionl Jounl of Conepoy eeh Vol 4 No ; Jnuy 204 Pil nd Wekly Pil ub ei odule lik Bineh ub l hei Depen Jodn Univeiy of iene nd Tehnology Ibid 220 Jodn Ab Le be ouive eiing wih ideniy nd n -ei odule

More information

CHAPTER? 29 ELECTRIC FIELD AND POTENTIAL EXERCISES = 2, N = (5.6) 1 = = = = = Newton

CHAPTER? 29 ELECTRIC FIELD AND POTENTIAL EXERCISES = 2, N = (5.6) 1 = = = = = Newton Downloe fo HPTER? ELETRI FIELD ND POTENTIL EXERISES. oulob Newton l M L T 4 k F.. istnce between k so, foce k ( F ( The weight of boy 4 N 4 N wt of boy.5 So, foce between chges 4 So, foce between chges

More information

Some algorthim for solving system of linear volterra integral equation of second kind by using MATLAB 7 ALAN JALAL ABD ALKADER

Some algorthim for solving system of linear volterra integral equation of second kind by using MATLAB 7 ALAN JALAL ABD ALKADER . Soe lgoi o solving syse o line vole inegl eqion o second ind by sing MATLAB 7 ALAN JALAL ABD ALKADER College o Edcion / Al- Msnsiiy Univesiy Depen o Meics تقديم البحث :-//7 قبول النشر:- //. Absc ( /

More information

Molecular Dynamics Simulations (Leach )

Molecular Dynamics Simulations (Leach ) Molecul Dynmics Simulions Lech 7.-7.5 compue hemlly eged popeies by smpling epesenie phse-spce jecoy i numeicl soluion of he clssicl equions of moion fo sysem of N inecing picles he coupled e.o.m. e: d

More information

CHAPTER 2 KINEMATICS IN ONE DIMENSION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS

CHAPTER 2 KINEMATICS IN ONE DIMENSION ANSWERS TO FOCUS ON CONCEPTS QUESTIONS Physics h Ediion Cunell Johnson Young Sdler Soluions Mnul Soluions Mnul, Answer keys, Insrucor's Resource Mnul for ll chpers re included. Compleed downlod links: hps://esbnkre.com/downlod/physics-h-ediion-soluions-mnulcunell-johnson-young-sdler/

More information

Elastic and Inelastic Collisions

Elastic and Inelastic Collisions laic and Inelaic Colliion In an LASTIC colliion, energy i conered (Kbefore = Kafer or Ki = Kf. In an INLASTIC colliion, energy i NOT conered. (Ki > Kf. aple: A kg block which i liding a 0 / acro a fricionle

More information

Physics 15 Second Hour Exam

Physics 15 Second Hour Exam hc 5 Second Hou e nwe e Mulle hoce / ole / ole /6 ole / ------------------------------- ol / I ee eone ole lee how ll wo n ode o ecee l ced. I ou oluon e llegle no ced wll e gen.. onde he collon o wo 7.

More information

ISSUES RELATED WITH ARMA (P,Q) PROCESS. Salah H. Abid AL-Mustansirya University - College Of Education Department of Mathematics (IRAQ / BAGHDAD)

ISSUES RELATED WITH ARMA (P,Q) PROCESS. Salah H. Abid AL-Mustansirya University - College Of Education Department of Mathematics (IRAQ / BAGHDAD) Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK www.e-onls.o ISSUES RELATED WITH ARMA PQ PROCESS Sl H. Ai AL-Msnsiy Univesiy - Collee Of Ecion Deen of Meics IRAQ

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information