Kinetics. Central Force Motion & Space Mechanics
|
|
- Nigel Johnson
- 5 years ago
- Views:
Transcription
1 Kintics Cntal Foc Motion & Spac Mcanics
2 Outlin Cntal Foc Motion Obital Mcanics Exampls
3 Cntal-Foc Motion If a paticl tavls un t influnc of a foc tat as a lin of action ict towas a fix point, tn t motion is call cntal-foc motion Exampls: plantay motion, lctostatic focs, cntifug
4 Cntal-Foc Motion P Consi a paticl of mass m act on by a foc F, wit cnt O θ O θ F 1 A Using t Equations of Motion fo Cylinical Cooinats, it can b sown tat (ivation omitt, stunt plas viw): θ θ F ma F m t t (13-11a) F F boy iagam F ma m t 0 t t (13-11b)
5 Cntal-Foc Motion W may -wit Eqn 13-11b in t fom 1 t t 0 tn by intgation t w is t constant of intgation (13-1)
6 Cntal-Foc Motion Sinc t paticl swps toug angl θ in tim intval t A t A 1 1 t A/t is call t aal vlocity. It mains constant fo a paticl in cntal-foc motion Tis mans t paticl swps toug qual aas in qual tim as it tavls along t pat
7 Cntal-Foc Motion Lt us iv t pat of motion as a function of θ By t cain ul (Calculus 101!) Lt us not t t t t t 1
8 Cntal-Foc Motion So tat w obtain also t squa of Eqn 13-1 bcoms Substituting t abov in Eqn 13-11a w obtain a iffntial quation wic can b solv to tmin t pat of motion t 4 t 3 m F m F OR (13-14)
9 Obital Mcanics Consi a spac vicl of mass m launc into f-fligt obit wit initial vlocity v o. Assum v o acts paalll to t tangnt to t at sufac Nglct gavitational attactions of sun an moon F-fligt tajctoy v 0 Spac vicl F launc Pow fligt tajctoy
10 Obital Mcanics At t instant just aft las into f fligt t only foc acting on it is t gavitational attaction fom t at Accoing to Nwton s law of gavitation; F G M m To obtain t obital pat, substitut into Eqn GM
11 Obital Mcanics T abov iffntial quation can b solv as t sum of t complmntay an paticula solutions (Rviw you Diffntial Equations ) Solution is: 1 GM C cos( ) (13-16)
12 Obital Mcanics Eqn is t quation of a conic sction [stunt, plas viw you P-Cal matials] By finition, Eccnticity 1 FP PA (PA) [ p cos( )] 1 p o cos( ) 1 p x x D A D ictix p P focus F
13 Obital Motion Compaing wit Eqn 13-16; an p C 1 C GM Povi θ is masu fom t x-axis wic is ppnicula to t ictix (an an axis of symmty), tn Ф = 0, an Eqn ucs to 1 (13-17) (13-18) GM C cos( ) (13-19)
14 Obital Motion T constants C an a tmin fom t bounay conitions at t n of t powfligt tajctoy At t bginning of f-fligt = o, v = v o ; if θ = Ф = 0, tn fom cuvilina motioncylinical componnts v t t o 0 v 0 (13-0)
15 Obital Motion Substituting Eqn 13-0, = o, θ = 0, into Eqn C 1 GM 1 0 0v 0 T quation fo t f-fligt tajctoy tfo bcoms (13-1) 1 1 GM GM 1 cos 0 0v (13-) 0 0v 0
16 Obital Motion T typ of pat tavl by t spac vicl pns on t valu of t ccnticity 0 cicl 1 1 paabola llip s (13-3) 1 ypbola [Stunts, plug in ts valus to t appopiat quations an vify ts conclusions]
17 Obital Motion Paabolic pat: T spaccaft is on t bolin of nv tuning to its stating point. T initial vlocity qui fo a paabolic pat is call t scap vlocity Plugging = 1, Eqns 13-1 an 13- into Eqn 1318; v GM 0 (13-4)
18 Obital Motion Similaly, fo Cicula Motion v GM c (13-5) 0 Not tat v o v will sult in vicl scaping at s gavitational pull On t ot an if v o < v c t vicl will fail to ac obit, nt at atmosp, an cas o bun up in t at of nty
19 Elliptical Obit All plants an most atificial satllits obit in an lliptical pat. Fo t spac caft t minimum istanc to t cnt of t at (wit at at a focus of t llips), p can b foun by plugging θ = 0 into Eqn 13. Using θ = 180 o w gt t max istanc a P O a b b a a
20 Elliptical Obit p 0 p is call t pig (gnally piapsis) a (GM 0 ) 1 a is call t apog (gnally apoapsis) Half t lngt of t majo axis a p a 0 v 0 (13-6) (13-8) (13-7)
21 Elliptical Obit It can also b sown tat b p a (13-9) (Stunts, vify on you own) By intgation, t aa of t llips is A ab ( p a ) p (13-30) a
22 Elliptical Motion T aal vlocity was fin in Eqn as A t o A t w T is t tim to mak on obital volution (aka obital pio). Fom 13-30: A T T ( p a ) pa (13-31)
23 Laws of Plantay Motion T toy vlop in tis capt was fist psnt by Joanns Kpl in 161, 6 cla cas bfo Nwton s Pincipia Kpl vlop t laws of plantay motion ov 0 yas by stuying plantay ata collct by is mnto Tyco Ba
24 Laws of Plantay Motion Plants tavl in lliptical obits wit t sun at a focus of t llips (Eqn 13-) Plants tavl in an obit suc tat ty swp qual aas in qual tim intvals (Eqn 13-13) T squa of t pio of any plant is ictly popotional to t cub of t majo axis of its obit (Eqns 13-31, 13-19, 13-8, 13-9)
25 Qustions & Commnts
GRAVITATION. (d) If a spring balance having frequency f is taken on moon (having g = g / 6) it will have a frequency of (a) 6f (b) f / 6
GVITTION 1. Two satllits and o ound a plant P in cicula obits havin adii 4 and spctivly. If th spd of th satllit is V, th spd of th satllit will b 1 V 6 V 4V V. Th scap vlocity on th sufac of th ath is
More information8 - GRAVITATION Page 1
8 GAVITATION Pag 1 Intoduction Ptolmy, in scond cntuy, gav gocntic thoy of plantay motion in which th Eath is considd stationay at th cnt of th univs and all th stas and th plants including th Sun volving
More informationGRAVITATION 4) R. max. 2 ..(1) ...(2)
GAVITATION PVIOUS AMCT QUSTIONS NGINING. A body is pojctd vtically upwads fom th sufac of th ath with a vlocity qual to half th scap vlocity. If is th adius of th ath, maximum hight attaind by th body
More informationGAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL
GAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL Ioannis Iaklis Haanas * and Michal Hany# * Dpatmnt of Physics and Astonomy, Yok Univsity 34 A Pti Scinc Building Noth Yok, Ontaio, M3J-P3,
More informationCHAPTER 5 CIRCULAR MOTION
CHAPTER 5 CIRCULAR MOTION and GRAVITATION 5.1 CENTRIPETAL FORCE It is known that if a paticl mos with constant spd in a cicula path of adius, it acquis a cntiptal acclation du to th chang in th diction
More informationCHAPTER 5 CIRCULAR MOTION AND GRAVITATION
84 CHAPTER 5 CIRCULAR MOTION AND GRAVITATION CHAPTER 5 CIRCULAR MOTION AND GRAVITATION 85 In th pious chapt w discussd Nwton's laws of motion and its application in simpl dynamics poblms. In this chapt
More informationMid Year Examination F.4 Mathematics Module 1 (Calculus & Statistics) Suggested Solutions
Mid Ya Eamination 3 F. Matmatics Modul (Calculus & Statistics) Suggstd Solutions Ma pp-: 3 maks - Ma pp- fo ac qustion: mak. - Sam typ of pp- would not b countd twic fom wol pap. - In any cas, no pp maks
More informationThe angle between L and the z-axis is found from
Poblm 6 This is not a ifficult poblm but it is a al pain to tansf it fom pap into Mathca I won't giv it to you on th quiz, but know how to o it fo th xam Poblm 6 S Figu 6 Th magnitu of L is L an th z-componnt
More informationNEWTON S THEORY OF GRAVITY
NEWTON S THEOY OF GAVITY 3 Concptual Qustions 3.. Nwton s thid law tlls us that th focs a qual. Thy a also claly qual whn Nwton s law of gavity is xamind: F / = Gm m has th sam valu whth m = Eath and m
More informationRadius of the Moon is 1700 km and the mass is 7.3x 10^22 kg Stone. Moon
xample: A 1-kg stone is thown vetically up fom the suface of the Moon by Supeman. The maximum height fom the suface eached by the stone is the same as the adius of the moon. Assuming no ai esistance and
More informationBasic oces an Keple s Laws 1. Two ientical sphees of gol ae in contact with each othe. The gavitational foce of attaction between them is Diectly popotional to the squae of thei aius ) Diectly popotional
More informationGMm. 10a-0. Satellite Motion. GMm U (r) - U (r ) how high does it go? Escape velocity. Kepler s 2nd Law ::= Areas Angular Mom. Conservation!!!!
F Satllt Moton 10a-0 U () - U ( ) 0 f ow g dos t go? scap locty Kpl s nd Law ::= Aas Angula Mo. Consaton!!!! Nwton s Unsal Law of Gaty 10a-1 M F F 1) F acts along t ln connctng t cnts of objcts Cntal Foc
More informationExperiment 09: Angular momentum
Expeiment 09: Angula momentum Goals Investigate consevation of angula momentum and kinetic enegy in otational collisions. Measue and calculate moments of inetia. Measue and calculate non-consevative wok
More informationGravitation. AP/Honors Physics 1 Mr. Velazquez
Gavitation AP/Honos Physics 1 M. Velazquez Newton s Law of Gavitation Newton was the fist to make the connection between objects falling on Eath and the motion of the planets To illustate this connection
More informationChapter 13: Gravitation
v m m F G Chapte 13: Gavitation The foce that makes an apple fall is the same foce that holds moon in obit. Newton s law of gavitation: Evey paticle attacts any othe paticle with a gavitation foce given
More informationAY 7A - Fall 2010 Section Worksheet 2 - Solutions Energy and Kepler s Law
AY 7A - Fall 00 Section Woksheet - Solutions Enegy and Keple s Law. Escape Velocity (a) A planet is obiting aound a sta. What is the total obital enegy of the planet? (i.e. Total Enegy = Potential Enegy
More information5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS
5.61 Fall 2007 Lctu #2 pag 1 Th DEMISE of CLASSICAL PHYSICS (a) Discovy of th Elcton In 1897 J.J. Thomson discovs th lcton and masus ( m ) (and inadvtntly invnts th cathod ay (TV) tub) Faaday (1860 s 1870
More informationGRAVITATION. Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18 PG 1
Einstein Classes, Unit No. 0, 0, Vahman Ring Roa Plaza, Vikas Pui Extn., New Delhi -8 Ph. : 96905, 857, E-mail einsteinclasses00@gmail.com, PG GRAVITATION Einstein Classes, Unit No. 0, 0, Vahman Ring Roa
More informationExtra notes for circular motion: Circular motion : v keeps changing, maybe both speed and
Exta notes fo cicula motion: Cicula motion : v keeps changing, maybe both speed and diection ae changing. At least v diection is changing. Hence a 0. Acceleation NEEDED to stay on cicula obit: a cp v /,
More informationGet Solution of These Packages & Learn by Video Tutorials on GRAVITATION
FEE Download Study Packag fom wbsit: www.tkoclasss.com & www.mathsbysuhag.com Gt Solution of Ths Packags & an by Vido Tutoials on www.mathsbysuhag.com. INTODUCTION Th motion of clstial bodis such as th
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 10-: MOTION IN A GRAVITATIONAL FIELD Questions Fom Reading Activity? Gavity Waves? Essential Idea: Simila appoaches can be taken in analyzing electical
More informationKEPLER S LAWS OF PLANETARY MOTION
EPER S AWS OF PANETARY MOTION 1. Intoduction We ae now in a position to apply what we have leaned about the coss poduct and vecto valued functions to deive eple s aws of planetay motion. These laws wee
More informationWhile flying from hot to cold, or high to low, watch out below!
STANDARD ATMOSHERE Wil flying fom ot to cold, o ig to low, watc out blow! indicatd altitud actual altitud STANDARD ATMOSHERE indicatd altitud actual altitud STANDARD ATMOSHERE Wil flying fom ot to cold,
More informationm1 m2 M 2 = M -1 L 3 T -2
GAVITATION Newton s Univesal law of gavitation. Evey paticle of matte in this univese attacts evey othe paticle with a foce which vaies diectly as the poduct of thei masses and invesely as the squae of
More informationF 12. = G m m 1 2 F 21 = F 12. = G m 1m 2. Review. Physics 201, Lecture 22. Newton s Law Of Universal Gravitation
Physics 201, Lectue 22 Review Today s Topics n Univesal Gavitation (Chapte 13.1-13.3) n Newton s Law of Univesal Gavitation n Popeties of Gavitational Foce n Planet Obits; Keple s Laws by Newton s Law
More informationBetween any two masses, there exists a mutual attractive force.
YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Univesal Law of Gavitation in wods Between any two masses, thee exists a mutual attactive foce. This foce
More informationHydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals
Hydogn atom Engy lvls and wav functions Obital momntum, lcton spin and nucla spin Fin and hypfin intaction Hydogn obitals Hydogn atom A finmnt of th Rydbg constant: R ~ 109 737.3156841 cm -1 A hydogn mas
More informationAP Calculus Multiple-Choice Question Collection
AP Calculus Multipl-Coic Qustion Collction 985 998 . f is a continuous function dfind for all ral numbrs and if t maimum valu of f () is 5 and t minimum valu of f () is 7, tn wic of t following must b
More informationGeneral Relativity Homework 5
Geneal Relativity Homewok 5. In the pesence of a cosmological constant, Einstein s Equation is (a) Calculate the gavitational potential point souce with = M 3 (). R µ Rg µ + g µ =GT µ. in the Newtonian
More informationRecap. Centripetal acceleration: v r. a = m/s 2 (towards center of curvature)
a = c v 2 Recap Centipetal acceleation: m/s 2 (towads cente of cuvatue) A centipetal foce F c is equied to keep a body in cicula motion: This foce poduces centipetal acceleation that continuously changes
More informationLecture 1a: Satellite Orbits
Lectue 1a: Satellite Obits Outline 1. Newton s Laws of Motion 2. Newton s Law of Univesal Gavitation 3. Calculating satellite obital paametes (assuming cicula motion) Scala & Vectos Scala: a physical quantity
More informationALLEN. è ø = MB = = (1) 3 J (2) 3 J (3) 2 3 J (4) 3J (1) (2) Ans. 4 (3) (4) W = MB(cosq 1 cos q 2 ) = MB (cos 0 cos 60 ) = MB.
at to Succss LLEN EE INSTITUTE KT (JSTHN) HYSIS 6. magntic ndl suspndd paalll to a magntic fild quis J of wok to tun it toug 60. T toqu ndd to mata t ndl tis position will b : () J () J () J J q 0 M M
More informationPHYS Dynamics of Space Vehicles
PHYS 4110 - Dynamics of Space Vehicles Chapte 3: Two Body Poblem Eath, Moon, Mas, and Beyond D. Jinjun Shan, Pofesso of Space Engineeing Depatment of Eath and Space Science and Engineeing Room 55, Petie
More informationChapter 7 Dynamic stability analysis I Equations of motion and estimation of stability derivatives - 4 Lecture 25 Topics
Chapt 7 Dynamic stability analysis I Equations of motion an stimation of stability ivativs - 4 ctu 5 opics 7.8 Expssions fo changs in aoynamic an populsiv focs an momnts 7.8.1 Simplifi xpssions fo changs
More informationThat is, the acceleration of the electron is larger than the acceleration of the proton by the same factor the electron is lighter than the proton.
PHY 8 Test Pactice Solutions Sping Q: [] A poton an an electon attact each othe electically so, when elease fom est, they will acceleate towa each othe. Which paticle will have a lage acceleation? (Neglect
More informationThat is, the acceleration of the electron is larger than the acceleration of the proton by the same factor the electron is lighter than the proton.
PHYS 55 Pactice Test Solutions Fall 8 Q: [] poton an an electon attact each othe electicall so, when elease fom est, the will acceleate towa each othe Which paticle will have a lage acceleation? (Neglect
More informationModeling Ballistics and Planetary Motion
Discipline Couses-I Semeste-I Pape: Calculus-I Lesson: Lesson Develope: Chaitanya Kuma College/Depatment: Depatment of Mathematics, Delhi College of Ats and Commece, Univesity of Delhi Institute of Lifelong
More informationGravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun
Chapte 12 Gavitation PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified by P. Lam 5_31_2012 Goals fo Chapte 12 To study Newton s Law
More information( )( )( ) ( ) + ( ) ( ) ( )
3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13
More informationLECTURE 14. m 1 m 2 b) Based on the second law of Newton Figure 1 similarly F21 m2 c) Based on the third law of Newton F 12
CTU 4 ] NWTON W O GVITY -The gavity law i foulated fo two point paticle with ae and at a ditance between the. Hee ae the fou tep that bing to univeal law of gavitation dicoveed by NWTON. a Baed on expeiental
More informationEE 5337 Computational Electromagnetics (CEM) Method of Lines
11/30/017 Instucto D. Ramon Rumpf (915) 747 6958 cumpf@utp.u 5337 Computational lctomagntics (CM) Lctu #4 Mto of Lins Lctu 4 Ts nots ma contain copigt matial obtain un fai us uls. Distibution of ts matials
More information5-9 THE FIELD CONCEPT. Answers to the Conceptual Questions. Chapter 5 Gravity 63
Chapt 5 Gavity 5-9 THE FIELD CONCEPT Goals Intoduc th notion of a fild. (Pobl Solvin) Calculat th Sun's avitational fild at Eath's location. Contnt Th psnc of a ass odifis spac. A valu can b assind to
More informationω = θ θ o = θ θ = s r v = rω
Unifom Cicula Motion Unifom cicula motion is the motion of an object taveling at a constant(unifom) speed in a cicula path. Fist we must define the angula displacement and angula velocity The angula displacement
More information4. Compare the electric force holding the electron in orbit ( r = 0.53
Electostatics WS Electic Foce an Fiel. Calculate the magnitue of the foce between two 3.60-µ C point chages 9.3 cm apat.. How many electons make up a chage of 30.0 µ C? 3. Two chage ust paticles exet a
More informationHW6 Physics 311 Mechanics
HW6 Physics 311 Mechanics Fall 015 Physics depatment Univesity of Wisconsin, Madison Instucto: Pofesso Stefan Westehoff By Nasse M. Abbasi June 1, 016 Contents 0.1 Poblem 1.........................................
More informationTrigonometric functions
Robrto s Nots on Diffrntial Calculus Captr 5: Drivativs of transcndntal functions Sction 5 Drivativs of Trigonomtric functions Wat you nd to know alrady: Basic trigonomtric limits, t dfinition of drivativ,
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More informationFree carriers in materials
Lctu / F cais in matials Mtals n ~ cm -3 Smiconductos n ~ 8... 9 cm -3 Insulatos n < 8 cm -3 φ isolatd atoms a >> a B a B.59-8 cm 3 ϕ ( Zq) q atom spacing a Lctu / "Two atoms two lvls" φ a T splitting
More informationPLANNING OF KEPLERIAN ORBITS: APPLICATION TO PERIODIC TRAJECTORIES
ANNING OF KEERIAN ORBITS: AICATION TO ERIODIC TRAJECTORIES Vann Mical Bnntt Dpatmnt o Matmatics Univsit o Hawai i at Manoa Honolulu, HI 968 ABSTRACT Satllits av numous uss anging om t tansmission o communications
More information10. Force is inversely proportional to distance between the centers squared. R 4 = F 16 E 11.
NSWRS - P Physics Multiple hoice Pactice Gavitation Solution nswe 1. m mv Obital speed is found fom setting which gives v whee M is the object being obited. Notice that satellite mass does not affect obital
More informationPhysics: Work & Energy Beyond Earth Guided Inquiry
Physics: Wok & Enegy Beyond Eath Guided Inquiy Elliptical Obits Keple s Fist Law states that all planets move in an elliptical path aound the Sun. This concept can be extended to celestial bodies beyond
More informationOSCILLATIONS AND GRAVITATION
1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,
More informationHistory of Astronomy - Part II. Tycho Brahe - An Observer. Johannes Kepler - A Theorist
Histoy of Astonomy - Pat II Afte the Copenican Revolution, astonomes stived fo moe obsevations to help bette explain the univese aound them Duing this time (600-750) many majo advances in science and astonomy
More informationPhysics 240: Worksheet 15 Name
Physics 40: Woksht 15 Nam Each of ths poblms inol physics in an acclatd fam of fnc Althouh you mind wants to ty to foc you to wok ths poblms insid th acclatd fnc fam (i.. th so-calld "won way" by som popl),
More informationChap 5. Circular Motion: Gravitation
Chap 5. Cicula Motion: Gavitation Sec. 5.1 - Unifom Cicula Motion A body moves in unifom cicula motion, if the magnitude of the velocity vecto is constant and the diection changes at evey point and is
More informationCentral Force Motion
Cental Foce Motion Cental Foce Poblem Find the motion of two bodies inteacting via a cental foce. Examples: Gavitational foce (Keple poblem): m1m F 1, ( ) =! G ˆ Linea estoing foce: F 1, ( ) =! k ˆ Two
More informationCh 13 Universal Gravitation
Ch 13 Univesal Gavitation Ch 13 Univesal Gavitation Why do celestial objects move the way they do? Keple (1561-1630) Tycho Bahe s assistant, analyzed celestial motion mathematically Galileo (1564-1642)
More informationWell, the aim of today s lesson is to understand how he came to this idea and how he interpreted the motion of the Moon around the Earth.
1) Inteogation oale d un élève su la patie : the gavity field, taitée au cous pécédent : Pévoi de faie paticipe les autes élèves au besoin. - Last time, we spoke about fields in physics; could you give
More informationMolecules and electronic, vibrational and rotational structure
Molculs and ctonic, ational and otational stuctu Max on ob 954 obt Oppnhim Ghad Hzbg ob 97 Lctu ots Stuctu of Matt: toms and Molculs; W. Ubachs Hamiltonian fo a molcul h h H i m M i V i fs to ctons, to
More information15. SIMPLE MHD EQUILIBRIA
15. SIMPLE MHD EQUILIBRIA In this Section we will examine some simple examples of MHD equilibium configuations. These will all be in cylinical geomety. They fom the basis fo moe the complicate equilibium
More informationD-Cluster Dynamics and Fusion Rate by Langevin Equation
D-Clust Dynamics an Fusion at by Langvin Equation kito Takahashi** an Noio Yabuuchi High Scintific sach Laboatoy Maunouchi-4-6, Tsu, Mi, 54-33 Japan **Osaka Univsity STCT Conns matt nucla ffct, spcially
More informationPhysics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM
Physics 0, Lctu 5 Today s Topics nnouncmnts: Homwok #3 on Wbssign by tonight Du (with Homwok #) on 9/4, 10 PM Rviw: (Ch. 5Pat I) Elctic Potntial Engy, Elctic Potntial Elctic Potntial (Ch. 5Pat II) Elctic
More informationAP Calculus BC AP Exam Problems Chapters 1 3
AP Eam Problms Captrs Prcalculus Rviw. If f is a continuous function dfind for all ral numbrs and if t maimum valu of f() is 5 and t minimum valu of f() is 7, tn wic of t following must b tru? I. T maimum
More informationMATHEMATICS PAPER IIB COORDINATE GEOMETRY AND CALCULUS. Note: This question paper consists of three sections A, B and C.
MATHEMATICS PAPER IIB COORDINATE GEOMETRY AND CALCULUS. Tim: 3hrs Ma. Marks.75 Not: This qustion papr consists of thr sctions A, B and C. SECTION -A Vry Short Answr Typ Qustions. 0 X = 0. Find th condition
More informationKepler's 1 st Law by Newton
Astonom 10 Section 1 MWF 1500-1550 134 Astonom Building This Class (Lectue 7): Gavitation Net Class: Theo of Planeta Motion HW # Due Fida! Missed nd planetaium date. (onl 5 left), including tonight Stadial
More informationMath Notes on Kepler s first law 1. r(t) kp(t)
Math 7 - Notes on Keple s fist law Planetay motion and Keple s Laws We conside the motion of a single planet about the sun; fo simplicity, we assign coodinates in R 3 so that the position of the sun is
More informationA Comparative Study and Analysis of an Optimized Control Strategy for the Toyota Hybrid System
Pag 563 Wol Elctic Vhicl Jounal Vol. 3 - ISSN 3-6653 - 9 AVERE EVS4 Stavang, Noway, May 13-16, 9 A Compaativ Stuy an Analysis of an Optimiz Contol Statgy fo th Toyota Hybi Systm Tho Hofman 1, Thijs Punot
More informationCBSE-XII-2013 EXAMINATION (MATHEMATICS) The value of determinant of skew symmetric matrix of odd order is always equal to zero.
CBSE-XII- EXAMINATION (MATHEMATICS) Cod : 6/ Gnal Instuctions : (i) All qustions a compulso. (ii) Th qustion pap consists of 9 qustions dividd into th sctions A, B and C. Sction A compiss of qustions of
More informationChapter 8. Accelerated Circular Motion
Chapte 8 Acceleated Cicula Motion 8.1 Rotational Motion and Angula Displacement A new unit, adians, is eally useful fo angles. Radian measue θ(adians) = s = θ s (ac length) (adius) (s in same units as
More informationUniform Circular Motion
Unifom Cicula Motion constant speed Pick a point in the objects motion... What diection is the velocity? HINT Think about what diection the object would tavel if the sting wee cut Unifom Cicula Motion
More informationMon. Tues. 6.2 Field of a Magnetized Object 6.3, 6.4 Auxiliary Field & Linear Media HW9
Fi. on. Tus. 6. Fild of a agntid Ojct 6.3, 6.4 uxiliay Fild & Lina dia HW9 Dipol t fo a loop Osvation location x y agntic Dipol ont Ia... ) ( 4 o I I... ) ( 4 I o... sin 4 I o Sa diction as cunt B 3 3
More informationThe local orthonormal basis set (r,θ,φ) is related to the Cartesian system by:
TIS in Sica Cooinats As not in t ast ct, an of t otntias tat w wi a wit a cnta otntias, aning tat t a jst fnctions of t istanc btwn a atic an so oint of oigin. In tis cas tn, (,, z as a t Coob otntia an
More informationMODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES VISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLIN MODUL 5 ADVANCD MCHANICS GRAVITATIONAL FILD: MOTION OF PLANTS AND SATLLITS SATLLITS: Obital motion of object of mass m about a massive object of mass M (m
More informationProblem Set 5: Universal Law of Gravitation; Circular Planetary Orbits
Poblem Set 5: Univesal Law of Gavitation; Cicula Planetay Obits Design Engineeing Callenge: Te Big Dig.007 Contest Evaluation of Scoing Concepts: Spinne vs. Plowe PROMBLEM 1: Daw a fee-body-diagam of a
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 informationAE 245 homework #9 solutions
AE 245 homewok #9 olution Tim Smith 13 Apil 2000 1 Poblem1 In the Apollo miion fom the Eath to the Moon, the Satun thid tage povided the tan-luna inetion bun that tanfeed the Apollo pacecaft fom a low
More informationCentral Force Problem. Central Force Motion. Two Body Problem: Center of Mass Coordinates. Reduction of Two Body Problem 8.01 W14D1. + m 2. m 2.
Cental oce Poblem ind the motion of two bodies inteacting via a cental foce. Cental oce Motion 8.01 W14D1 Examples: Gavitational foce (Keple poblem): 1 1, ( ) G mm Linea estoing foce: ( ) k 1, Two Body
More informationEquilibria of a cylindrical plasma
// Miscellaneous Execises Cylinical equilibia Equilibia of a cylinical plasma Consie a infinitely long cyline of plasma with a stong axial magnetic fiel (a geat fusion evice) Plasma pessue will cause the
More informationPractice. Understanding Concepts. Answers J 2. (a) J (b) 2% m/s. Gravitation and Celestial Mechanics 287
Pactice Undestanding Concepts 1. Detemine the gavitational potential enegy of the Eath Moon system, given that the aveage distance between thei centes is 3.84 10 5 km, and the mass of the Moon is 0.0123
More informationWhat Form of Gravitation Ensures Weakened Kepler s Third Law?
Bulletin of Aichi Univ. of Education, 6(Natual Sciences, pp. - 6, Mach, 03 What Fom of Gavitation Ensues Weakened Keple s Thid Law? Kenzi ODANI Depatment of Mathematics Education, Aichi Univesity of Education,
More informationLocal Effect of Space-Time Expansion ---- How Galaxies Form and Evolve
Intnational Jounal of Advancd Rsach in Physical Scinc (IJARPS) Volum Issu 5 06 PP 5-5 ISSN 49-7874 (Pint) & ISSN 49-788 (Onlin) www.acjounals.og Local Effct of Spac-Tim Expansion ---- How Galaxis Fom and
More informationGaia s Place in Space
Gaia s Place in Space The impotance of obital positions fo satellites Obits and Lagange Points Satellites can be launched into a numbe of diffeent obits depending on thei objectives and what they ae obseving.
More informationSPH4UI 28/02/2011. Total energy = K + U is constant! Electric Potential Mr. Burns. GMm
8//11 Electicity has Enegy SPH4I Electic Potential M. Buns To sepaate negative an positive chages fom each othe, wok must be one against the foce of attaction. Theefoe sepeate chages ae in a higheenegy
More informationr cos, and y r sin with the origin of coordinate system located at
Lectue 3-3 Kinematics of Rotation Duing ou peious lectues we hae consideed diffeent examples of motion in one and seeal dimensions. But in each case the moing object was consideed as a paticle-like object,
More informationCase Study 1 PHA 5127 Fall 2006 Revised 9/19/06
Cas Study Qustion. A 3 yar old, 5 kg patint was brougt in for surgry and was givn a /kg iv bolus injction of a muscl rlaxant. T plasma concntrations wr masurd post injction and notd in t tabl blow: Tim
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Revision Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Wok... 5 Gavitational field... 5 Potential enegy... 7 Kinetic enegy... 8 Pojectile... 9
More informationChapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields
Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets. two ba magnets can attact o epel epening on thei oientation this is ue to
More informationChapter 5: Uniform Circular Motion
Chapte 5: Unifom Cicula Motion Motion at constant speed in a cicle Centipetal acceleation Banked cuves Obital motion Weightlessness, atificial gavity Vetical cicula motion Centipetal Foce Acceleation towad
More informationDoublets and Other Allied Well Patterns
oults an Oth Alli Wll Pattns SUPRI TR- B William E. Bigham cm 000 Pfom un ontact Nums E-F6-00B5 an E-FG-96B99 Stanfo Univsit Stanfo, alifonia AKNOWLEGEMENTS Lt m stat ths acknowlgmnts with a isclaim.
More information1) Consider a particle moving with constant speed that experiences no net force. What path must this particle be taking?
Chapte 5 Test Cicula Motion and Gavitation 1) Conside a paticle moving with constant speed that expeiences no net foce. What path must this paticle be taking? A) It is moving in a paabola. B) It is moving
More informationFI 3103 Quantum Physics
7//7 FI 33 Quantum Physics Axan A. Iskana Physics of Magntism an Photonics sach oup Institut Tknoogi Banung Schoing Equation in 3D Th Cnta Potntia Hyognic Atom 7//7 Schöing quation in 3D Fo a 3D pobm,
More informationAH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion
AH Mechanics Checklist (Unit ) AH Mechanics Checklist (Unit ) Cicula Motion No. kill Done 1 Know that cicula motion efes to motion in a cicle of constant adius Know that cicula motion is conveniently descibed
More informationVaiatin f. A ydn balln lasd n t n ) Clibs u wit an acclatin f 6x.8s - ) Falls dwn wit an acclatin f.8x6s - ) Falls wit acclatin f.8 s - ) Falls wit an acclatin f.8 6 s-. T wit f an bjct in t cal in, sa
More informationWelcome to Aerospace Engineering
Welcome to Aeospace Engineeing DESIGN-CENTERED INTRODUCTION TO AEROSPACE ENGINEERING Notes 9 Topics 1. Couse Oganization. Today's Deams in Vaious Speed Ranges 3. Designing a Flight Vehicle: Route Map of
More informationMuch that has already been said about changes of variable relates to transformations between different coordinate systems.
MULTIPLE INTEGRLS I P Calculus Cooinate Sstems Much that has alea been sai about changes of vaiable elates to tansfomations between iffeent cooinate sstems. The main cooinate sstems use in the solution
More informationPhysics 201 Homework 4
Physics 201 Homewok 4 Jan 30, 2013 1. Thee is a cleve kitchen gadget fo dying lettuce leaves afte you wash them. 19 m/s 2 It consists of a cylindical containe mounted so that it can be otated about its
More informationInstrumentation for Characterization of Nanomaterials (v11) 11. Crystal Potential
Istumtatio o Chaactizatio o Naomatials (v). Cystal Pottial Dlta uctio W d som mathmatical tools to dvlop a physical thoy o lcto diactio om cystal. Idal cystals a iiit this, so th will b som iiitis lii
More informationAakash. For Class XII Studying / Passed Students. Physics, Chemistry & Mathematics
Aakash A UNIQUE PPRTUNITY T HELP YU FULFIL YUR DREAMS Fo Class XII Studying / Passd Studnts Physics, Chmisty & Mathmatics Rgistd ffic: Aakash Tow, 8, Pusa Road, Nw Dlhi-0005. Ph.: (0) 4763456 Fax: (0)
More informationChapter 11 Solutions ( ) 1. The wavelength of the peak is. 2. The temperature is found with. 3. The power is. 4. a) The power is
Chapt Solutios. Th wavlgth of th pak is pic 3.898 K T 3.898 K 373K 885 This cospods to ifad adiatio.. Th tpatu is foud with 3.898 K pic T 3 9.898 K 50 T T 5773K 3. Th pow is 4 4 ( 0 ) P σ A T T ( ) ( )
More informationkg 2 ) 1.9!10 27 kg = Gm 1
Section 6.1: Newtonian Gavitation Tutoial 1 Pactice, page 93 1. Given: 1.0 10 0 kg; m 3.0 10 0 kg;. 10 9 N; G 6.67 10 11 N m /kg Requied: Analysis: G m ; G m G m Solution: G m N m 6.67!10 11 kg ) 1.0!100
More information