mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !


 Magnus Cummings
 1 years ago
 Views:
Transcription
1 Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =! " & and so =! " &. Simplifying gives the esult. Fom poblem we know that = unit time i.e.! = ", i.e. =! ". Substituting, = Fom mv = G Mm we deduce that v = G M. Now = = 6900 km = 6.9! 0 6 m and so v = = 6.67! 0"! 6.0! 0 4 v =! " =! v 4!. he angula velocity is the angle swept pe (! ) 4! " = ". 6.9! 0 6 = 7.6! 0 ms ". he peiod is then found fom = s = 95 min. 4 he peiod has to be one day i.e. 4 hous. hen v =! deduce that v = G M. Combining the esults we get and fom mv = G Mm we = = 6.67 " 0 " 6.0 " 0 4 " (4 " 60 " 60) 4! = 4. " 0 7 m. 4! 5 (a) E P =! eath M moon (b) V =! eath (c) v = eath =! 6.67 " 0! " 5.98 " 0 4 " 7.5 " 0.84 " 0 8 =!7.64 " 0 8 J. =! 6.67 " 0! " 5.98 " " 0 8 =!.04 " 0 6 J kg!. = 6.67! 0"! 5.98! ! 0 8 =.0! 0 m s ". 6 We must plot the function E P =! eathm! moonm giving the gaph in the answes. d! Hee m is the mass of the spacecaft and d the sepaation of the eath and the moon (cente
2 tocente). Putting numbes in, E P =! 6.67 " 0! " 5.98 " 0 4 ".0 " 0 4. " 09.5 " 0 7 =!.84 " 0 8!! 6.67 " 0! " 7.5 " 0 ".0 " " 0 8! =. " 09 /.84 " 0 8!.5 " 07 /.84 " 0 8 /.84 " 0 8! /.84 " 0 8. " 00.9 " 08 =! x! x whee x =. In this way the function can be plotted on a calculato to give the 8.84! 0 gaph in the answes in the textbook. 7 (a) V =! 5 e (b) =! 6.67 " 0! " 5.98 " " 6.4 " 0 6 =!. " 0 7 J kg! E P =! m 5 e =! 6.67 " 0! " 5.98 " 0 4 " " 6.4 " 0 6 =!6. " 0 9 J 8 he net foce is the gavitational foce and this must point towads the cente of the eath. his happens only fo obit. 9 s shown in the text the eaction foce fom the spacecaft floo is zeo giving the impession of weightlessness. Moe simply, both spacecaft and astonaut ae in fee fall with the same acceleation. 0 he diffeence is!u = " m + h " " m & ( = m " m + h = m + h " ( + h) " h!u = m ( + h) &. When h is small compaed to this expession is appoximately!u = m h = m h = mgh. he wok done by an extenal agent in moving an object fom = a to = b at a small constant speed. & (.
3 (a) he potential at the suface of the planet is V =! =! 6.67 " 0! " M.0 " 0 5 =!4.9 " 0 J kg!. Hence M =.5! 0 8 kg. (b) he escape speed is obtained fom mv! m = 0, i.e. v =. But V =! and so =!V. Substituting, v =!V. (c) v =!V = " 4.9 " 0 =. " 0 6 m s! (d) he wok equied is W = m!v. his is W = 500! (".0! 0 " ("4.9! 0 )) = 5.8! 0 5 J. (e) We have that mv + mv = mv! v = (V " V ). his gives v = (!. " 0! (!4.9 " 0 )) =. " 0 6 m s!. (a) t = 0.75, g = P (0.75d)! m (0.5d) = 0. Hence M P = (0.75d) = 9. (b) he pobe M m (0.5d) must have enough enegy to get to the maximum of the gaph. Fom then on the moon will pull it in. hen W = mv = m!v " v =!V = (0. 0 (6.4 0 )) = m s. 4 (a) We deduced many times that v = and so = mv! m = m! m =! m. (b) =! 6.67 " 0! ".0 " 0 0 " 6.0 " 0 4 ".5 " 0 =!.7 " 0 J. 5 Using E K = m, E P =! m and =! m we deduce that (a) B has the lage kinetic enegy, (b) has the lage potential enegy and (c) has the lage total enegy. 6 he speed in obit is given fom mv then E K = mv = m is = m! m = G Mm to be v = G M. he potential enegy is E P =! m =! m. Since = 5, =! m 0.. he kinetic enegy is and so the total enegy 7 Fom poblem 6, =! m. Since we ae told that =! m 5 conseved,! m =! m 5 " = 5. and enegy is
4 8 he space station is in an obit with obit adius e and so has speed v = with e espect to the eath. Let the satellite be launched with speed u with espect to the space station. hen the speed with espect to the eath is u + v. Its total enegy is theefoe m(u + v)! m. t the escape speed this enegy must be zeo and so e u = e! v = e! e ". 0 ms!. 9 (a) he engines do positive wok inceasing the total enegy of the satellite. Since =! m it follows that the obit adius will incease. (b) Since the kinetic enegy is given by E K = m and the obit adius has inceased the speed in the new cicula obit will decease. (c) he fiing of the ockets when the satellite is in the lowe obit make the satellite move on an elliptical obit. fte half a evolution the satellite will be at and futhe fom the eath than in the oiginal position at P. s the satellite gets to its kinetic enegy is educed and the potential enegy inceases. t the speed is too low fo the new cicula obit and the engines must again be fied to incease the speed to that appopiate to the new obit. (If the engines ae not fied at then the satellite will emain in the elliptical obit and will etun to P.) 0 he tangential component at is in the diection of velocity and so the planet inceases its speed. t B it is opposite to the velocity and so the speed deceases. he nomal component does zeo wok since the angle between foce and displacement is a ight angle and cos90! = 0. he potential enegy is given by E P =! m. his is least when the distance to the sun is the smallest (emembe E P is negative). heefoe since the total enegy is conseved, the kinetic enegy and hence the speed ae geatest at P. (a) he atio is
5 B F moon F B sun! F moon! F sun this gives B F moon F B sun =! F moon! F sun = moon m (d moon! e )! m moon (d moon + e ) sun m (d sun! e )! = sunm (d sun + e ) M moon (d moon! e )! M moon (d moon + e ) 7.5 " 0 (.84 " 0 8! 6.4 " 0 6 )! 7.5 " 0 (.84 " " 0 6 ).99 " 0 0 (.5 " 0! 6.4 " 0 6 )!.99 " 0 0 (.5 " " 0 6 ) indicates the elative impotance of the moon. M sun (d sun! e )! M sun (d sun + e ). Numeically.. (b) his he escape speed is obtained fom mv! m and so = g. Substituting, v = g. = 0, i.e. v =. But g = 4 (a) he net gavitational field stength at the indicated position has magnitude g = G6m (4d / 5)! Gm (d / 5) = G5m! G5m = 0. (b) d d V =! G6m (4d / 5)! Gm (d / 5) =! G0m! G5m =! 5Gm. d d d 5 (a) See poblem. (b) = 4! M = 4!" 4!. Substituting, = G. Now! and! = M 4" 4!" =! G". 6 (a) We must use the fomula = 4! Now g =! = g. Substituting, = 4! g =!.4 " = M 4". Hence, that we have deived many times aleady. = 4! g. Hence =! g. (b) = 5.5 " 0 s = 9 min. (c) Fom = 4! we deduce that = hence 9 40 = (.4! 06 ) and so = 4.5! 0 6 m. he height is theefoe h = 4.5! 0 6 ".4! 0 6 =.! 0 6 m.
6 7 (a) F = 4 = = "!. (b) 4 4 &. Hence = 6! = Mv and so v = 4. But v =. (c) "! & and so 6! (.0 " 0 9 ) 6.67 " 0 ".5 ".0 " 0 0 =.8 " 04 s = 7.8 h. (d) = Mv + Mv!. Since v = 4 we have that E = M 4! " = 4 " = " 4. (e) Since enegy is being lost the total enegy will decease. his implies that the distance will decease. (Fom the peiod fomula in (b) the peiod will decease as well.) (f) (i) he total enegy is =! 4 and the peiod is = 6!. Combining the two gives =! 4 & o E / =!c!/ whee c is a constant. Woking as we do with 6" ( popagation of uncetainties (o using calculus) we have that! =! o! = is theefoe!. (ii)! =!.9! 0 "9 y " =.6! 08 y. = " 7 " 06 s y.8 " 0 4 s =.9 " 0 9 y (g) he lifetime 8 (a) he patten is not symmetical and so the masses must be diffeent. he spheical equipotential sufaces of the ight mass ae much less distoted and so this is the lage mass.(b) he gavitational field lines ae nomal to the equipotential sufaces. (c) Fom fa away it looks like we have a single mass of magnitude equal to the sum of the two individual masses. he equipotential sufaces of a single point mass ae spheical. 9 (a) he magnitude of the gavitational field stength is the slope of a potential distance gaph. Dawing a tangent to the cuve at d = 0.0 we find a slope of appoximately 4.7 N kg!. (b) t = 0.75 the slope of the gaph is zeo. But the slope of a potential d distance gaph is the magnitude of the gavitational field stength. Hence g is zeo at this point. (c) Since g = 0 =! Gm (d! ) = (0.75d)! Gm it follows that (d! 0.75d) M m = (0.75d) (0.5d) = 9.
Revision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams
More informationA) 2 B) 2 C) 2 2 D) 4 E) 8
Page 1 of 8 CTGavity1. m M Two spheical masses m and M ae a distance apat. The distance between thei centes is halved (deceased by a facto of 2). What happens to the magnitude of the foce of gavity between
More informationGravitation. AP Physics C
Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More information14. Gravitation Universal Law of Gravitation (Newton):
14. Gavitation 1 Univesal Law of Gavitation (ewton): The attactive foce between two paticles: F = G m 1m 2 2 whee G = 6.67 10 11 m 2 / kg 2 is the univesal gavitational constant. F m 2 m 1 F Paticle #1
More informationChapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43
Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.
More informationPHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013
PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationChapter 13 Gravitation
Chapte 13 Gavitation Newton, who extended the concept of inetia to all bodies, ealized that the moon is acceleating and is theefoe subject to a centipetal foce. He guessed that the foce that keeps the
More informationGRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players:
CHAPT 11 TH GAVITATIONAL FILD (GAVITY) GAVITATIONAL FILD: The goundwok fo Newton s geat contibution to undestanding gavity was laid by thee majos playes: Newton s Law of Gavitation o gavitational and inetial
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationESCAPE VELOCITY EXAMPLES
ESCAPE VELOCITY EXAMPLES 1. Escape velocity is the speed that an object needs to be taveling to beak fee of planet o moon's gavity and ente obit. Fo example, a spacecaft leaving the suface of Eath needs
More informationSamples of conceptual and analytical/numerical questions from chap 21, C&J, 7E
CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known
More informationMultiple choice questions [60 points]
1 Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect bubble on you scanton sheet. Each question has exactly one coect answe. All questions
More informationCh. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth
Ch. 8 Univesal Gavitation Pat 1: Keple s Laws Objectives: Section 8.1 Motion in the Heavens and on Eath Objectives Relate Keple s laws of planetay motion to Newton s law of univesal gavitation. Calculate
More informationSo we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1)
Lectue 17 Cicula Motion (Chapte 7) Angula Measue Angula Speed and Velocity Angula Acceleation We ve aleady dealt with cicula motion somewhat. Recall we leaned about centipetal acceleation: when you swing
More informationExam I. Spring 2004 Serway & Jewett, Chapters 15. Fill in the bubble for the correct answer on the answer sheet. next to the number.
Agin/Meye PART I: QUALITATIVE Exam I Sping 2004 Seway & Jewett, Chaptes 15 Assigned Seat Numbe Fill in the bubble fo the coect answe on the answe sheet. next to the numbe. NO PARTIAL CREDIT: SUBMIT ONE
More informationLesson 32: Measuring Circular Motion
Lesson 32: Measuing Cicula Motion Velocity hee should be a way to come up with a basic fomula that elates velocity in icle to some of the basic popeties of icle. Let s ty stating off with a fomula that
More informationrotation  Conservation of mechanical energy for rotation  Angular momentum  Conservation of angular momentum
Final Exam Duing class (13:55 pm) on 6/7, Mon Room: 41 FMH (classoom) Bing scientific calculatos No smat phone calculatos l ae allowed. Exam coves eveything leaned in this couse. Review session: Thusday
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation
More informationF G r. Don't confuse G with g: "Big G" and "little g" are totally different things.
G1 Gavity Newton's Univesal Law of Gavitation (fist stated by Newton): any two masses m 1 and m exet an attactive gavitational foce on each othe accoding to m m G 1 This applies to all masses, not just
More informationVoltage ( = Electric Potential )
V1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
More informationVoltage ( = Electric Potential )
V1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More information2008 QuarterFinal Exam Solutions
2008 Quatefinal Exam  Solutions 1 2008 QuateFinal Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of
More information12. Rolling, Torque, and Angular Momentum
12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.
More informationChapter 23: Gauss s Law
Chapte 3: Gauss s Law Homewok: Read Chapte 3 Questions, 5, 1 Poblems 1, 5, 3 Gauss s Law Gauss s Law is the fist of the fou Maxwell Equations which summaize all of electomagnetic theoy. Gauss s Law gives
More informationPhysics: Electromagnetism Spring PROBLEM SET 6 Solutions
Physics: Electomagnetism Sping 7 Physics: Electomagnetism Sping 7 PROBEM SET 6 Solutions Electostatic Enegy Basics: Wolfson and Pasachoff h 6 Poblem 7 p 679 Thee ae si diffeent pais of equal chages and
More informationPY1052 Problem Set 3 Autumn 2004 Solutions
PY1052 Poblem Set 3 Autumn 2004 Solutions C F = 8 N F = 25 N 1 2 A A (1) A foce F 1 = 8 N is exeted hoizontally on block A, which has a mass of 4.5 kg. The coefficient of static fiction between A and the
More informationPHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013
PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,
More informationGeneral Physics (PHY 2130)
Geneal Physics (PHY 130) Lectue 11 Rotational kinematics and unifom cicula motion Angula displacement Angula speed and acceleation http://www.physics.wayne.edu/~apetov/phy130/ Lightning Review Last lectue:
More informationExam 3: Equation Summary
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P
More information7 Circular Motion. 71 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary
7 Cicula Motion 71 Centipetal Acceleation and Foce Peiod, Fequency, and Speed Vocabulay Vocabulay Peiod: he time it takes fo one full otation o evolution of an object. Fequency: he numbe of otations o
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationPY1052 Problem Set 8 Autumn 2004 Solutions
PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ighthand end. If H 6.0 m and h 2.0 m, what
More informationPhysics HSC Course Stage 6. Space. Part 1: Earth s gravitational field
Physics HSC Couse Stage 6 Space Pat 1: Eath s gavitational field Contents Intoduction... Weight... 4 The value of g... 7 Measuing g...8 Vaiations in g...11 Calculating g and W...13 You weight on othe
More informationHour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and
Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon
More information81 Newton s Law of Universal Gravitation
81 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,
More informationPhysics 202, Lecture 4. Gauss s Law: Review
Physics 202, Lectue 4 Today s Topics Review: Gauss s Law Electic Potential (Ch. 25Pat I) Electic Potential Enegy and Electic Potential Electic Potential and Electic Field Next Tuesday: Electic Potential
More informationResources. Circular Motion: From Motor Racing to Satellites. Uniform Circular Motion. Sir Isaac Newton 3/24/10. Dr Jeff McCallum School of Physics
3/4/0 Resouces Cicula Motion: Fom Moto Racing to Satellites D Jeff McCallum School of Physics http://www.gapsystem.og/~histoy/mathematicians/ Newton.html http://www.fga.com http://www.clke.com/clipat
More informationLab 5: Circular Motion
Lab 5: Cicula motion Physics 193 Fall 2006 Lab 5: Cicula Motion I. Intoduction The lab today involves the analysis of objects that ae moving in a cicle. Newton s second law as applied to cicula motion
More information1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
More informationThe Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = W/q 0 1V [Volt] =1 Nm/C
Geneal Physics  PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit
More informationThe Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
More informationChapter 26  Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More information2. Orbital dynamics and tides
2. Obital dynamics and tides 2.1 The twobody poblem This efes to the mutual gavitational inteaction of two bodies. An exact mathematical solution is possible and staightfowad. In the case that one body
More informationChapter 3: Vectors and Coordinate Systems
Coodinate Systems Chapte 3: Vectos and Coodinate Systems Used to descibe the position of a point in space Coodinate system consists of a fied efeence point called the oigin specific aes with scales and
More information(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of
Homewok VI Ch. 7  Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the
More informationGravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2
F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,
More informationPhysics 111 Fall 2007 Electrostatic Forces and the Electric Field  Solutions
Physics 111 Fall 007 Electostatic Foces an the Electic Fiel  Solutions 1. Two point chages, 5 µc an 8 µc ae 1. m apat. Whee shoul a thi chage, equal to 5 µc, be place to make the electic fiel at the
More informationLab #7: Energy Conservation
Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 14 Intoduction: Pehaps one of the most unusual
More information2. An asteroid revolves around the Sun with a mean orbital radius twice that of Earth s. Predict the period of the asteroid in Earth years.
CHAPTR 7 Gavitation Pactice Poblems 7.1 Planetay Motion and Gavitation pages 171 178 page 174 1. If Ganymede, one of Jupite s moons, has a peiod of days, how many units ae thee in its obital adius? Use
More informationIn this section we shall look at the motion of a projectile MOTION IN FIELDS 9.1 PROJECTILE MOTION PROJECTILE MOTION
MOTION IN FIELDS MOTION IN FIELDS 9 9. Pojectile motion 9. Gavitational field, potential and enegy 9.3 Electic field, potential and enegy 9. PROJECTILE MOTION 9.. State the independence of the vetical
More information1.1 KINEMATIC RELATIONSHIPS
1.1 KINEMATIC RELATIONSHIPS Thoughout the Advanced Highe Physics couse calculus techniques will be used. These techniques ae vey poweful and knowledge of integation and diffeentiation will allow a deepe
More informationPhys 2101 Gabriela González. cos. sin. sin
1 Phys 101 Gabiela González a m t t ma ma m m T α φ ω φ sin cos α τ α φ τ sin m m α τ I We know all of that aleady!! 3 The figue shows the massive shield doo at a neuton test facility at Lawence Livemoe
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More informationChapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.
Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming
More informationProblems on Force Exerted by a Magnetic Fields from Ch 26 T&M
Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuentcaying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to
More informationAlgebra and Trig. I. A point is a location or position that has no size or dimension.
Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite
More informationLearning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds.
Lectue #0 Chapte Atomic Bonding Leaning Objectives Descibe ionic, covalent, and metallic, hydogen, and van de Waals bonds. Which mateials exhibit each of these bonding types? What is coulombic foce of
More informationIntroduction to Electric Potential
Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic
More informationTheory and measurement
Gavity: Theoy and measuement Reading: Today: p11  Theoy of gavity Use two of Newton s laws: 1) Univesal law of gavitation: ) Second law of motion: Gm1m F = F = mg We can combine them to obtain the gavitational
More informationGravity and the figure of the Earth
Gavity and the figue of the Eath Eic Calais Pudue Univesity Depatment of Eath and Atmospheic Sciences West Lafayette, IN 479071397 ecalais@pudue.edu http://www.eas.pudue.edu/~calais/ Objectives What is
More information1. CIRCULAR MOTION. ω =
1. CIRCULAR MOION 1. Calculate the angula elocity and linea elocity of a tip of minute hand of length 1 cm. 6 min. 6 6 s 36 s l 1 cm.1 m ω?? Fomula : ω π ω ω π 3.14 36 ω 1.744 1 3 ad/s ω.1 1.74 1 3 1.74
More informationAP Physics Electromagnetic Wrap Up
AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationIn the lecture on double integrals over nonrectangular domains we used to demonstrate the basic idea
Double Integals in Pola Coodinates In the lectue on double integals ove nonectangula domains we used to demonstate the basic idea with gaphics and animations the following: Howeve this paticula example
More informationSolutions to Homework Set #5 Phys2414 Fall 2005
Solution Set #5 1 Solutions to Homewok Set #5 Phys414 Fall 005 Note: The numbes in the boxes coespond to those that ae geneated by WebAssign. The numbes on you individual assignment will vay. Any calculated
More informationClassical Lifetime of a Bohr Atom
1 Poblem Classical Lifetime of a Boh Atom James D. Olsen and Kik T. McDonald Joseph Heny Laboatoies, Pinceton Univesity, Pinceton, NJ 85 (Mach 7, 5) In the Boh model of the hydogen atom s gound state,
More informationUNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100minute sessions
Name St.No.  Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,
More informationMagnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew  electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
More informationProblem Set 6: Solutions
UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 164 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente
More informationTRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles
TRIGONOMETRY REVIEW The Cosines and Sines of the Standad Angles P θ = ( cos θ, sin θ ) . ANGLES AND THEIR MEASURE In ode to define the tigonometic functions so that they can be used not only fo tiangula
More information2  ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1
 ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation
More informationDisplacement, Velocity And Acceleration
Displacement, Velocity And Acceleation Vectos and Scalas Position Vectos Displacement Speed and Velocity Acceleation Complete Motion Diagams Outline Scala vs. Vecto Scalas vs. vectos Scala : a eal numbe,
More informationOn the Relativistic Forms of Newton's Second Law and Gravitation
On the Relativistic Foms of Newton's Second Law and avitation Mohammad Bahami,*, Mehdi Zaeie 3 and Davood Hashemian Depatment of physics, College of Science, Univesity of Tehan,Tehan, Islamic Republic
More informationFluids Lecture 15 Notes
Fluids Lectue 15 Notes 1. Unifom flow, Souces, Sinks, Doublets Reading: Andeson 3.9 3.12 Unifom Flow Definition A unifom flow consists of a velocit field whee V = uî + vĵ is a constant. In 2D, this velocit
More informationChapter 8, Rotational Kinematics. Angular Displacement
Chapte 8, Rotational Kinematics Sections 1 3 only Rotational motion and angula displacement Angula velocity and angula acceleation Equations of otational kinematics 1 Angula Displacement! B l A The length
More informationChapter 4. Electric Potential
Chapte 4 Electic Potential 4.1 Potential and Potential Enegy... 43 4.2 Electic Potential in a Unifom Field... 47 4.3 Electic Potential due to Point Chages... 48 4.3.1 Potential Enegy in a System of
More informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chapte The lectic Field II: Continuous Chage Distibutions 1 [M] A unifom line chage that has a linea chage density l equal to.5 nc/m is on the x axis between x and x 5. m. (a) What is its total chage?
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
More informationIntroduction to Fluid Mechanics
Chapte 1 1 1.6. Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = 3.174 ft/s. (a) What is its mass in kg? (b) What will the weight of this body
More informationThe Grating Spectrometer and Atomic Spectra
PHY 19 Gating Spectomete 1 The Gating Spectomete and Atomic Specta Intoduction In the pevious expeiment diffaction and intefeence wee discussed and at the end a diffaction gating was intoduced. In this
More informationSection 53 Angles and Their Measure
5 5 TRIGONOMETRIC FUNCTIONS Section 5 Angles and Thei Measue Angles Degees and Radian Measue Fom Degees to Radians and Vice Vesa In this section, we intoduce the idea of angle and two measues of angles,
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson AddisonWesley.
Chapte 5. Foce and Motion In this chapte we study causes of motion: Why does the windsufe blast acoss the wate in the way he does? The combined foces of the wind, wate, and gavity acceleate him accoding
More informationEnergy Conservation. Energy Conservation. Work Done by Gravitational Force. Work Done by Gravitational Force. Work Done by Gravitational Force.
1. Consevative/Nonconsevative Foces Wok alon a path (Path inteal) Wok aound an closed path (Path inteal). Potential Ene (P.E.) Mechanical 3. Findin P.E. function 4. Ene Diaam Wok Done b Gavitational Foce
More informationCHAPTER 17 MAGNETIC DIPOLE MOMENT
1 CHAPTER 17 MAGNETIC DIPOLE MOMENT 17.1 Intoduction A numbe of diffeent units fo expessing magnetic dipole moment (heeafte simply magnetic moment ) ae commonly seen in the liteatue, including, fo example,
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More informationF = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a
.1 What ae the hoizontal and vetical components of the esultant electostatic foce on the chage in the lowe left cone of the squae if q =1. 1 7 and a =5.cm? +q q a +q a q F = kq 1q F 1 = k(q)(q) a F 13
More informationUNIVERSITY OF CALIFORNIA BERKELEY Structural Engineering, Professor: S. Govindjee. ElasticPerfectly Plastic Thick Walled Sphere
UNIVERSITY OF CALIFORNIA BERKELEY Stuctual Engineeing, Depatment of Civil Engineeing Mechanics and Mateials Fall 00 Pofesso: S Govindjee ElasticPefectly Plastic Thick Walled Sphee Conside a thick walled
More informationPHYSICS 218 Honors EXAM 2 Retest. Choose 5 of the following 6 problems. Indicate which problem is not to be graded.
PHYSICS 18 Honos EXAM Retest Choose 5 of the following 6 pobles. Indicate which poble is not to be gaded. 1. A ope is affixed at one end to the i of a pulley, and wapped five tuns aound the pulley. The
More informationAnalytical Proof of Newton's Force Laws
Analytical Poof of Newton s Foce Laws Page 1 1 Intouction Analytical Poof of Newton's Foce Laws Many stuents intuitively assume that Newton's inetial an gavitational foce laws, F = ma an Mm F = G, ae tue
More informationChapter 13. VectorValued Functions and Motion in Space 13.6. Velocity and Acceleration in Polar Coordinates
13.6 Velocity and Acceleation in Pola Coodinates 1 Chapte 13. VectoValued Functions and Motion in Space 13.6. Velocity and Acceleation in Pola Coodinates Definition. When a paticle P(, θ) moves along
More informationMultiple choice questions [70 points]
Multiple choice questions [70 points] Answe all of the following questions. Read each question caefull. Fill the coect bubble on ou scanton sheet. Each question has exactl one coect answe. All questions
More information6.2 Orbits and Kepler s Laws
Eath satellite in unstable obit 6. Obits and Keple s Laws satellite in stable obit Figue 1 Compaing stable and unstable obits of an atificial satellite. If a satellite is fa enough fom Eath s suface that
More informationGravity. A. Law of Gravity. Gravity. Physics: Mechanics. A. The Law of Gravity. Dr. Bill Pezzaglia. B. Gravitational Field. C.
Physics: Mechanics 1 Gavity D. Bill Pezzaglia A. The Law of Gavity Gavity B. Gavitational Field C. Tides Updated: 01Jul09 A. Law of Gavity 3 1a. Invese Squae Law 4 1. Invese Squae Law. Newton s 4 th law
More informationL19 Geomagnetic Field Part I
Intoduction to Geophysics L191 L19 Geomagnetic Field Pat I 1. Intoduction We now stat the last majo topic o this class which is magnetic ields and measuing the magnetic popeties o mateials. As a way o
More informationEconomics 326: Input Demands. Ethan Kaplan
Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly
More information