LECTURE 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

Size: px
Start display at page:

Download "LECTURE 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"

Transcription

1 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 infoation one potulate that gavitation poduce an attactive foce. b Baed on the econd law of Newton igue a _ o _ iilaly c Baed on the thid law of Newton It coe out that ( d Baed on expeiental eult Newton gueed that gavitation foce deceae with ditance a /. o, it coe out that oe peciely G ( eaueent how that G 6.67*0 - N /kg i the univeal contant of gavitation - The gavitational foce i a vecto diected veu the ouce that exet thi foce. o, it vecto fo i G (3 G i the unit vecto with tail at a the ouce of. i the unit vecto with tail at a the ouce of - To apy the gavitational law fo two bodie cloe to each othe one ut ue integation technique and the difficulty of calculi depend on the fo of the two bodie. But, if the bodied ae fa enough to each othe, one ay odel the by point paticle and apy the law in it oiginal fo. In paticula, with oe appoxiation, we ae able to odel the inteaction of eath with an object on it uface a if the whole a of the eath i concentated at it cente and the object ae at ditance eath. -any expeient have hown that; when eveal paticle inteact gavitationally between the the pincie of linea upepoition apie. o, inide a yte of paticle,, 3, n, the foce exeted on a i ] TH GVITTION ND TH INTI n i i (4 -When expeing the econd law of Newton we ue the inetial a NT in a (5 When foulating the gavitation law, Newton wa not ue that the a of paticle in thi law i the ae a thei inetial a. et veify thi iue. We tat by uppoing that the a in the gavitational law ay be diffeent fo in. o, we note it g. et conide now a body in fee fall cloe to eath g ath uface. The eath will exet on it the gavitational foce with agnitude g G (3 ath Hee we aue that the body i cloe to the uface o that it ditance fo eath cente i. ath Thei dienion ae <<< than the ditance between the.

2 thi i the net foce exeted on the body we apy the econd law of Newton g ath ath ath NT ina g G o, we get a G g in g ( g becaue G g ath ath ath g Then, a g (6 in big nube of eaueent how that the acceleation of fee bodie i equal to g 9.8/. Thi ean that g / in, and in g. o, the expeient confi that the gavitational a i the ae a the inetial a. - et apy the gavitation law fo the foce exeted by eath ove a a kg cloe to eath. ath ath G g (7 o, the g-vecto i equal to the gavitation foce exeted ( ath + h ath on a a kg. By eauing the foce exeted on the a kg in diffeent location on the eath one get a whole yte of g-vecto (fig.. The totality of thee vecto fo the gavitational field of the eath. igue (7 Note that the g-vecto agnitude deceae with the inceae of ditance h fo the eath but it i alway diected veu the cente of the eath. The gavitational field of the eath ha a pheical yety. In fact, it i not exactly pheical, becaue the odel of eath a a unifo denity phee i not vey pecie. Now, the object weight i equal to gavitational foce exeted by thi field W g (7 o, the weight of the ae object i a vecto that i diffeent in diffeent point of gavitational field of the eath. 3] K W ON NTY OTION - it law: The anet ove on elliptic obit aound the un that i located at one of it focue. igue 3 un b a eihelion phelion The ino axi i long b and the ajo axi i long a. The cloet ditance to un i called peihelion and the bigget ditance to un i called aphelion (fig.3. econd law: The line un- anet weep out equal aea fo equal inteval of tie. igue 4 Thid law: The quae of the peiod of anet otion i popotional to the cube of aveage ditance fo the un. Calculation how that the aveage of ditance un-anet i equal to half of ajo axi a. Then, atellite otion (ee ectue_8.5 tell that T κ a 3 (8 4π whee κ un G un

3 Note : Kee law ae valid fo elliptical path of any anet aound a cental body; fo exae the 4π oon oving aound the eath but in thi cae κ ath. G ath TH NGY O NT igue 5 - the a of othe anet i uch alle than the a of un we neglect thei action on the otion of the tudied anet. We conide that the yte un-anet i a conevative yte, i.e. the foce oiginated fo outide it ae zeo. In thee cicutance: a The toque of exteio foce i zeo and we can apy the pincie fo conevation of angula oentu. b The wok done by Net exteio foce i zeo and we can apy the pincie of enegy conevation fo the yte un-anet - The pincie of angula oentu conevation tell that (9 o x p B x p (0 0 0 The equality of agnitude bing to condition p in 90 p in 90 anet anet o, we get ( B -The pincie of enegy conevation tell that that ( the echanical enegy i K + U whee K (3 and U We get fte cancelling un By uing the equation ( and the fact that un un and finally un un G (4 un G un ( (5 (6 + a (7, afte oe calculation we find that G (8 and a G (9 a inally, by ubtituting one of thi expeion at the expeion of total enegy (at peihelion o aphelion un we get G (0 a 4] TH BOUND ND UNBOUND TJCTOI -et ee what happen with an object thown up with high initial velocity. The only foce exeted on it i ath the gavitational foce of the eath. G ( extenal net foce i zeo, the yte eath object coneve it enegy. o uch a yte U + K i a contant all tie. Note: the eath i the efeence fae, geneally one talk fo object enegy. 3

4 - By uing the wok done by the gavitation foce (exp. one ay find ath that U ( G ( U( > The gaph of thi function i hown in figue 6. Note that the zeo value of potential enegy of gavitational inteaction i et fo big -value. The zeo-value of potential enegy ean that thee i no inteaction U( between the yte pat, o oe peciely the pat ae not bound to each othe. When the object i on the eath uface, the ditance fo U( C of the eath (at oigin of gaph i equal to the eath adiu and K it potential enegy i U(. When we thow it vetically with initial igue 6 velocity, the echanical enegy of the object (i.e. of object eath yte i ( U( +K( (3 we know, the velocity of the object will deceae with height and will becoe zeo at it axiu height h, i.e. at ditance ( + h. When getting at thi ditance, all it enegy i potential enegy. o, ( U( (4 We ay that the kinetic enegy ake it clib up on a potential well (ee fig.6. The pincie of enegy conevation tell that ( ( (5 By uing thi equation we can find the axiu height a follow; ( +h ( ( +h U( +h and uing (3 we get U( +h ( U( +K( (6 o, ath ath G + and + h G ath ( + h G ath G ath G ath Then, ( _ a _ h << _ ( + h / h + h / G ath g we find that h (7 which i a known eult fo kineatic. g e - When the initial velocity of the body i uch that U( + K( < 0 the object will get to a given ditance fo eath but will eain all tie bound within the yte eath-object; If U( + K( 0 the object will get o fa that the inteaction with eath becoe zeo; it becoe an unbounded object to gavitational field of the eath. The liiting initial velocity neceay to unbind fo gavitational field of eath i known a ecape velocity ec. Thi velocity can be found by condition ec G U ( + K( ec 0 G + 0 ec (8 - uppoe that one ut end a ocket out of eath gavitational field; i.e. ake it unbound object to eath. The fit equieent i to give to ocket an initial velocity ec. ie calculation baed on expeion (8 how that ec 90 /. Thi value of initial velocity can be funihed only by eactive engine. Though a integal calculu. 4

5 What fo ha the tajectoy of an unbound ocket? The atheatical calculation how that if a > ec the ocket tajectoy will not be cloed and it i a hypebola. b ec the ocket tajectoy will not be cloed and it i a paabola. If the initial velocity of ocket < ec the object eain a bound object to the eath gavitation field and it tajectoy will be an ellipe (cloed obit. Note that if the initial velocity i too all << ec, thi obit ay co the eath, i.e. the ocket will tike on eath uface (figue 7. << ec ath < ec ellip -Conide an atificial atellite oving unifoly on a cicula obit at ditance fo C of the eath (fig.8. It otion ha a centipetal acceleation ac and the net foce exeted on it i the eath gavitation. o, G and ac We get G and G (9 What i the equied launch peed fo thi atellite? We apy the pincie of enegy conevation. ( ( (30 > ec ec paabolla G hipebola igue 7 o, G G ( (3 ath G G ( + ( h + h G ( h G ( + (3 o low obit atellite (ay height00-00k fo eath (6378k h/ and fo (3 we can find that igue 8 Cicula obite of atellite. G cicula low obit with adiu i o, the launch velocity fo a tationay G (33 5

Test 2 phy a) How is the velocity of a particle defined? b) What is an inertial reference frame? c) Describe friction.

Test 2 phy a) How is the velocity of a particle defined? b) What is an inertial reference frame? c) Describe friction. Tet phy 40 1. a) How i the velocity of a paticle defined? b) What i an inetial efeence fae? c) Decibe fiction. phyic dealt otly with falling bodie. d) Copae the acceleation of a paticle in efeence fae

More information

Perhaps the greatest success of his theory of gravity was to successfully explain the motion of the heavens planets, moons, &tc.

Perhaps the greatest success of his theory of gravity was to successfully explain the motion of the heavens planets, moons, &tc. AP Phyic Gavity Si Iaac Newton i cedited with the dicovey of gavity. Now, of coue we know that he didn t eally dicove the thing let face it, people knew about gavity fo a long a thee have been people.

More information

Honors Classical Physics I

Honors Classical Physics I Hono Claical Phyic I PHY141 Lectue 9 Newton Law of Gavity Pleae et you Clicke Channel to 1 9/15/014 Lectue 9 1 Newton Law of Gavity Gavitational attaction i the foce that act between object that have a

More information

( ) rad ( 2.0 s) = 168 rad

( ) rad ( 2.0 s) = 168 rad .) α 0.450 ω o 0 and ω 8.00 ω αt + ω o o t ω ω o α HO 9 Solution 8.00 0 0.450 7.8 b.) ω ω o + αδθ o Δθ ω 8.00 0 ω o α 0.450 7. o Δθ 7. ev.3 ev π.) ω o.50, α 0.300, Δθ 3.50 ev π 7π ev ω ω o + αδθ o ω ω

More information

Chapter 13 Gravitation

Chapter 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 information

Can a watch-sized electromagnet deflect a bullet? (from James Bond movie)

Can a watch-sized electromagnet deflect a bullet? (from James Bond movie) Can a peon be blown away by a bullet? et' ay a bullet of a 0.06 k i ovin at a velocity of 300 /. And let' alo ay that it ebed itelf inide a peon. Could thi peon be thut back at hih peed (i.e. blown away)?

More information

( ) Physics 1401 Homework Solutions - Walker, Chapter 9

( ) Physics 1401 Homework Solutions - Walker, Chapter 9 Phyic 40 Conceptual Quetion CQ No Fo exaple, ey likely thee will be oe peanent deoation o the ca In thi cae, oe o the kinetic enegy that the two ca had beoe the colliion goe into wok that each ca doe on

More information

= 4 3 π( m) 3 (5480 kg m 3 ) = kg.

= 4 3 π( m) 3 (5480 kg m 3 ) = kg. CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential

More information

Content 5.1 Angular displacement and angular velocity 5.2 Centripetal acceleration 5.3 Centripetal force. 5. Circular motion.

Content 5.1 Angular displacement and angular velocity 5.2 Centripetal acceleration 5.3 Centripetal force. 5. Circular motion. 5. Cicula otion By Liew Sau oh Content 5.1 Angula diplaceent and angula elocity 5. Centipetal acceleation 5.3 Centipetal foce Objectie a) expe angula diplaceent in adian b) define angula elocity and peiod

More information

m1 m2 M 2 = M -1 L 3 T -2

m1 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 information

1121 T Question 1

1121 T Question 1 1121 T1 2008 Question 1 ( aks) You ae cycling, on a long staight path, at a constant speed of 6.0.s 1. Anothe cyclist passes you, tavelling on the sae path in the sae diection as you, at a constant speed

More information

Homework Set 4 Physics 319 Classical Mechanics. m m k. x, x, x, x T U x x x x l 2. x x x x. x x x x

Homework Set 4 Physics 319 Classical Mechanics. m m k. x, x, x, x T U x x x x l 2. x x x x. x x x x Poble 78 a) The agangian i Hoewok Set 4 Phyic 319 Claical Mechanic k b) In te of the cente of a cooinate an x x1 x x1 x xc x x x x x1 xc x xc x x x x x1 xc x xc x, x, x, x T U x x x x l 1 1 1 1 1 1 1 1

More information

SPH4U Unit 6.3 Gravitational Potential Energy Page 1 of 9

SPH4U Unit 6.3 Gravitational Potential Energy Page 1 of 9 SPH4 nit 6.3 Gavitational Potential negy Page of Notes Physics ool box he gavitational potential enegy of a syste of two (spheical) asses is diectly popotional to the poduct of thei asses, and invesely

More information

Force & Motion: Newton s Laws

Force & Motion: Newton s Laws oce & otion: Newton Law ( t Law) If no net foce act on a body then the body velocity cannot change. Zeo net foce implie zeo acceleation. The ma of an object detemine how difficult it i to change the object

More information

Chapter 19 Webassign Help Problems

Chapter 19 Webassign Help Problems Chapte 9 Webaign Help Poblem 4 5 6 7 8 9 0 Poblem 4: The pictue fo thi poblem i a bit mileading. They eally jut give you the pictue fo Pat b. So let fix that. Hee i the pictue fo Pat (a): Pat (a) imply

More information

Chapter 4. Newton s Laws of Motion

Chapter 4. Newton s Laws of Motion Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto

More information

10. Force is inversely proportional to distance between the centers squared. R 4 = F 16 E 11.

10. 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 information

Radius of the Moon is 1700 km and the mass is 7.3x 10^22 kg Stone. Moon

Radius 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 information

Astronomy 421 Concepts of Astrophysics I. Astrophysics Talks at UNM. Course Logistics. Backgrounds. Other Opportunities

Astronomy 421 Concepts of Astrophysics I. Astrophysics Talks at UNM. Course Logistics. Backgrounds. Other Opportunities Astonoy 421 Concepts of Astophysics I Couse Logistics Goals: - Ipove knowledge of astophysics - develop eseach skills ain Aeas of Study: - Obital echanics - Radiation and atte - Relativity - Stas - Stella

More information

Ch 13 Universal Gravitation

Ch 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 information

Universal Gravitation

Universal Gravitation Add Ipotant Univeal Gavitation Pae: 7 Note/Cue Hee Unit: Dynaic (oce & Gavitation Univeal Gavitation Unit: Dynaic (oce & Gavitation NGSS Standad: HS-PS-4 MA Cuiculu aewok (00:.7 AP Phyic Leanin Objective:.B..,.B..,

More information

Gravitation. AP/Honors Physics 1 Mr. Velazquez

Gravitation. 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 information

OSCILLATIONS AND GRAVITATION

OSCILLATIONS 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 information

Chapter 13: Gravitation

Chapter 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 information

PHYSICS NOTES GRAVITATION

PHYSICS NOTES GRAVITATION GRAVITATION Newton s law of gavitation The law states that evey paticle of matte in the univese attacts evey othe paticle with a foce which is diectly popotional to the poduct of thei masses and invesely

More information

Rotational Kinetic Energy

Rotational Kinetic Energy Add Impotant Rotational Kinetic Enegy Page: 353 NGSS Standad: N/A Rotational Kinetic Enegy MA Cuiculum Famewok (006):.1,.,.3 AP Phyic 1 Leaning Objective: N/A, but olling poblem have appeaed on peviou

More information

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once.

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once. Honos Physics Fall, 2016 Cicula Motion & Toque Test Review Name: M. Leonad Instuctions: Complete the following woksheet. SHOW ALL OF YOUR WORK ON A SEPARATE SHEET OF PAPER. 1. Detemine whethe each statement

More information

ASTR 3740 Relativity & Cosmology Spring Answers to Problem Set 4.

ASTR 3740 Relativity & Cosmology Spring Answers to Problem Set 4. ASTR 3740 Relativity & Comology Sping 019. Anwe to Poblem Set 4. 1. Tajectoie of paticle in the Schwazchild geomety The equation of motion fo a maive paticle feely falling in the Schwazchild geomety ae

More information

Class 6 - Circular Motion and Gravitation

Class 6 - Circular Motion and Gravitation Class 6 - Cicula Motion and Gavitation pdf vesion [http://www.ic.sunysb.edu/class/phy141d/phy131pdfs/phy131class6.pdf] Fequency and peiod Fequency (evolutions pe second) [ o ] Peiod (tie fo one evolution)

More information

- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.

- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session. - 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU

More information

Between any two masses, there exists a mutual attractive force.

Between 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 information

MODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES VISUAL PHYSICS ONLINE

MODULE 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 information

Central Force Problem. Central Force Motion. Two Body Problem: Center of Mass Coordinates. Reduction of Two Body Problem 8.01 W14D1. + m 2. m 2.

Central 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 information

Equations of 2-body motion

Equations of 2-body motion Equation of -body motion The fundamental eqn. of claical atodynamic i Newton Law of Univeal Gavitation: F g = Gm i i i ˆ i (1) We ae inteeted in atellite in obit about ingle planet, o (1) educe to the

More information

CHAPTER 5: Circular Motion; Gravitation

CHAPTER 5: Circular Motion; Gravitation CHAPER 5: Cicula Motion; Gavitation Solution Guide to WebAssign Pobles 5.1 [1] (a) Find the centipetal acceleation fo Eq. 5-1.. a R v ( 1.5 s) 1.10 1.4 s (b) he net hoizontal foce is causing the centipetal

More information

GRAVITATION. Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18 PG 1

GRAVITATION. 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 information

r ˆr F = Section 2: Newton s Law of Gravitation m 2 m 1 Consider two masses and, separated by distance Gravitational force on due to is

r ˆr F = Section 2: Newton s Law of Gravitation m 2 m 1 Consider two masses and, separated by distance Gravitational force on due to is Section : Newton s Law of Gavitation In 1686 Isaac Newton published his Univesal Law of Gavitation. This explained avity as a foce of attaction between all atte in the Univese, causin e.. apples to fall

More information

AST 121S: The origin and evolution of the Universe. Introduction to Mathematical Handout 1

AST 121S: The origin and evolution of the Universe. Introduction to Mathematical Handout 1 Please ead this fist... AST S: The oigin and evolution of the Univese Intoduction to Mathematical Handout This is an unusually long hand-out and one which uses in places mathematics that you may not be

More information

Experiment 09: Angular momentum

Experiment 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 information

Objective Notes Summary

Objective Notes Summary Objective Notes Summay An object moving in unifom cicula motion has constant speed but not constant velocity because the diection is changing. The velocity vecto in tangent to the cicle, the acceleation

More information

Mon , (.12) Rotational + Translational RE 11.b Tues.

Mon , (.12) Rotational + Translational RE 11.b Tues. Mon..-.3, (.) Rotational + Tanlational RE.b Tue. EP0 Mon..4-.6, (.3) Angula Momentum & Toque RE.c Tue. Wed..7 -.9, (.) Toque EP RE.d ab Fi. Rotation Coue Eval.0 Quantization, Quiz RE.e Mon. Review fo Final

More information

Gravitation. Chapter 12. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman. Lectures by James Pazun

Gravitation. 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

ω = θ θ o = θ θ = s r v = rω

ω = 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 information

Chap 5. Circular Motion: Gravitation

Chap 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 information

HRW 7e Chapter 13 Page 1 of 5

HRW 7e Chapter 13 Page 1 of 5 HW 7e Chapte Pae o 5 Halliday/enick/Walke 7e Chapte Gaitation The manitude o the oce o one paticle on the othe i ien by F = Gm m /, whee m and m ae the mae, i thei epaation, and G i the unieal aitational

More information

Central Force Motion

Central 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 information

KEPLER S LAWS OF PLANETARY MOTION

KEPLER 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 information

AE 245 homework #9 solutions

AE 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 information

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL 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 information

SPH4U Magnetism Test Name: Solutions

SPH4U Magnetism Test Name: Solutions SPH4U Magneti et Nae: Solution QUESION 1 [4 Mak] hi and the following two quetion petain to the diaga below howing two cuent-caying wie. wo cuent ae flowing in the ae diection (out of the page) a hown.

More information

TRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the

TRAVELING WAVES. Chapter Simple Wave Motion. Waves in which the disturbance is parallel to the direction of propagation are called the Chapte 15 RAVELING WAVES 15.1 Simple Wave Motion Wave in which the ditubance i pependicula to the diection of popagation ae called the tanvee wave. Wave in which the ditubance i paallel to the diection

More information

(a) Calculate the apparent weight of the student in the first part of the journey while accelerating downwards at 2.35 m s 2.

(a) Calculate the apparent weight of the student in the first part of the journey while accelerating downwards at 2.35 m s 2. Chapte answes Heineann Physics 1 4e Section.1 Woked exaple: Ty youself.1.1 CALCULATING APPARENT WEIGHT A 79.0 kg student ides a lift down fo the top floo of an office block to the gound. Duing the jouney

More information

TAMPINES JUNIOR COLLEGE 2009 JC1 H2 PHYSICS GRAVITATIONAL FIELD

TAMPINES JUNIOR COLLEGE 2009 JC1 H2 PHYSICS GRAVITATIONAL FIELD TAMPINES JUNIOR COLLEGE 009 JC1 H PHYSICS GRAVITATIONAL FIELD OBJECTIVES Candidates should be able to: (a) show an undestanding of the concept of a gavitational field as an example of field of foce and

More information

Gravity. David Barwacz 7778 Thornapple Bayou SE, Grand Rapids, MI David Barwacz 12/03/2003

Gravity. David Barwacz 7778 Thornapple Bayou SE, Grand Rapids, MI David Barwacz 12/03/2003 avity David Bawacz 7778 Thonapple Bayou, and Rapid, MI 495 David Bawacz /3/3 http://membe.titon.net/daveb Uing the concept dicued in the peceding pape ( http://membe.titon.net/daveb ), I will now deive

More information

Rotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart

Rotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart Rotational Motion & Angula Momentum Rotational Motion Evey quantity that we have studied with tanslational motion has a otational countepat TRANSLATIONAL ROTATIONAL Displacement x Angula Position Velocity

More information

b) (5) What average force magnitude was applied by the students working together?

b) (5) What average force magnitude was applied by the students working together? Geneal Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibium Nov. 3, 2010 Name Rec. Inst. Rec. Time Fo full cedit, make you wok clea to the gade. Show fomulas used, essential steps, and esults

More information

Lecture 23: Central Force Motion

Lecture 23: Central Force Motion Lectue 3: Cental Foce Motion Many of the foces we encounte in natue act between two paticles along the line connecting the Gavity, electicity, and the stong nuclea foce ae exaples These types of foces

More information

Solutions Practice Test PHYS 211 Exam 2

Solutions Practice Test PHYS 211 Exam 2 Solution Pactice Tet PHYS 11 Exam 1A We can plit thi poblem up into two pat, each one dealing with a epaate axi. Fo both the x- and y- axe, we have two foce (one given, one unknown) and we get the following

More information

PS113 Chapter 5 Dynamics of Uniform Circular Motion

PS113 Chapter 5 Dynamics of Uniform Circular Motion PS113 Chapte 5 Dynamics of Unifom Cicula Motion 1 Unifom cicula motion Unifom cicula motion is the motion of an object taveling at a constant (unifom) speed on a cicula path. The peiod T is the time equied

More information

Ch 11 Particulate suspensions

Ch 11 Particulate suspensions Ch 11 Paticulate upenion Iue Stability (dipeion) edientation igation wall lip Had phee Only igid epulion peent when paticle coe into contact Zeo hea vicoity ( 1+. φ) 5 1+.5φ + 6.φ d.5 ( φ) dφ exp( 5φ /

More information

EN40: Dynamics and Vibrations. Midterm Examination Tuesday March

EN40: Dynamics and Vibrations. Midterm Examination Tuesday March EN4: Dynaics and Vibations Midte Exaination Tuesday Mach 8 16 School of Engineeing Bown Univesity NME: Geneal Instuctions No collaboation of any kind is peitted on this exaination. You ay bing double sided

More information

10. Universal Gravitation

10. Universal Gravitation 10. Univesal Gavitation Hee it is folks, the end of the echanics section of the couse! This is an appopiate place to complete the study of mechanics, because with his Law of Univesal Gavitation, Newton

More information

Extra notes for circular motion: Circular motion : v keeps changing, maybe both speed and

Extra 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 information

GRAVITATION. Thus the magnitude of the gravitational force F that two particles of masses m1

GRAVITATION. Thus the magnitude of the gravitational force F that two particles of masses m1 GAVITATION 6.1 Newton s law of Gavitation Newton s law of gavitation states that evey body in this univese attacts evey othe body with a foce, which is diectly popotional to the poduct of thei masses and

More information

F 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

F 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 information

Basic 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 information

Uniform Circular Motion

Uniform 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 information

AP * PHYSICS B. Circular Motion, Gravity, & Orbits. Teacher Packet

AP * PHYSICS B. Circular Motion, Gravity, & Orbits. Teacher Packet AP * PHYSICS B Cicula Motion, Gavity, & Obits Teache Packet AP* is a tademak of the College Entance Examination Boad. The College Entance Examination Boad was not involved in the poduction of this mateial.

More information

Math Notes on Kepler s first law 1. r(t) kp(t)

Math 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 information

MAGNETIC FIELD INTRODUCTION

MAGNETIC FIELD INTRODUCTION MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),

More information

Circular Orbits. and g =

Circular Orbits. and g = using analyse planetay and satellite motion modelled as unifom cicula motion in a univesal gavitation field, a = v = 4π and g = T GM1 GM and F = 1M SATELLITES IN OBIT A satellite is any object that is

More information

Circular-Rotational Motion Mock Exam. Instructions: (92 points) Answer the following questions. SHOW ALL OF YOUR WORK.

Circular-Rotational Motion Mock Exam. Instructions: (92 points) Answer the following questions. SHOW ALL OF YOUR WORK. AP Physics C Sping, 2017 Cicula-Rotational Motion Mock Exam Name: Answe Key M. Leonad Instuctions: (92 points) Answe the following questions. SHOW ALL OF YOUR WORK. ( ) 1. A stuntman dives a motocycle

More information

Recap. Centripetal acceleration: v r. a = m/s 2 (towards center of curvature)

Recap. 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 information

AH Mechanics Checklist (Unit 2) AH Mechanics Checklist (Unit 2) Circular Motion

AH 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 information

Paths of planet Mars in sky

Paths of planet Mars in sky Section 4 Gavity and the Sola System The oldest common-sense view is that the eath is stationay (and flat?) and the stas, sun and planets evolve aound it. This GEOCENTRIC MODEL was poposed explicitly by

More information

Newton s Laws, Kepler s Laws, and Planetary Orbits

Newton s Laws, Kepler s Laws, and Planetary Orbits Newton s Laws, Keple s Laws, and Planetay Obits PROBLEM SET 4 DUE TUESDAY AT START OF LECTURE 28 Septembe 2017 ASTRONOMY 111 FALL 2017 1 Newton s & Keple s laws and planetay obits Unifom cicula motion

More information

Chapter. s r. check whether your calculator is in all other parts of the body. When a rigid body rotates through a given angle, all

Chapter. s r. check whether your calculator is in all other parts of the body. When a rigid body rotates through a given angle, all conveted to adians. Also, be sue to vanced to a new position (Fig. 7.2b). In this inteval, the line OP has moved check whethe you calculato is in all othe pats of the body. When a igid body otates though

More information

Physics 110. Exam #1. September 30, 2016

Physics 110. Exam #1. September 30, 2016 Phyic 110 Exa #1 Septebe 30, 016 Nae Pleae ead and follow thee intuction caefully: Read all poble caefully befoe attepting to olve the. You wok ut be legible, and the oganization clea. You ut how all wok,

More information

Chap13. Universal Gravitation

Chap13. Universal Gravitation Chap13. Uniesal Gaitation Leel : AP Physics Instucto : Kim 13.1 Newton s Law of Uniesal Gaitation - Fomula fo Newton s Law of Gaitation F g = G m 1m 2 2 F21 m1 F12 12 m2 - m 1, m 2 is the mass of the object,

More information

Physics 111 Lecture 5 Circular Motion

Physics 111 Lecture 5 Circular Motion Physics 111 Lectue 5 Cicula Motion D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com Multiple Objects q A block of mass m1 on a ough, hoizontal suface is connected to a ball of mass m by a lightweight

More information

Niraj Sir. circular motion;; SOLUTIONS TO CONCEPTS CHAPTER 7

Niraj Sir. circular motion;; SOLUTIONS TO CONCEPTS CHAPTER 7 SOLUIONS O CONCEPS CHAPE 7 cicula otion;;. Distance between Eath & Moon.85 0 5 k.85 0 8 7. days 4 600 (7.) sec.6 0 6 sec.4.85 0 v 6.6 0 8 05.4/sec v (05.4) a 0.007/sec.7 0 /sec 8.85 0. Diaete of eath 800k

More information

1131 T Question 1

1131 T Question 1 1131 T1 2008 Question 1 ( aks) You ae cycling, on a long staight path, at a constant speed of 6.0.s 1. Anothe cyclist passes you, taelling on the sae path in the sae diection as you, at a constant speed

More information

Tidal forces. m r. m 1 m 2. x r 2. r 1

Tidal forces. m r. m 1 m 2. x r 2. r 1 Tidal foces Befoe we look at fee waves on the eath, let s fist exaine one class of otion that is diectly foced: astonoic tides. Hee we will biefly conside soe of the tidal geneating foces fo -body systes.

More information

Practice. Understanding Concepts. Answers J 2. (a) J (b) 2% m/s. Gravitation and Celestial Mechanics 287

Practice. 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 information

Determining solar characteristics using planetary data

Determining 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 investigation

More information

Formula Formula symbols Units. s = F A. e = x L. E = s ε. k = F δ. G = t γ. e = at. maximum load original cross sectional area. s M E = = N/m.

Formula Formula symbols Units. s = F A. e = x L. E = s ε. k = F δ. G = t γ. e = at. maximum load original cross sectional area. s M E = = N/m. A Lit of foulae fo ecanical engineeing pinciple Foula Foula ybol Unit Ste Stain applied foce co ectionalaea cange in lengt oiginal lengt F A e x L Young odulu of elaticity te tain Stiffne foce extenion

More information

Rotational Motion: Statics and Dynamics

Rotational Motion: Statics and Dynamics Physics 07 Lectue 17 Goals: Lectue 17 Chapte 1 Define cente of mass Analyze olling motion Intoduce and analyze toque Undestand the equilibium dynamics of an extended object in esponse to foces Employ consevation

More information

KEPLER S LAWS AND PLANETARY ORBITS

KEPLER S LAWS AND PLANETARY ORBITS KEPE S AWS AND PANETAY OBITS 1. Selected popeties of pola coodinates and ellipses Pola coodinates: I take a some what extended view of pola coodinates in that I allow fo a z diection (cylindical coodinates

More information

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 6- THE LAW OF GRAVITATION Essential Idea: The Newtonian idea of gavitational foce acting between two spheical bodies and the laws of mechanics

More information

Lecture 22. PE = GMm r TE = GMm 2a. T 2 = 4π 2 GM. Main points of today s lecture: Gravitational potential energy: Total energy of orbit:

Lecture 22. PE = GMm r TE = GMm 2a. T 2 = 4π 2 GM. Main points of today s lecture: Gravitational potential energy: Total energy of orbit: Lectue Main points of today s lectue: Gavitational potential enegy: Total enegy of obit: PE = GMm TE = GMm a Keple s laws and the elation between the obital peiod and obital adius. T = 4π GM a3 Midtem

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 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 information

2.2 This is the Nearest One Head Gravitational Potential Energy 14.8 Energy Considerations in Planetary and Satellite Motion

2.2 This is the Nearest One Head Gravitational Potential Energy 14.8 Energy Considerations in Planetary and Satellite Motion 2.2 This is the Neaest One Head 423 P U Z Z L E R Moe than 300 yeas ago, Isaac Newton ealized that the sae gavitational foce that causes apples to fall to the Eath also holds the Moon in its obit. In ecent

More information

Revision Guide for Chapter 11

Revision 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 information

Hoizontal Cicula Motion 1. A paticle of mass m is tied to a light sting and otated with a speed v along a cicula path of adius. If T is tension in the sting and mg is gavitational foce on the paticle then,

More information

Mark answers in spaces on the answer sheet

Mark answers in spaces on the answer sheet Mak answes in spaces 31-43 on the answe sheet PHYSICS 1 Summe 005 EXAM 3: July 5 005 9:50pm 10:50pm Name (pinted): ID Numbe: Section Numbe: INSTRUCTIONS: Some questions ae one point, othes ae two points,

More information

AP Physics - Coulomb's Law

AP Physics - Coulomb's Law AP Physics - oulomb's Law We ve leaned that electons have a minus one chage and potons have a positive one chage. This plus and minus one business doesn t wok vey well when we go in and ty to do the old

More information

MODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES VISUAL PHYSICS ONLINE

MODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES VISUAL PHYSICS ONLINE VISUAL PHYSICS ONLINE MODULE 5 ADVANCED MECHANICS GRAVITATIONAL FIELD: MOTION OF PLANETS AND SATELLITES SATELLITES: Obital motion of object of mass m about a massive object of mass M (m

More information

History of Astronomy - Part II. Tycho Brahe - An Observer. Johannes Kepler - A Theorist

History 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 information

CHAPTER 6: UNIFORM CIRCULAR MOTION AND GRAVITATION

CHAPTER 6: UNIFORM CIRCULAR MOTION AND GRAVITATION College Physics Student s Manual Chapte 6 CHAPTER 6: UIORM CIRCULAR MOTIO AD GRAVITATIO 6. ROTATIO AGLE AD AGULAR VELOCITY. Sei- taile tucks hae an odoete on one hub of a taile wheel. The hub is weighted

More information

Describing Circular motion

Describing Circular motion Unifom Cicula Motion Descibing Cicula motion In ode to undestand cicula motion, we fist need to discuss how to subtact vectos. The easiest way to explain subtacting vectos is to descibe it as adding a

More information