Episode 401: Newton s law of universal gravitation


 Damon Julius Shaw
 2 years ago
 Views:
Transcription
1 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 between objects. The meaning of invese squae law is discussed. Summay Discussion: Intoduction to Newton s law of univesal gavitation (5 minutes) Discussion: Newton s law of univesal gavitation: F = Gm 1 m / (10 minutes) Woked examples: Using F = Gm 1 m /. (5 minutes) Student questions: Moe pactice with F = Gm 1 m /. (0 minutes) Not to scale Discussion: Intoduction to Newton s law of univesal gavitation Hee ae some questions and answes which lead towads Newton s Law of Univesal Gavitation. What causes the weight that each student feels? (gavitational attaction by the Eath.) What affects the size of the Eath s pull on you? Why would you weigh a diffeent amount on the Moon? (You mass, and its mass.) If the Eath is pulling down on you, then what else must be occuing, by Newton s 3d Law? (You must be pulling up on the Eath with a foce equal to you weight.) What happens to the stength of the pull of the Eath as you go futhe away fom it? (It gets weake most students guess this coectly fom the incoect assumption that in space, astonauts ae weightless!) So, in summay the foce depends upon the masses of the Eath and you, and weakens with distance. This is all embodied in Newton s law of univesal gavitation Discussion: Newton s law of univesal gavitation Pesent the equation which epesents Newton s Law of Univesal Gavitation. F = Gm 1 m / F = gavitational foce of attaction (N) m 1, m ae the inteacting masses (kg) is the sepaation of the masses (m) 1
2 G is known as the univesal gavitational constant (NOT to be confused with little g). It sets the stength of the gavitational inteaction in the sense that if it wee doubled, so would all the gavitational foces. G = N m kg  Show how the units can be woked out by eaanging the oiginal equation. This law applies between point masses, but spheical masses can be teated as though they wee point masses with all thei mass concentated at thei cente. This foce is ALWAYS attactive. In some texts you will see a minus sign in the equation, so that F = Gm 1 m /. This minus sign is thee puely to indicate that the foce is attactive (it s a elic fom the moe coect, but well beyond the syllabus, vecto equation expessing Newton s Law of univesal gavitation). It s simplest to calculate the magnitude of the foce using F = Gm 1 m /, and the diection is given by the fact that the foce is always attactive. Evey object with a mass in the univese attacts evey othe accoding to this law. But the actual size of the foce becomes vey small fo objects vey fa away. Fo example, the Sun is about one million times moe massive than the Eath, but because it s so fa away, the pull on us fom the Sun is dwafed by the pull on us fom the Eath (which is aound 1650 times geate). As the sepaation of two objects inceases, the sepaation inceases even moe, damatically. The gavitational foce will decease by the same facto (since sepaation appeas in the denominato of the equation). This is an example of an invese squae law, so called because the foce of attaction vaies in invese popotion to the squae of the sepaation. Woked examples: Using F = Gm 1 m / You can wok though these examples, o you can set them as a task fo you students if you feel they will be able to tackle them. TAP 4011: Woked examples; F = Gm 1 m / Student questions: Moe pactice with F = Gm 1 m / TAP 401: Newton s gavitational law
3 TAP 4011: Woked examples; F = Gm 1 m / Woked examples Newton s Law of univesal gavitation teache s sheet Note: Remembe that a lot of students have difficulties in using standad fom coectly on a scientific calculato. You may need to tuto them in the use of the EXP button. Data equied: G = N m kg , mass of the Eath = kg, adius of the Eath = m, mass of the Sun = kg, aveage distance fom the Eath to the Sun = m. 1) Communications satellites obit the Eath at a height of km. How fa is this fom the cente of the Eath? If such a satellite has a mass of 50 kg, what is the foce of attaction on it fom the Eath? It is (3.6 x 10 7 m x 10 6 m) = 4.4 x 10 7 m fom the cente of the Eath. (They should eally give this as 4. x 10 7 m this may be an oppotunity to einfoce the ole of significant figues in physical calculations). The foce is F = Gm 1 m / = (6.67 x x 6.0 x 10 4 x 50)/ (4.4 x 10 7 ). This gives an answe of about 56 N, which fo infomation is about less than the weight as a one yea old toddle. ) What is the foce of attaction fom the Eath on you? What do we call this foce? What is the foce of attaction on the Eath fom you? They will need to estimate thei own mass in kg. If they need to convet, 1 stone is 6.4kg (and thee ae 14 pounds in a stone). They then use F=Gm 1 m / whee is the adius of the Eath. This foce is usually called thei weight. The foce on the Eath fom the student is exactly the same as thei fist answe, but in the opposite diection. 3) What is the foce of attaction fom the Sun on you? How many times smalle is this than the foce of attaction fom the Eath on you? Again, they will need to use thei own mass, and the equation F=Gm 1 m /, but this time is the aveage distance fom the Sun to the Eath. This foce should be about 1650 times less than thei weight, of the ode of N. Small, but not negligible. 3
4 4) The aveage foce of attaction on the Moon fom the Sun is N. Taking the distance fom the Sun to the Moon to be about the same as that fom the Sun to the Eath, what value of mass does this give fo the Moon? m = F /Gm 1 = (4.4 x 10 0 x (1.5 x ) )/(6.67 x x.0 x ) = 7.4 x 10 kg 5) Using the mass of the Moon you calculated in question 4, what is the pull of the Eath on the Moon, if the Moon is km away? How does this compae with the pull of the Sun on the Moon? F = Gm 1 m / = (6.67 x x 6.0 x 10 4 x 7.4 x 10 )/ (3.8 x 10 8 ) =.1 x 10 0 N This is actually smalle than the pull of the Sun on the Moon. You could discuss whethe that means the Moon is obiting the Sun athe than the Eath. In fact, it depends on the most useful fame of efeence in a paticula situation fom the Sun s point of view, the Moon and the Eath obit the Sun, in a way that is affected by the pesence of the othe; fom the Moon s point of view, both the Sun and the Eath obit the Moon, in a way that is affected by the pesence of the othe, etc. 6. What is the foce of attaction between two people, one of mass 80 kg and the othe 100 kg if they ae 0.5m apat? F = Gm 1 m / F = G x 100 x 80 / 0.5 =.14 x 106 N. This is a vey small foce but it does incease as the people get close togethe! Actually this example is not accuate because Newton's law eally only applies to spheical objects, o at least objects so fa apat that they can be effectively consideed as spheical. 7. What is the foce of attaction between the Eath and the Sun? Mass of the Sun = x kg, mass of the Eath = 6 x 10 4 kg, distance fom the Eath to the Sun = 1.5 x m F = Gm 1 m / F = G x x x 6 x 10 4 / [1.5 x ] = 6.7 x N an enomous foce! 4
5 Extenal efeence Questions 6 and 7 taken fom Resouceful Physics 5
6 TAP 401: Newton s gavitational law These questions ae intended to give you pactice in using the gavitational law. They will give you a feeling fo typical foces with a ange of masses and also how sensitive foce is to distance. Useful data G = N m kg Eath s mass = kg Moon s mass = kg Sun s mass is kg Radius of the Moon = m Radius of the Eath = m Eath Moon distance = km Eath Sun distance = km 1. You may sometimes find it difficult to get up fom the sofa afte watching a TV pogamme. Assuming the foce of gavity acts between the cente of you body and the cente of the sofa, estimate the attaction between you and you sofa.. Calculate the size of the gavitational pull of a sphee of mass 10 kg on a mass.0 kg when thei centes ae 00 mm apat. What is the foce of the.0 kg mass on the 10 kg mass? 3. At what distance apat would two equal masses of 150 kg need to be placed fo the foce between them to be N? 6
7 4. Calculate the gavitational pull of the Eath on each of the following bodies: the Moon; satellite A with mass 100 kg at a distance fom the Eath s cente m; and satellite B mass 80 kg at a distance fom the Eath s cente m. 5. Show that the unit fo G, the univesal gavitational constant, can be expessed as m 3 s kg Calculate the weight of an astonaut whose mass (including spacesuit) is 7 kg on the Moon? What is the astonaut's weight on Eath? 7
8 Comment on the diffeence. 7. Show that pull of the Sun on the Moon is about. times lage than the pull of the Eath on the Moon. 8. Why then does the Moon obit the Eath? Fomatted: Bullets and Numbeing The Ameican space agency, NASA, plans to send a manned mission to Mas late this centuy. Mas has a mass 6.4 x 10 3 kg and a adius 3.38 x 10 6 m. G = 6.67 x N m kg  9 (a) The mass of a typical astonaut plus spacesuit is 80 kg. What would be the gavitational foce acting on such an astonaut standing on the suface of Mas? (b) State whethe an astonaut on Mas would feel lighte o heavie than on Eath. 8
9 Pactical advice This esouce could be used fo eithe class wok o homewok. Answes and woked solutions 1. Fo the values estimated in the answes: GMm ( N kg m ) 60 kg 100 kg 6 = ( 0.5 m) N.. Pull on the.0 kg mass GMm ( N kg m ) 10 kg.0 kg 9 = ( 0.00 m) The pull on the 10 kg mass will be equal but opposite in diection. N. 3. = Gm F = m G F = 150 kg Nkg 5 N m = 0.7 m. 4. GMm ( Nkg m ) ( kg) ( kg) 0 =.0 10 N. GMm ( Nkg 8 ( m) m ) ( ( m) 6 ( m) 4 4 kg) 100 kg = 3 N. GMm ( Nkg m ) ( kg) 80 kg = N N kg m = kg m s kg m = m s kg. 6. Moon GMm ( Nkg m ) 7 kg ( kg) = N. 6 ( m) 9
10 Eath 4 GMm ( N kg m ) 7 kg ( kg) = Sun Moon 6 ( m) N. GMm ( Nkg m ) (.0 10 kg) ( kg) 0 = N. Eath Moon ( m) 4 GMm N kg m ) ( kg) ( kg) =.0 10 ( 0 8 ( m) N atio of attactions = N =. N 8. The Moon does of couse obit the Sun, as pat of the Eath Moon system. You can think of the Moon s obit of the Eath as supeimposed on its obit of the Sun. 9 F = (Gm astom x M mas ) / F = (6.67 x N m kg  ) x 80 kg x (6.4 x 10 3 kg) / (3.38 x 10 6 m) = 300 N (b) Would feel lighte. Extenal efeences Questions 18: This is taken fom Advancing Physics Chapte 11, 80W Question 9: This is taken fom Saltes Hones Advanced Physics, section STA, additional sheet 8 and 9 10
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 !
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 =!
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 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 informationRevision 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 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 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 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 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 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 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 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 informationThe force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
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 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 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 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 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 informationToday in Physics 217: multipole expansion
Today in Physics 17: multipole expansion Multipole expansions Electic multipoles and thei moments Monopole and dipole, in detail Quadupole, octupole, Example use of multipole expansion as appoximate solution
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 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 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 informationCHAPTER 5 GRAVITATIONAL FIELD AND POTENTIAL
CHATER 5 GRAVITATIONAL FIELD AND OTENTIAL 5. Intoduction. This chapte deals with the calculation of gavitational fields and potentials in the vicinity of vaious shapes and sizes of massive bodies. The
More informationGravitational Mechanics of the MarsPhobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the MasPhobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationTrigonometric Functions of Any Angle
Tigonomet Module T2 Tigonometic Functions of An Angle Copight This publication The Nothen Albeta Institute of Technolog 2002. All Rights Reseved. LAST REVISED Decembe, 2008 Tigonometic Functions of An
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 informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationOrbital Motion & Gravity
Astonomy: Planetay Motion 1 Obital Motion D. Bill Pezzaglia A. Galileo & Fee Fall Obital Motion & Gavity B. Obits C. Newton s Laws Updated: 013Ma05 D. Einstein A. Galileo & Fee Fall 3 1. Pojectile Motion
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 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 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 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 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 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 informationExperiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuentcaying conducto is basic to evey electic moto  tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
More informationFarming: It s a Fact! Career & Technical Education, Introduction
Faming: It s a Fact! Caee & Technical Education, Intoduction Whee Does You Food Dolla Go? Mateials Compute Lab o Compute & Pojecto fo Pesentation Compute Speakes o Headphones Compute Intenet Access o Agicultual
More informationChapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6
Chapte 9 lectic Chages, Foces, an Fiels 6 9. One in a million (0 ) ogen molecules in a containe has lost an electon. We assume that the lost electons have been emove fom the gas altogethe. Fin the numbe
More informationELECTRIC CHARGES AND FIELDS
Chapte One ELECTRIC CHARGES AND FIELDS 1.1 INTRODUCTION All of us have the expeience of seeing a spak o heaing a cackle when we take off ou synthetic clothes o sweate, paticulaly in dy weathe. This is
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 informationPHY002 Lecture Notes for PreDegree Science
PHY00 Lectue Notes fo PeDegee Science Couse Contents: Magnets, Magnetic fields and Electostatic By Odusote Y. A Depatment of Physics Fedeal Univesity of Technology P. M.B. 704, Akue, Ondo State. 1 MAGNETS
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 informationCharges, Coulomb s Law, and Electric Fields
Q&E 1 Chages, Coulomb s Law, and Electic ields Some expeimental facts: Expeimental fact 1: Electic chage comes in two types, which we call (+) and ( ). An atom consists of a heavy (+) chaged nucleus suounded
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 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 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 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 informationNewton s Shell Theorem
Newton Shell Theoem Abtact One of the pincipal eaon Iaac Newton wa motivated to invent the Calculu wa to how that in applying hi Law of Univeal Gavitation to pheicallyymmetic maive bodie (like planet,
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationFigure 2. So it is very likely that the Babylonians attributed 60 units to each side of the hexagon. Its resulting perimeter would then be 360!
1. What ae angles? Last time, we looked at how the Geeks intepeted measument of lengths. Howeve, as fascinated as they wee with geomety, thee was a shape that was much moe enticing than any othe : the
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationLesson C3 2. Exploring Genetics. Performance Standard: 2. Discuss the implications of genetic variation.
Lesson C3 2 Exploing Genetics Unit C. Basic Pinciples of Agicultual/Hoticultual Science Poblem Aea 3. Undestanding Cells, Genetics, and Repoduction Lesson 2. Exploing Genetics New Mexico Content Standad:
More informationLecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3
Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each
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 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 information10. Collisions. Before During After
10. Collisions Use conseation of momentum and enegy and the cente of mass to undestand collisions between two objects. Duing a collision, two o moe objects exet a foce on one anothe fo a shot time: F(t)
More information2.2. Trigonometric Ratios of Any Angle. Investigate Trigonometric Ratios for Angles Greater Than 90
. Tigonometic Ratios of An Angle Focus on... detemining the distance fom the oigin to a point (, ) on the teminal am of an angle detemining the value of sin, cos, o tan given an point (, ) on the teminal
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 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 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 informationUniversal Cycles. Yu She. Wirral Grammar School for Girls. Department of Mathematical Sciences. University of Liverpool
Univesal Cycles 2011 Yu She Wial Gamma School fo Gils Depatment of Mathematical Sciences Univesity of Livepool Supeviso: Pofesso P. J. Giblin Contents 1 Intoduction 2 2 De Buijn sequences and Euleian Gaphs
More informationChapter 4. Gauss s Law
Chapte 4 Gauss s Law 4.1 lectic Flux...44. Gauss s Law...43 xample 4.1: Infinitely Long Rod of Unifom Chage Density...48 xample 4.: Infinite Plane of Chage...49 xample 4.3: Spheical Shell...41 xample
More informationChapter 17 The Kepler Problem: Planetary Mechanics and the Bohr Atom
Chapte 7 The Keple Poblem: Planetay Mechanics and the Boh Atom Keple s Laws: Each planet moves in an ellipse with the sun at one focus. The adius vecto fom the sun to a planet sweeps out equal aeas in
More informationMon., 3/9 Tues., 3/10 Wed., 3/11 Thurs., 3/12 Fri., 3/ 13. RE19 HW19:RQ.42, 49, 52; P.61, 66, 69 RE20, Exp new RE ,34 Magnetic Force
Mon., 3/9 Tues., 3/10 Wed., 3/11 Thus., 3/12 Fi., 3/ 13 Mon., 3/16 Tues., 3/17 Wed., 3/18 Thus., 3/19 Fi., 3/20 20.1,34 Magnetic Foce 20.2,5 Cuent and Motional Emf Quiz Ch 19, Lab 8 Cycloton & Electon
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 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 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 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 informationSemipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
More informationPhysics 107 HOMEWORK ASSIGNMENT #14
Physics 107 HOMEWORK ASSIGNMENT #14 Cutnell & Johnson, 7 th edition Chapte 17: Poblem 44, 60 Chapte 18: Poblems 14, 18, 8 **44 A tube, open at only one end, is cut into two shote (nonequal) lengths. The
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
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 information