Part 1. Electric Charges, Forces and Fields. Forces of nature or A short journey back to Physics 111. Chapter 17. Forces of Nature.

Size: px
Start display at page:

Download "Part 1. Electric Charges, Forces and Fields. Forces of nature or A short journey back to Physics 111. Chapter 17. Forces of Nature."

Transcription

1 Foces of Natue Electic Chages, Foces and Fields Chapte 17 Electic Chage Coulomb s Law Electic Field Electic Field Lines Flux of an Electic Field Physics 111: Analysis of motion - 3 key ideas Pat 1 Foces of natue o A shot jouney back to Physics 111 Newton s laws of motion Consevation of Enegy Consevation of Momentum 4 Newton s laws of motion Newton s Fist Law: If no foce acts on a body, then the body s velocity cannot change Newton s laws of motion (applications) Special case: motion with constant acceleation (1D, D o 3D motion) Newton s Second Law: F = ma Newton s laws of motion allow us to analyze many kinds of motion. F = ma at x = x + vt + v = v + at Obsevables: time foce position velocity acceleation 5 Examples of poblems: pojectile motion, 6 1

2 Consevation of enegy The total enegy of an isolated system cannot change In an isolated system whee only consevative foces cause enegy changes, the kinetic enegy and potential enegy can change, but thei sum cannot change K + U = K + U i i f f 7 Consevation of momentum Consevation of linea momentum If no net extenal foce acts on a system of paticles, the total linea momentum of the system cannot change P = m v + m v m v 1 1 n n = const Consevation of angula momentum If the net extenal toque acting on a system is zeo, the angula momentum of the system emains constant, no matte what changes take place within the system L i = L f 8 What foces do we know fom ou expeience and Physics 111 Thee ae ONLY fou fundamental foces of natue Gavitational Foce Fictional Foce Sping Foce (Hook s Law) Nomal Foce Tension foce in a sting Aeodynamic Dag Foce 9 1 FOUR o ONE Many scientists think that all fou of the fundamental foces ae, the manifestations of a single foce which has yet to be discoveed. Gavitational and electo-magnetic foces: this what we expeience!!! Fictional foce, sping foce, nomal foce, tension foce in a sting, aeodynamic foce ae esults of electomagnetic foce Just as electicity, magnetism, and the weak foce wee unified into the electoweak inteaction, they wok to unify all of the fundamental foces. 11 1

3 Electic chage Pat Electic Chage Electic Chage is an intinsic chaacteistic of the fundamental paticles making up objects aound us (including us). The odinay matte consists of thee (only!) paticles: electon (e) poton (p) neuton (n) mass kg kg kg chage C C. The SI unit of electic chage is the Coulomb 14 Impotant chaacteistic of electic chage An electic chage has a magnitude and sign. It is eithe positive o negative. Electon has negative electic chage Poton has positive electic chage Atoms and molecules ae made up fom electons, potons and neutons! A classical (sola system) model of an atom (Lithium) A quantum model of an atom (Lithium) If the chages have the same sign, the foces between them ae epulsive Chages of opposite sign Atoms ae combinations of equal amounts of electons and potons. expeience attactive foces15 16 Sizes and masses Atoms ae combinations of equal amounts of electons and potons. The neutons povide the glue to stick togethe the potons in the nucleus. The poton and the neuton ae about times heavie than the electon, so the vast majoity of an atom s mass esides in the nucleus. Atoms ae mostly empty. We live in almost empty space Net electic chage fo a system of n paticles net = q1 + q + q3 + Kq n The total (net) electic chage of an isolated system is conseved. The only way to change it is to add o emove chaged paticles. Example: tennis ball and a gain of sand q The total electic chage of the univese is constant. the net electic chage of atoms and molecules is zeo (equal amounts of electons and potons) emoving an electon fom a neutal atom ceates a positive ion negative ions 3

4 Example: 19 Maco objects (many atoms o molecules) To make an unchaged object have a negative chage we must: A) add some atoms B) add some potons C) add some electons D) add some neutons E) wite down a negative sign Mateials two exteme models Insulatos a mateial in which chages do not move feely though the inteio of the sample. Examples: Glass, wood, ubbe, plastics, stone, bick, etc Conductos mateial whee fee chages can move though the mateial. Examples: Ionized gases (plasmas), metals, ionic solutions if salts in wate Semi-conductos a mateial intemediate between the two exteme models GaAs, Ge, Si, ae the classic examples. 1 Maco objects can be chaged by chage tansfe o chage sepaation Chage tansfe happens when electic chages (usually electons) tansfe fom one object to anothe Chage sepaation occus when two mateial ae ubbed togethe o when objects collide Chage is quantized Expeiments show that any positive o negative chage q that can be detected can be witten as q = n e, n = ± 1, ±, ± 3, K e = C whee e is the elementay chage

5 fom a simple to complex Univese human beings cells condense matte, gases molecules atoms Note: ALL electons ae identical, as well as potons, neutons Pat 3 A foce between chages electons, potons, neutons fundamental paticles: electons, quaks, 5 Coulomb s Law The electostatic foce between two chages q 1 and q sepaated by a distance has the magnitude q F = k 1 q 1 9 k = = N m /C 4 πε k is the electomagnetic constant ε is the pemittivity constant The diagam shows two pais of heavily chaged plastic cubes. Cubes 1 and attact each othe and so do cubes 1 and 3. Which of the following illustates the foces of on 3 and 3 on Whee is the 3 d Newton s law 7 8 Compaing the gavitational and electostatic foces Let s calculate the atio of the electical to the gavitational foce inside a hydogen atoms. GM pm e keq pqe Fg =, F e = R kqq e p e Fe kqq e p e = = F GM g pm e GM pm e 9 19 Fe (9 1 )(1.6 1 ) = Fg ( )( )( ) 39 =.7 1 So we can foget gavity as compaed to electostatic A contadiction to a simple obsevation If F e /F Gl = then, why the gavity foce plays any obsevable ole The foce of gavity play essentially NO ole in atomic and molecula systems Howeve macoscopic objects ae neutal o almost neutal (the net electic chage is close to zeo) Theefoe the foce of gavity play stong ole fo macoscopic objects foces at least on the atomic scale 9 3 5

6 An example with two coins Let s find an electostatic foce between two coins sepaated by a distance of 1 mete a) foce between electons b) foce between electons in the two coins c) the net foce between electons and potons in the two coins about 5 millions!!! q q F = k 1 9 k = N m /C -19 e = C N 1 electons coin.3*1-8 N.3*1 16 N. N 31 Coulomb s law and the pinciple of supeposition The pinciple of supeposition: the net effect is the sum of the individual effects Fo n inteacting paticles the net foce on paticle 1 can be witten as = F + F + F + K F1, net F1 n being pactical see chapte 3 Vectos in Physics (adding vectos using components) 3 Net Foce and the supeposition pinciple Net Foce Chages Q, Q, and q ae placed at the vetices of an equilateal tiangle as shown. The total foce exeted on the chage q is: A) towad chage Q B) towad chage Q C) away fom chage Q D) at ight angles to the line joining Q and Q E) paallel to the line joining Q and Q Two point chages ae aanged as shown, whee Q 1 = -C, Q = 1C. In which egion could a thid chage +1 C be placed so that the net electostatic foce on it is zeo A) I only B) I and II only C) III only D) I and III only E) II only Always daw a fee body diagam! What if the thid chage is q=-1c What if the paticles have chages Q and -Q 33 What if the paticles have chages Q and Q 34 Net Foce Net Foce Conside the thee electic chages shown in the figue. List the chages in ode of the magnitude of the foce they expeience, stating with the smallest (Note: the distance fom A to B is the same as the distance fom B to C.) Fou identical point chages ae placed at the cones of a squae. A fifth point chage placed at the cente of the squae expeiences zeo net foce. Is this a stable equilibium fo the fifth chage good to use PhET compute simulation as an illustation

7 Example: 3 electic chages in a line poblem poblem Given that q = +1 mc and d = 16 cm, (a) find the diection and magnitude of the net electostatic foce exeted on the point chage q in Figue below (b) How would you answes to pat (a) change if the distance d wee tipled F blue F ed 1 3.q.q 9 3.q.q = = 9 1 4πε d d 1 1.q.q 9 1.q.q = = 9 1 4πε d d F 3.q.q 1.q.q = 9 1 to the ight d d 9 esultant poblem A tale of two paticles poblem An electon and a poton ae eleased fom est in space, fa fom any othe object. The paticles move towad each othe, due to thei mutual attaction. When they meet, is the kinetic enegy of the electon geate than, less than, o the same as the kinetic enegy of the poton Explain A couple simple questions Pat 4 Electic Field The Coulomb law q q F = k 1 How does q 1 know of the pesence of q Since the chages do not touch, how can q 1 exet a foce on q Action on a distance! Othe examples 4 7

8 Electic Fields o Action on a Distance We can say that q 1 sets up an electic field in the space suounding it. 1. At any given point P in that space the field has both magnitude and diection.. The magnitude depends on the magnitude of q 1 and the distance between P and q The diection depends on the diection fom q 1 to P and the electical sign of q Thus when we place q at P, q 1 inteacts with q 43 though the electic field at P. The electic field is a vecto field The electic field consists of a distibution of vectos, one fo each point in the egion aound a chaged object. A way to define the electic field at some point P 1. Place a positive chage q, called a test chage, at the point P. Measue the electostatic foce F that acts on the test chage 3. Define the electic field at the point P due to the chaged object as F E = q The SI unit fo the electic field is 44 the newton pe coulomb (N/C) A paticle in an electic field The electic field due to a point electic chage 1. If we know the electic field vecto at a given point, the foce that a chage q expeiences at that point is F = qe. The diection of the foce: positive paticles in the diection of the field negative paticles in the opposite diection of the field F F + E 45 Fom Coulomb s law, the magnitude of the electostatic foce acting on q is q q 1 q q F = k = 4πε The diection of the foce is diectly away fom the point chage if q is positive, and diectly towad the point chage is q is negative. Then the magnitude of the electic field fom a point chage is q 1 q E = k = 4πε 46 Example Electic field aound a positive electic chage The electic field due to moe than one point electic chage Using the supeposition pinciple we can find the net foce F, net = F1 + F + F3 + KF n Theefoe the net electic field at the position of the test chage is F, net F1 F F3 F n E = = K q q q q q E = E 1 + E + E 3 + KE n

9 Net Field A poton p and an electon e ae on the x axis. Find the diections of the electic field at points 1,, and 3 espectively Conside two identical negative chages as shown. At which letteed point is the magnitude of the electic field geatest Least a b c d Go to PhET 49 5 Conceptual question Conceptual question A poton moves in a egion of constant electic field. Does it follow that the poton s velocity is paallel to the electic field Does it follow that the poton s acceleation is paallel to the electic field The foce expeienced by chage 1 at point A is diffeent in diection and magnitude fom the foce expeienced by chage at point B. Can we conclude that the electic fields at point A and point B ae diffeent 51 5 Example: a point chage in an electic field Tools (equations) to descibe motion of electons The essential featues of an ink-jet pinte atoms molecules quantum mechanics Schodinge equation Diac equation F = qe = ma then motion with constant acceleation (see physics 111) gases, plasma, classical mechanics Second Newton s law F = qe = ma

10 Pat 5 Electic Field Lines Electic field lines povide a nice way to visualize pattens in electic fields 1. At any point, the diection of a staight field line gives the diection of the electic field at that point. Electic fields extend away fom positive chage and towad negative chage 3. No field lines coss. 4. The field lines ae dawn so that the numbe of lines pe unit aea is popotional to the magnitude of the electic field. 56 Examples Poblem The electic field lines suounding thee chages ae shown in the Figue. The cente chage is q = - 1. mc. (a) What ae the signs of q 1 and q 3 (b) Find q 1. Note that twice as many field lines oiginate fom the +q chage than the +q o q chages. 57 (c) Find q Flux Pat 6 Flux of an Electic Field Example: a wide ai steam of unifom velocity at a small squae loop of aea A. Let Φ epesents the volume flow ate (volume pe unit time) at which ai flows though the loop. The ate depends on the angle between the velocity and the plane of the loop. Φ = ( v cosθ ) A = vacosθ 6 1

11 Flux of an Electic Field Φ = EAcosθ θ is the angle between the electic field and the line pependicula to the suface. SI units: N m /C Fo a non-unifom fields we have to integate ove a suface The electic flux though a suface is popotional to the net numbe of electic field lines passing though that suface. 61 Gauss Law Gauss law elates the net flux Φ of an electic field though a closed suface to the net chage q enc that is enclosed by that suface ε Φ = q enc Gauss law and Coulomb s law Demonstation fo a point chage 1 q 1 q q E = Φ = EA = 4π = 4πε 4πε ε A = 4π 6 Example In the following figue, the dashed line denotes a Gaussian suface enclosing pat of a distibution of fou positive chages. (a) Which chages contibute to the electic field at P (b) Is the value of the flux though the suface, calculated using only the electic field due to q1 and q, geate than, equal to, o less than that obtained using the field due to all fou chages A pactical conclusion fom the Gauss s Law Faaday s cage 63 Duing a thundestom stay in you ca!!! 64 Epilogue Inteactive Compute Simulation A vey good collection of inteactive simulations to lean physics fom the Physics Education Technology poject at the Univesity of Coloado

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges

The 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 information

Charges, Coulomb s Law, and Electric Fields

Charges, 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 information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 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 information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic 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 information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 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 information

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6

Chapter 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 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

(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 information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 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 information

12. Rolling, Torque, and Angular Momentum

12. 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 information

Exam 3: Equation Summary

Exam 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 information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The 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 information

The Role of Gravity in Orbital Motion

The 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 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

Episode 401: Newton s law of universal gravitation

Episode 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 information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 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 information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 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 plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection 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 information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 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 information

Forces & Magnetic Dipoles. r r τ = μ B r

Forces & Magnetic Dipoles. r r τ = μ B r Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector 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 information

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 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 ight-hand end. If H 6.0 m and h 2.0 m, what

More information

Gravitation. AP Physics C

Gravitation. 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 information

Solution Derivations for Capa #8

Solution Derivations for Capa #8 Solution Deivations fo Capa #8 1) A ass spectoete applies a voltage of 2.00 kv to acceleate a singly chaged ion (+e). A 0.400 T field then bends the ion into a cicula path of adius 0.305. What is the ass

More information

Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2

Gravitation 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 information

Multiple choice questions [60 points]

Multiple 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 information

Gravity. A. Law of Gravity. Gravity. Physics: Mechanics. A. The Law of Gravity. Dr. Bill Pezzaglia. B. Gravitational Field. C.

Gravity. 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 information

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

1240 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 information

Displacement, Velocity And Acceleration

Displacement, 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 information

AP Physics Electromagnetic Wrap Up

AP 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 information

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary 7 Cicula Motion 7-1 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 information

Phys 2101 Gabriela González. cos. sin. sin

Phys 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 information

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 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 information

Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 10 Solutions

Pearson Physics Level 30 Unit VI Forces and Fields: Chapter 10 Solutions Peason Physics Level 30 Unit VI Foces and Fields: hapte 10 Solutions Student Book page 518 oncept heck 1. It is easie fo ebonite to eove electons fo fu than fo silk.. Ebonite acquies a negative chage when

More information

UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

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 inestigation

More information

Lesson 7 Gauss s Law and Electric Fields

Lesson 7 Gauss s Law and Electric Fields Lesson 7 Gauss s Law and Electic Fields Lawence B. Rees 7. You may make a single copy of this document fo pesonal use without witten pemission. 7. Intoduction While it is impotant to gain a solid conceptual

More information

Lab #7: Energy Conservation

Lab #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 1-4 Intoduction: Pehaps one of the most unusual

More information

Experiment 6: Centripetal Force

Experiment 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 information

F G r. Don't confuse G with g: "Big G" and "little g" are totally different things.

F G r. Don't confuse G with g: Big G and little g are totally different things. G-1 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 information

Chapter 2. Electrostatics

Chapter 2. Electrostatics Chapte. Electostatics.. The Electostatic Field To calculate the foce exeted by some electic chages,,, 3,... (the souce chages) on anothe chage Q (the test chage) we can use the pinciple of supeposition.

More information

TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION

TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION MISN-0-34 TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION shaft TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION by Kiby Mogan, Chalotte, Michigan 1. Intoduction..............................................

More information

A r. (Can you see that this just gives the formula we had above?)

A r. (Can you see that this just gives the formula we had above?) 24-1 (SJP, Phys 1120) lectic flux, and Gauss' law Finding the lectic field due to a bunch of chages is KY! Once you know, you know the foce on any chage you put down - you can pedict (o contol) motion

More information

Chapte 3 Is Gavitation A Results Of Asymmetic Coulomb Chage Inteactions? Jounal of Undegaduate Reseach èjurè Univesity of Utah è1992è, Vol. 3, No. 1, pp. 56í61. Jeæey F. Gold Depatment of Physics, Depatment

More information

Mechanics 1: Motion in a Central Force Field

Mechanics 1: Motion in a Central Force Field Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.

More information

Chapter 30: Magnetic Fields Due to Currents

Chapter 30: Magnetic Fields Due to Currents d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.

More information

10. Collisions. Before During After

10. 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 information

2. Orbital dynamics and tides

2. Orbital dynamics and tides 2. Obital dynamics and tides 2.1 The two-body 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 information

Multiple choice questions [70 points]

Multiple 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 information

Experiment MF Magnetic Force

Experiment MF Magnetic Force Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuent-caying conducto is basic to evey electic moto -- tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating

More information

Electrostatic properties of conductors and dielectrics

Electrostatic properties of conductors and dielectrics Unit Electostatic popeties of conductos and dielectics. Intoduction. Dielectic beaking. onducto in electostatic equilibium..3 Gound connection.4 Phenomena of electostatic influence. Electostatic shields.5

More information

Chapter 17 The Kepler Problem: Planetary Mechanics and the Bohr Atom

Chapter 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 information

Figure 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!

Figure 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 information

Moment and couple. In 3-D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r

Moment and couple. In 3-D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r Moment and couple In 3-D, because the detemination of the distance can be tedious, a vecto appoach becomes advantageous. o k j i M k j i M o ) ( ) ( ) ( + + M o M + + + + M M + O A Moment about an abita

More information

NUCLEAR MAGNETIC RESONANCE

NUCLEAR MAGNETIC RESONANCE 19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic

More information

Physics HSC Course Stage 6. Space. Part 1: Earth s gravitational field

Physics 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 information

CHAPTER 5 GRAVITATIONAL FIELD AND POTENTIAL

CHAPTER 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 information

Solutions for Physics 1301 Course Review (Problems 10 through 18)

Solutions for Physics 1301 Course Review (Problems 10 through 18) Solutions fo Physics 1301 Couse Review (Poblems 10 though 18) 10) a) When the bicycle wheel comes into contact with the step, thee ae fou foces acting on it at that moment: its own weight, Mg ; the nomal

More information

Lab M4: The Torsional Pendulum and Moment of Inertia

Lab M4: The Torsional Pendulum and Moment of Inertia M4.1 Lab M4: The Tosional Pendulum and Moment of netia ntoduction A tosional pendulum, o tosional oscillato, consists of a disk-like mass suspended fom a thin od o wie. When the mass is twisted about the

More information

VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY OF BIO-DIESEL FUELS VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use

More information

Lecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3

Lecture 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 information

Do Vibrations Make Sound?

Do Vibrations Make Sound? Do Vibations Make Sound? Gade 1: Sound Pobe Aligned with National Standads oveview Students will lean about sound and vibations. This activity will allow students to see and hea how vibations do in fact

More information

SELF-INDUCTANCE AND INDUCTORS

SELF-INDUCTANCE AND INDUCTORS MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................

More information

Mechanics 1: Work, Power and Kinetic Energy

Mechanics 1: Work, Power and Kinetic Energy Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).

More information

Structure and evolution of circumstellar disks during the early phase of accretion from a parent cloud

Structure and evolution of circumstellar disks during the early phase of accretion from a parent cloud Cente fo Tubulence Reseach Annual Reseach Biefs 2001 209 Stuctue and evolution of cicumstella disks duing the ealy phase of accetion fom a paent cloud By Olusola C. Idowu 1. Motivation and Backgound The

More information

Chapter 4: Fluid Kinematics

Chapter 4: Fluid Kinematics Oveview Fluid kinematics deals with the motion of fluids without consideing the foces and moments which ceate the motion. Items discussed in this Chapte. Mateial deivative and its elationship to Lagangian

More information

An Introduction to Omega

An 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 isk-ewad chaacteistics? The Finance Development Cente 2002 1 Fom

More information

Chapter 2 Coulomb s Law

Chapter 2 Coulomb s Law Chapte Coulomb s Law.1 lectic Chage...-3. Coulomb's Law...-3 Animation.1: Van de Gaaff Geneato...-4.3 Pinciple of Supeposition...-5 xample.1: Thee Chages...-5.4 lectic Field...-7 Animation.: lectic Field

More information

Introduction to Fluid Mechanics

Introduction 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 information

Problems of the 2 nd and 9 th International Physics Olympiads (Budapest, Hungary, 1968 and 1976)

Problems of the 2 nd and 9 th International Physics Olympiads (Budapest, Hungary, 1968 and 1976) Poblems of the nd and 9 th Intenational Physics Olympiads (Budapest Hungay 968 and 976) Péte Vankó Institute of Physics Budapest Univesity of Technology and Economics Budapest Hungay Abstact Afte a shot

More information

GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS ` E MISN-0-133. CHARGE DISTRIBUTIONS by Peter Signell, Michigan State University

GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS ` E MISN-0-133. CHARGE DISTRIBUTIONS by Peter Signell, Michigan State University MISN-0-133 GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS GAUSS S LAW APPLIED TO CYLINDRICAL AND PLANAR CHARGE DISTRIBUTIONS by Pete Signell, Michigan State Univesity 1. Intoduction..............................................

More information

Carter-Penrose diagrams and black holes

Carter-Penrose diagrams and black holes Cate-Penose 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 information

Model Question Paper Mathematics Class XII

Model Question Paper Mathematics Class XII Model Question Pape Mathematics Class XII Time Allowed : 3 hous Maks: 100 Ma: Geneal Instuctions (i) The question pape consists of thee pats A, B and C. Each question of each pat is compulsoy. (ii) Pat

More information

Skills Needed for Success in Calculus 1

Skills 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 information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 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 information

PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary

PAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII - SPETO - 1995. pod patronatem. Summary PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8 - TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC

More information

Explicit, analytical solution of scaling quantum graphs. Abstract

Explicit, analytical solution of scaling quantum graphs. Abstract Explicit, analytical solution of scaling quantum gaphs Yu. Dabaghian and R. Blümel Depatment of Physics, Wesleyan Univesity, Middletown, CT 06459-0155, USA E-mail: ydabaghian@wesleyan.edu (Januay 6, 2003)

More information

Fluids Lecture 15 Notes

Fluids 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 2-D, this velocit

More information

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers

Concept and Experiences on using a Wiki-based System for Software-related Seminar Papers Concept and Expeiences on using a Wiki-based System fo Softwae-elated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wth-aachen.de,

More information

Gravitation and Kepler s Laws

Gravitation and Kepler s Laws 3 Gavitation and Keple s Laws In this chapte we will ecall the law of univesal gavitation and will then deive the esult that a spheically symmetic object acts gavitationally like a point mass at its cente

More information

The Binomial Distribution

The Binomial Distribution The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

Magnetic Bearing with Radial Magnetized Permanent Magnets

Magnetic Bearing with Radial Magnetized Permanent Magnets Wold Applied Sciences Jounal 23 (4): 495-499, 2013 ISSN 1818-4952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich

More information

Week 3-4: Permutations and Combinations

Week 3-4: Permutations and Combinations Week 3-4: Pemutations and Combinations Febuay 24, 2016 1 Two Counting Pinciples Addition Pinciple Let S 1, S 2,, S m be disjoint subsets of a finite set S If S S 1 S 2 S m, then S S 1 + S 2 + + S m Multiplication

More information

Semipartial (Part) and Partial Correlation

Semipartial (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 information

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications

TECHNICAL DATA. JIS (Japanese Industrial Standard) Screw Thread. Specifications JIS (Japanese Industial Standad) Scew Thead Specifications TECNICAL DATA Note: Although these specifications ae based on JIS they also apply to and DIN s. Some comments added by Mayland Metics Coutesy

More information

est 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.

est 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 information

12.1. FÖRSTER RESONANCE ENERGY TRANSFER

12.1. FÖRSTER RESONANCE ENERGY TRANSFER ndei Tokmakoff, MIT epatment of Chemisty, 3/5/8 1-1 1.1. FÖRSTER RESONNCE ENERGY TRNSFER Föste esonance enegy tansfe (FR) efes to the nonadiative tansfe of an electonic excitation fom a dono molecule to

More information

Lesson 8 Ampère s Law and Differential Operators

Lesson 8 Ampère s Law and Differential Operators Lesson 8 Ampèe s Law and Diffeential Opeatos Lawence Rees 7 You ma make a single cop of this document fo pesonal use without witten pemission 8 Intoduction Thee ae significant diffeences between the electic

More information

Uniform Rectilinear Motion

Uniform Rectilinear Motion Engineeing Mechanics : Dynamics Unifom Rectilinea Motion Fo paticle in unifom ectilinea motion, the acceleation is zeo and the elocity is constant. d d t constant t t 11-1 Engineeing Mechanics : Dynamics

More information

Symmetric polynomials and partitions Eugene Mukhin

Symmetric polynomials and partitions Eugene Mukhin Symmetic polynomials and patitions Eugene Mukhin. Symmetic polynomials.. Definition. We will conside polynomials in n vaiables x,..., x n and use the shotcut p(x) instead of p(x,..., x n ). A pemutation

More information

Analytical Proof of Newton's Force Laws

Analytical 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 information

2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES

2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES . TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES In ode to etend the definitions of the si tigonometic functions to geneal angles, we shall make use of the following ideas: In a Catesian coodinate sstem, an

More information

Comparing Availability of Various Rack Power Redundancy Configurations

Comparing Availability of Various Rack Power Redundancy Configurations Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance the availability

More information

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w

Quantity Formula Meaning of variables. 5 C 1 32 F 5 degrees Fahrenheit, 1 bh A 5 area, b 5 base, h 5 height. P 5 2l 1 2w 1.4 Rewite Fomulas and Equations Befoe You solved equations. Now You will ewite and evaluate fomulas and equations. Why? So you can apply geometic fomulas, as in Ex. 36. Key Vocabulay fomula solve fo a

More information

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning

Gravitational Mechanics of the Mars-Phobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning Gavitational Mechanics of the Mas-Phobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This

More information

DYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES

DYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation

More information

Supplementary Material for EpiDiff

Supplementary Material for EpiDiff Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module

More information

CHAPTER 9 THE TWO BODY PROBLEM IN TWO DIMENSIONS

CHAPTER 9 THE TWO BODY PROBLEM IN TWO DIMENSIONS 9. Intoduction CHAPTER 9 THE TWO BODY PROBLEM IN TWO DIMENSIONS In this chapte we show how Keple s laws can be deived fom Newton s laws of motion and gavitation, and consevation of angula momentum, and

More information

Impulse and Linear Momentum 5

Impulse and Linear Momentum 5 Implse and Linea Momentm 5 How does jet poplsion wok? How can yo mease the speed of a bllet? Wold a meteoite collision significantly change Eath s obit? In pevios chaptes we discoveed that the pshing inteaction

More information

Chapter 4: Fluid Kinematics

Chapter 4: Fluid Kinematics 4-1 Lagangian g and Euleian Desciptions 4-2 Fundamentals of Flow Visualization 4-3 Kinematic Desciption 4-4 Reynolds Tanspot Theoem (RTT) 4-1 Lagangian and Euleian Desciptions (1) Lagangian desciption

More information