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

Size: px
Start display at page:

Download "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"

Transcription

1 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 Joule J) In electicity, it is usually moe convenient to use the Electic Potential V (o Voltage) is electic potential enegy pe unit chage, measued in joules pe coulomb (Unit Volt V) A chaged paticle q exets an electic foce (a consevative foce) in an electic field. If the chage q is not static then wok is done in an electic field by moving the chage q. The wok is popotional to the magnitude of chage (Moe wok is needed to move a bigge chage). This is simila to lift/dop an object against/with gavity. Geneal Physics - PH Winte 6 Bjoen Seipel Definition: The electic potential is electic potential enegy pe chage (like we deived the electic field). V = U/q The change in electic potential enegy pe chage is known as potential diffeence o voltage and is measued in Volt. Only changes of electic potential ae meaningful. V = U/q = -W/q 1V [Volt] =1 Nm/C When we dealing with small chages, thee is anothe unit fo enegy: electon volt = enegy of one electon possesses when it has moved though a potential diffeence of 1 Volt 1 ev = J [Joule] Connection between electic field and electic potential (E=const.) V = U/q = -W/q = q Ed/q = Ed F=q E F=mg U=E el =qed (W=Fs cosθ and U=-W) U=E pot =mgh (when E-field is homogeneous, E is constant vecto eveywhee) Electic Potential Enegy Gavitational Potential Enegy The electic potential enegy incease/decease in the same way as like the gavitational enegy. Only diffeences in potential enegy ae impotant E = V/d= V/ s If E=const. The change in the potential pe distance is constant Example: Paallel Plate Capacito Fo calculating physical quantities it is the diffeence in potential which has significance, not the potential itself. Theefoe, we may choose any abitay point as having zeo potential 1

2 Geneal Physics - PH Winte 6 Bjoen Seipel Enegy consevation When we move a chage in an electic field the total enegy the electic foce is consevative must be conseved. (E kin + E el ) initial = (E kin +E el ) final (½ mv +U) initial =(½ mv +U) final (½ mv +qv) initial =(½ mv +qv) final ½ mv final=(½ mv ) initial + q(v final -V initial ) v final=v initial+ q( V)/m ules: positives chages acceleate in the diection of deceasing electical potential negative chages in the opposite diection In both cases the chage moves to a egion with a lowe potential enegy Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential of Point Chages q q 1 Electic foce F = k 1 1 If we elease test chage it will move (acceleate) away At point B: U A -U B =(qed) A -(qed) B = (Fd) A -(Fd) B = kq q/ A - kq q/ B o V A -V B = (U A -U B )/ q = kq/ A - kq/ B if then V B = Definition: The electic potential fo a point chage kq V = [V ] The electic potential enegy fo a point chage q q U = q V = k [ J ] 3 4

3 Geneal Physics - PH Winte 6 Bjoen Seipel Supeposition of two o moe point chages The potential at a given point in space due to seveal chages can be found by adding the potential fom each chage Geneal Physics - PH Winte 6 Bjoen Seipel Anothe way to daw electic potentials: Contou Maps V A q = k q k q k 3... The dense the lines the moe geat is the change in the potential (Equipotential sufaces, Equipotential lines) The electic field points always in the diection of the deceasing lines No wok is equied to move a chage along an equipotential suface, the electic field at evey point on an equipotential suface is pependicula to the suface. 5 6

4 Geneal Physics - PH Winte 6 Bjoen Seipel The ideal conducto Geneal Physics - PH Winte 6 Bjoen Seipel If both sphees have the same potential Evey point on o within such a conducto is at the same potential. Ideal conductos ae equipotential objects. The electic field is stonge whee the conducto is shaply cuved. Why? Let s assume we have to chaged metal sphees both with the same electic potential. Lage sphee: kσ 4π V = kσ 4π E = Small sphee: = kσ 4π = kσ 4π k?4π 4 V = = k?4π Theefoe:?=σ small sphee = σ kσ 4π E = 4 = kσ 4π 4 highe chage density The potential of a metal sphee is given by kq V = The electic field is given by kq E = Q is the chage distibuted unifomly ove the suface A with a cetain chage density σ Q= σ A = σ 4π 7 8

5 Geneal Physics - PH Winte 6 Bjoen Seipel Capacitos A capacito is a device that stoes enegy associated with a configuation of chages. In geneal, a capacito consists of two conductos, one with a chage +Q and the othe with a chage -Q. Geneal Physics - PH Winte 6 Bjoen Seipel Dielectics A way to incease the capacitance is with an insulting mateial between the plates a dielectic Dielectic slab Capacity is the ability to stoe chage and enegy. The capacitance C is defined as the atio of the magnitude of the chage on eithe conducto to the magnitude of the potential diffeence between the conductos: Q = C V o C = Q/V C: Capacitance [F = Faad] The paallel-plate capacito We can calculated accoding to Gauss law fo a paallel plate capacito the electic field as Q σ A Q E = = = ε ε ε A Qd V = ε A We can calculate the potential as V=Ed Q ε A C = = Qd d ε A Capacitance of a paallel-plate capacito Field lines teminate on negative chage and stat at positive chage on polaized slab. Less field lines ae going though the entie capacito. We educe E-field by a mateial dependent facto the dielectic constant κ E E = Vacuum κ=1; H O= 8.4 κ We know E V V = Ed = d = κ κ V decease with inceasing κ C = Q Q Q = = κ = κ C C incease with inceasing κ V V V κ We can expand the equation fo the paallel capacito: ε A C = κ d 9 1

6 Geneal Physics - PH Winte 6 Bjoen Seipel => Capacitance dependence also on the suface aea A of the plates and the distance d. That how a keyboad woks A dielectic beakdown appeas when the Electic field is too stong. That means stong enough to tea atoms apat. Geneal Physics - PH Winte 6 Bjoen Seipel Electical Enegy Stoage Situation: Paallel plate capacito with a chage Q on its plates and potential diffeence of V. Now we tansfe small packages of chage fom one play to the othe. The change in electic potential enegy would be U = Q V Attention! V is not constant. If we would tansfe anothe chage package we have to calculate with anothe V U= QV av = ½ QV Substance Mica Teflon Pape Pyex glass Neopene ubbe Ai Dielectic stength (V/m) 1 x x x x x x 1 6 With Q = CV U = ½ CV V = Q/C U = ½ Q /C Fo a paallel plate capacito Q = ε E A and V = Ed Theefoe U = ½ Q V = ½ (ε E A) (Ed)= ½ ε E A d A d is the volume between the plates so we can define a density (i.e. a quantity divided by its volume) Electic enegy density U E = electic enegy/ volume = ½ ε E Next time you walk acoss a capet and get a shock fom the dooknob think about the fact that you just have poduced an electic field of oughly 3 million V/m. 11 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(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

Electric Potential. otherwise to move the object from initial point i to final point f

Electric Potential. otherwise to move the object from initial point i to final point f PHY2061 Enched Physcs 2 Lectue Notes Electc Potental Electc Potental Dsclame: These lectue notes ae not meant to eplace the couse textbook. The content may be ncomplete. Some topcs may be unclea. These

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

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

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

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

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

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

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

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

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

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

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

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

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

www.sakshieducation.com

www.sakshieducation.com Viscosity. The popety of viscosity in gas is due to ) Cohesive foces between the moecues ) Coisions between the moecues ) Not having a definite voume ) Not having a definite size. When tempeatue is inceased

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

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

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

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & 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 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

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

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

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

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.

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

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

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,

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

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

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH

YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav

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

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

dz + η 1 r r 2 + c 1 ln r + c 2 subject to the boundary conditions of no-slip side walls and finite force over the fluid length u z at r = 0

dz + η 1 r r 2 + c 1 ln r + c 2 subject to the boundary conditions of no-slip side walls and finite force over the fluid length u z at r = 0 Poiseuille Flow Jean Louis Maie Poiseuille, a Fench physicist and physiologist, was inteested in human blood flow and aound 1840 he expeimentally deived a law fo flow though cylindical pipes. It s extemely

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

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

Coordinate Systems L. M. Kalnins, March 2009

Coordinate 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 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

Dipole moments 1 2.10 DETERMINATION OF DIPOLE MOMENT FROM RELATIVE PERMITTIVITY AND REFRACTIVE INDEX. Plates applying external electric field

Dipole moments 1 2.10 DETERMINATION OF DIPOLE MOMENT FROM RELATIVE PERMITTIVITY AND REFRACTIVE INDEX. Plates applying external electric field Dipole moments 1.10 DETERMINATION OF DIPOLE MOMENT FROM RELATIVE PERMITTIVITY AND REFRACTIVE INDEX (4 points) Plates applying extenal electic field Suface chages on dielectic block Figue 1. Polaization

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

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

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

An Epidemic Model of Mobile Phone Virus

An Epidemic Model of Mobile Phone Virus An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity

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

Excitation energies for molecules by Time-Dependent. based on Effective Exact Exchange Kohn-Sham potential

Excitation energies for molecules by Time-Dependent. based on Effective Exact Exchange Kohn-Sham potential Excitation enegies fo molecules by Time-Dependent Density-Functional Theoy based on Effective Exact Exchange Kohn-Sham potential Fabio Della Sala National Nanotechnology Laboatoies Lecce Italy A. Göling

More information

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE

INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE 1 INVESTIGATION OF FLOW INSIDE AN AXIAL-FLOW PUMP OF GV IMP TYPE ANATOLIY A. YEVTUSHENKO 1, ALEXEY N. KOCHEVSKY 1, NATALYA A. FEDOTOVA 1, ALEXANDER Y. SCHELYAEV 2, VLADIMIR N. KONSHIN 2 1 Depatment of

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

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt

Instituto Superior Técnico Av. Rovisco Pais, 1 1049-001 Lisboa E-mail: virginia.infante@ist.utl.pt FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB-30 AIRCRAFT - PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado

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

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

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

Gravitation. Definition of Weight Revisited. Newton s Law of Universal Gravitation. Newton s Law of Universal Gravitation. Gravitational Field

Gravitation. Definition of Weight Revisited. Newton s Law of Universal Gravitation. Newton s Law of Universal Gravitation. Gravitational Field Defnton of Weght evsted Gavtaton The weght of an object on o above the eath s the gavtatonal foce that the eath exets on the object. The weght always ponts towad the cente of mass of the eath. On o above

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation

More information

Advanced Control of Active Filters. in a Battery Charger Application. Martin Bojrup

Advanced Control of Active Filters. in a Battery Charger Application. Martin Bojrup Advanced Contol of Active Filtes in a Battey Chage Application Matin Bojup Lund 999 ii Cove pictue Measuement on the dynamic esponse of the MRI hamonic filte contolle: load cuent (top), esulting line cuent

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

3.11 Recitation #9 November 4, 2003. Rubber Elasticity

3.11 Recitation #9 November 4, 2003. Rubber Elasticity 3.11 Recitation #9 Novembe 4, 2003 Moe Disode Rubbe Elasticity The Entopic Sping Entopy - a natual law that expesses the diving foce towads disode Less Disode Rubbe bands ae made fom polymes, but the chains

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

DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION

DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION DIFFERENT TYPES OF HUMAN HEAD SHAPES FOR CELLULAR PHONE EXPOSURE ON ELECTROMAGNETIC ABSORPTION Mohammad Rashed Iqbal Fauque* #1, Mohammad Taiqul Islam* 2, Nobahiah Misan* #3 * Institute of Space Science

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

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

LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions.

LATIN SQUARE DESIGN (LS) -With the Latin Square design you are able to control variation in two directions. Facts about the LS Design LATIN SQUARE DESIGN (LS) -With the Latin Squae design you ae able to contol vaiation in two diections. -Teatments ae aanged in ows and columns -Each ow contains evey teatment.

More information

Strength Analysis and Optimization Design about the key parts of the Robot

Strength Analysis and Optimization Design about the key parts of the Robot Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Pint): 2320-9356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.25-29 Stength Analysis and Optimization Design

More information

CHAPTER 26 ELECTROSTATIC ENERGY AND CAPACITORS

CHAPTER 26 ELECTROSTATIC ENERGY AND CAPACITORS CHAPTER 6 ELECTROSTATIC ENERGY AND CAPACITORS. Three point charges, each of +q, are moved from infinity to the vertices of an equilateral triangle of side l. How much work is required? The sentence preceding

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 White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dual-path powe distibution to IT equipment ae used to enhance

More information