Rotating DC Motors Part II


 Lora Watkins
 4 years ago
 Views:
Transcription
1 Rotting Motors rt II II.1 Motor Equivlent Circuit The next step in our consiertion of motors is to evelop n equivlent circuit which cn be use to better unerstn motor opertion. The rmtures in rel motors usully consist of mny winings of reltively thin wire. Recll tht thin wires hve lrger resistnce thn thick wires. The equivlent circuit then must inclue resistor R which ccounts for the totl resistnce of the rmture wining. Figure 1 shows the equivlent circuit for motor. V represents the pplie voltge which cuses the rmture current to flow, R is the resistnce of the rmture, n E is the generte or inuce bck EMF in the rmture. I R V E = K υ  Figure 1: ermnent Mgnet Motor Equivlent Circuit Figure 1 shows tht rmture current, I, flows from the positive terminl of the voltge source, V, n the vlue of I is etermine by I = ( V E )/ R. The bck EMF cts to limit the flow of rmture current, but E g must lwys be less thn V in orer for I to be positive. The equivlent circuit for the motor cn be nlyze using ny circuit technique lerne erlier in this course. II. ower in Motors The power input to motor is simply the input current multiplie by the pplie voltge: = I V. Due to electricl n mechnicl losses in the motor, the mechnicl power out of the motor must be less thn the electricl power in. The most obvious electricl loss is ue to the rmture resistnce, elec loss = I R. As iscusse in previous sections, power losses lso occur ue to:  friction between prts of the mchine
2  mgnetic inefficiencies of the mteril use  ir resistnce (winge) of the rotting rmture  smll resistnce cross the brushes use to couple current onto the commuttor These losses cn be pproximte collectively by specifying n overll vlue for mechnicl power lost,. As with ny other system which oes not store energy, the electricl power input to motor must equl the sum of the mechnicl power output n the vrious loss mechnisms: = + + The output power cn be clculte from the power blnce eqution bove, or from the prouct of output torque n ngulr velocity: = T lo Mechnicl power is often expresse in units of horsepower, hp. This is nonsi unit of power equl to 746 wtts. If torque is expresse in N m n ngulr velocity is expresse in units of rins per secon, then the units out of = T lo will be expresse in wtts. To convert to horsepower, simply ivie the nswer in wtts by 746. A power conversion igrm is useful tool to ocument the power flow in motor. It clerly shows tht the input power is electricl n tht the output power is mechnicl. The power evelope,, enotes the chnge from electricl to mechnicl power. = V I = EI = T = T lo = I R = T Figure : ower Conversion Digrm II.3 Efficiency Efficiency of system cn be generlly efine s the rtio of power output reltive to power input. In motors this becomes the mechnicl power out reltive to the electricl power in: η = /
3 The expression for power out, = T lo, cn be recst to provie simple eqution for efficiency s follows. Erlier in this chpter, evelope torque ws given s T = K. Multiplying both sies of this eqution by the ngulr velocity,, gives: I T = K v I But T equls the power evelope,. Thus: = K v I Bck EMF ws lso efine erlier s E = K. Hence, we cn rrive t new eqution for mechnicl power evelope s shown t the she line in Figure bove: = T = KI = EI In mny cses the friction losses will be smll compre to the rmture loss. If we ssume tht mechnicl losses cn be ignore, the efficiency of motor cn be expresse simply s the rtio of bck EMF to pplie voltge becuse: T = T + T lo n if: T = 0 then: T = T lo hence: = T = T = KI = EI lo n EI E η = (100%) = (100%) = (100%) V I V Agin, this finl eqution ssumes ll mechnicl losses re ignore.
4 Here is summry of the rotting motor equtions: Rotting Motor Equtions in = mechnicl If no lo, then out n T out = 0, n =, T = T electricl = out ower eqution ( out = lo ) T T = T out Torque eqution (T out = T lo ) energy conversion here (T = /, or, = T ) ( subscript mens evelope ) in = V I = I R = E * I = T = K v I E = K v T = K v I η = out / in
5 Exmple II1: A permnent mgnet motor is rte for 5 V, A n 1300 rpm. If the mchine is 90% efficient t rte conitions fin R n K if T = N m. SOLUTION: We use the given rte electricl informtion to etermine the power into the motor. = V I = ( 5V )( A) = 50 W The efficiency vlue then enbles us to clculte the output power t rte conitions. = ( 0.90)(50 W ) = 45 W We cn clculte the power loss t rte conitions by The power evelope must be = + Now, we cn solve for To fin R : = T 1300 rev 1min π r = ( N m) min 60 s 1rev = 4.55 W = 4.55 W + 45 W = W K. = T = K I π W = K ( A) 1300rpm 30 K = 0.18 V s V = RI + E V = RI + K π 5 = R ( A) + (0.18 V s)(1300) 30 R = 0.11 Ω
6 A power conversion igrm shows nother pproch to this problem if we consier electricl power loss in the rmture. = V I = EI = T = T lo = I R = T From the power conversion igrm. 50 W = 0.45 W R = = 0.45 W = I R = (A) = 0.11 Ω W + 45 W R
4. DC MOTORS. Understand the basic principles of operation of a DC motor. Understand the operation and basic characteristics of simple DC motors.
4. DC MOTORS Almost every mechnicl movement tht we see round us is ccomplished by n electric motor. Electric mchines re mens o converting energy. Motors tke electricl energy nd produce mechnicl energy.
More informationRotating DC Motors Part I
Rotting DC Motors Prt I he previous lesson introduced the simple liner motor. Liner motors hve some prcticl pplictions, ut rotting DC motors re much more prolific. he principles which eplin the opertion
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationWeek 11  Inductance
Week  Inductnce November 6, 202 Exercise.: Discussion Questions ) A trnsformer consists bsiclly of two coils in close proximity but not in electricl contct. A current in one coil mgneticlly induces n
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More information, and the number of electrons is 19. e e 1.60 10 C. The negatively charged electrons move in the direction opposite to the conventional current flow.
Prolem 1. f current of 80.0 ma exists in metl wire, how mny electrons flow pst given cross section of the wire in 10.0 min? Sketch the directions of the current nd the electrons motion. Solution: The chrge
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationPolynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 9 The Force Method of Anlysis: Bems (Continued) Version CE IIT, Khrgpur Instructionl Objectives
More informationCOMPONENTS: COMBINED LOADING
LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments  they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationAlgebra Review. How well do you remember your algebra?
Algebr Review How well do you remember your lgebr? 1 The Order of Opertions Wht do we men when we write + 4? If we multiply we get 6 nd dding 4 gives 10. But, if we dd + 4 = 7 first, then multiply by then
More information9.3. The Scalar Product. Introduction. Prerequisites. Learning Outcomes
The Sclr Product 9.3 Introduction There re two kinds of multipliction involving vectors. The first is known s the sclr product or dot product. This is soclled becuse when the sclr product of two vectors
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nmwide region t x
More informationMATH 150 HOMEWORK 4 SOLUTIONS
MATH 150 HOMEWORK 4 SOLUTIONS Section 1.8 Show tht the product of two of the numbers 65 1000 8 2001 + 3 177, 79 1212 9 2399 + 2 2001, nd 24 4493 5 8192 + 7 1777 is nonnegtive. Is your proof constructive
More informationLINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES
LINEAR TRANSFORMATIONS AND THEIR REPRESENTING MATRICES DAVID WEBB CONTENTS Liner trnsformtions 2 The representing mtrix of liner trnsformtion 3 3 An ppliction: reflections in the plne 6 4 The lgebr of
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More information15.6. The mean value and the rootmeansquare value of a function. Introduction. Prerequisites. Learning Outcomes. Learning Style
The men vlue nd the rootmensqure vlue of function 5.6 Introduction Currents nd voltges often vry with time nd engineers my wish to know the verge vlue of such current or voltge over some prticulr time
More informationIntegration. 148 Chapter 7 Integration
48 Chpter 7 Integrtion 7 Integrtion t ech, by supposing tht during ech tenth of second the object is going t constnt speed Since the object initilly hs speed, we gin suppose it mintins this speed, but
More informationReview guide for the final exam in Math 233
Review guide for the finl exm in Mth 33 1 Bsic mteril. This review includes the reminder of the mteril for mth 33. The finl exm will be cumultive exm with mny of the problems coming from the mteril covered
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationUnderstanding Basic Analog Ideal Op Amps
Appliction Report SLAA068A  April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp).
More informationMA 15800 Lesson 16 Notes Summer 2016 Properties of Logarithms. Remember: A logarithm is an exponent! It behaves like an exponent!
MA 5800 Lesson 6 otes Summer 06 Rememer: A logrithm is n eponent! It ehves like n eponent! In the lst lesson, we discussed four properties of logrithms. ) log 0 ) log ) log log 4) This lesson covers more
More informationand thus, they are similar. If k = 3 then the Jordan form of both matrices is
Homework ssignment 11 Section 7. pp. 24925 Exercise 1. Let N 1 nd N 2 be nilpotent mtrices over the field F. Prove tht N 1 nd N 2 re similr if nd only if they hve the sme miniml polynomil. Solution: If
More informationUnderstanding Life Cycle Costs How a Northern Pump Saves You Money
Understnding Life Cycle Costs How Nrn Pump Sves You Money Reference: Hydrulic Institute (www.s.g) Introduction Wht Life Cycle Cost (LCC) Clculting Totl LCC LCC Components Wht Life Cycle Cost Life Cycle
More informationRegular Sets and Expressions
Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationCOMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, crossclssified
More informationMATH PLACEMENT REVIEW GUIDE
MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your
More informationSpace Vector Pulse Width Modulation Based Induction Motor with V/F Control
Interntionl Journl of Science nd Reserch (IJSR) Spce Vector Pulse Width Modultion Bsed Induction Motor with V/F Control Vikrmrjn Jmbulingm Electricl nd Electronics Engineering, VIT University, Indi Abstrct:
More informationTutorial on How to Create Electric Machine Models
PSIM Sotwre Tutoril on How to Crete Electric Mchine Models Powersi Inc. Septber 2009 www.powersitech.co Tutoril on Creting Electric Mchine Models Users cn crete electric chine odels using the bsic unction
More informationThe Velocity Factor of an Insulated TwoWire Transmission Line
The Velocity Fctor of n Insulted TwoWire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the
More information1.2 The Integers and Rational Numbers
.2. THE INTEGERS AND RATIONAL NUMBERS.2 The Integers n Rtionl Numers The elements of the set of integers: consist of three types of numers: Z {..., 5, 4, 3, 2,, 0,, 2, 3, 4, 5,...} I. The (positive) nturl
More informationLectures 8 and 9 1 Rectangular waveguides
1 Lectures 8 nd 9 1 Rectngulr wveguides y b x z Consider rectngulr wveguide with 0 < x b. There re two types of wves in hollow wveguide with only one conductor; Trnsverse electric wves
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationIntegration by Substitution
Integrtion by Substitution Dr. Philippe B. Lvl Kennesw Stte University August, 8 Abstrct This hndout contins mteril on very importnt integrtion method clled integrtion by substitution. Substitution is
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More information5.2. LINE INTEGRALS 265. Let us quickly review the kind of integrals we have studied so far before we introduce a new one.
5.2. LINE INTEGRALS 265 5.2 Line Integrls 5.2.1 Introduction Let us quickly review the kind of integrls we hve studied so fr before we introduce new one. 1. Definite integrl. Given continuous relvlued
More informationAnswer, Key Homework 10 David McIntyre 1
Answer, Key Homework 10 Dvid McIntyre 1 This printout should hve 22 questions, check tht it is complete. Multiplechoice questions my continue on the next column or pge: find ll choices efore mking your
More informationc. Values in statements are broken down by fiscal years; many projects are
Lecture 18: Finncil Mngement (Continued)/Csh Flow CEE 498 Construction Project Mngement L Schedules A. Schedule.of Contrcts Completed See Attchment # 1 ll. 1. Revenues Erned 2. Cost of Revenues 3. Gross
More informationThe Definite Integral
Chpter 4 The Definite Integrl 4. Determining distnce trveled from velocity Motivting Questions In this section, we strive to understnd the ides generted by the following importnt questions: If we know
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine soclled volumes of
More informationBabylonian Method of Computing the Square Root: Justifications Based on Fuzzy Techniques and on Computational Complexity
Bbylonin Method of Computing the Squre Root: Justifictions Bsed on Fuzzy Techniques nd on Computtionl Complexity Olg Koshelev Deprtment of Mthemtics Eduction University of Texs t El Pso 500 W. University
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationCapacitance and Dielectrics
2.2 This is the Nerest One He 803 P U Z Z L E R Mny electronic components crry wrning lel like this one. Wht is there insie these evices tht mkes them so ngerous? Why wouln t you e sfe if you unplugge
More informationRIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS
RIGHT TRIANGLES AND THE PYTHAGOREAN TRIPLETS Known for over 500 yers is the fct tht the sum of the squres of the legs of right tringle equls the squre of the hypotenuse. Tht is +b c. A simple proof is
More information6.5  Areas of Surfaces of Revolution and the Theorems of Pappus
Lecture_06_05.n 1 6.5  Ares of Surfces of Revolution n the Theorems of Pppus Introuction Suppose we rotte some curve out line to otin surfce, we cn use efinite integrl to clculte the re of the surfce.
More informationCypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:
Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationRadius of the Earth  Radii Used in Geodesy James R. Clynch February 2006
dius of the Erth  dii Used in Geodesy Jmes. Clynch Februry 006 I. Erth dii Uses There is only one rdius of sphere. The erth is pproximtely sphere nd therefore, for some cses, this pproximtion is dequte.
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More informationPHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationWeek 7  Perfect Competition and Monopoly
Week 7  Perfect Competition nd Monopoly Our im here is to compre the industrywide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in pointdirection nd twopoint
More informationPSYCHROMETRICS: HEATING & HUMIDIFYING or COOLING & DEHUMIDIFYING
PSYCHROMETRICS: HEATING & HUMIDIYING or COOLING & DEHUMIDIYING I) Objective The objective of this experiment is to exmine the stte of moist ir s it enters nd psses through the ir hndling unit. When ether
More informationaddition, there are double entries for the symbols used to signify different parameters. These parameters are explained in this appendix.
APPENDIX A: The ellipse August 15, 1997 Becuse of its importnce in both pproximting the erth s shpe nd describing stellite orbits, n informl discussion of the ellipse is presented in this ppendix. The
More informationUNIVERSITY OF OSLO FACULTY OF MATHEMATICS AND NATURAL SCIENCES
UNIVERSITY OF OSLO FACULTY OF MATHEMATICS AND NATURAL SCIENCES Solution to exm in: FYS30, Quntum mechnics Dy of exm: Nov. 30. 05 Permitted mteril: Approved clcultor, D.J. Griffiths: Introduction to Quntum
More information200506 Second Term MAT2060B 1. Supplementary Notes 3 Interchange of Differentiation and Integration
Source: http://www.mth.cuhk.edu.hk/~mt26/mt26b/notes/notes3.pdf 256 Second Term MAT26B 1 Supplementry Notes 3 Interchnge of Differentition nd Integrtion The theme of this course is bout vrious limiting
More information10.6 Applications of Quadratic Equations
10.6 Applictions of Qudrtic Equtions In this section we wnt to look t the pplictions tht qudrtic equtions nd functions hve in the rel world. There re severl stndrd types: problems where the formul is given,
More information50 MATHCOUNTS LECTURES (10) RATIOS, RATES, AND PROPORTIONS
0 MATHCOUNTS LECTURES (0) RATIOS, RATES, AND PROPORTIONS BASIC KNOWLEDGE () RATIOS: Rtios re use to ompre two or more numers For n two numers n ( 0), the rtio is written s : = / Emple : If 4 stuents in
More informationBypassing Space Explosion in Regular Expression Matching for Network Intrusion Detection and Prevention Systems
Bypssing Spce Explosion in Regulr Expression Mtching for Network Intrusion Detection n Prevention Systems Jignesh Ptel, Alex Liu n Eric Torng Dept. of Computer Science n Engineering Michign Stte University
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationAC 20111184: BASIC CLASS MATERIALS AND LABORATORY PROJECTS WITH DC MOTORS IN AN INTRODUCTORY UNDERGRADUATE ECE CLASS FOR NONMAJORS
AC 20111184: BASC CLASS MATERALS AND LABORATORY PROJECTS WTH DC MOTORS N AN NTRODUCTORY UNDERGRADUATE ECE CLASS FOR NONMAJORS Sergey N. Mkrov, Worcester Polytechnic nstitute Submitting uthor: Sergey
More informationEvaluation of Prediction Models for Marketing Campaigns
Evlution of Preiction Moels for Mrketing Cmpigns Shron Rosset Amocs Lt n Stnfor University shronr@mocscom Nurit Vtnik Amocs (Isrel Lt nuritv@mocscom Eint Neumnn Amocs (Isrel Lt n TelAviv University eintn@mocscom
More informationSOLUTIONS TO CONCEPTS CHAPTER 5
1. m k S 10m Let, ccelertion, Initil velocity u 0. S ut + 1/ t 10 ½ ( ) 10 5 m/s orce: m 5 10N (ns) 40000. u 40 km/hr 11.11 m/s. 3600 m 000 k ; v 0 ; s 4m v u ccelertion s SOLUIONS O CONCEPS CHPE 5 0 11.11
More informationTechnical Appendix: MultiProduct Firms and Trade Liberalization (Not For Publication)
Technicl Appenix: MultiProuct Firms n Tre Liberlition (Not For Publiction) Anrew B. Bernr Tuck School of Business t Drtmouth, CEPR & NBER Stephen J. Reing Princeton University & CEPR Peter K. Schott Yle
More informationModule Summary Sheets. C3, Methods for Advanced Mathematics (Version B reference to new book) Topic 2: Natural Logarithms and Exponentials
MEI Mthemtics in Ection nd Instry Topic : Proof MEI Structured Mthemtics Mole Summry Sheets C, Methods for Anced Mthemtics (Version B reference to new book) Topic : Nturl Logrithms nd Eponentils Topic
More informationAngles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example
2.1 Angles Reognise lternte n orresponing ngles Key wors prllel lternte orresponing vertilly opposite Rememer, prllel lines re stright lines whih never meet or ross. The rrows show tht the lines re prllel
More information4.11 Inner Product Spaces
314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces
More informationN V V L. R a L I. Transformer Equation Notes
Tnsfome Eqution otes This file conts moe etile eivtion of the tnsfome equtions thn the notes o the expeiment 3 witeup. t will help you to unestn wht ssumptions wee neee while eivg the iel tnsfome equtions
More informationTwo hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE. Date: Friday 16 th May 2008. Time: 14:00 16:00
COMP20212 Two hours UNIVERSITY OF MANCHESTER SCHOOL OF COMPUTER SCIENCE Digitl Design Techniques Dte: Fridy 16 th My 2008 Time: 14:00 16:00 Plese nswer ny THREE Questions from the FOUR questions provided
More informationUplift Capacity of KSeries Open Web Steel Joist Seats. Florida, Gainesville, FL 32611; email: psgreen@ce.ufl.edu
Uplift Cpcity of KSeries Open Web Steel Joist Sets Perry S. Green, Ph.D, M.ASCE 1 nd Thoms Sputo, Ph.D., P.E., M.ASCE 2 1 Assistnt Professor, Deprtment of Civil nd Costl Engineering, University of Florid,
More informationTITLE THE PRINCIPLES OF COINTAP METHOD OF NONDESTRUCTIVE TESTING
TITLE THE PRINCIPLES OF COINTAP METHOD OF NONDESTRUCTIVE TESTING Sung Joon Kim*, DongChul Che Kore Aerospce Reserch Institute, 45 EoeunDong, YouseongGu, Dejeon, 35333, Kore Phone : 824286231 FAX
More informationChapter Outline How do atoms arrange themselves to form solids? Types of Solids
Chpter Outline How do toms rrnge themselves to form solids? Fundmentl concepts nd lnguge Unit cells Crystl structures Fcecentered cubic Bodycentered cubic Hexgonl closepcked Close pcked crystl structures
More informationProject 6 Aircraft static stability and control
Project 6 Aircrft sttic stbility nd control The min objective of the project No. 6 is to compute the chrcteristics of the ircrft sttic stbility nd control chrcteristics in the pitch nd roll chnnel. The
More informationA.7.1 Trigonometric interpretation of dot product... 324. A.7.2 Geometric interpretation of dot product... 324
A P P E N D I X A Vectors CONTENTS A.1 Scling vector................................................ 321 A.2 Unit or Direction vectors...................................... 321 A.3 Vector ddition.................................................
More informationAn Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process
An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct
More informationThe Principle of No Punishment Without a Law for It LEARNING OBJECTIVES: CRLA.GAAN:15.01.0701.07
True / Flse 1. An ex post fcto lw is lw which hs retroctive effect.. True b. Flse True 2. An lcoholic cnnot be convicte for the offense of being runk in public plce bse upon the Eighth n Fourteenth Amenments..
More informationSimulation of operation modes of isochronous cyclotron by a new interative method
NUKLEONIKA 27;52(1):29 34 ORIGINAL PAPER Simultion of opertion modes of isochronous cyclotron y new intertive method Ryszrd Trszkiewicz, Mrek Tlch, Jcek Sulikowski, Henryk Doruch, Tdeusz Norys, Artur Srok,
More informationRatio and Proportion
Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty
More informationSensorless Force Estimation for Robots with Friction
Proc. Austrlsin Conference on Rootics nd Automtion Aucklnd, 79 Novemer Sensorless orce Estimtion for Roots with riction John W.L Simpson, Chris D Cook, Zheng Li School of Electricl, Computer nd Telecommunictions
More informationSPECIAL PRODUCTS AND FACTORIZATION
MODULE  Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationCHAPTER 11 Numerical Differentiation and Integration
CHAPTER 11 Numericl Differentition nd Integrtion Differentition nd integrtion re bsic mthemticl opertions with wide rnge of pplictions in mny res of science. It is therefore importnt to hve good methods
More information1. In the Bohr model, compare the magnitudes of the electron s kinetic and potential energies in orbit. What does this imply?
Assignment 3: Bohr s model nd lser fundmentls 1. In the Bohr model, compre the mgnitudes of the electron s kinetic nd potentil energies in orit. Wht does this imply? When n electron moves in n orit, the
More informationPhysics 6010, Fall 2010 Symmetries and Conservation Laws: Energy, Momentum and Angular Momentum Relevant Sections in Text: 2.6, 2.
Physics 6010, Fll 2010 Symmetries nd Conservtion Lws: Energy, Momentum nd Angulr Momentum Relevnt Sections in Text: 2.6, 2.7 Symmetries nd Conservtion Lws By conservtion lw we men quntity constructed from
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationLearn to Recognize Sptil Structure Through Compre Recognition
StrokeBse Performnce Metrics for Hnwritten Mthemticl Expressions Richr Znii rlz@cs.rit.eu Amit Pilly p2731@rit.eu eprtment of Computer Science Rochester Institute of Technology, NY, SA Hrol Mouchère hrol.mouchere@univnntes.fr
More informationSolution to Problem Set 1
CSE 5: Introduction to the Theory o Computtion, Winter A. Hevi nd J. Mo Solution to Prolem Set Jnury, Solution to Prolem Set.4 ). L = {w w egin with nd end with }. q q q q, d). L = {w w h length t let
More informationThe remaining two sides of the right triangle are called the legs of the right triangle.
10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right
More informationLECTURE #05. Learning Objectives. How does atomic packing factor change with different atom types? How do you calculate the density of a material?
LECTURE #05 Chpter : Pcking Densities nd Coordintion Lerning Objectives es How does tomic pcking fctor chnge with different tom types? How do you clculte the density of mteril? 2 Relevnt Reding for this
More informationAREA OF A SURFACE OF REVOLUTION
AREA OF A SURFACE OF REVOLUTION h cut r πr h A surfce of revolution is formed when curve is rotted bout line. Such surfce is the lterl boundr of solid of revolution of the tpe discussed in Sections 7.
More information