v o a y = = * Since H < 1m, the electron does not reach to the top plate.


 Theodore Patrick
 2 years ago
 Views:
Transcription
1 . The uniom electic ield between two conducting chged pltes shown in the igue hs mgnitude o.40 N/C. The plte seption is m, nd we lunch n electon om the bottom plte diectl upwd with v o 6 m/s. Will the electon ech the top plte? Justi ou nswe b poviding numeicl dt. v o * m * ν ( ) ν ο ο m / s H H 0. 90m * Since H < m, the electon does not ech to the top plte.. Thee point chges, µc ech, e plced on thee cones o n euiltel tingle with side m. Wite the net electic ield t the middle point, in tems o unit vectos m * k k N C nd * cos0. k N C 4 * sin 0 6. k N C 0 *.4( k N C) i 6.0( k N C) j ˆ ˆ
2 . long nonconducting clinde with dius 0.5 m hs volume chge densit ρ 5 nc/m. Find the mgnitude o electic ield (in N/C) t distnce 0. m om its is. enc d ε ο d πl enc π L L d 9 ρ N.5 ε ο C 4. ve long line o chge hving uniom chge densit λ is t distnce o d 0.4 m om positive point chge (Q 4 µc) s shown in the igue. I the net electic ield t point is zeo, ind the vlue o λ (sign nd mgnitude). Q λ d 0. m (due to the chged b) must be upwd to cncel the downwd ield (due to Q). Thus, λ should hve positive vlue. Q k λ Q k λ o Q 0.m λ µ C m λ µ C m 5. solid bll o dius R hs uniom volume chge densit ρ nd poduces cetin electic ield with mgnitude t point, which is t distnce R om the bll s cente (ig.). I coe o dius R/ is emoved om the bll (ig.), the ield mgnitude t point chnges to. Wht is the tio /? R Fig. Fig. k k, 4 π R 4 π R ( R ). ρ ρ
3 6. oints ( m, 0 m) nd ( 6 m, m) e in uniom electic ield ) ) 00 ( N / C) i 500( N / C) j. Clculte the potentil dieence V V. X X V V 6 d dl d dl V V V. kv dl dl 7. Thee pticles with eul mss but dieent chge e elesed om thei positions shown below (Q  µc, 9 cm). Wht is the highest kinetic eneg the pticle with chge Q cn obtin? Q Q Q U i k kq 6 kq 9. J U K U K i i. 0 0 K K. J *Since the pticles hve the sme mss K Q K.7 J. lectic chge Q nc is distibuted unioml long thin od o length 4 cm, s shown in the igue. Tke the electic potentil to be zeo t ininit. Clculte the electic potentil t the oigin. Q k d d dv kλ.5 cm 4.0 cm d V kλ kλ ln V 9 ln. 4 kv cm d Q
4 ultiplechoice Questions. Two ininitel lge conducting pltes e positivel chged so tht the suce chge densit o is twice tht o (σ σ ). Which o the ollowing sttements is coect? Region Region Region σ σ ) The net electic ield in egion is zeo. b) The net electic ield in egions nd is zeo. c) The diections o net electic ield in egions nd e the sme. d) The mgnitudes o the net electic ield in egions nd e eul.. point chge o mss m nd chge Q nd nothe point chge o mss m nd chge Q e elesed on ictionless tble. I the chge Q hs n initil cceletion o, wht will be the initil cceletion o Q? ) b) c) / d) 4. The two metl sphees shown in the igue hng om nlon theds close to ech othe. The chge o one sphee is Q, nd the othe is unchged. I the sphees e elesed om est, which o the ollowing sttements is tue: ) The ttct, touch ech othe, nd st in touch. b) The ttct, touch ech othe, nd then epel c) The do not ttct o epel ech othe. d) The epel ech othe until the stop t gete distnce. 4. n empt cone is plced inside uniom electic ield s shown in the igue. The electic lu, Φ, pssing though the cuved suce (S ) o the cone is: R ) Zeo b) πr c) 4πR d) πr se suce S Cuved suce S
5 5. chged conducting spheicl shell with net chge o  hs dii nd b. I point chge o is plced t the cente, then the suce chge densit on the oute suce o the conducting shell is: ) Zeo b) /(4πb ) c) /(4πb ) d) /(4πb ) b 6. Fou Closed suces S, S, S nd S 4 togethe with the chges Q, 5Q nd Q e sketched s shown in the igue. I Q.5 pc then the net electic lu (in Nm /C) though the suce S is: S ) 0 b) c) d) 4 S Q S Q 5Q S 4 7. The wok done b the electic ield to move chge Q om point to point long thee dieent pths with length L, L nd L is denoted b W, W nd W, espectivel. I L L L, then: ) W W W b) W.5 W c) W W W d) W W W L L L. conducting spheicl shell with inne dius nd oute dius b cies chge Q. The electic potentil (with espect to ininit) t the cente o the shell is: ) kq/(b) b) Zeo c) kq/ d) kq/b b
(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?
Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the
More informationExam in physics, Elgrunder (Electromagnetism), 20140326, kl 9.0015.00
Umeå Univesitet, Fysik 1 Vitly Bychkov Em in physics, Elgunde (Electomgnetism, 146, kl 9.15. Hjälpmedel: Students my use ny book(s. Mino notes in the books e lso llowed. Students my not use thei lectue
More informationChapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.
Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming
More informationChapter 23 Electrical Potential
hpte Electicl Potentil onceptul Polems [SSM] A poton is moved to the left in unifom electic field tht points to the ight. Is the poton moving in the diection of incesing o decesing electic potentil? Is
More informationGRAVITATION 1. BASIC FORCES IN NATURE
GRAVITATION. BASIC ORCES IN NATURE POINTS TO REMEMBER. Bsing on the ntue nd eltive stength the bsic foces in ntue e clssified into fou ctegoies. They e ) Gvittionl foce ) Electomgnetic foce 3) Stong Nucle
More information2.016 Hydrodynamics Prof. A.H. Techet
.016 Hydodynmics Reding #5.016 Hydodynmics Po. A.H. Techet Fluid Foces on Bodies 1. Stedy Flow In ode to design oshoe stuctues, suce vessels nd undewte vehicles, n undestnding o the bsic luid oces cting
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationMath 1105: Calculus II (Math/Sci majors) MWF 11am / 12pm, Campion 235 Written homework 5
Mth 5: Clculus II Mth/Sci mjos) MWF m / pm, Cmpion 35 Witten homewok 5 6.6, p. 458 3,33), 6.7, p. 467 8,3), 6.875), 7.58,6,6), 7.44,48) Fo pctice not to tun in): 6.6, p. 458,8,,3,4), 6.7, p. 467 4,6,8),
More informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chpte The lectic Field II: Continuous Chge Distibutions Conceptul Poblems [SSM] Figue 7 shows n Lshped object tht hs sides which e equl in length. Positive chge is distibuted unifomly long the length
More informationIntro to Circle Geometry By Raymond Cheong
Into to Cicle Geomety By Rymond Cheong Mny poblems involving cicles cn be solved by constucting ight tingles then using the Pythgoen Theoem. The min chllenge is identifying whee to constuct the ight tingle.
More informationUniversity Physics AI No. 1 Rectilinear Motion
Uniesity Physics AI No. Rectiline Motion Clss Numbe Nme I.Choose the Coect Answe. An object is moing long the is with position s function of time gien by (. Point O is t. The object is efinitely moing
More informationSummary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:
Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos
More informationA package travels along a conveyor belt as shown in Figure Q1(a). At the instant shown, it has a speed of 0.5 m/s and a rate of increase in speed of
pckge tels long coneyo belt s shown in Figue Q(). t the instnt shown, it hs speed of.5 /s nd te of incese in speed of t =.3 /s. (i) Deteine its speed when it ies t point (ii) Deteine the gnitude of its
More informationLaplace s Equation on a Disc
LECTURE 15 Lplce s Eqution on Disc Lst time we solved the Diichlet poblem fo Lplce s eqution on ectngul egion. Tody we ll look t the coesponding Diichlet poblem fo disc. Thus, we conside disc of dius 1
More informationSamples of conceptual and analytical/numerical questions from chap 21, C&J, 7E
CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known
More informationChapter 26  Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field
More information12. Rolling, Torque, and Angular Momentum
12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.
More informationChapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6
Chapte 9 lectic Chages, Foces, an Fiels 6 9. One in a million (0 ) ogen molecules in a containe has lost an electon. We assume that the lost electons have been emove fom the gas altogethe. Fin the numbe
More informationAnswer, Key Homework 8 David McIntyre 1
Answer, Key Homework 8 Dvid McIntyre 1 This printout should hve 17 questions, check tht it is complete. Multiplechoice questions my continue on the net column or pge: find ll choices before mking your
More informationDouble Integrals over General Regions
Double Integrls over Generl egions. Let be the region in the plne bounded b the lines, x, nd x. Evlute the double integrl x dx d. Solution. We cn either slice the region verticll or horizontll. ( x x Slicing
More informationMultiple choice questions [60 points]
1 Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect bubble on you scanton sheet. Each question has exactly one coect answe. All questions
More informationVersion 001 CIRCUITS holland (1290) 1
Version CRCUTS hollnd (9) This printout should hve questions Multiplechoice questions my continue on the next column or pge find ll choices efore nswering AP M 99 MC points The power dissipted in wire
More informationCircles and Tangents with Geometry Expressions
icles nd Tngents with eomety xpessions IRLS N TNNTS WITH OMTRY XPRSSIONS... INTROUTION... 2 icle common tngents... 3 xmple : Loction of intesection of common tngents... 4 xmple 2: yclic Tpezium defined
More informationr 2 F ds W = r 1 qe ds = q
Chpter 4 The Electric Potentil 4.1 The Importnt Stuff 4.1.1 Electricl Potentil Energy A chrge q moving in constnt electric field E experiences force F = qe from tht field. Also, s we know from our study
More informationMechanics 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 informationr (1+cos(θ)) sin(θ) C θ 2 r cos θ 2
icles xmple 66: Rounding one ssume we hve cone of ngle θ, nd we ound it off with cuve of dius, how f wy fom the cone does the ound stt? nd wht is the chod length? (1+cos(θ)) sin(θ) θ 2 cos θ 2 xmple 67:
More informationReview of Coordinate Systems
Review o Coodinate Sstems good undestanding o coodinate sstems can be ve helpul in solving poblems elated to Mawell s Equations. The thee most common coodinate sstems ae ectangula (,, ), clindical (,,
More informationDivergence and Curl of a Vector Function
Divegence and Cul o a Vecto unction This unit is based on Section 9.7 Chapte 9. All assigned eadings and eecises ae om the tetbook Obectives: Make cetain that ou can deine and use in contet the tems concepts
More informationPROBLEMS 13  APPLICATIONS OF DERIVATIVES Page 1
PROBLEMS  APPLICATIONS OF DERIVATIVES Pge ( ) Wter seeps out of conicl filter t the constnt rte of 5 cc / sec. When the height of wter level in the cone is 5 cm, find the rte t which the height decreses.
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 informationSolution 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 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 informationr Curl is associated w/rotation X F
13.5 ul nd ivegence ul is ssocited w/ottion X F ivegence is F Tody we define two opetions tht cn e pefomed on vecto fields tht ply sic ole in the pplictions of vecto clculus to fluid flow, electicity,
More informationPhysics 107 HOMEWORK ASSIGNMENT #14
Physics 107 HOMEWORK ASSIGNMENT #14 Cutnell & Johnson, 7 th edition Chapte 17: Poblem 44, 60 Chapte 18: Poblems 14, 18, 8 **44 A tube, open at only one end, is cut into two shote (nonequal) lengths. The
More informationProblems on Force Exerted by a Magnetic Fields from Ch 26 T&M
Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuentcaying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to
More informationMAGNETIC FIELD AROUND CURRENTCARRYING WIRES. point in space due to the current in a small segment ds. a for field around long wire
MAGNETC FELD AROUND CURRENTCARRYNG WRES How will we tckle this? Pln: 1 st : Will look t contibution d to the totl mgnetic field t some point in spce due to the cuent in smll segment of wie iotsvt Lw
More information9. Mathematics Practice Paper for Class XII (CBSE) Available Online Tutoring for students of classes 4 to 12 in Physics, Chemistry, Mathematics
Available Online Tutoing fo students of classes 4 to 1 in Physics, 9. Mathematics Class 1 Pactice Pape 1 3 1. Wite the pincipal value of cos.. Wite the ange of the pincipal banch of sec 1 defined on the
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 informationAAPT UNITED STATES PHYSICS TEAM AIP 2010
2010 F = m Exm 1 AAPT UNITED STATES PHYSICS TEAM AIP 2010 Enti non multiplicnd sunt preter necessittem 2010 F = m Contest 25 QUESTIONS  75 MINUTES INSTRUCTIONS DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD
More informationPhysics 2102 Lecture 2. Physics 2102
Physics 10 Jonthn Dowling Physics 10 Lecture Electric Fields ChrlesAugustin de Coulomb (17361806) Jnury 17, 07 Version: 1/17/07 Wht re we going to lern? A rod mp Electric chrge Electric force on other
More informationOrbits and Kepler s Laws
Obits nd Keple s Lws This web pge intoduces some of the bsic ides of obitl dynmics. It stts by descibing the bsic foce due to gvity, then consides the ntue nd shpe of obits. The next section consides how
More informationCurvature. (Com S 477/577 Notes) YanBin Jia. Oct 8, 2015
Cuvtue Com S 477/577 Notes YnBin Ji Oct 8, 205 We wnt to find mesue of how cuved cuve is. Since this cuvtue should depend only on the shpe of the cuve, it should not be chnged when the cuve is epmetized.
More information1+(dy/dx) 2 dx. We get dy dx = 3x1/2 = 3 x, = 9x. Hence 1 +
Mth.9 Em Solutions NAME: #.) / #.) / #.) /5 #.) / #5.) / #6.) /5 #7.) / Totl: / Instructions: There re 5 pges nd totl of points on the em. You must show ll necessr work to get credit. You m not use our
More informationLesson 10. Parametric Curves
Return to List of Lessons Lesson 10. Prmetric Curves (A) Prmetric Curves If curve fils the Verticl Line Test, it cn t be expressed by function. In this cse you will encounter problem if you try to find
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 informationPHYS 4110 Dynamics of Space Vehicles
PHYS 40 Dynmics of Sce Vehicles Chte 7: Obitl Mneues Eth, Moon, Ms, nd eyond D. Jinjun Shn, Pofesso of Sce Engineeing Detment of Eth nd Sce Science nd Engineeing Room 55, Petie Science nd Engineeing uilding
More informationMechanics 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 informationm, where m = m 1 + m m n.
Lecture 7 : Moments nd Centers of Mss If we hve msses m, m 2,..., m n t points x, x 2,..., x n long the xxis, the moment of the system round the origin is M 0 = m x + m 2 x 2 + + m n x n. The center of
More informationYour Thoughts. Does the moment of inertia play a part in determining the amount of time it takes an object to get to the bottom of an incline.
Your Thoughts Suppose bll rolls down rmp with coefficient of friction just big enough to keep the bll from slipping. An identicl bll rolls down n identicl rmp with coefficient of friction of. Do both blls
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More 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 informationMath 22B Solutions Homework 1 Spring 2008
Mth 22B Solutions Homework 1 Spring 2008 Section 1.1 22. A sphericl rindrop evportes t rte proportionl to its surfce re. Write differentil eqution for the volume of the rindrop s function of time. Solution
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 information1. 1 m/s m/s m/s. 5. None of these m/s m/s m/s m/s correct m/s
Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 1 This printout should he 30 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. The due time
More informationv T R x m Version PREVIEW Practice 7 carroll (11108) 1
Version PEVIEW Prctice 7 crroll (08) his printout should he 5 questions. Multiplechoice questions y continue on the next colun or pge find ll choices before nswering. Atwood Mchine 05 00 0.0 points A
More informationGauss Law in dielectrics
Gauss Law in dielectics We fist deive the diffeential fom of Gauss s law in the pesence of a dielectic. Recall, the diffeential fom of Gauss Law is This law is always tue. E In the pesence of dielectics,
More informationRandom Variables and Distribution Functions
Topic 7 Rndom Vibles nd Distibution Functions 7.1 Intoduction Fom the univese of possible infomtion, we sk question. To ddess this question, we might collect quntittive dt nd ognize it, fo emple, using
More informationPY1052 Problem Set 8 Autumn 2004 Solutions
PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ighthand end. If H 6.0 m and h 2.0 m, what
More 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 informationChapter 6 Solving equations
Chpter 6 Solving equtions Defining n eqution 6.1 Up to now we hve looked minly t epressions. An epression is n incomplete sttement nd hs no equl sign. Now we wnt to look t equtions. An eqution hs n = sign
More informationPoynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions
Poynting Vecto an Enegy Flow in a Capacito Challenge Poblem Solutions Poblem 1: A paallelplate capacito consists of two cicula plates, each with aius R, sepaate by a istance. A steay cuent I is flowing
More informationOnline Homework 12 Solution
Online Homewok Solution Electic nd Mgnetic Field Vectos Conceptul Question Pt A The electic nd mgnetic field vectos t specific point in spce nd time e illustted. Bsed on this infomtion, in wht diection
More informationPHY 140A: Solid State Physics. Solution to Homework #2
PHY 140A: Solid Stte Physics Solution to Homework # TA: Xun Ji 1 October 14, 006 1 Emil: jixun@physics.ucl.edu Problem #1 Prove tht the reciprocl lttice for the reciprocl lttice is the originl lttice.
More information( )( 10!12 ( 0.01) 2 2 = 624 ( ) Exam 1 Solutions. Phy 2049 Fall 2011
Phy 49 Fall 11 Solutions 1. Three charges form an equilateral triangle of side length d = 1 cm. The top charge is q =  4 μc, while the bottom two are q1 = q = +1 μc. What is the magnitude of the net force
More informationSection 74 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 74 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More informationAP QUIZ #2 GRAPHING MOTION 1) POSITION TIME GRAPHS DISPLACEMENT Each graph below shows the position of an object as a function of time.
AP QUIZ # GRAPHING MOTION ) POSITION TIME GRAPHS DISPLAEMENT Ech grph below shows the position of n object s function of time. A, B,, D, Rnk these grphs on the gretest mgnitude displcement during the time
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 informationChapter 4 Newton s Laws
Chpte 4 Newton s Lws Conceptul Pobles While on ve sooth level tnscontinentl plne fliht, ou coffee cup sits otionless on ou t. Ae thee foces ctin on the cup? If so, how do the diffe fo the foces tht would
More informationSection 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables
The Clculus of Functions of Severl Vribles Section 2.3 Motion Along Curve Velocity ccelertion Consider prticle moving in spce so tht its position t time t is given by x(t. We think of x(t s moving long
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 informationUnit 6: Exponents and Radicals
Eponents nd Rdicls : The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N):  counting numers. {,,,,, } Whole Numers (W):  counting numers with 0. {0,,,,,, } Integers (I): 
More informationrotation  Conservation of mechanical energy for rotation  Angular momentum  Conservation of angular momentum
Final Exam Duing class (13:55 pm) on 6/7, Mon Room: 41 FMH (classoom) Bing scientific calculatos No smat phone calculatos l ae allowed. Exam coves eveything leaned in this couse. Review session: Thusday
More informationPhys 207. Announcements. Hwk3 is posted on course website Quizzes & answers will be posted on course website Formula sheets.
Phys 07 Announcements Hwk3 is posted on course website Quizzes & nswers will be posted on course website ormul sheets Newton s 3 lws Tody s Agend How nd why do objects move? Dynmics 1 Dynmics Isc Newton
More informationSection 3.3: Geometric Sequences and Series
ectio 3.3: Geometic equeces d eies Geometic equeces Let s stt out with defiitio: geometic sequece: sequece i which the ext tem is foud by multiplyig the pevious tem by costt (the commo tio ) Hee e some
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationTwo special Righttriangles 1. The
Mth Right Tringle Trigonometry Hndout B (length of )  c  (length of side ) (Length of side to ) Pythgoren s Theorem: for tringles with right ngle ( side + side = ) + = c Two specil Righttringles. The
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 informationHarvard College. Math 21a: Multivariable Calculus Formula and Theorem Review
Hrvrd College Mth 21: Multivrible Clculus Formul nd Theorem Review Tommy McWillim, 13 tmcwillim@college.hrvrd.edu December 15, 2009 1 Contents Tble of Contents 4 9 Vectors nd the Geometry of Spce 5 9.1
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 informationLecture 5. Inner Product
Lecture 5 Inner Product Let us strt with the following problem. Given point P R nd line L R, how cn we find the point on the line closest to P? Answer: Drw line segment from P meeting the line in right
More informationwww.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values)
www.mthsbo.org.uk CORE SUMMARY NOTES Functions A function is rule which genertes ectl ONE OUTPUT for EVERY INPUT. To be defined full the function hs RULE tells ou how to clculte the output from the input
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More 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 informationVoltage ( = Electric Potential )
V1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
More 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 informationNet Change and Displacement
mth 11, pplictions motion: velocity nd net chnge 1 Net Chnge nd Displcement We hve seen tht the definite integrl f (x) dx mesures the net re under the curve y f (x) on the intervl [, b] Any prt of the
More informationVEHICLE PLANAR DYNAMICS BICYCLE MODEL
Auptions Do, VEHE PANA DYNAMS BYE MODE o tel, (esued o instntneous cente o ottion O) o Yw, (wt Globl Ais) ongitudinl elocit is ued to be constnt. Sll slip ngles, i.e. ties opete in the line egion. No
More informationHCP crystal planes are described using the MillerBravais indices, (hkil) Draw the hexagonal crystal planes whose MillerBravais indices are:
.6 How re crystllogrphic plnes indicted in HCP unit cells? In HCP unit cells, crystllogrphic plnes re indicted using four indices which correspond to four xes: three bsl xes of the unit cell,,, nd, which
More information2008 QuarterFinal Exam Solutions
2008 Quatefinal Exam  Solutions 1 2008 QuateFinal Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of
More informationTheories of light and Interference S BALASUBRAMANYA SGL IN PHYSICS SARVODAYA PU COLLEGE, TUMKUR Important paints
Theories of light nd nterference S BALASUBRAMANYA SGL N PHYSCS SARVODAYA PU COLLEGE, TUMKUR mportnt pints Theories of Light Newton s Corpusculr theory (1675) Christin Huygen s Wve theory (1678) Mxwell
More informationPhys222 W12 Quiz 2: Chapters 23, 24. Name: = 80 nc, and q = 30 nc in the figure, what is the magnitude of the total electric force on q?
Nme: 1. A pricle (m = 5 g, = 5. µc) is relesed from res when i is 5 cm from second pricle (Q = µc). Deermine he mgniude of he iniil ccelerion of he 5g pricle.. 54 m/s b. 9 m/s c. 7 m/s d. 65 m/s e. 36
More informationA Simple Method for Generating Rational Triangles
A Simple Method fo Geneting Rtionl Tingles Konstntine Zelto Deptment Of Mthemtics College Of Ats And Sciences Mil Stop 94 Univesity Of Toledo Toledo,OH 436063390 U.S.A. Intoduction The pupose of this
More informationAP Physics Gravity and Circular Motion
AP Phyic Gity nd icul Motion Newton theoy i ey iple. Gity i foce of ttction between ny two object tht he. Two object itting on dektop ttct ech othe with foce tht we cll gity. They don t go flying togethe
More informationApplications to Physics and Engineering
Section 7.5 Applictions to Physics nd Engineering Applictions to Physics nd Engineering Work The term work is used in everydy lnguge to men the totl mount of effort required to perform tsk. In physics
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 informationScalar and Vector Quantities. A scalar is a quantity having only magnitude (and possibly phase). LECTURE 2a: VECTOR ANALYSIS Vector Algebra
Sclr nd Vector Quntities : VECTO NLYSIS Vector lgebr sclr is quntit hving onl mgnitude (nd possibl phse). Emples: voltge, current, chrge, energ, temperture vector is quntit hving direction in ddition to
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. W02D3_0 Group Problem: Pulleys and Ropes Constraint Conditions
MSSCHUSES INSIUE OF ECHNOLOGY Deprtment of hysics 8.0 W02D3_0 Group roblem: ulleys nd Ropes Constrint Conditions Consider the rrngement of pulleys nd blocks shown in the figure. he pulleys re ssumed mssless
More informationCONIC SECTIONS. Chapter 11
CONIC SECTIONS Chpter 11 11.1 Overview 11.1.1 Sections of cone Let l e fied verticl line nd m e nother line intersecting it t fied point V nd inclined to it t n ngle α (Fig. 11.1). Fig. 11.1 Suppose we
More information(1) continuity equation: 0. momentum equation: u v g (2) u x. 1 a
Comment on The effect of vible viscosity on mied convection het tnsfe long veticl moving sufce by M. Ali [Intentionl Jounl of Theml Sciences, 006, Vol. 45, pp. 6069] Asteios Pntoktos Associte Pofesso
More informationAnswer, Key Homework 4 David McIntyre Mar 25,
Answer, Key Homework 4 Dvid McIntyre 45123 Mr 25, 2004 1 his printout should hve 18 questions. Multiplechoice questions my continue on the next column or pe find ll choices before mkin your selection.
More information