Gradebook & Midterm & Office Hours
|
|
- Leslie Shelton
- 6 years ago
- Views:
Transcription
1 Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing that I had nvr sn bfor, rgarding th nw dfinition of potntial nrgy. It's confusing, but cool Whovr got so mad about th appl problm (.g. th guy who's txt got put up during th lctur) nds to shap up and larn som humility. Whovr has th nrv to tll a profssor "you should hav known bttr" on a CHECKPOINT QUESTION nds to rconsidr thir prioritis. W'r all hr bcaus w'r smart, you don't nd to go around bing an arrogant (it got bttr but I can t put it hr) Could w go ovr mchanical nrgy and consrvativ forcs? Ovrall, vrything mad sns, I would just lik it if you quickly xplaind again how potntial nrgy is mixd in with kintic nrgy and work. I found vrything to b difficult bcaus it is th first tim I am larning ths concpts. Still waiting to find out whr to purchas "It is what it has to b to do what it dos" t- shirts/mugs/assortd mrchandis.
2 Gradbook & Midtrm & Offic Hours A littl commntary on th xam coming up on Oct. Around half th problms purly concptual: Undrstanding concpts is in fact th ky to solving all of th problms. Hav a look at th practic xams. Th first xam is in 2 wks (Wdnsday Oct. 3 at 7pm s plannr) If you hav a conflict you can sign up for th conflict xam in your grad-book. Don t forgt w hav xtra offic hours during xam wk. Mchanics Lctur 8, Slid 2
3 Physics 211 Lctur 8 Today's Concpts: a) Potntial Enrgy b) Mchanical Enrgy Mchanics Lctur 8, Slid 3
4 Work don by a Spring Can you spnd mor tim xplaining th spring problms. If you r worrid about th sign: Us formula to gt th magnitud Us situation and knowldg of dfinition of work to gt th sign
5 Clickr Qustion A box attachd at rst to a spring at its quilibrium lngth. You now push th box with your hand so that th spring is comprssd a distanc D, and you hold th box at rst in this nw location. D During this motion, th spring dos: A) Positiv Work B) Ngativ Work C) Zro work
6 Clickr Qustion A box attachd at rst to a spring at its quilibrium lngth. You now push th box with your hand so that th spring is comprssd a distanc D, and you hold th box at rst in this nw location. D During this motion, your hand dos: A) Positiv Work B) Ngativ Work C) Zro work
7 Clickr Qustion A box attachd at rst to a spring at its quilibrium lngth. You now push th box with your hand so that th spring is comprssd a distanc D, and you hold th box at rst in this nw location. During this motion, th total work don on th box is: A) Positiv B) Ngativ C) Zro D
8 Homwork Problm W spring = ½ k x 2 = ½ (4111) (0.456) 2 = 427 J Mchanics Lctur 8, Slid 8
9 Homwork Problm W tot = DK W spring = 427J = ½ mv 2 v 2 = 2 * 427 / 12 v = 8.44 m/s Mchanics Lctur 8, Slid 9
10 Homwork Problm W friction = -mmgd W friction = - (0.45)(12)(9.81)(2.1) W friction = J Mchanics Lctur 8, Slid 10
11 Homwork Problm W tot = DK W spring + W friction = 427 J J = ½ mv 2 v 2 = 2 * ( ) / 12 v = 7.25 m/s Mchanics Lctur 8, Slid 11
12 Summary DK Wtotal Lctur 7 Work Kintic Enrgy thorm D U W Lctur 8 For springs & gravity (consrvativ forcs) E K U DE W NC Total Mchanical Enrgy E = Kintic + Potntial Work don by any forc othr than gravity and springs will chang E Mchanics Lctur 8, Slid 12
13 Rlax. Thr is nothing nw hr It s just r-writing th work-ke thorm: DK W tot DK DU DU W gravity springs N C Dfin Mchanical Enrgy: E K U DK DU W NC W W W gravity springs N C DU DU W gravity springs N C DE W NC In P211 vrything xcpt gravity and springs is NC DE 0 If othr forcs arn't doing work So what xactly is th point of potntial nrgy thn? Also, why is 'U' th charactr usd to rprsnt it? Mchanics Lctur 8, Slid 13
14 Homwork Problm DE = W NC E f - E i = W friction (U f + K f ) - (U i + K i ) = W friction ½ mv J = v 2 = 2 * ( ) / 12 v = 7.25 m/s Mchanics Lctur 8, Slid 14
15 Finding th potntial nrgy chang: Us formulas to find th magnitud Chck th sign by undrstanding th problm Mchanics Lctur 8, Slid 15
16 ChckPoint Thr balls of qual mass ar fird simultanously with qual spds from th sam hight h abov th ground. Ball 1 is fird straight up, ball 2 is fird straight down, and ball 3 is fird horizontally. Rank in ordr from largst to smallst thir spds v 1, v 2, and v 3 just bfor ach ball hits th ground. 2 A) v 1 > v 2 > v 3 B) v 3 > v 2 > v 1 C) v 2 > v 3 > v 1 D) v 1 = v 2 = v 3 h 1 3 Thy hav th sam U and K to start with and dlta_u is th sam
17 ChckPoint A box sliding on a horizontal frictionlss surfac runs into a fixd spring, comprssing it a distanc x 1 from its rlaxd position whil momntarily coming to rst. If th initial spd of th box wr doubld, how far x 2 would th spring comprss? A) x 2 x 2 1 B) x 2 x 2 1 C) x 4 x x 2 1 Mchanics Lctur 8, Slid 17
18 ChckPoint K 1 2 m v 2 x U 1 2 kx 2 2 x x 2 x A) x B) C) x x A) Bcaus w is proportional to x^2, I thought th doubld spd would rsult in squar root of x. B) Both vlocity and th distanc comprssd ar squard so thy will changs with a 1 to 1 ratio C) bcaus th v is squard, thrfor doubling it, quadrupls th rsult Mchanics Lctur 8, Slid 18
19 DE DK D U 0 DK 1 2 m v 2 DU 1 2 kx mv kx x v m k Mchanics Lctur 8, Slid 19
20 Vrtical Springs M kx 2 x DU = ½ kd 2 - mgd = ½ ky 2 Equilibrium without mass Equilibrium with mass d Thy both look th sam!! Mchanics Lctur 8, Slid 20
21 From Tusday s lctur Why did you li about th appl? I didn t - w can xplain this in a diffrnt way now and still gt th sam answr: DE = W NC DK + DU 0 W hand DU = W hand Th chang in potntial nrgy of th appl is du to just th work don on it by your hand as you lift it.
22 From Tusday s lctur Why did you li about th appl? Last tim w usd th Work Kintic Enrgy thorm to xplain this and it says th sam thing: W tot = DK W hand + W gravity = 0 W hand = - W gravity W hand = DU gravity Sam rsult: Th chang in potntial nrgy of th appl is du to just th work don on it by your hand as you lift it.
23 Fun with balls rolling along tracks track A track B A) Ball on track A wins th rac B) Ball on track B wins th rac C) It s a ti balls arriv at th nd at th sam tim I will ask for voluntrs to xplain th rasoning lading to your slction.
24 Fun with balls rolling along tracks Explanation for why ball B wins rac Lt s now considr a slightly diffrnt scnario
25 It s gtting funnr and funnr A) Ball on track A wins th rac B) Ball on track B wins th rac C) It s a ti balls arriv at th nd at th sam tim I will ask for voluntrs to xplain th rasoning lading to your slction.
26 ChckPoint In Cas 1 w rlas an objct from a hight abov th surfac of th arth qual to 1 arth radius, and w masur its kintic nrgy just bfor it hits th arth to b K 1. In Cas 2 w rlas an objct from a hight abov th surfac of th arth qual to 2 arth radii, and w masur its kintic nrgy just bfor it hits th arth to b K 2. Compar K 1 and K 2. A) K 2 = 2K 1 B) K 2 = 4K 1 C) K 2 = 4K 1 /3 D) K 2 = 3K 1 /2 wrong Mchanics Lctur 8, Slid 26
27 Lts look at U For gravity: U ( r) G M m +U 0 r R E 2R E 3R E Mchanics Lctur 8, Slid 27
28 U ( r) What is th potntial nrgy of an objct of on th arths surfac: Clickr Qustion G M m r R E 2R E 3R E A) B) C) U surfac = U surfac = U surfac = GM m 0 GM m R E GM m 2R E R E Mchanics Lctur 8, Slid 28
29 U ( r) Clickr Qustion G M m What is th potntial nrgy of a objct starting at th hight of Cas 1? A) B) C) U U U E r G M m R G M m 2 R 3R E G M m E R E 2R E 3R E R E Mchanics Lctur 8, Slid 29
30 What is th potntial nrgy of a objct starting at th hight of Cas 2? A) B) C) U ( r) U U U G M m R E G M m 2 R G M m 3R E E Clickr Qustion G M m r R E 2R E 3R E R E Mchanics Lctur 8, Slid 30
31 GM m G M m U surfac U U 1 2 What is th chang R in potntial 2 Rin Cas 1? What is th chang in potntial in Cas 1? E E G M m 3R E A) B) G M m DU G M m cas1 2R R 2 R D G M m U G M m cas1 R 2 2 R R R E Mchanics Lctur 8, Slid 31
32 GM m G M m U surfac U U 1 2 What is th chang R in potntial 2 Rin Cas 2? What is th chang in potntial in Cas 2? E E G M m 3R E A) D G M m U G M m cas 2 R 3 3 R R B) D G M m U G M m cas 2 R 3 3 R R R E Mchanics Lctur 8, Slid 32
33 GM m D U cas1 DU cas 2 2 R 2G M m 3R What is th ratio DK DK DU 2 2 DU A) 2 B) 4 C) 4/3 D) 3/2 Mchanics Lctur 8, Slid 33
34 In Cas 1 w rlas an objct from a hight abov th surfac of th arth qual to 1 arth radius, and w masur its kintic nrgy just bfor it hits th arth to b K 1. In Cas 2 w rlas an objct from a hight abov th surfac of th arth qual to 2 arth radii, and w masur its kintic nrgy just bfor it hits th arth to b K 2. Compar K 1 and K 2. Chckpoint A) K 2 = 2K 1 B) K 2 = 4K 1 C) K 2 = 4K 1 /3 D) K 2 = 3K 1 /2 Mchanics Lctur 8, Slid 34
A Propagating Wave Packet Group Velocity Dispersion
Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to
More informationEEO 401 Digital Signal Processing Prof. Mark Fowler
EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1
More informationMath 34A. Final Review
Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right
More informationHigher order derivatives
Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of
More informationas a derivative. 7. [3.3] On Earth, you can easily shoot a paper clip straight up into the air with a rubber band. In t sec
MATH6 Fall 8 MIDTERM II PRACTICE QUESTIONS PART I. + if
More informationLecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields
Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration
More informationEngineering 323 Beautiful HW #13 Page 1 of 6 Brown Problem 5-12
Enginring Bautiful HW #1 Pag 1 of 6 5.1 Two componnts of a minicomputr hav th following joint pdf for thir usful liftims X and Y: = x(1+ x and y othrwis a. What is th probability that th liftim X of th
More informationcycle that does not cross any edges (including its own), then it has at least
W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th
More information1 Minimum Cut Problem
CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms
More informationThe pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n
More informationFourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.
Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform
More informationCalculus II (MAC )
Calculus II (MAC232-2) Tst 2 (25/6/25) Nam (PRINT): Plas show your work. An answr with no work rcivs no crdit. You may us th back of a pag if you nd mor spac for a problm. You may not us any calculators.
More informationMassachusetts Institute of Technology Department of Mechanical Engineering
Massachustts Institut of Tchnolog Dpartmnt of Mchanical Enginring. Introduction to Robotics Mid-Trm Eamination Novmbr, 005 :0 pm 4:0 pm Clos-Book. Two shts of nots ar allowd. Show how ou arrivd at our
More informationSundials and Linear Algebra
Sundials and Linar Algbra M. Scot Swan July 2, 25 Most txts on crating sundials ar dirctd towards thos who ar solly intrstd in making and using sundials and usually assums minimal mathmatical background.
More informationDavisson Germer experiment Announcements:
Davisson Grmr xprimnt Announcmnts: Homwork st 7 is du Wdnsday. Problm solving sssions M3-5, T3-5. Th 2 nd midtrm will b April 7 in MUEN E0046 at 7:30pm. BFFs: Davisson and Grmr. Today w will go ovr th
More informationAtomic energy levels. Announcements:
Atomic nrgy lvls Announcmnts: Exam solutions ar postd. Problm solving sssions ar M3-5 and Tusday 1-3 in G-140. Will nd arly and hand back your Midtrm Exam at nd of class. http://www.colorado.du/physics/phys2170/
More informationSupplementary Materials
6 Supplmntary Matrials APPENDIX A PHYSICAL INTERPRETATION OF FUEL-RATE-SPEED FUNCTION A truck running on a road with grad/slop θ positiv if moving up and ngativ if moving down facs thr rsistancs: arodynamic
More informationDifferentiation of Exponential Functions
Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of
More informationu 3 = u 3 (x 1, x 2, x 3 )
Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.
More informationBrief Introduction to Statistical Mechanics
Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.
More informationExam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.
Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r
More informationThe van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012
Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor
More informationEXST Regression Techniques Page 1
EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy
More informationWhere k is either given or determined from the data and c is an arbitrary constant.
Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is
More informationProblem 22: Journey to the Center of the Earth
Problm : Journy to th Cntr of th Earth Imagin that on drilld a hol with smooth sids straight through th ntr of th arth If th air is rmod from this tub (and it dosn t fill up with watr, liquid rok, or iron
More informationContemporary, atomic, nuclear, and particle physics
Contmporary, atomic, nuclar, and particl physics 1 Blackbody radiation as a thrmal quilibrium condition (in vacuum this is th only hat loss) Exampl-1 black plan surfac at a constant high tmpratur T h is
More informationExam 2 Thursday (7:30-9pm) It will cover material through HW 7, but no material that was on the 1 st exam.
Exam 2 Thursday (7:30-9pm) It will covr matrial through HW 7, but no matrial that was on th 1 st xam. What happns if w bash atoms with lctrons? In atomic discharg lamps, lots of lctrons ar givn kintic
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More information7.4 Potential Difference and Electric Potential
7.4 Potntial Diffrnc and Elctric Potntial In th prvious sction, you larnd how two paralll chargd surfacs produc a uniform lctric fild. From th dfinition of an lctric fild as a forc acting on a charg, it
More informationChemical Physics II. More Stat. Thermo Kinetics Protein Folding...
Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg
More informationCollisions between electrons and ions
DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision
More informationMor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration
More informationFirst derivative analysis
Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points
More informationIntroduction to the quantum theory of matter and Schrödinger s equation
Introduction to th quantum thory of mattr and Schrödingr s quation Th quantum thory of mattr assums that mattr has two naturs: a particl natur and a wa natur. Th particl natur is dscribd by classical physics
More informationCS 361 Meeting 12 10/3/18
CS 36 Mting 2 /3/8 Announcmnts. Homwork 4 is du Friday. If Friday is Mountain Day, homwork should b turnd in at my offic or th dpartmnt offic bfor 4. 2. Homwork 5 will b availabl ovr th wknd. 3. Our midtrm
More informationDealing with quantitative data and problem solving life is a story problem! Attacking Quantitative Problems
Daling with quantitati data and problm soling lif is a story problm! A larg portion of scinc inols quantitati data that has both alu and units. Units can sa your butt! Nd handl on mtric prfixs Dimnsional
More informationLimiting value of higher Mahler measure
Limiting valu of highr Mahlr masur Arunabha Biswas a, Chris Monico a, a Dpartmnt of Mathmatics & Statistics, Txas Tch Univrsity, Lubbock, TX 7949, USA Abstract W considr th k-highr Mahlr masur m k P )
More informationPHYS-333: Problem set #2 Solutions
PHYS-333: Problm st #2 Solutions Vrsion of March 5, 2016. 1. Visual binary 15 points): Ovr a priod of 10 yars, two stars sparatd by an angl of 1 arcsc ar obsrvd to mov through a full circl about a point
More informationu x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula
7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting
More informationPartial Derivatives: Suppose that z = f(x, y) is a function of two variables.
Chaptr Functions o Two Variabls Applid Calculus 61 Sction : Calculus o Functions o Two Variabls Now that ou hav som amiliarit with unctions o two variabls it s tim to start appling calculus to hlp us solv
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!
More informationorbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the
Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly
More informationMCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)
MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl
More informationThere is an arbitrary overall complex phase that could be added to A, but since this makes no difference we set it to zero and choose A real.
Midtrm #, Physics 37A, Spring 07. Writ your rsponss blow or on xtra pags. Show your work, and tak car to xplain what you ar doing; partial crdit will b givn for incomplt answrs that dmonstrat som concptual
More informationHigh Energy Physics. Lecture 5 The Passage of Particles through Matter
High Enrgy Physics Lctur 5 Th Passag of Particls through Mattr 1 Introduction In prvious lcturs w hav sn xampls of tracks lft by chargd particls in passing through mattr. Such tracks provid som of th most
More informationDifferential Equations
Prfac Hr ar m onlin nots for m diffrntial quations cours that I tach hr at Lamar Univrsit. Dspit th fact that ths ar m class nots, th should b accssibl to anon wanting to larn how to solv diffrntial quations
More informationPH300 Modern Physics SP11 Final Essay. Up Next: Periodic Table Molecular Bonding
PH Modrn Physics SP11 Final Essay Thr will b an ssay portion on th xam, but you don t nd to answr thos qustions if you submit a final ssay by th day of th final: Sat. 5/7 It dosnʼt mattr how smart you
More informationMSLC Math 151 WI09 Exam 2 Review Solutions
Eam Rviw Solutions. Comput th following rivativs using th iffrntiation ruls: a.) cot cot cot csc cot cos 5 cos 5 cos 5 cos 5 sin 5 5 b.) c.) sin( ) sin( ) y sin( ) ln( y) ln( ) ln( y) sin( ) ln( ) y y
More informationLast time. Resistors. Circuits. Question. Quick Quiz. Quick Quiz. ( V c. Which bulb is brighter? A. A B. B. C. Both the same
Last tim Bgin circuits Rsistors Circuits Today Rsistor circuits Start rsistor-capacitor circuits Physical layout Schmatic layout Tu. Oct. 13, 2009 Physics 208 Lctur 12 1 Tu. Oct. 13, 2009 Physics 208 Lctur
More informationHydrogen Atom and One Electron Ions
Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial
More informationThus, because if either [G : H] or [H : K] is infinite, then [G : K] is infinite, then [G : K] = [G : H][H : K] for all infinite cases.
Homwork 5 M 373K Solutions Mark Lindbrg and Travis Schdlr 1. Prov that th ring Z/mZ (for m 0) is a fild if and only if m is prim. ( ) Proof by Contrapositiv: Hr, thr ar thr cass for m not prim. m 0: Whn
More informationSECTION where P (cos θ, sin θ) and Q(cos θ, sin θ) are polynomials in cos θ and sin θ, provided Q is never equal to zero.
SETION 6. 57 6. Evaluation of Dfinit Intgrals Exampl 6.6 W hav usd dfinit intgrals to valuat contour intgrals. It may com as a surpris to larn that contour intgrals and rsidus can b usd to valuat crtain
More informationAssignment 4 Biophys 4322/5322
Assignmnt 4 Biophys 4322/5322 Tylr Shndruk Fbruary 28, 202 Problm Phillips 7.3. Part a R-onsidr dimoglobin utilizing th anonial nsmbl maning rdriv Eq. 3 from Phillips Chaptr 7. For a anonial nsmbl p E
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!
More informationSAFE HANDS & IIT-ian's PACE EDT-15 (JEE) SOLUTIONS
It is not possibl to find flu through biggr loop dirctly So w will find cofficint of mutual inductanc btwn two loops and thn find th flu through biggr loop Also rmmbr M = M ( ) ( ) EDT- (JEE) SOLUTIONS
More information6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved.
6.1 Intgration by Parts and Prsnt Valu Copyright Cngag Larning. All rights rsrvd. Warm-Up: Find f () 1. F() = ln(+1). F() = 3 3. F() =. F() = ln ( 1) 5. F() = 6. F() = - Objctivs, Day #1 Studnts will b
More informationRecall that by Theorems 10.3 and 10.4 together provide us the estimate o(n2 ), S(q) q 9, q=1
Chaptr 11 Th singular sris Rcall that by Thorms 10 and 104 togthr provid us th stimat 9 4 n 2 111 Rn = SnΓ 2 + on2, whr th singular sris Sn was dfind in Chaptr 10 as Sn = q=1 Sq q 9, with Sq = 1 a q gcda,q=1
More informationCOMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.
C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH
More informationSearch sequence databases 3 10/25/2016
Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an
More informationPHYS ,Fall 05, Term Exam #1, Oct., 12, 2005
PHYS1444-,Fall 5, Trm Exam #1, Oct., 1, 5 Nam: Kys 1. circular ring of charg of raius an a total charg Q lis in th x-y plan with its cntr at th origin. small positiv tst charg q is plac at th origin. What
More informationATMO 551a Homework 6 solutions Fall 08
. A rising air parcl in th cor of a thundrstorm achivs a vrtical vlocity of 8 m/s similar to th midtrm whn it rachs a nutral buoyancy altitud at approximatly 2 km and 2 mb. Assum th background atmosphr
More informationLecture 28 Title: Diatomic Molecule : Vibrational and Rotational spectra
Lctur 8 Titl: Diatomic Molcul : Vibrational and otational spctra Pag- In this lctur w will undrstand th molcular vibrational and rotational spctra of diatomic molcul W will start with th Hamiltonian for
More informationCoupled Pendulums. Two normal modes.
Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron
More informationCOHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.
MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function
More informationGeneral Notes About 2007 AP Physics Scoring Guidelines
AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation
More informationLecture Outline. Skin Depth Power Flow 8/7/2018. EE 4347 Applied Electromagnetics. Topic 3e
8/7/018 Cours Instructor Dr. Raymond C. Rumpf Offic: A 337 Phon: (915) 747 6958 E Mail: rcrumpf@utp.du EE 4347 Applid Elctromagntics Topic 3 Skin Dpth & Powr Flow Skin Dpth Ths & Powr nots Flow may contain
More informationAlpha and beta decay equation practice
Alpha and bta dcay quation practic Introduction Alpha and bta particls may b rprsntd in quations in svral diffrnt ways. Diffrnt xam boards hav thir own prfrnc. For xampl: Alpha Bta α β alpha bta Dspit
More informationy = 2xe x + x 2 e x at (0, 3). solution: Since y is implicitly related to x we have to use implicit differentiation: 3 6y = 0 y = 1 2 x ln(b) ln(b)
4. y = y = + 5. Find th quation of th tangnt lin for th function y = ( + ) 3 whn = 0. solution: First not that whn = 0, y = (1 + 1) 3 = 8, so th lin gos through (0, 8) and thrfor its y-intrcpt is 8. y
More information3 2x. 3x 2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Math B Intgration Rviw (Solutions) Do ths intgrals. Solutions ar postd at th wbsit blow. If you hav troubl with thm, sk hlp immdiatly! () 8 d () 5 d () d () sin d (5) d (6) cos d (7) d www.clas.ucsb.du/staff/vinc
More informationClassical Magnetic Dipole
Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg
More informationPair (and Triplet) Production Effect:
Pair (and riplt Production Effct: In both Pair and riplt production, a positron (anti-lctron and an lctron (or ngatron ar producd spontanously as a photon intracts with a strong lctric fild from ithr a
More informationCS 6353 Compiler Construction, Homework #1. 1. Write regular expressions for the following informally described languages:
CS 6353 Compilr Construction, Homwork #1 1. Writ rgular xprssions for th following informally dscribd languags: a. All strings of 0 s and 1 s with th substring 01*1. Answr: (0 1)*01*1(0 1)* b. All strings
More informationREGISTER!!! The Farmer and the Seeds (a parable of scientific reasoning) Class Updates. The Farmer and the Seeds. The Farmer and the Seeds
How dos light intract with mattr? And what dos (this say about) mattr? REGISTER!!! If Schrödingr s Cat walks into a forst, and no on is around to obsrv it, is h rally in th forst? sourc unknown Phys 1010
More informationCalculus concepts derivatives
All rasonabl fforts hav bn mad to mak sur th nots ar accurat. Th author cannot b hld rsponsibl for any damags arising from th us of ths nots in any fashion. Calculus concpts drivativs Concpts involving
More informationClassical Mechanics Lecture 8
Classical Mechanics Lecture 8 Today's Concepts: a) Poten2al Energy b) Mechanical Energy Mechanics Lecture 8, Slide 1 Stuff you asked about: Gravity is the law. violators will be brought down. How were
More informationSeptember 23, Honors Chem Atomic structure.notebook. Atomic Structure
Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning
More informationECE602 Exam 1 April 5, You must show ALL of your work for full credit.
ECE62 Exam April 5, 27 Nam: Solution Scor: / This xam is closd-book. You must show ALL of your work for full crdit. Plas rad th qustions carfully. Plas chck your answrs carfully. Calculators may NOT b
More informationComputing and Communications -- Network Coding
89 90 98 00 Computing and Communications -- Ntwork Coding Dr. Zhiyong Chn Institut of Wirlss Communications Tchnology Shanghai Jiao Tong Univrsity China Lctur 5- Nov. 05 0 Classical Information Thory Sourc
More informationPHYSICS 489/1489 LECTURE 7: QUANTUM ELECTRODYNAMICS
PHYSICS 489/489 LECTURE 7: QUANTUM ELECTRODYNAMICS REMINDER Problm st du today 700 in Box F TODAY: W invstigatd th Dirac quation it dscribs a rlativistic spin /2 particl implis th xistnc of antiparticl
More informationMAXIMA-MINIMA EXERCISE - 01 CHECK YOUR GRASP
EXERCISE - MAXIMA-MINIMA CHECK YOUR GRASP. f() 5 () 75 f'() 5. () 75 75.() 7. 5 + 5. () 7 {} 5 () 7 ( ) 5. f() 9a + a +, a > f'() 6 8a + a 6( a + a ) 6( a) ( a) p a, q a a a + + a a a (rjctd) or a a 6.
More informationAbstract Interpretation: concrete and abstract semantics
Abstract Intrprtation: concrt and abstract smantics Concrt smantics W considr a vry tiny languag that manags arithmtic oprations on intgrs valus. Th (concrt) smantics of th languags cab b dfind by th funzcion
More informationY 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall
Staning Wav Intrfrnc btwn th incint & rflct wavs Staning wav A string with on n fix on a wall Incint: y, t) Y cos( t ) 1( Y 1 ( ) Y (St th incint wav s phas to b, i.., Y + ral & positiv.) Rflct: y, t)
More informationPhysics 312 First Pledged Problem Set
Physics 31 First Pldgd Problm St 1. Th ground stat of hydrogn is dscribd by th wavfunction whr a is th Bohr radius. (a) Comput th charg dnsity à (r) = 1 p ¼ µ 1 a 3 r=a ; ½ (r) = jã (r)j : and plot 4¼r
More informationAddition of angular momentum
Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat
More informationAS 5850 Finite Element Analysis
AS 5850 Finit Elmnt Analysis Two-Dimnsional Linar Elasticity Instructor Prof. IIT Madras Equations of Plan Elasticity - 1 displacmnt fild strain- displacmnt rlations (infinitsimal strain) in matrix form
More informationBasic Polyhedral theory
Basic Polyhdral thory Th st P = { A b} is calld a polyhdron. Lmma 1. Eithr th systm A = b, b 0, 0 has a solution or thr is a vctorπ such that π A 0, πb < 0 Thr cass, if solution in top row dos not ist
More informationVoltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes
Lctur 1. oltag, Currnt, Powr, Sris sistanc, Paralll sistanc, and Diods Whn you start to dal with lctronics thr ar thr main concpts to start with: Nam Symbol Unit oltag volt Currnt ampr Powr W watt oltag
More information1 Isoparametric Concept
UNIVERSITY OF CALIFORNIA BERKELEY Dpartmnt of Civil Enginring Spring 06 Structural Enginring, Mchanics and Matrials Profssor: S. Govindj Nots on D isoparamtric lmnts Isoparamtric Concpt Th isoparamtric
More informationChapter 8: Electron Configurations and Periodicity
Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how
More informationSection 6.1. Question: 2. Let H be a subgroup of a group G. Then H operates on G by left multiplication. Describe the orbits for this operation.
MAT 444 H Barclo Spring 004 Homwork 6 Solutions Sction 6 Lt H b a subgroup of a group G Thn H oprats on G by lft multiplication Dscrib th orbits for this opration Th orbits of G ar th right costs of H
More informationPHA 5127 Answers Homework 2 Fall 2001
PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring
More informationRadiation Physics Laboratory - Complementary Exercise Set MeBiom 2016/2017
Th following qustions ar to b answrd individually. Usful information such as tabls with dtctor charactristics and graphs with th proprtis of matrials ar availabl in th cours wb sit: http://www.lip.pt/~patricia/fisicadaradiacao.
More information1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by:
Elctromagntic Induction. Lorntz forc on moving charg Point charg moving at vlocity v, F qv B () For a sction of lctric currnt I in a thin wir dl is Idl, th forc is df Idl B () Elctromotiv forc f s any
More informationPropositional Logic. Combinatorial Problem Solving (CPS) Albert Oliveras Enric Rodríguez-Carbonell. May 17, 2018
Propositional Logic Combinatorial Problm Solving (CPS) Albrt Olivras Enric Rodríguz-Carbonll May 17, 2018 Ovrviw of th sssion Dfinition of Propositional Logic Gnral Concpts in Logic Rduction to SAT CNFs
More informationObjective Mathematics
x. Lt 'P' b a point on th curv y and tangnt x drawn at P to th curv has gratst slop in magnitud, thn point 'P' is,, (0, 0),. Th quation of common tangnt to th curvs y = 6 x x and xy = x + is : x y = 8
More informationDerivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian
Drivation of Elctron-Elctron Intraction Trms in th Multi-Elctron Hamiltonian Erica Smith Octobr 1, 010 1 Introduction Th Hamiltonian for a multi-lctron atom with n lctrons is drivd by Itoh (1965) by accounting
More information10. The Discrete-Time Fourier Transform (DTFT)
Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w
More informationCollisions. In had on lastic collision of two bodis of qual ass ) Th fastr body spds up furthr and th slowr body slows down. ) Th fastr body slows down and th slowr body spds up. 3) Both of th abov. 4)
More informationAddition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
More information