Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

1 Page

Review-1

Course: PHYSICS 112, Summer 2009
School: Iowa State
Rating:

Word Count: 661

Document Preview

112 PHYSICS - REVIEW FOR EXAM 1 ELECTRIC CHARGES Electric charges are positive, negative, or zero; they are measured in coulombs (symbol: C). Electric charges are quantized: every object in the universe has a electric charge ; oe ,, 8/, where 8 oe 0, 1, 2, . . . is an integer and / oe 1.6 , 1019 C. Electrons, neutrons, and protons have charges / 0, / respectively. Electrical and magnetic forces act on charged...

Register Now

Unformatted Document Excerpt

Coursehero >> Iowa >> Iowa State >> PHYSICS 112

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
112 PHYSICS - REVIEW FOR EXAM 1 ELECTRIC CHARGES Electric charges are positive, negative, or zero; they are measured in coulombs (symbol: C). Electric charges are quantized: every object in the universe has a electric charge ; oe ,, 8/, where 8 oe 0, 1, 2, . . . is an integer and / oe 1.6 , 1019 C. Electrons, neutrons, and protons have charges / 0, / respectively. Electrical and magnetic forces act on charged particles. ELECTRIC FORCES Coulomb's law: The electric force beween two particles of electric charge ;1 and ;2 separated by a distance < has magnitude J oe The forces on two positive or two negative charges is repulsive, directly straight away from each other. The forces between a positive and a negative charge are attractive, directed towards each other. ELECTRIC FIELDS t t t t The electric field I at a point where the electric force on a small charge ; (positive or negative) is J is given by I oe J . ; t t The electric field has units of N/C. Consequently, the force on a charge in an electric field is J oe ;I . The electric force on a positive charge is in the direction of the electric field; the electric force on a negative charge is opposite to the direction of the electric field. 5 |U| t The electric field due to a charge U at a distance < from the charge has magnitude lIl oe e # and is directed straight away < from a positive charge and straight towards a negative charge. The electric field at a general point can be determined by the Principle of Superposition, by adding the electric field vectors at that point due to all the charges in the universe. The electric field in space can be represented by electric field lines. 5e ;1 ;# , where 5 oe 9 , 109 N-m2 /C2 is a universal constant. <# ELECTRIC POTENTIAL ENERGY Energy formulas from Physics 111: Kinetic energy: OI oe " 7@2 # Work: [ oe J . cos ) (in terms of a force and a displacement) Total work: oe [total [c [nc (work by conservative forces + work by nonconservative forces) Work by a conservative force: [c oe ?T I . Work-energy theorem: [total oe ?OI Mechanical energy: X I oe OI T I ?X I oe ?OI ?T I oe [total [c oe [nc The electric potential energy of a system of two charges ;1 and ;2 a distance < apart is PE oe <1 2 (note the single power of < in the denominator). Like any energy, it is measured in joules (J). This is positive if the two charges have the same sign and is negative if they have opposite signs. The electric potential energy of a system of many charges is the sum of the two-charge electric potential energies of each pair of charges. (Count each pair once: For 3 particles, use terms for 1 & 2, 1 & 3 and 2 & 3.) ELECTRIC POTENTIAL: Electric potential Z is defined as the potential energy per charge: Z oe T I; is the electric potential ; at a certain point, where T I; is the electric potential energy added to the system when a small charge ; is placed at that point. The unit of electric potential is the J/C or V (volt). The electric potential at a distance < from a point charge ; is Z oe 5;<, which can be positive or negative depending on the sign of ; . The Principle of Superposition applied to electric potential: Z at a point in space is the sum of the electric potentials at that point due to all the charges in the universe. The change in the electric potential energy of a system when a charge ; is moved from an initial point 3 to a final point 0 is ?T I oe ; ?Z oe ;Zf Zi The sign of the change in electric potential energy depends on the signs of ; and of ?Z , and can be positive or negative. An equipotential surface is one on which the electric potential is a constant; equipotential surfaces are perpendicular to electric field lines. Capacitance: Capacitance G is defined by U oe G ?Z . Energy stored is " G?Z 2 . # 5; ;
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Iowa State - PHYSICS - 112
PHYSICS 112 - REVIEW FOR EXAM 2CURRENT M rate at which electic charge is flowing in a wire M oe ?UX RESISTANCE V and POTENTIAL DIFFERENCE ?Z related by Ohm's law: ?Z oe MV . The power dissipated in a resistor has magnitude T oe M ?Z oe M 2 V oe ?Z 2 V .
Iowa State - PHYSICS - 112
PHYSICS 112 - REVIEW FOR EXAM 3t MAGNETIC FLUX: The magnetic flux through a plane circuit is F oe FE cos ), where ) is the angle between F 2 and the normal ( perpendicular) to the plane of the circuit. Units: T-m . MAGNETIC INDUCTION The current induced
Iowa State - PHYSICS - 112
PHYSICS 112 - SPRING 2003 - EXAM 1 - February 12, 2003 Name: _ Recitation Section Number: _ SHOW YOUR WORK! Although some of these problems are multiple-choice, full credit will be given only if you explain how you arrived at your answer. Either show your
Iowa State - PHYSICS - 112
PHYSICS 112 - SPRING 2003 - EXAM 3 SHOW YOUR WORK! Full credit will be given only if you explain how you arrived at your answer. Either show your work (especially in a calculation) or give a short explanation. Nothing elaborate is required, but the grader
Iowa State - PHYSICS - 112
PHYSICS 112 - EXAM 4 (first part of final exam) - SPRING 2003Use only a right-handed coordinate system ( B C D along thumb, forefinger, and middle finger of your right hand when these three fingers are perpendicular to one another). Show your calculation
Iowa State - PHYSICS - 112
PHYSICS 112 - SPRING 2004 - EXAM 2 NO CALCULATORS. SHOW YOUR WORK! Full credit will be given only if you explain how you arrived at your answer. Either show your work (especially in a calculation) or give a short explanation. Nothing elaborate is required
Iowa State - PHYSICS - 112
PHYSICS 112 - FINAL EXAM (second, comprehensive part) - SPRING 2005cos2 0 oe 1 cos2 30 oe 0.75 cos2 45 oe 0.50 cos2 60 oe 0.25 cos2 90 oe 0.1. [9 points total] An electric charge of 2.0 .C is placed at a point 3.0 m from a fixed electric charge of 3.0 .
Iowa State - PHYSICS - 112
PHYSICS 112 - SUMMER 2005 - EXAM 3 Name: _ Recitation Section: _NO CALCULATORS ALLOWED - BUT, LUCKILY, NO CALCULATORS NEEDED. SHOW YOUR WORK! Full credit will be given only if you explain how you arrived at your answer. Either show your work (especially
Iowa State - PHYSICS - 112
USEFUL INFORMATIONIMPORTANT PHYSICAL CONSTANTS - 299,792,458 m/s 300 , 10) m/s K oe 6.673 , 10&quot; N m# /kg# 5/ oe1 41%0(speed of light) (gravitational constant) (electrical constant) (Planck's constant) (permittivity of free space) (fundamental electric
Iowa State - PHYSICS - 112
TOPIC 1. REVIEWINTRODUCTIONIn Physics 112 we will be making heavy use of vectors, so we will start with a review of vectors. The important vector quantities we will be discussing are electric forces, electric fields, electric currents, magnetic forces,
Iowa State - PHYSICS - 112
TOPIC 2. ELECTRICITY Topic 2A. Electric Charges and ForcesELECTRIC CHARGEObjects, including elementary particles like the electron and proton, have a number of properties. The one we have studied the most so far is mass. The mass of an object is importa
Iowa State - PHYSICS - 112
TOPIC 3. Electric Currents ELECTRIC CURRENTSWhat causes charges to flow, and what hinders the free flow of charge? The most important practical applications of electrical phenomena are in the innumerable forms of electronic devices. In these, it is the m
Iowa State - PHYSICS - 112
Topic 4. Magnetic Forces and FieldsDo currents exert forces on each other in the same way that charges do? Our study of electric forces and electric fields began with a simple experimental observation: charged particles exert forces on each other. From t
Iowa State - STAT - 511
IntroductionOne possible model: yij = i +ijIntroduction (continued)The first part of Stat 511 re-examines methods from Stat 500 from a linear models perspective.A simple study: does a proprietary food additive increase milk production in dairy cows?
Iowa State - STAT - 511
IntroductionThe first part of Stat 511 re-examines methods from Stat 500 from a linear models perspective. A simple study: does a proprietary food additive increase milk production in dairy cows? 6 cows, housed one per stall. Randomly choose 3 to get foo
Iowa State - STAT - 511
Geometry of the Gauss-Markov Linear ModelX is a linear combination of the columns of X: 1 . X = [x1 , . . . , xp ] . = 1 x1 + + p xp . . p The set of all possible linear combinations of the columns of X is called the column space of X and is denoted by C
Iowa State - STAT - 511
Geometry of the Gauss-Markov Linear ModelReminder from the last section of the notes: y = X + We saw two possible X matrices for the t-test. This section focuses on the Q: does it matter which X we use? Important pieces of information for what follows: X
Iowa State - STAT - 511
Estimating Estimable Functions of In the Gauss-Markov or Normal Theory Gauss-Markov Linear Model, the distribution of y depends on only through X, i.e., y (X, 2 I) or y N(X, 2 I)The Response Depends on Only through XWe now shift attention from E(y) to
Iowa State - STAT - 511
Estimating Estimable Functions of We now shift attention from E(y) to the parameter vector . Remember our t-test questions about 1 - 2 and 1 - 2 ? y y Those are questions about or linear combinations of . We've seen some models where there is a unique so
Iowa State - STAT - 511
Proof of the Gauss-Markov TheoremSuppose dy is any linear unbiased estimator other than the OLS ^ estimator C. ^ Need to show Var(dy) &gt; Var(C). ^ ^ Can relate the two Var by writing Var(dy) = Var(dy - C + C) ^ ^ Var(dy) = Var(dy - C + C) ^ ^ ^ ^ = Var(dy
Iowa State - STAT - 511
Proof of the Gauss-Markov TheoremGauss-Markov Th'm: ^ The OLS estimator, C, is the unique BLUE of C in GM model: y = X + , N(0, 2 I) ^ Need to show Var(C) is strictly less than the variance of any other linear unbiased estimator of C for all IRp and 2 IR
Iowa State - STAT - 511
Estimating Estimable Functions of : 11 12 22 23 33 41 42An Examplecustomer1 2 3 4 Which movie is best? y= X +movie 1 2 3 4 1 ? ? 3 5 ? ? 3 3 1 ? Can we guess ratings for customer/movie combinations not in the dataset? = + 4 1 3 5 3 3 11 1 1 1 1 1
Iowa State - STAT - 511
Estimating Estimable Functions of :An Example movie 1 2 3 4 1 ? ? 3 5 ? ? 3 3 1 ? customer i's rating of movie j + Ci + mj +ijcustomer1 2 3 4 =Can we guess ratings for customer/movie combinations not in the dataset? Which movie is best?YijYij=Cop
Iowa State - STAT - 511
Alternative ParameterizationsFor example yij i = 1, 2, 3 j = 1, 2Recall that the Gauss-Markov Linear Model simply says that E(y) C(X) and Var(y) = 2 I for some 2 &gt; 0.Treatment Effects E(yij ) = + i 1 2 3 Cell Means E(yij ) = iThus, as long as C(X) = C
Iowa State - STAT - 511
Inference Under the Normal Theory Gauss-Markov Linear Model Inference (cont.)Remember our dairy cow study (2 treatments, 3 reps per trt) and our questions (Introduction, slide 3) We've answered all questions except the last one: y 3) When does t = [(1 -
Iowa State - STAT - 511
Inference Under the Normal Theory Gauss-Markov Linear ModelRemember our dairy cow study (2 treatments, 3 reps per trt) and our questions (Introduction, slide 3) We've answered all questions except the last one: 3) When does t = [(1 - 2 ) - (1 - 2 )] / s2
Iowa State - STAT - 511
Practical Data AnalysisA not uncommon situation: A client brings you data from a food development study: 3 treatments:Old &quot;on market&quot; formulation of soup new formulation, Same salt content as old new formulation, Reduced salt contentThey recruited 25 p
Iowa State - STAT - 511
Practical Data AnalysisPractical Data AnalysisHow would you analyze the data? (N.B. all analyses account for blocking / pairing of obs. within subject) 1. ANOVA F test of O = S = R , report p-value and trt. means 2. 3 paired t-tests: O = S , O = R , and
Iowa State - STAT - 511
POWER OF THE F-TESTA very common consulting question: &quot;I'm planning a study to do .&quot;. How many replicates (per treatment) should I use? I know 5 ways that can be used to determine an appropriate sample sizeAs many as you can afford (time, money) n = 3 p
Iowa State - STAT - 511
POWER OF THE F-TESTSuppose C is a q p matrix such that C is testable. Earlier, we established that the quadratic form incorporating ^ C - d has a non-central F distribution ^ F = (C - d) Fq,n-k where 2 = (C - d) [C(X X)- C ] 2-1 ( 2 )A very common cons
Iowa State - STAT - 511
REDUCED vs. FULL MODEL F-TESTTests of C - d = 0 lead to F tests, but that's not the only way to an F test 500/402: big emphasis on model comparison SS in ANOVA tables usually explained in terms of model comparison e.g. SS for AB interaction is the differ
Iowa State - STAT - 511
REDUCED vs. FULL MODEL F-TESTWhy does model comparison lead to F tests? If you test Ho using a C test or using a model comparison test, do you get the same answer? Again, will answer using a general setup (Normal GM model) y = X + , N(0, 2 I)Questions a
Iowa State - STAT - 511
Equivalence of model comparison and Cb F testsSummary of results from Cb estimates and testsContinuation of the Storage time example from Part 9. Data: Storage Temperature 20 C 30 C 2 5 Time Ho: 6 6 7 7 Temp Ho: 16 9 12 15 These correspond to tests of:
Iowa State - STAT - 511
Equivalence of model comparison and Cb F testsContinuation of the Storage time example from Part 9. Data: Storage Time 3 months 6 months Storage Temperature 20 C 30 C 2 5 6 6 7 7 9 12 15 16Copyright c 2011 Dept. of Statistics (Iowa State University)Sta
Iowa State - STAT - 511
ANalysis Of VAriance (ANOVA) for a sequence of models Some examplesMultiple RegressionModel comparison can be generalized to a sequence of models (not just one full and one reduced model) N(0, 2 I)X1 = 1, X2 = [1, x1 ], X3 = [1, x1 , x2 ], . . . Xm = [
Iowa State - STAT - 511
ANalysis Of VAriance (ANOVA) for a sequence of modelsModel comparison can be generalized to a sequence of models (not just one full and one reduced model) Context: usual nGM model: y = X + , Let X1 = 1 and Xm = X. But now, we have a sequence of models &quot;i
Iowa State - STAT - 511
THE AITKEN MODELAnalysis of averagesExamples - 1y = X + , (0, 2 V)Identical to the Gauss-Markov Linear Model except that Var ( ) = 2 V instead of 2 I.V is assumed to be a known nonsingular Variance matrix.The Normal Theory Aitken Model adds an assu
Iowa State - STAT - 511
THE AITKEN MODELy = X + , (0, 2 V)Identical to the Gauss-Markov Linear Model except that Var ( ) = 2 V instead of 2 I. V is assumed to be a known nonsingular Variance matrix. The Normal Theory Aitken Model adds an assumption of normality: N(0, 2 V) Obs
Iowa State - STAT - 511
the bootstrapProcess optimization Many physical processes can be described (at least approximately) as quadratic functions of input variable(s)ExamplesWe've seen a lot about inference on C in a nGM (or nAitken) modelA huge number of questions can be a
Iowa State - STAT - 511
the bootstrapWe've seen a lot about inference on C in a nGM (or nAitken) model A huge number of questions can be answered by appropriate choice of C key point is that C is a linear function of y What if quantity of interest is not a linear function of y?
Iowa State - STAT - 511
Randomization/permutation testsBootstrapping preserves the fixed effectsRandomization / Permutation testsResampling from a single pool of observations tests HoR : F1 (x) = F2 (x)Notice a subtle point: HoR is slightly more general than Ho:1 = 2H0R is
Iowa State - STAT - 511
Randomization / Permutation testsBootstrapping preserves the fixed effectsDifference of two means: resample Y1i and resample Y2i bootstrap estimates, 1B - 2B , are centered on/near Y1 - Y2 , ^ ^ which estimates 1 - 2 Regression bootstrap: ^ resample ^i
Iowa State - STAT - 511
LINEAR MIXED-EFFECT MODELSSeedling weight in 2 genotype study from Aitken model section. Seedling weight measured on each seedling. Two (potential) sources of variation: among flats and among seedlings within a flat. Yijk = + i + Tij + Tij ijk ijkExamp
Iowa State - STAT - 511
LINEAR MIXED-EFFECT MODELSStudies / data / models seen previously in 511 assumed a single source of &quot;error&quot; variation y = X + . are fixed constants (in the frequentist approach to inference) is the only random effect What if there are multiple sources of
Iowa State - STAT - 511
Experimental Designs and LME'sOne example:LME models provide one way to model correlations among observationsVery useful for experimental designs where there is more than one size of experimental unitOr designs where the observation unit is not the sa
Iowa State - STAT - 511
Experimental Designs and LME'sLME models provide one way to model correlations among observations Very useful for experimental designs where there is more than one size of experimental unit Or designs where the observation unit is not the same as the exp
Iowa State - STAT - 511
THE ANOVA APPROACH TO THE ANALYSIS OF LINEAR MIXED EFFECTS MODELSThis is the commonly-used model for a CRD with t treatments, n experimental units per treatment, and m observations per experimental unit. We can write the model as y = X + Zu + , where X=[
Iowa State - STAT - 511
THE ANOVA APPROACH TO THE ANALYSIS OF LINEAR MIXED EFFECTS MODELSA model for expt. data with subsampling yijk = + i + uij + eijk , (i = 1, ., t; j = 1, ., n; k = 1, ., m) = (, i , ., t ) , u = (u11 , u12 , ., utn ) , = (e111 , e112 , ., etnm ) , IRt+1 ,
Iowa State - STAT - 511
Two approaches for E MSRCBD with random blocks and multiple obs. per blockijkYijk = + i + j + ij +where i cfw_1, . . . , B, j cfw_1, . . . , T, k cfw_1, . . . , N.with ANOVA table:Expected Mean Squares from two different sources Source 1: Searle (19
Iowa State - STAT - 511
Two approaches for E MSRCBD with random blocks and multiple obs. per block Yijk = + i + j + ij +ijkwhere i cfw_1, . . . , B, j cfw_1, . . . , T, k cfw_1, . . . , N. with ANOVA table: Source Blocks Treatments BlockTrt Error C. total df B-1 T-1 (B-1)(T-1
Iowa State - STAT - 511
ANOVA ANALYSIS OF A BALANCED SPLIT-PLOT EXPERIMENTFieldBlock 1 0 100 150 50 150 100 50 100 150 0 50Plot Genotype B0Genotype CGenotype AExample: the corn genotype and fertilization response studyBlock 2 150 100 Block 3 100 50 0 0 150 50 0 0Main pl
Iowa State - STAT - 511
ANOVA ANALYSIS OF A BALANCED SPLIT-PLOT EXPERIMENTExample: the corn genotype and fertilization response study Main plots: genotypes, in blocks Split plots: fertilization 2 way factorial treatment structure split plot variability nested in main plot varia
Iowa State - STAT - 511
IDENTIFYING AN APPROPRIATE MODELGiven a description of a study, how do you construct an appropriate model?Context: more than one size of e.u.A made-up example, intended to be complicated (but far from being the most complicated I've seen)A study of th
Iowa State - STAT - 511
IDENTIFYING AN APPROPRIATE MODELGiven a description of a study, how do you construct an appropriate model? Context: more than one size of e.u. A made-up example, intended to be complicated (but far from being the most complicated I've seen) A study of th
Iowa State - STAT - 511
MAXIMUM LIKELIHOOD and REML ESTIMATION IN THE GENERAL LINEAR MODELGiven a value of the parameter vector , f (w|) is a real-valued function of w.Suppose f (w|) is the probability density function (pdf ) or probability mass function (pmf ) of a random vec
Iowa State - STAT - 511
MAXIMUM LIKELIHOOD and REML ESTIMATION IN THE GENERAL LINEAR MODELc 2011 Dept. Statistics (Iowa State University)Stat 511 section 211 / 23Suppose f (w|) is the probability density function (pdf ) or probability mass function (pmf ) of a random vector
Iowa State - STAT - 511
Prediction of random variablesKey distinction between fixed and random effects:Estimate means of fixed effects Estimate variance of random effectsBut in some instances, want to predict FUTURE values of a random effectExample (from Efron and Morris, 19
Iowa State - STAT - 511
Prediction of random variablesKey distinction between fixed and random effects:Estimate means of fixed effects Estimate variance of random effectsBut in some instances, want to predict FUTURE values of a random effect Example (from Efron and Morris, 19
Iowa State - STAT - 511
A collection of potentially useful modelsWe've already seen two very common mixed models:for subsampling for designed experiments with multiple experimental unitsHere are three more general classes of modelsRandom coefficient models, aka multi-level m
Iowa State - STAT - 511
A collection of potentially useful modelsA regression where all coefficients vary between groups Example: Strength of parachute lines.Random coefficient modelsWe've already seen two very common mixed models:for subsampling for designed experiments wit
Iowa State - STAT - 511
Choosing among possible random effects structuresGoal is a model that:Fits the data reasonably well Is not too complicatedINFORMATION CRITERIA: AIC and BICSometimes random effects structure specified by the experimental designe.g. for experimental st