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### CE-18-SS2005

Course: PHYSICS 112, Summer 2009
School: Iowa State
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Word Count: 142

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EXERCISE CLASS #18 - 19 July 2005 A spherical mirror has a radius of curvature of 20 cm. An object is placed on the principal axis on the concave side a distance of 5.0 cm from the vertex of the mirror. Determine the focal length of this mirror and then make a sketch showing the object and image as determined by three different rays. Then use the mirror formula to determine the image location the and...

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EXERCISE CLASS #18 - 19 July 2005 A spherical mirror has a radius of curvature of 20 cm. An object is placed on the principal axis on the concave side a distance of 5.0 cm from the vertex of the mirror. Determine the focal length of this mirror and then make a sketch showing the object and image as determined by three different rays. Then use the mirror formula to determine the image location the and magnification, and characterize the image (real or virtual, etc.) The focal length 0 oe V2 oe 20 cm2 oe 10 cm and the object distance 9 oe 5.0 cm. 13 oe 10 19 oe 110 cm 15 cm oe (1 2)10 cm oe 110 cm so 3 oe 10 cm. The magnfication 7 oe 39 oe 10 cm5.0 cm oe 2. The image is virtual (because 3 is negative), erect (because 7 is positive), and twice as large as the object.
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Iowa State - PHYSICS - 112
CLASS EXERCISE #19 - 20 July 2005You are supposed to make a slide projector using a single convergent lens. The projector projects an image of a slide (which is placed near the lens, in the projector). Suppose you want the slide to be magnified 100 times
Iowa State - PHYSICS - 112
CLASS EXERCISE #20 - 25 July 2005Light of wavelength 500 nm is incident on a pair of slits. On a screen 2.0 m away, the interference maxima are found to be 2.0 mm apart. (a) Determine the angle ) (in radians and in degrees) corresponding to the first int
Iowa State - PHYSICS - 112
CLASS EXERCISE #22 - 27 July 2005Initially unpolarized light passes through four different polarizers, all of them letting through light polarized in a horizontal plane (like polarizers sitting on an overhead projector). The first lets through light pola
Iowa State - PHYSICS - 112
CLASS EXERCISE #23 - 28 July 2005Light of wavelength 520 nm is incident normally (perpendicularly) from air onto an interface with a thin oil film (8 oe 1.30) that is floating on water (8 oe 1.33). (a) What is the frequency of this light?0 oe - oe 3 , 1
Iowa State - PHYSICS - 112
CLASS EXERCISE #24 - 1 August 2005 An atom undergoes a transition from a state of energy 14.7 eV to a state of energy 10.6 eV. Determine whether a photon was absorbed or emitted, and determine that photon's energy (in both eV and joules) and frequency. Th
Iowa State - PHYSICS - 112
PHYSICS 112 - EXAM 4 (first part of final exam) - FALL 2003 Name _ Section _Use 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 y
Iowa State - PHYSICS - 112
P-1PHYSICS 112 SUMMER 2005 Homework for June 14, 2005 Due in recitation during the first five minutes; after that, worth only 50% as much.Name SectionIn parts (1a) through (1c), consider the two dimensionless vectors t t E oe (3.10, 2.40) and F oe ( 3.
Iowa State - PHYSICS - 112
Homework Assignment #2 - Thursday June 16, 20051. (a) On a piece of graph paper (remember that some are available on the course web page) place a 3 .C charge at the origin and a 2.C at the point B oe 3.0 m C oe 0. (b) Determine the magnitude of the elect
Iowa State - PHYSICS - 112
HOMEWORK #3 for Tuesday, June 21, 2005Name _ Section _ 1. A 4-.C charge is located at the point (0 m, 3 m), and a 5-.C charge is located at the point (0 m, 2 m). No other charges are around.A. What is the magnitude of the electrical force on the 4-.C ch
Iowa State - PHYSICS - 112
Homework #4 for Thursday, June 23, 2005Name _ Section _The figure above shows a (rectangular) region of space with a uniform magnetic field: the electric field everywhere has the same magnitude and direction. The direction of the electric field is indic
Iowa State - PHYSICS - 112
HOMEWORK - TUESDAY, JUNE 28, 20051. A piece of an electric circuit consists of five resistors connected as shown below. The electric potential at two points is shown.(a) Determine the electric current in this part of the circuit and show its direction o
Iowa State - PHYSICS - 112
HOMEWORK for JUNE 30, 2005 For the following circuits, draw the circuit and fill out the V M ?Z T table (including the battery or batteries). Also mark a point between each pair of circuit elements (resistors or batteries) and determine the electric poten
Iowa State - PHYSICS - 112
HOMEWORK for JUNE 30, 2005 For the following circuits, draw the circuit and fill out the V M ?Z T table (including the battery or batteries). Also mark a point between each pair of circuit elements (resistors or batteries) and determine the electric poten
Iowa State - PHYSICS - 112
HOMEWORK for TUESDAY, JULY 5, 2005Determine the currents in the following circuits, and construct the V M ?Z T table for each circuit. Check that the powers are correct. Also, determine the electric potentials at the points marked.
Iowa State - PHYSICS - 112
Determine the currents in the following circuits, and construct the V M ?Z T table for each circuit. Check that the powers are correct. Also, determine the electric potentials at the points marked.V 6H 12 H 4HM 2A 1A 3A?Z 12 V 12 V 12 VT 24 W 12 W 36
Iowa State - PHYSICS - 112
HOMEWORK for THURSDAY JULY 7, 2005 1. Determine the magnitude and direction of the magnetic force on the following charges in a magnetic field of 0.20 T directed east: (a) A charge ; oe 4.0 .C moving north at 35 m/s.(b) An electron moving vertically upwa
Iowa State - PHYSICS - 112
HOMEWORK for TUESDAY, JULY 12, 2005For each of the following situations two circuit loops are shown in a uniform t external magnetic field F . Let the one on the left have a clockwise current and the one on the right have a counterclockwise current. Dete
Iowa State - PHYSICS - 112
HOMEWORK for TUESDAY, JULY 12, 2005For each of the following situations two circuit loops are shown in a uniform t external magnetic field F ext . Let the one on the left have a clockwise current and the one on the right have a counterclockwise current.
Iowa State - PHYSICS - 112
Homework for Thursday, July 14, 2005 (Bastille Day) Name _ Section _For each of the following situations a circuit loop is shown in a uniform t external magnetic field F . Determine in each case the direction (clockwise or counterclockwise) of the induce
Iowa State - PHYSICS - 112
C 1. t F ext BThe magnitude F of the magnetic field is increasing.Flux: increasing due to increasing F . t F loop must be down ( OE ) to counteract upward increasing flux; current is then clockwise.C 2. t OE F ext BThe magnitude F of the magnetic fiel
Iowa State - PHYSICS - 112
HOMEWORK FOR TUESDAY, JULY 19, 2005 In this problem we will consider the path of light rays from air into glass and vice versa. The glass has a flat, horizontal surface, and the air is above it. We want to determine the angles for the reflected and refrac
Iowa State - PHYSICS - 112
HOMEWORK SOLUTIONS FOR JULY 21 1. An object is placed 10 cm from the vertex of a concave mirror of radius of curvature 12 cm. Find the image distance and the magnification, and characterize the image in the usual way. Check your results by ray tracing usi
Iowa State - PHYSICS - 112
HOMEWORK ASSIGNMENT FOR JULY 26, 2005Consider the interference between two slits separated by a distance . on which light of wavelength - shines, producing a pattern of dark and bright fringes on a screen a distance H away from the slits. First draw a sk
Iowa State - PHYSICS - 112
Consider the interference between two slits separated by a distance . on which light of wavelength - shines, producing a pattern of dark and bright fringes on a screen a distance H away from the slits. First draw a sketch of this physical situation, showi
Iowa State - PHYSICS - 112
HOMEWORK FOR THURSDAY, JULY 28, 20051. A diffraction grating has lines spaced 2.00 .m apart. Let's consider white visible light (wavelengths ranging from 0.400 .m for violet light to 0.700 .m for red light) shining on it. (a) Determine all the angles for
Iowa State - PHYSICS - 112
SOLUTIONS 1. A diffraction grating has lines spaced 2.00 .m apart. Let's consider white visible light (wavelengths ranging from 0.400 .m for violet light to 0.700 .m for red light) shining on it. (a) Determine all the angles for which interference maxima
Iowa State - PHYSICS - 112
HOMEWORK FOR TUESDAY, AUGUST 2, 20051. Consider the atom denoted by 183 Au 79 The common name of this element is _. It has _ electrons, _ protons, _ neutrons, and _ quarks. This atom is radioactive and decays by alpha decay with a half-life of 49 seconds
Iowa State - PHYSICS - 112
1. Consider the atom denoted by 183 Au 79 The common name of this element is: gold It has 79 electrons, 79 protons, and 183 79 oe 104 neutrons. This atom is radioactive and decays by alpha decay with a half-life of 49 seconds. Determine the fraction of it
Iowa State - PHYSICS - 112
REFRACTION WORKSHEET &quot;Triangle&quot; Diagram: On other pages in this set you will find a large triangle that represents a triangular prism. We want to follow the path of a light ray striking one of the surfaces as it passes through the prism and exits one of t
Iowa State - PHYSICS - 112
PHYSICS 112 - REVIEW FOR EXAM 1ELECTRIC 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,
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