Note: Please use the actual date you accessed this material in your citation.

Size: px
Start display at page:

Download "Note: Please use the actual date you accessed this material in your citation."

Transcription

1 MIT OpenCourseWare Electromagnetic Fields, Forces, and Motion, Spring 25 Please use the following citation format: Markus Zahn, Electromagnetic Fields, Forces, and Motion, Spring 25. (Massachusetts Institute of Technology: MIT OpenCourseWare). (accessed MM DD, YYYY). License: Creative Commons Attribution-Noncommercial-Share Alike. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit:

2 Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Electromagnetic Fields, Forces, and Motion Final Exam May, Spring 24, 1:3-4:3PM Formula Sheet Attached in the study materials section. You are also allowed to use the formula sheets that you prepared for Qui 1, Qui 2, and an additional 8 ½ x 11 formula sheet (both sides) that you have prepared for the Final. Problem 1 (25 points) σ =, ε Φ (x =, y y) = V cos ky σ =, ε x s A potential sheet of infinite extent in the y and directions is placed at x = and has potential distribution Φ (x =, y) = V cos ky. Free space with no conductivity ( σ = ) and permittivity ε is present for x < while for < x <s a perfectly insulating dielectric ( σ = ) with permittivity ε is present. The region for x > s is a grounded perfect conductor at ero potential. a) What are the potential distributions for x < and < x < s? b) What are the surface charge densities at x =, σ f (x =, y), and at x = s, σ f (x = s, y)? c) What is the force, magnitude and direction, on a section of the perfect conductor at x = s π that extends over the region < y < and < < D? k Hint: cos2 ydy = y / 2 + (sin 2 y ) / 4 1

3 Problem 2 (25 points) I µ h E, ρ δ ( x, t) A δ ( A, t ) Depth D -a A x y Parallel plate electrodes with spacing h and depth D are excited by a DC current source I. An elastic rod surrounded by free space has mass density ρ, modulus of elasticity E, equilibrium length A when I =, and has infinite ohmic conductivity σ. The elastic rod end at x = is fixed while the deflections of the rod are described as δ ( x, t ) and are assumed small δ ( xt, ) A. The rod width A δ ( A, t) changes as I is changed because of the magnetic force. The DC current flows as a surface current on the x = (A δ ( A, t )) end of the perfectly conducting rod. a) Calculate H in the free space region a< x < (A δ ( A, t )). Neglect fringing field effects and assume h a and h D. b) Using the Maxwell Stress Tensor calculate the magnetic force per unit area on the x = (A δ ( A, t )) end of the rod. c) Calculate the steady state change in rod length δ (x = A). d) Noise creates fluctuations δ (x, t ) in longitudinal displacement. What are the natural frequencies of the rod? 2

4 Problem 3 (25 points) it (, = ) = I < < A vt (, = ) = Z Z, T = A c A An electrical transmission line of length A has characteristic impedance Z. Electromagnetic waves can travel on the line at speed c, so that the time to travel one-way over the line length A is T = A / c. The line is matched at = and is short circuited at = A. At time t =, a lightning bolt strikes the entire line so that there is a uniform current along the line but with ero voltage: it (, = ) = I < <A vt (, = ) = Since the voltage and current obey the telegrapher s relations: v i 1 = L, c = t LC i v = C, Z = L/ C t the voltage and current along the line are related as d v+ iz = c + on = c dt d v iz = c on = c dt a) The solutions for vt (, ) and it (, ) can be found using the method of characteristics within each region shown below. Within regions 1-9 give the values of c+, c, v and iz. A c short circuited d f g i j e matched T h 2T k 3T t 3

5 b) Plot vt (, = T/ 4) and i( t, = T/ 4). vt (, = T/4) it (, =T/4) I Z I IZ I 2 2 A /4 A /2 3 A /4 A A /4 A /2 3 A /4 A I Z I 2 2 I Z I c) How long a time does it take for the transmission line to have vt (,) = and it (,) = everywhere for < < A for all further time? 4

6 Problem 4 (25 points) A x g h ξ ( x, t) Mass per unit area σ m kg/m 2 Tension S N/m H µ Depth D A perfectly conducting membrane of depth D with mass per unit area σ m and tension S is a distance h above a rigid perfect conductor. The membrane and rigid conductor are in free space and support currents such that when the membrane is flat, ξ ( xt, ) =, the static uniform magnetic field intensity is H. As the membrane deforms, the flux through the region between membrane and rigid conductor is conserved. The system is in a downward gravity field with gravitational acceleration g = gi. The membrane deflection has no dependence on y and is fixed at its two ends at x = and x = A. a) Assuming that ξ (x, t ) h and that the only significant magnetic field component is x directed, how is Hx ( x, t ) approximately related to ξ ( x, t ) to linear terms in ξ ( x, t )? b) Using the Maxwell Stress tensor and the result of part (a), to linear terms in small displacement ξ (x, t ), what is the directed magnetic force per unit area, F, on the membrane? c) To linear terms in small displacement ξ (x, t ), express the membrane equation of motion in the form 2 ξ 2 ξ a = b + cξ + d 2 2 t x What are a, b, c, and d? d) What value of H is needed so that in static equilibrium, the membrane has no sag, ξ ( xt, ) =. Continue to next page for parts (e)-(g) 5

7 Prob. 4 continued. e) About the equilibrium of part (d), what is the ω k dispersion relation for membrane deflections of the form j(ωt k x) ξ ( xt, ) = Re[ ξˆe ]? Solve for k as a function of ω and system parameters. f) Using all the values of k found in part (e), find a superposition of solutions of the form of ξ ( x, t ) given in (e), that satisfy the ero deflection boundary conditions at the ends of the membrane at x = and x = A. What are the allowed values for k? g) Is this system always stable or under what conditions can it be unstable? When stable, what are the natural frequencies and if unstable what are the growth rates of the instability? 6

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

More information

Lecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion

Lecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion S. Widnall 6.07 Dynamics Fall 009 Version.0 Lecture L - Degrees of Freedom and Constraints, Rectilinear Motion Degrees of Freedom Degrees of freedom refers to the number of independent spatial coordinates

More information

DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING

DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING SESSION WEEK COURSE: Physics II DEGREE: Bachelor's Degree in Industrial Electronics and Automation COURSE: 1º TERM: 2º WEEKLY PLANNING DESCRIPTION GROUPS (mark ) Indicate YES/NO If the session needs 2

More information

Structural Axial, Shear and Bending Moments

Structural Axial, Shear and Bending Moments Structural Axial, Shear and Bending Moments Positive Internal Forces Acting Recall from mechanics of materials that the internal forces P (generic axial), V (shear) and M (moment) represent resultants

More information

Magnetostatics (Free Space With Currents & Conductors)

Magnetostatics (Free Space With Currents & Conductors) Magnetostatics (Free Space With Currents & Conductors) Suggested Reading - Shen and Kong Ch. 13 Outline Review of Last Time: Gauss s Law Ampere s Law Applications of Ampere s Law Magnetostatic Boundary

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #4 March 15, 2007 Time: 90 minutes NAME: (Last) Please Print (Given) STUDENT NO.: LECTURE SECTION (please

More information

Lecture L22-2D Rigid Body Dynamics: Work and Energy

Lecture L22-2D Rigid Body Dynamics: Work and Energy J. Peraire, S. Widnall 6.07 Dynamics Fall 008 Version.0 Lecture L - D Rigid Body Dynamics: Work and Energy In this lecture, we will revisit the principle of work and energy introduced in lecture L-3 for

More information

Practice Test SHM with Answers

Practice Test SHM with Answers Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one

More information

6 J - vector electric current density (A/m2 )

6 J - vector electric current density (A/m2 ) Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J - vector electric current density (A/m2 ) M - vector magnetic current density (V/m 2 ) Some problems

More information

AP Physics C. Oscillations/SHM Review Packet

AP Physics C. Oscillations/SHM Review Packet AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete

More information

PHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator.

PHYS 222 Spring 2012 Final Exam. Closed books, notes, etc. No electronic device except a calculator. PHYS 222 Spring 2012 Final Exam Closed books, notes, etc. No electronic device except a calculator. NAME: (all questions with equal weight) 1. If the distance between two point charges is tripled, the

More information

PHY3128 / PHYM203 (Electronics / Instrumentation) Transmission Lines. Repeated n times I L

PHY3128 / PHYM203 (Electronics / Instrumentation) Transmission Lines. Repeated n times I L Transmission Lines Introduction A transmission line guides energy from one place to another. Optical fibres, waveguides, telephone lines and power cables are all electromagnetic transmission lines. are

More information

Acceleration levels of dropped objects

Acceleration levels of dropped objects Acceleration levels of dropped objects cmyk Acceleration levels of dropped objects Introduction his paper is intended to provide an overview of drop shock testing, which is defined as the acceleration

More information

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13

EE301 Lesson 14 Reading: 10.1-10.4, 10.11-10.12, 11.1-11.4 and 11.11-11.13 CAPACITORS AND INDUCTORS Learning Objectives EE301 Lesson 14 a. Define capacitance and state its symbol and unit of measurement. b. Predict the capacitance of a parallel plate capacitor. c. Analyze how

More information

PHYSICAL QUANTITIES AND UNITS

PHYSICAL QUANTITIES AND UNITS 1 PHYSICAL QUANTITIES AND UNITS Introduction Physics is the study of matter, its motion and the interaction between matter. Physics involves analysis of physical quantities, the interaction between them

More information

CLASS TEST GRADE 11. PHYSICAL SCIENCES: PHYSICS Test 3: Electricity and magnetism

CLASS TEST GRADE 11. PHYSICAL SCIENCES: PHYSICS Test 3: Electricity and magnetism CLASS TEST GRADE 11 PHYSICAL SCIENCES: PHYSICS Test 3: Electricity and magnetism MARKS: 45 TIME: 1 hour INSTRUCTIONS AND INFORMATION 1. Answer ALL the questions. 2. You may use non-programmable calculators.

More information

39th International Physics Olympiad - Hanoi - Vietnam - 2008. Theoretical Problem No. 3

39th International Physics Olympiad - Hanoi - Vietnam - 2008. Theoretical Problem No. 3 CHANGE OF AIR TEMPERATURE WITH ALTITUDE, ATMOSPHERIC STABILITY AND AIR POLLUTION Vertical motion of air governs many atmospheric processes, such as the formation of clouds and precipitation and the dispersal

More information

Electromagnetism Laws and Equations

Electromagnetism Laws and Equations Electromagnetism Laws and Equations Andrew McHutchon Michaelmas 203 Contents Electrostatics. Electric E- and D-fields............................................. Electrostatic Force............................................2

More information

Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings

Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings 1 of 11 9/7/2012 1:06 PM Logged in as Julie Alexander, Instructor Help Log Out Physics 210 Q1 2012 ( PHYSICS210BRIDGE ) My Courses Course Settings Course Home Assignments Roster Gradebook Item Library

More information

COMPETENCY GOAL 1: The learner will develop abilities necessary to do and understand scientific inquiry.

COMPETENCY GOAL 1: The learner will develop abilities necessary to do and understand scientific inquiry. North Carolina Standard Course of Study and Grade Level Competencies, Physics I Revised 2004 139 Physics PHYSICS - Grades 9-12 Strands: The strands are: Nature of Science, Science as Inquiry, Science and

More information

Force on Moving Charges in a Magnetic Field

Force on Moving Charges in a Magnetic Field [ Assignment View ] [ Eðlisfræði 2, vor 2007 27. Magnetic Field and Magnetic Forces Assignment is due at 2:00am on Wednesday, February 28, 2007 Credit for problems submitted late will decrease to 0% after

More information

Chapter 4. Electrostatic Fields in Matter

Chapter 4. Electrostatic Fields in Matter Chapter 4. Electrostatic Fields in Matter 4.1. Polarization A neutral atom, placed in an external electric field, will experience no net force. However, even though the atom as a whole is neutral, the

More information

Precision Miniature Load Cell. Models 8431, 8432 with Overload Protection

Precision Miniature Load Cell. Models 8431, 8432 with Overload Protection w Technical Product Information Precision Miniature Load Cell with Overload Protection 1. Introduction The load cells in the model 8431 and 8432 series are primarily designed for the measurement of force

More information

Statics of Structural Supports

Statics of Structural Supports Statics of Structural Supports TYPES OF FORCES External Forces actions of other bodies on the structure under consideration. Internal Forces forces and couples exerted on a member or portion of the structure

More information

Experiment 8: Undriven & Driven RLC Circuits

Experiment 8: Undriven & Driven RLC Circuits Experiment 8: Undriven & Driven RLC Circuits Answer these questions on a separate sheet of paper and turn them in before the lab 1. RLC Circuits Consider the circuit at left, consisting of an AC function

More information

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).

Edmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H). INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes

More information

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x

www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. 8.02 Spring 2013 Conflict Exam Two Solutions

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics. 8.02 Spring 2013 Conflict Exam Two Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 802 Spring 2013 Conflict Exam Two Solutions Problem 1 (25 points): answers without work shown will not be given any credit A uniformly charged

More information

STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION

STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION Chapter 11 STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION Figure 11.1: In Chapter10, the equilibrium, kinematic and constitutive equations for a general three-dimensional solid deformable

More information

Bending, Forming and Flexing Printed Circuits

Bending, Forming and Flexing Printed Circuits Bending, Forming and Flexing Printed Circuits John Coonrod Rogers Corporation Introduction: In the printed circuit board industry there are generally two main types of circuit boards; there are rigid printed

More information

The purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.

The purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law. 260 17-1 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this

More information

Digital Systems Ribbon Cables I CMPE 650. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip.

Digital Systems Ribbon Cables I CMPE 650. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip. Ribbon Cables A ribbon cable is any cable having multiple conductors bound together in a flat, wide strip. Each dielectric configuration has different high-frequency characteristics. All configurations

More information

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22 BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

More information

CHAPTER 24 GAUSS S LAW

CHAPTER 24 GAUSS S LAW CHAPTER 4 GAUSS S LAW 4. The net charge shown in Fig. 4-40 is Q. Identify each of the charges A, B, C shown. A B C FIGURE 4-40 4. From the direction of the lines of force (away from positive and toward

More information

Candidate Number. General Certificate of Education Advanced Level Examination June 2014

Candidate Number. General Certificate of Education Advanced Level Examination June 2014 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 214 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Wednesday

More information

12.510 Introduction to Seismology Spring 2008

12.510 Introduction to Seismology Spring 2008 MIT OpenCourseWare http://ocw.mit.edu 12.510 Introduction to Seismology Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 04/30/2008 Today s

More information

Fundamentals of Electromagnetic Fields and Waves: I

Fundamentals of Electromagnetic Fields and Waves: I Fundamentals of Electromagnetic Fields and Waves: I Fall 2007, EE 30348, Electrical Engineering, University of Notre Dame Mid Term II: Solutions Please show your steps clearly and sketch figures wherever

More information

1 The basic equations of fluid dynamics

1 The basic equations of fluid dynamics 1 The basic equations of fluid dynamics The main task in fluid dynamics is to find the velocity field describing the flow in a given domain. To do this, one uses the basic equations of fluid flow, which

More information

Exam 2 Practice Problems Part 1 Solutions

Exam 2 Practice Problems Part 1 Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Exam Practice Problems Part 1 Solutions Problem 1 Electric Field and Charge Distributions from Electric Potential An electric potential V ( z

More information

Physics 30 Worksheet #10 : Magnetism From Electricity

Physics 30 Worksheet #10 : Magnetism From Electricity Physics 30 Worksheet #10 : Magnetism From Electricity 1. Draw the magnetic field surrounding the wire showing electron current below. x 2. Draw the magnetic field surrounding the wire showing electron

More information

Boardworks AS Physics

Boardworks AS Physics Boardworks AS Physics Vectors 24 slides 11 Flash activities Prefixes, scalars and vectors Guide to the SI unit prefixes of orders of magnitude Matching powers of ten to their SI unit prefixes Guide to

More information

PS-6.2 Explain the factors that determine potential and kinetic energy and the transformation of one to the other.

PS-6.2 Explain the factors that determine potential and kinetic energy and the transformation of one to the other. PS-6.1 Explain how the law of conservation of energy applies to the transformation of various forms of energy (including mechanical energy, electrical energy, chemical energy, light energy, sound energy,

More information

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level

Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level *0123456789* PHYSICS 9702/02 Paper 2 AS Level Structured Questions For Examination from 2016 SPECIMEN

More information

Science Standard Articulated by Grade Level Strand 5: Physical Science

Science Standard Articulated by Grade Level Strand 5: Physical Science Concept 1: Properties of Objects and Materials Classify objects and materials by their observable properties. Kindergarten Grade 1 Grade 2 Grade 3 Grade 4 PO 1. Identify the following observable properties

More information

Fluid Mechanics: Static s Kinematics Dynamics Fluid

Fluid Mechanics: Static s Kinematics Dynamics Fluid Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three

More information

Chapter 7: Polarization

Chapter 7: Polarization Chapter 7: Polarization Joaquín Bernal Méndez Group 4 1 Index Introduction Polarization Vector The Electric Displacement Vector Constitutive Laws: Linear Dielectrics Energy in Dielectric Systems Forces

More information

PHY114 S11 Term Exam 3

PHY114 S11 Term Exam 3 PHY4 S Term Exam S. G. Rajeev Mar 2 20 2:0 pm to :45 pm PLEASE write your workshop number and your workshop leader s name at the top of your book, so that you can collect your graded exams at the workshop.

More information

arxiv:1111.4354v2 [physics.acc-ph] 27 Oct 2014

arxiv:1111.4354v2 [physics.acc-ph] 27 Oct 2014 Theory of Electromagnetic Fields Andrzej Wolski University of Liverpool, and the Cockcroft Institute, UK arxiv:1111.4354v2 [physics.acc-ph] 27 Oct 2014 Abstract We discuss the theory of electromagnetic

More information

Basic Equations, Boundary Conditions and Dimensionless Parameters

Basic Equations, Boundary Conditions and Dimensionless Parameters Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were

More information

AS COMPETITION PAPER 2008

AS COMPETITION PAPER 2008 AS COMPETITION PAPER 28 Name School Town & County Total Mark/5 Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question

More information

MCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements

MCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements MCE380: Measurements and Instrumentation Lab Chapter 9: Force, Torque and Strain Measurements Topics: Elastic Elements for Force Measurement Dynamometers and Brakes Resistance Strain Gages Holman, Ch.

More information

Sample Questions for the AP Physics 1 Exam

Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiple-choice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each

More information

Magnetic Circuits. Outline. Ampere s Law Revisited Review of Last Time: Magnetic Materials Magnetic Circuits Examples

Magnetic Circuits. Outline. Ampere s Law Revisited Review of Last Time: Magnetic Materials Magnetic Circuits Examples Magnetic Circuits Outline Ampere s Law Revisited Review of Last Time: Magnetic Materials Magnetic Circuits Examples 1 Electric Fields Magnetic Fields S ɛ o E da = ρdv B V = Q enclosed S da =0 GAUSS GAUSS

More information

CHAPTER - 1. Chapter ONE: WAVES CHAPTER - 2. Chapter TWO: RAY OPTICS AND OPTICAL INSTRUMENTS. CHAPTER - 3 Chapter THREE: WAVE OPTICS PERIODS PERIODS

CHAPTER - 1. Chapter ONE: WAVES CHAPTER - 2. Chapter TWO: RAY OPTICS AND OPTICAL INSTRUMENTS. CHAPTER - 3 Chapter THREE: WAVE OPTICS PERIODS PERIODS BOARD OF INTERMEDIATE EDUCATION, A.P., HYDERABAD REVISION OF SYLLABUS Subject PHYSICS-II (w.e.f 2013-14) Chapter ONE: WAVES CHAPTER - 1 1.1 INTRODUCTION 1.2 Transverse and longitudinal waves 1.3 Displacement

More information

Experiment 9. The Pendulum

Experiment 9. The Pendulum Experiment 9 The Pendulum 9.1 Objectives Investigate the functional dependence of the period (τ) 1 of a pendulum on its length (L), the mass of its bob (m), and the starting angle (θ 0 ). Use a pendulum

More information

ANALYTICAL METHODS FOR ENGINEERS

ANALYTICAL METHODS FOR ENGINEERS UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations

More information

VERTICAL STRESS INCREASES IN SOIL TYPES OF LOADING. Point Loads (P) Line Loads (q/unit length) Examples: - Posts. Examples: - Railroad track

VERTICAL STRESS INCREASES IN SOIL TYPES OF LOADING. Point Loads (P) Line Loads (q/unit length) Examples: - Posts. Examples: - Railroad track VERTICAL STRESS INCREASES IN SOIL Point Loads (P) TYPES OF LOADING Line Loads (q/unit length) Revised 0/015 Figure 6.11. Das FGE (005). Examples: - Posts Figure 6.1. Das FGE (005). Examples: - Railroad

More information

Mode Patterns of Parallel plates &Rectangular wave guides Mr.K.Chandrashekhar, Dr.Girish V Attimarad

Mode Patterns of Parallel plates &Rectangular wave guides Mr.K.Chandrashekhar, Dr.Girish V Attimarad International Journal of Scientific & Engineering Research Volume 3, Issue 8, August-2012 1 Mode Patterns of Parallel plates &Rectangular wave guides Mr.K.Chandrashekhar, Dr.Girish V Attimarad Abstract-Parallel

More information

INTERACTION BETWEEN MOVING VEHICLES AND RAILWAY TRACK AT HIGH SPEED

INTERACTION BETWEEN MOVING VEHICLES AND RAILWAY TRACK AT HIGH SPEED INTERACTION BETWEEN MOVING VEHICLES AND RAILWAY TRACK AT HIGH SPEED Prof.Dr.Ir. C. Esveld Professor of Railway Engineering TU Delft, The Netherlands Dr.Ir. A.W.M. Kok Associate Professor of Railway Engineering

More information

physics 111N work & energy

physics 111N work & energy physics 111N work & energy conservation of energy entirely gravitational potential energy kinetic energy turning into gravitational potential energy gravitational potential energy turning into kinetic

More information

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is

Lecture 17. Last time we saw that the rotational analog of Newton s 2nd Law is Lecture 17 Rotational Dynamics Rotational Kinetic Energy Stress and Strain and Springs Cutnell+Johnson: 9.4-9.6, 10.1-10.2 Rotational Dynamics (some more) Last time we saw that the rotational analog of

More information

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

More information

An equivalent circuit of a loop antenna.

An equivalent circuit of a loop antenna. 3.2.1. Circuit Modeling: Loop Impedance A loop antenna can be represented by a lumped circuit when its dimension is small with respect to a wavelength. In this representation, the circuit parameters (generally

More information

Eatman Associates 2014 Rockwall TX 800-388-4036 rev. October 1, 2014. Striplines and Microstrips (PCB Transmission Lines)

Eatman Associates 2014 Rockwall TX 800-388-4036 rev. October 1, 2014. Striplines and Microstrips (PCB Transmission Lines) Eatman Associates 2014 Rockwall TX 800-388-4036 rev. October 1, 2014 Striplines and Microstrips (PCB Transmission Lines) Disclaimer: This presentation is merely a compilation of information from public

More information

Physics Notes Class 11 CHAPTER 6 WORK, ENERGY AND POWER

Physics Notes Class 11 CHAPTER 6 WORK, ENERGY AND POWER 1 P a g e Work Physics Notes Class 11 CHAPTER 6 WORK, ENERGY AND POWER When a force acts on an object and the object actually moves in the direction of force, then the work is said to be done by the force.

More information

AS COMPETITION PAPER 2007 SOLUTIONS

AS COMPETITION PAPER 2007 SOLUTIONS AS COMPETITION PAPER 2007 Total Mark/50 SOLUTIONS Section A: Multiple Choice 1. C 2. D 3. B 4. B 5. B 6. A 7. A 8. C 1 Section B: Written Answer Question 9. A mass M is attached to the end of a horizontal

More information

Physics 202, Lecture 3. The Electric Field

Physics 202, Lecture 3. The Electric Field Physics 202, Lecture 3 Today s Topics Electric Field Quick Review Motion of Charged Particles in an Electric Field Gauss s Law (Ch. 24, Serway) Conductors in Electrostatic Equilibrium (Ch. 24) Homework

More information

FLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS - CB0235 2014_1

FLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS - CB0235 2014_1 COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE FLUID MECHANICS IM0235 3 LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 32 HOURS LABORATORY, 112 HOURS OF INDEPENDENT

More information

PROVA DINAMICA SU PALI IN ALTERNATIVA ALLA PROVA STATICA. Pile Dynamic Load test as alternative to Static Load test

PROVA DINAMICA SU PALI IN ALTERNATIVA ALLA PROVA STATICA. Pile Dynamic Load test as alternative to Static Load test PROVA DINAMICA SU PALI IN ALTERNATIVA ALLA PROVA STATICA Pile Dynamic Load test as alternative to Static Load test Gorazd Strnisa, B.Sc.Civ.Eng. SLP d.o.o. Ljubljana ABSTRACT Pile Dynamic test is test

More information

4 SENSORS. Example. A force of 1 N is exerted on a PZT5A disc of diameter 10 mm and thickness 1 mm. The resulting mechanical stress is:

4 SENSORS. Example. A force of 1 N is exerted on a PZT5A disc of diameter 10 mm and thickness 1 mm. The resulting mechanical stress is: 4 SENSORS The modern technical world demands the availability of sensors to measure and convert a variety of physical quantities into electrical signals. These signals can then be fed into data processing

More information

Human Exposure to Outdoor PLC System

Human Exposure to Outdoor PLC System 1602 PIERS Proceedings, Marrakesh, MOROCCO, March 20 23, 2011 Human Exposure to Outdoor PLC System Vicko Doric 1, Dragan Poljak 1, and Khalil El Khamlichi Drissi 2 1 University of Split, Croatia 2 Blaise

More information

SOLUTIONS TO CONCEPTS CHAPTER 15

SOLUTIONS TO CONCEPTS CHAPTER 15 SOLUTIONS TO CONCEPTS CHAPTER 15 1. v = 40 cm/sec As velocity of a wave is constant location of maximum after 5 sec = 40 5 = 00 cm along negative x-axis. [(x / a) (t / T)]. Given y = Ae a) [A] = [M 0 L

More information

Proof of the conservation of momentum and kinetic energy

Proof of the conservation of momentum and kinetic energy Experiment 04 Proof of the conservation of momentum and kinetic energy By Christian Redeker 27.10.2007 Contents 1.) Hypothesis...3 2.) Diagram...7 3.) Method...7 3.1) Apparatus...7 3.2) Procedure...7 4.)

More information

COURSE: PHYSICS DEGREE: COMPUTER ENGINEERING year: 1st SEMESTER: 1st

COURSE: PHYSICS DEGREE: COMPUTER ENGINEERING year: 1st SEMESTER: 1st COURSE: PHYSICS DEGREE: COMPUTER ENGINEERING year: 1st SEMESTER: 1st WEEKLY PROGRAMMING WEE K SESSI ON DESCRIPTION GROUPS GROUPS Special room for LECTU PRAC session RES TICAL (computer classroom, audiovisual

More information

Physics 41 HW Set 1 Chapter 15

Physics 41 HW Set 1 Chapter 15 Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,

More information

Chapter 15, example problems:

Chapter 15, example problems: Chapter, example problems: (.0) Ultrasound imaging. (Frequenc > 0,000 Hz) v = 00 m/s. λ 00 m/s /.0 mm =.0 0 6 Hz. (Smaller wave length implies larger frequenc, since their product,

More information

Wireless Power Transfer System Design. Julius Saitz ANSYS

Wireless Power Transfer System Design. Julius Saitz ANSYS Wireless Power Transfer System Design Julius Saitz ANSYS 1 WPT System 2 Wireless Power Transfer (WPT) Near-Field (Inductive coupling, resonant) Do not rely on propagating EM waves Operate at distances

More information

In-situ Load Testing to Evaluate New Repair Techniques

In-situ Load Testing to Evaluate New Repair Techniques In-situ Load Testing to Evaluate New Repair Techniques W.J. Gold 1 and A. Nanni 2 1 Assistant Research Engineer, Univ. of Missouri Rolla, Dept. of Civil Engineering 2 V&M Jones Professor, Univ. of Missouri

More information

APPLIED MATHEMATICS ADVANCED LEVEL

APPLIED MATHEMATICS ADVANCED LEVEL APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications

More information

Solved with COMSOL Multiphysics 4.0a. COPYRIGHT 2010 COMSOL AB.

Solved with COMSOL Multiphysics 4.0a. COPYRIGHT 2010 COMSOL AB. Permanent Magnet Introduction This example shows how to model the magnetic field surrounding a permanent magnet. It also computes the force with which it acts on a nearby iron rod. Thanks to the symmetry

More information

Online Courses for High School Students 1-888-972-6237

Online Courses for High School Students 1-888-972-6237 Online Courses for High School Students 1-888-972-6237 PHYSICS Course Description: This course provides a comprehensive survey of all key areas: physical systems, measurement, kinematics, dynamics, momentum,

More information

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger

Slide 1 / 26. Inductance. 2011 by Bryan Pflueger Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one

More information

Candidate Number. General Certificate of Education Advanced Level Examination June 2012

Candidate Number. General Certificate of Education Advanced Level Examination June 2012 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 212 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Monday

More information

XX. Introductory Physics, High School

XX. Introductory Physics, High School XX. Introductory Physics, High School High School Introductory Physics Test The spring 2013 high school Introductory Physics test was based on learning standards in the Physics content strand of the Massachusetts

More information

Objectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials.

Objectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials. Lab 3 Tension Test Objectives Concepts Background Experimental Procedure Report Requirements Discussion Objectives Experimentally determine the yield strength, tensile strength, and modules of elasticity

More information

MAS.836 HOW TO BIAS AN OP-AMP

MAS.836 HOW TO BIAS AN OP-AMP MAS.836 HOW TO BIAS AN OP-AMP Op-Amp Circuits: Bias, in an electronic circuit, describes the steady state operating characteristics with no signal being applied. In an op-amp circuit, the operating characteristic

More information

Energy transformations

Energy transformations Energy transformations Objectives Describe examples of energy transformations. Demonstrate and apply the law of conservation of energy to a system involving a vertical spring and mass. Design and implement

More information

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces.

Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion. Physics is about forces and how the world around us reacts to these forces. Physics 111: Lecture 4: Chapter 4 - Forces and Newton s Laws of Motion Physics is about forces and how the world around us reacts to these forces. Whats a force? Contact and non-contact forces. Whats a

More information

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) In this lecture How does turbulence affect the ensemble-mean equations of fluid motion/transport? Force balance in a quasi-steady turbulent boundary

More information

Overview. also give you an idea of ANSYS capabilities. In this chapter, we will define Finite Element Analysis and. Topics covered: B.

Overview. also give you an idea of ANSYS capabilities. In this chapter, we will define Finite Element Analysis and. Topics covered: B. 2. FEA and ANSYS FEA and ANSYS Overview In this chapter, we will define Finite Element Analysis and also give you an idea of ANSYS capabilities. Topics covered: A. What is FEA? B. About ANSYS FEA and ANSYS

More information

8.2 Elastic Strain Energy

8.2 Elastic Strain Energy Section 8. 8. Elastic Strain Energy The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for

More information

Candidate Number. General Certificate of Education Advanced Level Examination June 2010

Candidate Number. General Certificate of Education Advanced Level Examination June 2010 entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 1 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Friday 18

More information

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of

More information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

Indiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance.

Indiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance. .1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations

More information

Engineering g Problem Solving Process

Engineering g Problem Solving Process Engineering g Problem Solving Process GIVEN State briefly and concisely (in your own words) the information given. FIND State the information that you have to find. DIAGRAM A drawing showing the physical

More information

FRICTION, WORK, AND THE INCLINED PLANE

FRICTION, WORK, AND THE INCLINED PLANE FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle

More information

Practice Exam Three Solutions

Practice Exam Three Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Practice Exam Three Solutions Problem 1a) (5 points) Collisions and Center of Mass Reference Frame In the lab frame,

More information

Exam 1 Practice Problems Solutions

Exam 1 Practice Problems Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8 Spring 13 Exam 1 Practice Problems Solutions Part I: Short Questions and Concept Questions Problem 1: Spark Plug Pictured at right is a typical

More information

LECTURE 6: Fluid Sheets

LECTURE 6: Fluid Sheets LECTURE 6: Fluid Sheets The dynamics of high-speed fluid sheets was first considered by Savart after his early work on electromagnetism with Biot, and was subsequently examined in a series of papers by

More information