Projectile Motion with Air Resistance (Numerical Modeling, Euler s Method)
|
|
- Priscilla Phelps
- 6 years ago
- Views:
Transcription
1 Projectile Motion with Air Resistance (Nuerical Modeling, Euler s Method) Theory Euler s ethod is a siple way to approxiate the solution of ordinary differential equations (ode s) nuerically. Specifically, those ode s for which initial conditions are known. Consider the ode which has solution dy dx = f (x) (1) and reference Figure 1. y = f(x) Figure 1: Euler s ethod. The Euler ethod is a nuerical ethod; with known (x o, y o ), a chosen x, and the approxiation Equation 1 becoes dy dx y x 1
2 y = f (x) x Thus x 1 = x o + x y 1 = y + f (x o ) x The process is then be repeated; the general algorith is x n = x n 1 + x () y n = y n 1 + f (x n 1 ) x (3) Physics is all about rates of change so this ethod can be used to solve a wide variety of physics probles. Reeber that a = dv dt and v = dx dt and consider an object oving in one diension subject to a constant rate of acceleration a; it starts fro rest (x o = v o = t o = 0). Then t 1 = 0 + t x 1 = t v 1 = 0 + a t a 1 = a and in general t n = t n 1 + t x n = x n 1 + v n 1 t v n = v n 1 + a n 1 t a n = a This is rearkably easy to ipleent in a spreadsheet such as Excel. The first 10 steps of the proble are shown in Figure ; here, the forulas are displayed in the cells rather than the results to better deonstrate the process [you can also check your solution analytically]. Note that the forulas in Row 3 were copied down the rest of the way. This is the beauty of Excel - with judicious use of relative and absolute cell references the first iterative row can be copied down as far as needed - which ay be several thousand steps! Although the ethod will work on any ode it is ost often eployed on those difficult or ipossible to solve analytically. The acceleration of the object need not be constant; it could be a function of any nuber of variables - position, velocity, or tie. As long as initial values can be quantified it can be used. But, a word of warning - all nuerical ethods give but approxiate solutions and are subject to accuulation error. You can iniize this with very sall t.
3 Figure : Excel ipleentation of the Euler ethod. Air Resistance on a Projectile Assue that air resistance for a projectile is proportional to the square of the projectile velocity; i.e., the drag force on the projectile is given by where F = Dv and v = v x + v y D = ρca Here, ρ is the density of air, C a diensionless constant called the drag coefficient (0. to 1.0 for baseballs, tennis balls, etc.), and A the cross-sectional area of the projectile. At any point in the otion of the projectile, the drag force is directed opposite to the direction of the velocity, as shown in Figure 3. Figure 3: Drag Force on Projectile 3
4 The net force on the projectile in each diension is Fx = Dv cos θ = a x = Dv(v cos θ) Fy = g Dv sin θ = a y = g Dv(v sin θ) thus the corresponding accelerations are just a x = vv x a y = g vv y Fro an Euler ethod standpoint this would be ipleented as a nx = v n v nx (4) a ny = g v n v ny (5) Obviously the x and y diensions ust be solved separately. If you know the initial values x o, y o, v xo, and v yo then the ethod can be used. Procedure In this experient you will solve the probles below involving projectiles subject to air resistance. You will do this with an Euler ethod worksheet. At the top of the worksheet will be the basic paraeters g, r, C, ρ,, v o, θ (in degrees!), and t. Include the interediate paraeters A and D calculated with these values. Below this start the table of Euler calculations; it will contain 8 coluns - Step, t, x, v x, a x, y, v y, and a y. The first row is initial values for all quantities; subsequent iterations (rows) are deterined with the Euler equations. These equations should reference the cells at the top of the worksheet; this way you can solve all of the probles by just changing the paraeters and/or initial values at the top. Each tie, scan your table to obtain the answer and write it at the top of the table to the right of your constants (include the t used in the proble). Before you eail e your Excel file, delete all but about 5 rows of your Euler table - this will be easier to eail. When I open your file I will recopy your forulas down. 1. As a test progra find the trajectory of a baseball with and without (D = 0) air resistance. The radius of the baseball is , and A = πr. Its ass is 0.145kg, the drag coefficient is 0.5 and the density of air is 1.kg/ 3. The baseball is given an initial velocity of 50/s at an angle of 35 above the +x-axis. With drag the range of the baseball is just over 100; without drag the range is alost 40.. The hoe field for the Colorado Rockies is in Denver (altitude 1 ile), where the air density is only 1.0kg/ 3. How uch farther will the baseball in the trial progra go copared to sea level? 4
5 3. Estiate the axiu distance a huan being can throw a ping-pong ball. A ping-pong ball has a radius of and a ass of 0.004kg. Use a drag coefficient of 0.5 and a density of 1.kg/ 3. The fastest pitchers can throw at about 100i/h. Why can a baseball be thrown uch farther than a ping-pong ball? 4. In tennis, 100i/h is a very good serving speed. How fast is the ball oving when it crosses the baseline in the opposite court, about 4 distant? Use a ass of 0.055kg, a radius of 0.031, a drag coefficient of 0.75, and a density of 1.kg/ 3. The ball leaves the racquet oving horizontally and does not hit the ground until after it crosses the opposite court baseline. 5. Decide whether or not air resistance really is negligible in a typical Projectile Motion lab experient. The projectile sphere has a ass of 16g, a diaeter of 1.5c, a sall C (i.e., closer to 0. than 1), and an initial velocity of 5.00/s. For a launch angle of 45, exaine the otion in both cases drag and no drag. What is the ratio Is air resistance negligible or not? range drag? range 5
Ph 20.3 Numerical Solution of Ordinary Differential Equations
Ph 20.3 Nuerical Solution of Ordinary Differential Equations Due: Week 5 -v20170314- This Assignent So far, your assignents have tried to failiarize you with the hardware and software in the Physics Coputing
More informationLAB MECH8.COMP From Physics with Computers, Vernier Software & Technology, 2003.
LAB MECH8.COMP Fro Physics with Coputers, Vernier Software & Technology, 003. INTRODUCTION You have probably watched a ball roll off a table and strike the floor. What deterines where it will land? Could
More informationModel Fitting. CURM Background Material, Fall 2014 Dr. Doreen De Leon
Model Fitting CURM Background Material, Fall 014 Dr. Doreen De Leon 1 Introduction Given a set of data points, we often want to fit a selected odel or type to the data (e.g., we suspect an exponential
More informationHORIZONTAL MOTION WITH RESISTANCE
DOING PHYSICS WITH MATLAB MECHANICS HORIZONTAL MOTION WITH RESISTANCE Ian Cooper School of Physics, Uniersity of Sydney ian.cooper@sydney.edu.au DOWNLOAD DIRECTORY FOR MATLAB SCRIPTS ec_fr_b. This script
More informationAn Approximate Model for the Theoretical Prediction of the Velocity Increase in the Intermediate Ballistics Period
An Approxiate Model for the Theoretical Prediction of the Velocity... 77 Central European Journal of Energetic Materials, 205, 2(), 77-88 ISSN 2353-843 An Approxiate Model for the Theoretical Prediction
More informationBALLISTIC PENDULUM. EXPERIMENT: Measuring the Projectile Speed Consider a steel ball of mass
BALLISTIC PENDULUM INTRODUCTION: In this experient you will use the principles of conservation of oentu and energy to deterine the speed of a horizontally projected ball and use this speed to predict the
More informationPhysics 201, Lecture 15
Physics 0, Lecture 5 Today s Topics q More on Linear Moentu And Collisions Elastic and Perfect Inelastic Collision (D) Two Diensional Elastic Collisions Exercise: Billiards Board Explosion q Multi-Particle
More informationMassachusetts Institute of Technology Quantum Mechanics I (8.04) Spring 2005 Solutions to Problem Set 4
Massachusetts Institute of Technology Quantu Mechanics I (8.04) Spring 2005 Solutions to Proble Set 4 By Kit Matan 1. X-ray production. (5 points) Calculate the short-wavelength liit for X-rays produced
More informationUSEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS. By: Ian Blokland, Augustana Campus, University of Alberta
1 USEFUL HINTS FOR SOLVING PHYSICS OLYMPIAD PROBLEMS By: Ian Bloland, Augustana Capus, University of Alberta For: Physics Olypiad Weeend, April 6, 008, UofA Introduction: Physicists often attept to solve
More informationToday s s topics are: Collisions and Momentum Conservation. Momentum Conservation
Today s s topics are: Collisions and P (&E) Conservation Ipulsive Force Energy Conservation How can we treat such an ipulsive force? Energy Conservation Ipulsive Force and Ipulse [Exaple] an ipulsive force
More informationANALYSIS OF HALL-EFFECT THRUSTERS AND ION ENGINES FOR EARTH-TO-MOON TRANSFER
IEPC 003-0034 ANALYSIS OF HALL-EFFECT THRUSTERS AND ION ENGINES FOR EARTH-TO-MOON TRANSFER A. Bober, M. Guelan Asher Space Research Institute, Technion-Israel Institute of Technology, 3000 Haifa, Israel
More informationCh 12: Variations on Backpropagation
Ch 2: Variations on Backpropagation The basic backpropagation algorith is too slow for ost practical applications. It ay take days or weeks of coputer tie. We deonstrate why the backpropagation algorith
More informationy scalar component x scalar component A. 770 m 250 m file://c:\users\joe\desktop\physics 2A\PLC Assignments - F10\2a_PLC7\index.
Page 1 of 6 1. A certain string just breaks when it is under 400 N of tension. A boy uses this string to whirl a 10-kg stone in a horizontal circle of radius 10. The boy continuously increases the speed
More informationPhysics 2107 Oscillations using Springs Experiment 2
PY07 Oscillations using Springs Experient Physics 07 Oscillations using Springs Experient Prelab Read the following bacground/setup and ensure you are failiar with the concepts and theory required for
More informationFigure 1: Equivalent electric (RC) circuit of a neurons membrane
Exercise: Leaky integrate and fire odel of neural spike generation This exercise investigates a siplified odel of how neurons spike in response to current inputs, one of the ost fundaental properties of
More informationSpine Fin Efficiency A Three Sided Pyramidal Fin of Equilateral Triangular Cross-Sectional Area
Proceedings of the 006 WSEAS/IASME International Conference on Heat and Mass Transfer, Miai, Florida, USA, January 18-0, 006 (pp13-18) Spine Fin Efficiency A Three Sided Pyraidal Fin of Equilateral Triangular
More informationQuantum Chemistry Exam 2 Take-home Solutions
Cheistry 60 Fall 07 Dr Jean M Standard Nae KEY Quantu Cheistry Exa Take-hoe Solutions 5) (0 points) In this proble, the nonlinear variation ethod will be used to deterine an approxiate solution for the
More informationTHE EFFECT OF SOLID PARTICLE SIZE UPON TIME AND SEDIMENTATION RATE
Bulletin of the Transilvania University of Braşov Series II: Forestry Wood Industry Agricultural Food Engineering Vol. 5 (54) No. 1-1 THE EFFECT OF SOLID PARTICLE SIZE UPON TIME AND SEDIMENTATION RATE
More informationDETECTION OF NONLINEARITY IN VIBRATIONAL SYSTEMS USING THE SECOND TIME DERIVATIVE OF ABSOLUTE ACCELERATION
DETECTION OF NONLINEARITY IN VIBRATIONAL SYSTEMS USING THE SECOND TIME DERIVATIVE OF ABSOLUTE ACCELERATION Masaki WAKUI 1 and Jun IYAMA and Tsuyoshi KOYAMA 3 ABSTRACT This paper shows a criteria to detect
More informationChemistry 432 Problem Set 11 Spring 2018 Solutions
1. Show that for an ideal gas Cheistry 432 Proble Set 11 Spring 2018 Solutions P V 2 3 < KE > where is the average kinetic energy of the gas olecules. P 1 3 ρ v2 KE 1 2 v2 ρ N V P V 1 3 N v2 2 3 N
More informationSome Perspective. Forces and Newton s Laws
Soe Perspective The language of Kineatics provides us with an efficient ethod for describing the otion of aterial objects, and we ll continue to ake refineents to it as we introduce additional types of
More informationName Class Date. two objects depends on the masses of the objects.
CHAPTER 12 2 Gravity SECTION Forces KEY IDEAS As you read this section keep these questions in ind: What is free fall? How are weight and ass related? How does gravity affect the otion of objects? What
More informationPY /005 Practice Test 1, 2004 Feb. 10
PY 205-004/005 Practice Test 1, 2004 Feb. 10 Print nae Lab section I have neither given nor received unauthorized aid on this test. Sign ature: When you turn in the test (including forula page) you ust
More informationCOULD A VARIABLE MASS OSCILLATOR EXHIBIT THE LATERAL INSTABILITY?
Kragujevac J. Sci. 3 (8) 3-44. UDC 53.35 3 COULD A VARIABLE MASS OSCILLATOR EXHIBIT THE LATERAL INSTABILITY? Nebojša Danilović, Milan Kovačević and Vukota Babović Institute of Physics, Faculty of Science,
More informationTake-Home Midterm Exam #2, Part A
Physics 151 Due: Friday, March 20, 2009 Take-Hoe Midter Exa #2, Part A Roster No.: Score: NO exa tie liit. Calculator required. All books and notes are allowed, and you ay obtain help fro others. Coplete
More information2. What two units of measurement are necessary for describing speed? Ans. Distance and time.
Conceptual Physics-9 th edition Answers by R. E. Treblay Ch. 3 Pg.51 Review questions. What two units of easureent are necessary for describing speed? Ans. Distance and tie. 3. What kind of speed is registered
More informationThe ballistic pendulum
(ta initials) first nae (print) last nae (print) brock id (ab17cd) (lab date) Experient 4 The ballistic pendulu In this Experient you will learn how to deterine the speed of a projectile as well as the
More informationA Simplified Analytical Approach for Efficiency Evaluation of the Weaving Machines with Automatic Filling Repair
Proceedings of the 6th SEAS International Conference on Siulation, Modelling and Optiization, Lisbon, Portugal, Septeber -4, 006 0 A Siplified Analytical Approach for Efficiency Evaluation of the eaving
More informationDonald Fussell. October 28, Computer Science Department The University of Texas at Austin. Point Masses and Force Fields.
s Vector Moving s and Coputer Science Departent The University of Texas at Austin October 28, 2014 s Vector Moving s Siple classical dynaics - point asses oved by forces Point asses can odel particles
More informationQuestion 1. [14 Marks]
6 Question 1. [14 Marks] R r T! A string is attached to the dru (radius r) of a spool (radius R) as shown in side and end views here. (A spool is device for storing string, thread etc.) A tension T is
More informationPhysics 41 HW Set 1 Chapter 15 Serway 7 th Edition
Physics HW Set Chapter 5 Serway 7 th Edition Conceptual Questions:, 3, 5,, 6, 9 Q53 You can take φ = π, or equally well, φ = π At t= 0, the particle is at its turning point on the negative side of equilibriu,
More informationAnalysis of Impulsive Natural Phenomena through Finite Difference Methods A MATLAB Computational Project-Based Learning
Analysis of Ipulsive Natural Phenoena through Finite Difference Methods A MATLAB Coputational Project-Based Learning Nicholas Kuia, Christopher Chariah, Mechatronics Engineering, Vaughn College of Aeronautics
More informationExplicit Analytic Solution for an. Axisymmetric Stagnation Flow and. Heat Transfer on a Moving Plate
Int. J. Contep. Math. Sciences, Vol. 5,, no. 5, 699-7 Explicit Analytic Solution for an Axisyetric Stagnation Flow and Heat Transfer on a Moving Plate Haed Shahohaadi Mechanical Engineering Departent,
More informationUNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics
UNIVERSITY OF SASKATCHEWAN Departent of Physics and Engineering Physics 05 Saskatchewan High School Physics Scholarship Copetition May, 05 Tie allowed: 90 inutes This copetition is based on the Saskatchewan
More informationSRI LANKAN PHYSICS OLYMPIAD MULTIPLE CHOICE TEST 30 QUESTIONS ONE HOUR AND 15 MINUTES
SRI LANKAN PHYSICS OLYMPIAD - 5 MULTIPLE CHOICE TEST QUESTIONS ONE HOUR AND 5 MINUTES INSTRUCTIONS This test contains ultiple choice questions. Your answer to each question ust be arked on the answer sheet
More informationASSIGNMENT BOOKLET Bachelor s Degree Programme (B.Sc./B.A./B.Com.) MATHEMATICAL MODELLING
ASSIGNMENT BOOKLET Bachelor s Degree Prograe (B.Sc./B.A./B.Co.) MTE-14 MATHEMATICAL MODELLING Valid fro 1 st January, 18 to 1 st Deceber, 18 It is copulsory to subit the Assignent before filling in the
More informationReading from Young & Freedman: For this topic, read the introduction to chapter 25 and sections 25.1 to 25.3 & 25.6.
PHY10 Electricity Topic 6 (Lectures 9 & 10) Electric Current and Resistance n this topic, we will cover: 1) Current in a conductor ) Resistivity 3) Resistance 4) Oh s Law 5) The Drude Model of conduction
More informationPhysically Based Modeling CS Notes Spring 1997 Particle Collision and Contact
Physically Based Modeling CS 15-863 Notes Spring 1997 Particle Collision and Contact 1 Collisions with Springs Suppose we wanted to ipleent a particle siulator with a floor : a solid horizontal plane which
More informationCOS 424: Interacting with Data. Written Exercises
COS 424: Interacting with Data Hoework #4 Spring 2007 Regression Due: Wednesday, April 18 Written Exercises See the course website for iportant inforation about collaboration and late policies, as well
More information2.003 Engineering Dynamics Problem Set 2 Solutions
.003 Engineering Dynaics Proble Set Solutions This proble set is priarily eant to give the student practice in describing otion. This is the subject of kineatics. It is strongly recoended that you study
More informationLecture #8-3 Oscillations, Simple Harmonic Motion
Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.
More informationUNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics
UNIVERSITY OF SASKATCHEWAN Departent of Physics and Engineering Physics 017 Saskatchewan High School Physics Scholarship Copetition Wednesday May 10, 017 Tie allowed: 90 inutes This copetition is based
More informationOcean 420 Physical Processes in the Ocean Project 1: Hydrostatic Balance, Advection and Diffusion Answers
Ocean 40 Physical Processes in the Ocean Project 1: Hydrostatic Balance, Advection and Diffusion Answers 1. Hydrostatic Balance a) Set all of the levels on one of the coluns to the lowest possible density.
More informationm A 1 m mgd k m v ( C) AP Physics Multiple Choice Practice Oscillations
P Physics Multiple Choice Practice Oscillations. ass, attached to a horizontal assless spring with spring constant, is set into siple haronic otion. Its axiu displaceent fro its equilibriu position is.
More informationNB1140: Physics 1A - Classical mechanics and Thermodynamics Problem set 2 - Forces and energy Week 2: November 2016
NB1140: Physics 1A - Classical echanics and Therodynaics Proble set 2 - Forces and energy Week 2: 21-25 Noveber 2016 Proble 1. Why force is transitted uniforly through a assless string, a assless spring,
More informationKinematics and dynamics, a computational approach
Kineatics and dynaics, a coputational approach We begin the discussion of nuerical approaches to echanics with the definition for the velocity r r ( t t) r ( t) v( t) li li or r( t t) r( t) v( t) t for
More information1 (40) Gravitational Systems Two heavy spherical (radius 0.05R) objects are located at fixed positions along
(40) Gravitational Systes Two heavy spherical (radius 0.05) objects are located at fixed positions along 2M 2M 0 an axis in space. The first ass is centered at r = 0 and has a ass of 2M. The second ass
More information2. Which of the following best describes the relationship between force and potential energy?
Work/Energy with Calculus 1. An object oves according to the function x = t 5/ where x is the distance traveled and t is the tie. Its kinetic energy is proportional to (A) t (B) t 5/ (C) t 3 (D) t 3/ (E)
More informationPHY307F/407F - Computational Physics Background Material for Expt. 3 - Heat Equation David Harrison
INTRODUCTION PHY37F/47F - Coputational Physics Background Material for Expt 3 - Heat Equation David Harrison In the Pendulu Experient, we studied the Runge-Kutta algorith for solving ordinary differential
More informationPhys101 Lectures 13, 14 Momentum and Collisions
Phs0 Lectures 3, 4 Moentu and ollisions Ke points: Moentu and ipulse ondition for conservation of oentu and wh How to solve collision probles entre of ass Ref: 7-,,3,4,5,6,7,8,9,0. Page Moentu is a vector:
More informationPhysicsAndMathsTutor.com
. A raindrop falls vertically under gravity through a cloud. In a odel of the otion the raindrop is assued to be spherical at all ties and the cloud is assued to consist of stationary water particles.
More informatione-companion ONLY AVAILABLE IN ELECTRONIC FORM
OPERATIONS RESEARCH doi 10.1287/opre.1070.0427ec pp. ec1 ec5 e-copanion ONLY AVAILABLE IN ELECTRONIC FORM infors 07 INFORMS Electronic Copanion A Learning Approach for Interactive Marketing to a Custoer
More informationEULER EQUATIONS. We start by considering how time derivatives are effected by rotation. Consider a vector defined in the two systems by
EULER EQUATIONS We now consider another approach to rigid body probles based on looking at the change needed in Newton s Laws if an accelerated coordinate syste is used. We start by considering how tie
More informationQ5 We know that a mass at the end of a spring when displaced will perform simple m harmonic oscillations with a period given by T = 2!
Chapter 4.1 Q1 n oscillation is any otion in which the displaceent of a particle fro a fixed point keeps changing direction and there is a periodicity in the otion i.e. the otion repeats in soe way. In
More informationUNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics
UNIVERSITY OF SASKATCHEWAN Departent of Physics and Engineering Physics Physics 115.3 MIDTERM TEST October 22, 2008 Tie: 90 inutes NAME: (Last) Please Print (Given) STUDENT NO.: LECTURE SECTION (please
More informationSupervised assessment: Modelling and problem-solving task
Matheatics C 2008 Saple assessent instruent and indicative student response Supervised assessent: Modelling and proble-solving tas This saple is intended to infor the design of assessent instruents in
More informationNumerical Solution of the MRLW Equation Using Finite Difference Method. 1 Introduction
ISSN 1749-3889 print, 1749-3897 online International Journal of Nonlinear Science Vol.1401 No.3,pp.355-361 Nuerical Solution of the MRLW Equation Using Finite Difference Method Pınar Keskin, Dursun Irk
More information3.2 Projectile Motion
Motion in 2-D: Last class we were analyzing the distance in two-dimensional motion and revisited the concept of vectors, and unit-vector notation. We had our receiver run up the field then slant Northwest.
More informationWhen we throw a ball :
PROJECTILE MOTION When we throw a ball : There is a constant velocity horizontal motion And there is an accelerated vertical motion These components act independently of each other PROJECTILE MOTION A
More informationExplicit Approximate Solution for Finding the. Natural Frequency of the Motion of Pendulum. by Using the HAM
Applied Matheatical Sciences Vol. 3 9 no. 1 13-13 Explicit Approxiate Solution for Finding the Natural Frequency of the Motion of Pendulu by Using the HAM Ahad Doosthoseini * Mechanical Engineering Departent
More informationProblem T1. Main sequence stars (11 points)
Proble T1. Main sequence stars 11 points Part. Lifetie of Sun points i..7 pts Since the Sun behaves as a perfectly black body it s total radiation power can be expressed fro the Stefan- Boltzann law as
More informationChapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant
Chapter 7 Ipulse and Moentu So far we considered only constant force/s BUT There are any situations when the force on an object is not constant Force varies with tie 7. The Ipulse-Moentu Theore DEFINITION
More information= T. Oscillations and Waves. Example of an Oscillating System IB 12 IB 12
Oscillation: the vibration of an object Oscillations and Waves Eaple of an Oscillating Syste A ass oscillates on a horizontal spring without friction as shown below. At each position, analyze its displaceent,
More informationma x = -bv x + F rod.
Notes on Dynaical Systes Dynaics is the study of change. The priary ingredients of a dynaical syste are its state and its rule of change (also soeties called the dynaic). Dynaical systes can be continuous
More informationPeriodic Motion is everywhere
Lecture 19 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand and use energy conservation
More informationPhysics 140 D100 Midterm Exam 2 Solutions 2017 Nov 10
There are 10 ultiple choice questions. Select the correct answer for each one and ark it on the bubble for on the cover sheet. Each question has only one correct answer. (2 arks each) 1. An inertial reference
More informationThe Euler-Maclaurin Formula and Sums of Powers
DRAFT VOL 79, NO 1, FEBRUARY 26 1 The Euler-Maclaurin Forula and Sus of Powers Michael Z Spivey University of Puget Sound Tacoa, WA 98416 spivey@upsedu Matheaticians have long been intrigued by the su
More informationPhysics 11 HW #6 Solutions
Physics HW #6 Solutions Chapter 6: Focus On Concepts:,,, Probles: 8, 4, 4, 43, 5, 54, 66, 8, 85 Focus On Concepts 6- (b) Work is positive when the orce has a coponent in the direction o the displaceent.
More informationTactics Box 2.1 Interpreting Position-versus-Time Graphs
1D kineatic Retake Assignent Due: 4:32p on Friday, October 31, 2014 You will receive no credit for ites you coplete after the assignent is due. Grading Policy Tactics Box 2.1 Interpreting Position-versus-Tie
More informationThe ballistic pendulum
(ta initials) first nae (print) last nae (print) brock id (ab17cd) (lab date) Experient 3 The ballistic pendulu Prelab preparation Print a copy of this experient to bring to your scheduled lab session.
More information6.2 Grid Search of Chi-Square Space
6.2 Grid Search of Chi-Square Space exaple data fro a Gaussian-shaped peak are given and plotted initial coefficient guesses are ade the basic grid search strateg is outlined an actual anual search is
More informationName: Partner(s): Date: Angular Momentum
Nae: Partner(s): Date: Angular Moentu 1. Purpose: In this lab, you will use the principle of conservation of angular oentu to easure the oent of inertia of various objects. Additionally, you develop a
More informationChapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant
Chapter 7 Ipulse and Moentu So far we considered only constant force/s BUT There are any situations when the force on an object is not constant JUST IN TIME TEACHING E-ail or bring e your questions prior
More information2. Electric Current. E.M.F. of a cell is defined as the maximum potential difference between the two electrodes of the
2. Electric Current The net flow of charges through a etallic wire constitutes an electric current. Do you know who carries current? Current carriers In solid - the electrons in outerost orbit carries
More informationMomentum. Conservation of Linear Momentum. Slide 1 / 140 Slide 2 / 140. Slide 3 / 140. Slide 4 / 140. Slide 6 / 140. Slide 5 / 140.
Slide 1 / 140 Slide 2 / 140 Moentu www.njctl.org Slide 3 / 140 Slide 4 / 140 Table of Contents Click on the topic to go to that section Conservation of Linear Moentu Ipulse - Moentu Equation Collisions
More informationMonitoring and system identification of suspension bridges: An alternative approach
Monitoring and syste identification of suspension bridges: An alternative approach Erdal Şafak Boğaziçi University, Kandilli Observatory and Earthquake Reseach Institute, Istanbul, Turkey Abstract This
More informationProjectile Motion. Chin- Sung Lin STEM GARAGE SCIENCE PHYSICS
Projectile Motion Chin- Sung Lin Introduction to Projectile Motion q What is Projectile Motion? q Trajectory of a Projectile q Calculation of Projectile Motion Introduction to Projectile Motion q What
More informationSIMPLE HARMONIC MOTION: NEWTON S LAW
SIMPLE HARMONIC MOTION: NEWTON S LAW siple not siple PRIOR READING: Main 1.1, 2.1 Taylor 5.1, 5.2 http://www.yoops.org/twocw/it/nr/rdonlyres/physics/8-012fall-2005/7cce46ac-405d-4652-a724-64f831e70388/0/chp_physi_pndul.jpg
More informationP235 Midterm Examination Prof. Cline
P235 Mier Exaination Prof. Cline THIS IS A CLOSED BOOK EXAMINATION. Do all parts of all four questions. Show all steps to get full credit. 7:00-10.00p, 30 October 2009 1:(20pts) Consider a rocket fired
More informationPH 221-1D Spring Oscillations. Lectures Chapter 15 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)
PH 1-1D Spring 013 Oscillations Lectures 35-37 Chapter 15 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 15 Oscillations In this chapter we will cover the following topics: Displaceent,
More informationCOMPONENT MODE SYNTHESIS, FIXED-INTERFACE MODEL Revision A
COMPONEN MODE SYNHESS, FXED-NERFACE MODEL Revision A By o rvine Eail: toirvine@aol.co February, ntroduction Coponent ode synthesis is a ethod for analyzing the dynaic behavior of a syste consisting of
More informationPhysics 2210 Fall smartphysics 20 Conservation of Angular Momentum 21 Simple Harmonic Motion 11/23/2015
Physics 2210 Fall 2015 sartphysics 20 Conservation of Angular Moentu 21 Siple Haronic Motion 11/23/2015 Exa 4: sartphysics units 14-20 Midter Exa 2: Day: Fri Dec. 04, 2015 Tie: regular class tie Section
More informationMAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START
Laboratory Section: Last Revised on Deceber 15, 2014 Partners Naes: Grade: EXPERIMENT 8 Electron Beas 0. Pre-Laboratory Work [2 pts] 1. Nae the 2 forces that are equated in order to derive the charge to
More informationI. Understand get a conceptual grasp of the problem
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departent o Physics Physics 81T Fall Ter 4 Class Proble 1: Solution Proble 1 A car is driving at a constant but unknown velocity,, on a straightaway A otorcycle is
More information821. Study on analysis method for deepwater TTR coupled vibration of parameter vibration and vortex-induced vibration
81. Study on analysis ethod for deepwater TTR coupled vibration of paraeter vibration and vortex-induced vibration Wu Xue-Min 1, Huang Wei-Ping Shandong Key aboratory of Ocean Engineering, Ocean University
More informationEgyptian Mathematics Problem Set
(Send corrections to cbruni@uwaterloo.ca) Egyptian Matheatics Proble Set (i) Use the Egyptian area of a circle A = (8d/9) 2 to copute the areas of the following circles with given diaeter. d = 2. d = 3
More informationDefinition of Work, The basics
Physics 07 Lecture 16 Lecture 16 Chapter 11 (Work) v Eploy conservative and non-conservative forces v Relate force to potential energy v Use the concept of power (i.e., energy per tie) Chapter 1 v Define
More information(Newton s 2 nd Law for linear motion)
PHYSICS 3 Final Exaination ( Deeber Tie liit 3 hours Answer all 6 questions You and an assistant are holding the (opposite ends of a long plank when oops! the butterfingered assistant drops his end If
More informationHonors Lab 4.5 Freefall, Apparent Weight, and Friction
Nae School Date Honors Lab 4.5 Freefall, Apparent Weight, and Friction Purpose To investigate the vector nature of forces To practice the use free-body diagras (FBDs) To learn to apply Newton s Second
More informationProjectile Motion Lab Report
Projectile Motion Lab Report Yadesh Prashad, Tiothy Yang, Saad Salee, Mai Wageh, Thanoja Gnanatheeva M r. M u r z a k u N o v e b e r 1 1 t h, 2 0 1 1 Using a Projectile Launcher to Verify that Increasing
More informationEnergy and Momentum: The Ballistic Pendulum
Physics Departent Handout -10 Energy and Moentu: The Ballistic Pendulu The ballistic pendulu, first described in the id-eighteenth century, applies principles of echanics to the proble of easuring the
More informationNewton's Laws. Lecture 2 Key Concepts. Newtonian mechanics and relation to Kepler's laws The Virial Theorem Tidal forces Collision physics
Lecture 2 Key Concepts Newtonian echanics and relation to Kepler's laws The Virial Theore Tidal forces Collision physics Newton's Laws 1) An object at rest will reain at rest and an object in otion will
More informationP (t) = P (t = 0) + F t Conclusion: If we wait long enough, the velocity of an electron will diverge, which is obviously impossible and wrong.
4 Phys520.nb 2 Drude theory ~ Chapter in textbook 2.. The relaxation tie approxiation Here we treat electrons as a free ideal gas (classical) 2... Totally ignore interactions/scatterings Under a static
More informationPhysics 207 Lecture 18. Physics 207, Lecture 18, Nov. 3 Goals: Chapter 14
Physics 07, Lecture 18, Nov. 3 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand
More informationRelativity and Astrophysics Lecture 25 Terry Herter. Momenergy Momentum-energy 4-vector Magnitude & components Invariance Low velocity limit
Mo Mo Relativity and Astrophysics Lecture 5 Terry Herter Outline Mo Moentu- 4-vector Magnitude & coponents Invariance Low velocity liit Concept Suary Reading Spacetie Physics: Chapter 7 Hoework: (due Wed.
More informationFOUNDATION STUDIES EXAMINATIONS January 2016
1 FOUNDATION STUDIES EXAMINATIONS January 2016 PHYSICS Seester 2 Exa July Fast Track Tie allowed 2 hours for writing 10 inutes for reading This paper consists of 4 questions printed on 11 pages. PLEASE
More informationChapter 10 Atmospheric Forces & Winds
Chapter 10 Atospheric Forces & Winds Chapter overview: Atospheric Pressure o Horizontal pressure variations o Station vs sea level pressure Winds and weather aps Newton s 2 nd Law Horizontal Forces o Pressure
More informationCalculations Manual 5-1
Calculations Manual 5-1 Although you ay be anxious to begin building your rocket, soe iportant decisions need to be ade about launch conditions that can help ensure a ore accurate launch. Reeber: the goal
More informationPhysics 4A Solutions to Chapter 15 Homework
Physics 4A Solutions to Chapter 15 Hoework Chapter 15 Questions:, 8, 1 Exercises & Probles 6, 5, 31, 41, 59, 7, 73, 88, 90 Answers to Questions: Q 15- (a) toward -x (b) toward +x (c) between -x and 0 (d)
More informationPY241 Solutions Set 9 (Dated: November 7, 2002)
PY241 Solutions Set 9 (Dated: Noveber 7, 2002) 9-9 At what displaceent of an object undergoing siple haronic otion is the agnitude greatest for the... (a) velocity? The velocity is greatest at x = 0, the
More information