PHY2053 Lecture 11 Conservation of Energy. Conservation of Energy Kinetic Energy Gravitational Potential Energy
|
|
- Ethel Lloyd
- 6 years ago
- Views:
Transcription
1 PHY2053 Lecture 11 Conservation of Energy Conservation of Energy Kinetic Energy Gravitational Potential Energy
2 Symmetries in Physics Symmetry - fundamental / descriptive property of the Universe itself [ vacuum ] Colloquial: Symmetric Laws of Physics are the same at any point in space [ translational invariance ] Conservation of Momentum [Ch 7] Laws of Physics are the same at any point in time [ time invariance ] Conservation of Energy [today s lecture] Physics term: Parity 2
3 More practical aspect there are different, mathematically equivalent ways to formulate Newton s laws all these calculations predict certain quantities will be conserved for a closed system (0 net external force) energy, momentum, angular momentum.. existence of conserved quantities simplifies otherwise complicated calculations Key concepts: learn to recognize and exploit conserved quantities conserved quantities derived from Newton s laws solutions immediately satisfy Newton s laws 3
4 Energy Conservation term closed system means: no net external force is acting upon any element of the system The total energy of a closed system does not change over time: total energy before = total energy after textbook implies that the Universe is a closed system The total energy in the Universe is unchanged by any physical process next: define change of energy (work), energy itself 4
5 Concept of Work colloquial meaning of work: effort which produces a result. analogy in terms of mechanics: Effort Force, F Result Displacement r interested in displacement due to force F θ r W = F r cos( ) angular term cos(θ) projects force displacement SI unit: Joule [ J ]; relation to calorie: 1 cal = 4.2 J 5
6 Work: signed scalar quantity Work can be positive, negative, and zero depending on the orientation of the force to the displacement F θ θ = 90 r F r F θ r θ < 90 cosθ > 0 W > 0 θ = 90 cosθ = 0 W = 0 θ > 90 cosθ < 0 W < 0 6
7 Total Work in a Closed System start with total work on a particular object i W i = i F i r cos( i )= recall the definition of a closed system i F i =0 r i vector sum, has to be zero in all directions i F i cos( i ) F i cos( i )=0 i W i = r i F i cos( i ) =0 7
8 Kinetic Energy, Definition consider impact of work on the velocity of an! object start from 1D motion, works in all three (x, y, z) W = F x x = ma x x a x x = v2 f,x W = ma x x = m v2 f,x v 2 i,x 2! 2 = m v2 f,x 2 v 2 i,x! 2 m v2 i,x 2 K = m v2 2 v 2 W = K f K i = K Work Energy Theorem 8
9 Example #1: Mass Driver A mass driver is a device which uses magnetic fields to accelerate a container (mass). Predicted commercial uses include launching people and cargo to bases on the Moon. The common way to specify mass drivers is to quote the kinetic energy that an object will have when leaving the driver, if it started from rest. For a 1 MJ mass driver, compute the muzzle velocity of a) a 0.5 kg projectile b) a 50 kg projectile 9
10 Mass driver notes pt 1 10
11 Mass driver notes pt 2 11
12 Gravitational Potential Energy Near Earth near Earth, the usual orientation of coordinate systems is so that the positive y axis points up the force of gravity has only one component, in the y-direction: Fy = mg only y displacement, y matters for computing work: W = FG,y y = mg y consider a vertical shot upwards, vf = 0 W = K = Kf Ki = 0 ½mvf 2, also = mg y gravity did negative work, removing kinetic energy 12
13 Energy Conservation Law where did the kinetic energy go? temporarily stored in gravitational field define potential energy Ugrav = Wgrav = mg y computes how much kinetic energy could be released if we let gravity work across y work-energy theorem: W = K; K W = 0 K + U = 0 ( K + U ) = 0 sum of kinetic and potential energy does not change define E = K + U, then E is constant in time 13
14 Choice of Zero Point, Near Earth Due to conservation of energy, only changes in potential energy are really relevant for kinematics The absolute value of potential energy at a point in space is arbitrary - up to an additive constant We have the freedom to pick a convenient point in space and declare that the potential energy at that point equals 0 J All other potential energies are then computed relative to that point, based on U = U(y) U(0) U(y) = U + U(0) = mg y + 0 = mg (y 0) 14
15 Example #1: Rollercoaster A roller-coaster is barely moving as it starts down a ramp of height h. The first figure it encounters is a loop of radius R. How high must the ramp be so that the roller-coaster never loses contact with the rails? h R 15
16 Rollercoaster notes pt 1 16
17 Rollercoaster notes pt 2 Comment: Given that the total height of the loop is 2R, this is not really much taller than the loop itself. The ratio of the height of the ramp and the height of the loop is 2.5R / 2R = the ramp has to be only 25% taller than the loop for the rollercoaster to clear the highest point in the loop and stay in contact with the rails. 17
18 More Realistic: Dissipative (Non-conservative) Forces friction converts mechanical energy into heat heat does not store mechanical energy therefore, there is no point in defining a heat or frictional potential energy friction always opposes motion, so Wfriction < 0 extend the law of energy conservation to account for non-conservative forces: (Ki + Ui) + WNC = (Kf + Uf) 18
19 Gravitational Potential Energy, Planetary Scales derivation requires math beyond baseline calculus U grav = G m 1 m 2 for gravitational potential at planetary scales, there already exists a usual convention: potential energy infinitely far away from a planet is = 0 convention: an object with positive total energy can escape a planet (will not fall back to the planet) allows easy computation of escape velocities for objects starting from any R from the planet s center r 19
20 Example #2: Hyperbolic Comet A comet not bound to the Sun will only pass by the Sun once. It will trace a hyperbolic trajectory through the Solar system. Compute the minimum velocity of a hyperbolic comet when it is roughly 1 A.U. away from the Sun. The mass of the Sun is MS = kg. 1 Astronomical Unit is the distance from the Earth to the Sun, 150 million km. Does the velocity depend on the mass of the comet? 20
21 Hyperbolic Comet notes 21
22 Next Lecture: Hooke s Law, Elastic Potential Energy Power
Chapter 5 Gravitation Chapter 6 Work and Energy
Chapter 5 Gravitation Chapter 6 Work and Energy Chapter 5 (5.6) Newton s Law of Universal Gravitation (5.7) Gravity Near the Earth s Surface Chapter 6 (today) Work Done by a Constant Force Kinetic Energy,
More informationIn vertical circular motion the gravitational force must also be considered.
Vertical Circular Motion In vertical circular motion the gravitational force must also be considered. An example of vertical circular motion is the vertical loop-the-loop motorcycle stunt. Normally, the
More informationAstro Lecture 12. Energy and Gravity (Cont d) 13/02/09 Habbal Astro Lecture 12 1
Astro 110-01 Lecture 12 Energy and Gravity (Cont d) 13/02/09 Habbal Astro110-01 Lecture 12 1 Energy due to movement of Kinetic Energy: object E k = ½ m v 2 13/02/09 Habbal Astro110-01 Lecture 12 2 Gravitational
More informationEnergy Problem Solving Techniques.
1 Energy Problem Solving Techniques www.njctl.org 2 Table of Contents Introduction Gravitational Potential Energy Problem Solving GPE, KE and EPE Problem Solving Conservation of Energy Problem Solving
More informationStudy of work done by a variable force. Overview of energy. Study of work done by a constant force. Understanding of energy conservation.
Chap. 7: Work and Energy Overview of energy. Study of work done by a constant force as defined in physics. Relation between work and kinetic energy. Study of work done by a variable force. Study of potential
More informationOther Examples of Energy Transfer
Chapter 7 Work and Energy Overview energy. Study work as defined in physics. Relate work to kinetic energy. Consider work done by a variable force. Study potential energy. Understand energy conservation.
More informationAP Physics C - Mechanics
Slide 1 / 84 Slide 2 / 84 P Physics C - Mechanics Energy Problem Solving Techniques 2015-12-03 www.njctl.org Table of Contents Slide 3 / 84 Introduction Gravitational Potential Energy Problem Solving GPE,
More informationChapter 5 Work and Energy
Chapter 5 Work and Energy Work and Kinetic Energy Work W in 1D Motion: by a Constant orce by a Varying orce Kinetic Energy, KE: the Work-Energy Theorem Mechanical Energy E and Its Conservation Potential
More informationPhysics 100A Summer 2016 Chapter 8
Physics 00A Summer 06 Chapter 8 Solutions are provided only for problems from your textbook. The other problems already have so much guidance and notes that you should be able to understand where you have
More informationToday. Laws of Motion. Conservation Laws. Gravity. tides
Today Laws of Motion Conservation Laws Gravity tides Newton s Laws of Motion Our goals for learning: Newton s three laws of motion Universal Gravity How did Newton change our view of the universe? He realized
More informationChapter 8. Dynamics II: Motion in a Plane
Chapter 8. Dynamics II: Motion in a Plane Chapter Goal: To learn how to solve problems about motion in a plane. Slide 8-2 Chapter 8 Preview Slide 8-3 Chapter 8 Preview Slide 8-4 Chapter 8 Preview Slide
More informationMore examples: Summary of previous lecture
More examples: 3 N Individual Forces Net Force 5 N 37 o 4 N Summary of previous lecture 1 st Law A net non zero force is required to change the velocity of an object. nd Law What happens when there is
More informationRecall: Gravitational Potential Energy
Welcome back to Physics 15 Today s agenda: Work Power Physics 15 Spring 017 Lecture 10-1 1 Recall: Gravitational Potential Energy For an object of mass m near the surface of the earth: U g = mgh h is height
More informationGame Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost
Game and Media Technology Master Program - Utrecht University Dr. Nicolas Pronost Essential physics for game developers Introduction The primary issues Let s move virtual objects Kinematics: description
More information4.3 Conservation Laws in Astronomy
4.3 Conservation Laws in Astronomy Our goals for learning: Why do objects move at constant velocity if no force acts on them? What keeps a planet rotating and orbiting the Sun? Where do objects get their
More informationChapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Copyright 2009 Pearson Education, Inc.
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves speed = distance time
More informationPhysics 110 Homework Solutions Week #5
Physics 110 Homework Solutions Week #5 Wednesday, October 7, 009 Chapter 5 5.1 C 5. A 5.8 B 5.34. A crate on a ramp a) x F N 15 F 30 o mg Along the x-axis we that F net = ma = Fcos15 mgsin30 = 500 cos15
More informationPHY 101. Work and Kinetic Energy 7.1 Work Done by a Constant Force
PHY 101 DR M. A. ELERUJA KINETIC ENERGY AND WORK POTENTIAL ENERGY AND CONSERVATION OF ENERGY CENTRE OF MASS AND LINEAR MOMENTUM Work is done by a force acting on an object when the point of application
More informationForces. Dynamics FORCEMAN
1 Forces Dynamics FORCEMAN 2 What causes things to move? Forces What is a force? A push or a pull that one body exerts on another. 3 Balanced No change in motion 4 5 Unbalanced If the forces acting on
More informationPHYSICS. Chapter 8 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 8 Lecture RANDALL D. KNIGHT Chapter 8. Dynamics II: Motion in a Plane IN THIS CHAPTER, you will learn to solve problems about motion
More informationAP Physics 1. 2 Dimensional Work and Energy.
1 AP Physics 1 2 Dimensional Work and Energy 2016 05 12 www.njctl.org 2 Table of Contents Click on the topic to go to that section Review of One Dimensional Forces, Work and Energy Two Dimensional Forces
More informationPhysics 2211 ABC Quiz #4 Solutions Spring 2017
Physics 22 ABC Quiz #4 Solutions Spring 207 I. (6 points) Corentine is driving her car of mass m around a curve when suddenly, all systems fail! The engine quits, she can t brake, she can t steer, and
More informationChapter 6 Work and Energy
Chapter 6 Work and Energy Units of Chapter 6 Work Done by a Constant Force Work Done by a Varying Force Kinetic Energy, and the Work-Energy Principle Potential Energy Conservative and Nonconservative Forces
More informationUniversal gravitation
Universal gravitation Physics 211 Syracuse University, Physics 211 Spring 2015 Walter Freeman February 22, 2017 W. Freeman Universal gravitation February 22, 2017 1 / 14 Announcements Extra homework help
More informationGeneral Physics (PHY 2130)
General Physics (PHY 130) Lecture 0 Rotational dynamics equilibrium nd Newton s Law for rotational motion rolling Exam II review http://www.physics.wayne.edu/~apetrov/phy130/ Lightning Review Last lecture:
More informationChapter 5: Energy. Energy is one of the most important concepts in the world of science. Common forms of Energy
Chapter 5: Energy Energy is one of the most important concepts in the world of science. Common forms of Energy Mechanical Chemical Thermal Electromagnetic Nuclear One form of energy can be converted to
More informationMidterm 3 Thursday April 13th
Welcome back to Physics 215 Today s agenda: rolling friction & review Newtonian gravity Planetary orbits Gravitational Potential Energy Physics 215 Spring 2017 Lecture 13-1 1 Midterm 3 Thursday April 13th
More informationToday: Work, Kinetic Energy, Potential Energy. No Recitation Quiz this week
Today: Work, Kinetic Energy, Potential Energy HW #4 due Thursday, 11:59 p.m. pm No Recitation Quiz this week 1 What is Energy? Mechanical Electromagnetic PHY 11 PHY 13 Chemical CHE 105 Nuclear PHY 555
More informationPhys101 Lectures 9 and 10 Conservation of Mechanical Energy
Phys101 Lectures 9 and 10 Conservation of Mechanical Energy Key points: Conservative and Nonconservative Forces Potential Energy Generalized work-energy principle Mechanical Energy and Its Conservation
More informationRegular Physics Semester 1
Regular Physics Semester 1 1.1.Can define major components of the scientific method 1.2.Can accurately carry out conversions using dimensional analysis 1.3.Can utilize and convert metric prefixes 1.4.Can
More informationLecture 11. Impulse/Momentum. Conservation of Momentum. Cutnell+Johnson: Impulse and Momentum
Lecture 11 Impulse/Momentum Conservation of Momentum Cutnell+Johnson: 7.1-7.3 Impulse and Momentum We learned about work, which is the force times distance (times the cosine of the angle in between the
More information4) Vector = and vector = What is vector = +? A) B) C) D) E)
1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In
More informationChapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Copyright 2012 Pearson Education, Inc.
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 1 4.1 Describing Motion: Examples from Everyday Life Our goals for learning: How do we describe motion? How is mass different
More information9/13/ Describing Motion: Examples from Everyday Life. Chapter 4: Making Sense of the Universe Understanding Motion, Energy, and Gravity
9/13/17 Lecture Outline 4.1 Describing Motion: Examples from Everyday Life Chapter 4: Making Sense of the Universe Understanding Motion, Energy, and Gravity Our goals for learning: How do we describe motion?
More informationPHYSICS. Chapter 13 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 13 Lecture RANDALL D. KNIGHT Chapter 13 Newton s Theory of Gravity IN THIS CHAPTER, you will learn to understand the motion of satellites
More informationOutline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy. Hello!
PHY131H1F - Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe
More informationAdios Cassini! Crashed into Saturn 9/15/17 after 20 years in space. https://saturn.jpl.nasa.gov/mission/grand-finale/overview/
Adios Cassini! Crashed into Saturn 9/15/17 after 20 years in space https://saturn.jpl.nasa.gov/mission/grand-finale/overview/ Laws of Motion Conservation Laws Gravity tides Today Why are astronauts weightless
More informationElectricity and Magnetism. Electric Potential Energy and Voltage
Electricity and Magnetism Electric Potential Energy and Voltage Work and Potential Energy Recall from Mechanics that E mech = K + U is a conserved quantity for particles that interact via conservative
More informationPLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)
PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2) We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when
More informationWelcome back to Physics 215
Welcome back to Physics 215 Today s agenda: More rolling without slipping Newtonian gravity Planetary orbits Gravitational Potential Energy Physics 215 Spring 2018 Lecture 13-1 1 Rolling without slipping
More informationProgressive Science Initiative. Click to go to website:
Slide 1 / 140 New Jersey Center for Teaching and Learning Progressive Science Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and
More informationAnnouncements. 1. Do not bring the yellow equation sheets to the miderm. Idential sheets will be attached to the problems.
Announcements 1. Do not bring the yellow equation sheets to the miderm. Idential sheets will be attached to the problems. 2. Some PRS transmitters are missing. Please, bring them back! 1 Kinematics Displacement
More informationNewton s Laws of Motion
Chapter 4 Newton s Second Law: in vector form Newton s Laws of Motion σ റF = m റa in component form σ F x = ma x σ F y = ma y in equilibrium and static situations a x = 0; a y = 0 Strategy for Solving
More informationPH201 Chapter 7 Solutions
PH0 Chapter 7 Solutions 7.6. Set Up: Use W F s ( F cos ) s Calculate the work done by each force. In each case, identify the angle In part (d), the net work is the algebraic sum of the work done by each
More informationLecture PowerPoints. Chapter 6 Physics: Principles with Applications, 7 th edition Giancoli
Lecture PowerPoints Chapter 6 Physics: Principles with Applications, 7 th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching
More informationW = Fd cos θ. W = (75.0 N)(25.0 m) cos (35.0º) = 1536 J = J. W 2400 kcal =
8 CHAPTER 7 WORK, ENERGY, AND ENERGY RESOURCES generator does negative work on the briefcase, thus removing energy from it. The drawing shows the latter, with the force from the generator upward on the
More informationThe Cosmic Perspective Seventh Edition. Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Chapter 4 Lecture
Chapter 4 Lecture The Cosmic Perspective Seventh Edition Making Sense of the Universe: Understanding Motion, Energy, and Gravity 2014 Pearson Education, Inc. Making Sense of the Universe: Understanding
More information4.1 Describing Motion. How do we describe motion? Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion Our goals for learning: How do we describe motion? How is mass different from weight? How do we describe
More informationLecture Presentation. Chapter 6 Preview Looking Ahead. Chapter 6 Circular Motion, Orbits, and Gravity
Chapter 6 Preview Looking Ahead Lecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity Text: p. 160 Slide 6-2 Chapter 6 Preview Looking Back: Centripetal Acceleration In Section 3.8, you learned
More information(A) 10 m (B) 20 m (C) 25 m (D) 30 m (E) 40 m
PSI AP Physics C Work and Energy (Algebra Based) Multiple Choice Questions (use g = 10 m/s 2 ) 1. A student throws a ball upwards from the ground level where gravitational potential energy is zero. At
More informationWork changes Energy. Do Work Son!
1 Work changes Energy Do Work Son! 2 Do Work Son! 3 Work Energy Relationship 2 types of energy kinetic : energy of an object in motion potential: stored energy due to position or stored in a spring Work
More informationWork and Energy continued
Chapter 6 Work and Energy continued 6.2 The Work-Energy Theorem and Kinetic Energy Chapters 1 5 Motion equations were been developed, that relate the concepts of velocity, speed, displacement, time, and
More information/////// ///////////// Module ONE /////////////// ///////// Space
// // / / / / //// / ////// / /// / / // ///// ////// ////// Module ONE Space 1 Gravity Knowledge and understanding When you have finished this chapter, you should be able to: define weight as the force
More informationHow do we describe motion?
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion: Examples from Everyday Life Our goals for learning: How do we describe motion? How is mass different
More informationChapter 13. Gravitation. PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow
Chapter 13 Gravitation PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Next one week Today: Ch 13 Wed: Review of Ch 8-11, focusing
More informationAP Physics 1 Chapter 7 Circular Motion and Gravitation
AP Physics 1 Chapter 7 Circular Motion and Gravitation Chapter 7: Circular Motion and Angular Measure Gravitation Angular Speed and Velocity Uniform Circular Motion and Centripetal Acceleration Angular
More informationLecture I: Basic Physics
1 Velocity: Instantaneous change in position! = $% ' $& Suppose object position ( ) and constant velocity!. After time step +: ( ) + + + = ( ) + +! + ( ) = ( ) + + + ( ) + =! +.! is never constant in practice
More informationLecture 13 REVIEW. Physics 106 Spring What should we know? What should we know? Newton s Laws
Lecture 13 REVIEW Physics 106 Spring 2006 http://web.njit.edu/~sirenko/ What should we know? Vectors addition, subtraction, scalar and vector multiplication Trigonometric functions sinθ, cos θ, tan θ,
More informationDynamics. Dynamics of mechanical particle and particle systems (many body systems)
Dynamics Dynamics of mechanical particle and particle systems (many body systems) Newton`s first law: If no net force acts on a body, it will move on a straight line at constant velocity or will stay at
More informationLecture 15 - Orbit Problems
Lecture 15 - Orbit Problems A Puzzle... The ellipse shown below has one focus at the origin and its major axis lies along the x-axis. The ellipse has a semimajor axis of length a and a semi-minor axis
More informationEXAM 3 SOLUTIONS. NAME: SECTION: AU Username: Read each question CAREFULLY and answer all parts. Work MUST be shown to receive credit.
EXAM 3 SOLUTIONS NAME: SECTION: AU Username: Print your name: Printing your name above acknowledges that you are subject to the AU Academic Honesty Policy Instructions: Read each question CAREFULLY and
More informationThe Moon does not fall to Earth because
The Moon does not fall to Earth because 1. It is in Earth s gravitational field. 2. The net force on it is zero. 3. It is beyond the main pull of Earth s gravity. 4. It is being pulled by the Sun and planets
More informationConcepts in Physics. Friday, October 16th
1206 - Concepts in Physics Friday, October 16th Notes Assignment #4 due Wednesday, October 21 st in class (no later than noon) There are still assignments #1 and #2 in my office to be picked up... If you
More informationThe content contained in all sections of chapter 6 of the textbook is included on the AP Physics B exam.
WORK AND ENERGY PREVIEW Work is the scalar product of the force acting on an object and the displacement through which it acts. When work is done on or by a system, the energy of that system is always
More informationWhat are two forms of Potential Energy that we commonly use? Explain Conservation of Energy and how we utilize it for problem-solving technics.
Bell Ringer Define Kinetic Energy, Potential Energy, and Work. What are two forms of Potential Energy that we commonly use? Explain Conservation of Energy and how we utilize it for problem-solving technics.
More information2010 Pearson Education, Inc. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion: Examples from Daily Life Some of the topics we will explore: How do we describe motion? (Speed,
More informationChapter 12 Gravity. Copyright 2010 Pearson Education, Inc.
Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationPhysics 211 Week 5. Work and Kinetic Energy: Block on Ramp
Physics 211 Week 5 Work and Kinetic Energy: Block on Ramp A block starts with a speed of 15 m/s at the bottom of a ramp that is inclined at an angle of 30 o with the horizontal. The coefficient of kinetic
More informationPhys101 Lectures 9 and 10 Conservation of Mechanical Energy
Phys101 Lectures 9 and 10 Conservation of Mechanical Energy Key points: Conservative and Nonconservative Forces Potential Energy Generalized work-energy principle Mechanical Energy and Its Conservation
More informationAnnouncements 15 Oct 2013
Announcements 15 Oct 2013 1. While you re waiting for class to start, see how many of these blanks you can fill out. Tangential Accel.: Direction: Causes speed to Causes angular speed to Therefore, causes:
More informationPS113 Chapter 4 Forces and Newton s laws of motion
PS113 Chapter 4 Forces and Newton s laws of motion 1 The concepts of force and mass A force is described as the push or pull between two objects There are two kinds of forces 1. Contact forces where two
More informationNewton s Gravitational Law
1 Newton s Gravitational Law Gravity exists because bodies have masses. Newton s Gravitational Law states that the force of attraction between two point masses is directly proportional to the product of
More informationLECTURE 18: Uniform Circular Motion (UCM)
Lectures Page 1 LECTURE 18: Uniform Circular Motion (UCM) Select LEARNING OBJECTIVES: i. ii. iii. iv. v. vi. vii. viii. ix. x. xi. xii. xiii. xiv. xv. Understand the definition of UCM, specifically that
More informationAngle recap. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration:
Angle recap Angular position: Angular displacement: s Angular velocity: Angular Acceleration: Every point on a rotating rigid object has the same angular, but not the same linear motion! Today s lecture
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued Clicker Question 4.3 A mass at rest on a ramp. How does the friction between the mass and the table know how much force will EXACTLY balance the gravity
More informationPhysics Unit 4:Work & Energy Name:
Name: Review and Preview We have come a long way in our study of mechanics. We started with the concepts of displacement and time, and built up to the more complex quantities of velocity and acceleration.
More informationME 230 Kinematics and Dynamics
ME 230 Kinematics and Dynamics Wei-Chih Wang Department of Mechanical Engineering University of Washington Lecture 8 Kinetics of a particle: Work and Energy (Chapter 14) - 14.1-14.3 W. Wang 2 Kinetics
More informationAH Mechanics Checklist (Unit 1) AH Mechanics Checklist (Unit 1) Rectilinear Motion
Rectilinear Motion No. kill Done 1 Know that rectilinear motion means motion in 1D (i.e. along a straight line) Know that a body is a physical object 3 Know that a particle is an idealised body that has
More informationOutline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy
PHY131H1F - Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe
More informationChapter 12 Gravity. Copyright 2010 Pearson Education, Inc.
Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationPhysics 101: Lecture 08. Common Incorrect Forces (Spooky Rules!) Items below are NOT forces Acceleration: F Net = ma Centripetal Acceleration
Physics 101: Lecture 08 Circular Motion Review of Newton s Laws Checkpoint 4, Lecture 7 In the game of tetherball, a rope connects a ball to the top of a vertical pole as shown. In one case, a ball of
More informationBe on time Switch off mobile phones. Put away laptops. Being present = Participating actively
A couple of house rules Be on time Switch off mobile phones Put away laptops Being present = Participating actively Het basisvak Toegepaste Natuurwetenschappen http://www.phys.tue.nl/nfcmr/natuur/collegenatuur.html
More informationUniform Circular Motion
Circular Motion Uniform Circular Motion Uniform Circular Motion Traveling with a constant speed in a circular path Even though the speed is constant, the acceleration is non-zero The acceleration responsible
More informationWork Done by a Constant Force
Work and Energy Work Done by a Constant Force In physics, work is described by what is accomplished when a force acts on an object, and the object moves through a distance. The work done by a constant
More informationPhysics 12. Unit 5 Circular Motion and Gravitation Part 2
Physics 12 Unit 5 Circular Motion and Gravitation Part 2 1. Newton s law of gravitation We have seen in Physics 11 that the force acting on an object due to gravity is given by a well known formula: F
More informationTest 3 solution. Problem 1: Short Answer Questions / Multiple Choice a. => 1 b. => 4 c. => 9 d. => 8 e. => 9
Test 3 solution Problem 1: Short Answer Questions / Multiple Choice a. > 1 b. > 4 c. > 9 d. > 8 e. > 9 Problem : Estimation Problem (a GOAL Approach student solution) While this is a good GOAL approach
More informationChapter 8 Conservation of Energy. Copyright 2009 Pearson Education, Inc.
Chapter 8 Conservation of Energy Units of Chapter 8 Conservative and Nonconservative Forces Potential Energy Mechanical Energy and Its Conservation Problem Solving Using Conservation of Mechanical Energy
More informationPhysics Mechanics Lecture 30 Gravitational Energy
Physics 170 - Mechanics Lecture 30 Gravitational Energy Gravitational Potential Energy Gravitational potential energy of an object of mass m a distance r from the Earth s center: Gravitational Potential
More informationHow do we describe motion?
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity If I have seen farther than others, it is because I have stood on the shoulders of giants. Sir Isaac Newton (1642 1727)
More informationSummary of Chapters 1-3. Equations of motion for a uniformly acclerating object. Quiz to follow
Summary of Chapters 1-3 Equations of motion for a uniformly acclerating object Quiz to follow An unbalanced force acting on an object results in its acceleration Accelerated motion in time, t, described
More informationChapter 5 Circular Motion; Gravitation
Chapter 5 Circular Motion; Gravitation Kinematics of Uniform Circular Motion Dynamics of Uniform Circular Motion Highway Curves, Banked and Unbanked Non-uniform Circular Motion Centrifugation Will be covered
More informationToday s lecture. WEST VIRGINIA UNIVERSITY Physics
Today s lecture Review of chapters 1-14 Note: I m taking for granted that you ll still know SI/cgs units, order-of-magnitude estimates, etc., so I m focusing on problems. Velocity and acceleration (1d)
More informationStudy Guide Solutions
Study Guide Solutions Table of Contents Chapter 1 A Physics Toolkit... 3 Vocabulary Review... 3 Section 1.1: Mathematics and Physics... 3 Section 1.2: Measurement... 3 Section 1.3: Graphing Data... 4 Chapter
More informationSolving Physics Problems
Solving Physics Problems Vectors Characteristic Displacement, velocity, acceleration, forces, momentum, impulse, electric field, magnetic field Break each vector into x and y components Add up x components
More informationPhysics 1A. Lecture 8A
Physics 1A Lecture 8A Review of Last Lecture A closed system is one which does not exchange (mechanical) energy with its environment total mechanical energy is conserved in this system Force is the negative
More informationPhysics 1 Second Midterm Exam (AM) 2/25/2010
Physics Second Midterm Eam (AM) /5/00. (This problem is worth 40 points.) A roller coaster car of m travels around a vertical loop of radius R. There is no friction and no air resistance. At the top of
More informationChapter 7 Potential Energy and Energy Conservation
Chapter 7 Potential Energy and Energy Conservation We saw in the previous chapter the relationship between work and kinetic energy. We also saw that the relationship was the same whether the net external
More informationPhys 102 Lecture 4 Electric potential energy & work
Phys 102 Lecture 4 Electric potential energy & work 1 Today we will... Learn about the electric potential energy Relate it to work Ex: charge in uniform electric field, point charges Apply these concepts
More informationIn this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion.
1 PHYS:100 LECTURE 9 MECHANICS (8) In this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion. 9 1. Conservation of Energy. Energy is one of the most fundamental
More informationEnd-of-Chapter Exercises
End-of-Chapter Exercises Exercises 1 12 are conceptual questions that are designed to see if you have understood the main concepts of the chapter. 1. Figure 11.21 shows four different cases involving a
More information