pring force (conservative forces) do work,(No friction, no resistance (in air, on ice, not water ),no external forces or energy source does work, (no human,animal, motor, lift, push ) K U will stay unchanged.Kinetic EnergyU mgyPotential EnergyK ½mv2U ½k( x) 2Got Conservation of Mechanical Energy, when Wnc 0Copyright Dr. Weining Man and Pearson
8-3 Conservation of Mechanical EnergyEnergy conservation can make kinematicsproblems much easier to solve:When there is no work done bynon-conservative forces,Ki Ui Kf Uf; (happily)You don’t need to calculate workhere, because work done bygravity and spring forces areincluded in the change of potentialenergy. K - U Work of gravity or springCopyright Dr. Weining Man and Pearson
8-3 Conservation of Mechanical EnergyYou can solve v easily if h is known.Q1: If initial height was lower, thefinal speed to hit the ground wouldbe more or less?Q2: Had the initial height wasdoubled, the final speed to hit theground would becomeHalf, Twice,, or 4 times ?Similarly, if an object was thrownUPWARD with v0, maximum heightcan be easily found.Copyright Dr. Weining Man and Pearson
Figure 8-9When no work is done bynon-conservative forces,Ki Ui Kf Uf;When we look for changeof KE or PE, only initialand final height matters.½ mv02 mgh0 ½ mvf2 mghfNo matter which direction velocities are.If no friction, K U does not change. It’s true forall middle positions, not only the start and the end.You have ½ mv02 mgh0 ½ mvf2 mghf ½mv12 mgh1 ½ mv22 mgh2,or any middle position at 1,2,3, . regardlessvelocity directions.
For A object launched at angle θ and V0, throughthe entire motion, for all points in between.½ mv02 mgh0 ½ mvf2 mghf ½mv12 mgh1 ½ mv22 mgh2At maximum height,½ mv02 mgh0 ½mvtop2 mghmaxIs vtop 0 ?Sure, vtop y 0,But vtop vtop x v0cosθ; ax 0.But for a pendulum, or an object sliding up alone aincline, track etc, total v IS zero at maximum height.Copyright 2010 Pearson Education, Inc.Copyright Dr. Weining Man
Example, A truck slide down for distance Lfrom rest, on an incline. (θ)LIf there is no friction,After distance L what willhθbe its final speed?Don’t memorize conclusionslike v2 2gh0 mgh0 ½ mvf2 0 It only works without frictionand when initial or final v 0h0 L sinθLearn the physics,mg L sinθ ½ mvf2 UNDERSTAND it,UNDERSTAND when to useg L sinθ ½ vf2vf2 2g L sinθ the sweetKi Ui Kf Uf;Copyright 2010 Pearson Education, Inc.
Total Energy conservation:Energy cannot be created or destroyed. It onlychange forms.When Energy seems to be created/ destroyed, itactually is being converted from/to other forms.When friction does work, it reduces kineticenergy and convert that into Heat.Copyright Dr. Weining Man
When nonconservative forces do work, the total mechanicalenergy is not conserved: we need to calculate work done byNon-Conservative forces. (Wnc sum of all work except formg and spring’s work)Wexternal, Wpush, pull, wind, man, wave, elevator, Kinetic EnergyU mgyPotential EnergyK ½mv2U ½k( x) 2Wkinetic-friction – fkdCopyright Dr. Weining Man and Pearson
8-4 Work Done by Nonconservative ForcesIn this example, thenonconservative forceis water resistance:By comparing Ef and EiYou can find Wnc,which is otherwise hardto calculate since waterresistance may not beconstant force.Copyright Dr. Weining Man and Pearson
m 1000kg, v0 0, µk 0.2φ 30ο, d 0.5m,Find vfN mgcosφfk µkN µkmgcosφfk 0.2 9800 cos30 1697(Ν)New Problem solving strategy :1.Ananlyze all forces and decide whether NonConservative force does work or not.2. Only compute total work down by NC forces3. Set equationYeah! No need to calculate ALL work anymore, when I understand conservative andnon-conservative forces.WNC Wfk – fk d – 1697*0.5 – 849 J ;Kf Uf Ki Ui WNC½mvf2 0 0 mgh – fk d ;h d sin φ½mvf2 mg d sin30 – fk d 1601Jvf 1.79m/s
Summary of Chapter 8 Conservative forces conserve mechanicalenergy. They do work to convert energy betweenKinetic Energy and Potential Energy. Conservative force does zero work on anyclosed path Work done by a conservative force isindependent of path Conservative forces: gravity, spring force. Nonconservative forces convert mechanicalenergy into other forms.Copyright Dr. Weining Man and Pearson
Summary of Chapter 8 Work done by nonconservative force on closedpath is not zero, and depends on the path Nonconservative forces: friction, air resistance,pull, push, most other forces Energy in the form of potential energy can beconverted to kinetic or other forms Work done by a conservative force is thenegative of the change in the potential energy Gravity: U mgy Spring: U ½ k( x)2Copyright Dr. Weining Man and Pearson
Summary of Chapter 8 Mechanical energy is the sum of the kinetic andpotential energies; it is conserved only insystems with purely conservative forces to dowork. Nonconservative forces change a system’smechanical energy Work done by nonconservative forces equalschange in a system’s mechanical energy (K U) Gravitational Potential energy at distance r fromearth center:U GMearth m/rCopyright Dr. Weining Man and Pearson
Copyright Dr. Weining Man
Copyright Dr. Weining Man
reduces Kinetic Energy and increase Potential Energy A: The energy is stored as potential energy. PE is like your saving account. Potential energy gain (mg h) during the rising part. We can get that energy back as kinetic E if the ball falls back off. During falling, Kinetic Energy will increase mg h. Potential energy will reduce mg h.
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
About the husband’s secret. Dedication Epigraph Pandora Monday Chapter One Chapter Two Chapter Three Chapter Four Chapter Five Tuesday Chapter Six Chapter Seven. Chapter Eight Chapter Nine Chapter Ten Chapter Eleven Chapter Twelve Chapter Thirteen Chapter Fourteen Chapter Fifteen Chapter Sixteen Chapter Seventeen Chapter Eighteen
18.4 35 18.5 35 I Solutions to Applying the Concepts Questions II Answers to End-of-chapter Conceptual Questions Chapter 1 37 Chapter 2 38 Chapter 3 39 Chapter 4 40 Chapter 5 43 Chapter 6 45 Chapter 7 46 Chapter 8 47 Chapter 9 50 Chapter 10 52 Chapter 11 55 Chapter 12 56 Chapter 13 57 Chapter 14 61 Chapter 15 62 Chapter 16 63 Chapter 17 65 .
HUNTER. Special thanks to Kate Cary. Contents Cover Title Page Prologue Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter
Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 . Within was a room as familiar to her as her home back in Oparium. A large desk was situated i
Which idea describes a change from potential energy to kinetic energy? 4. Not all of a roller coaster’s energy transfers back and forth between potential energy and kinetic energy. According to the law of conservation of energy, however, the leftover potential energy must exist somewhere. Identify another form of energy that both potential .
Energy comes in many forms, but rollercoasters mostly use Potential Energy and Kinetic Energy. Potential Energy is stored energy. Rollercoasters use gravitational potential energy which is stored when objects go up high. The equation for gravitational potential energy is Kinetic Energy is the energy of a moving object.
The Hunger Games Book 2 Suzanne Collins Table of Contents PART 1 – THE SPARK Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8. Chapter 9 PART 2 – THE QUELL Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapt
Chapter 8: Potential Energy and Conservation of Energy Work and kinetic energy are energies of motion. We need to introduce an energy that depends on location or position.This energy is called potential energy.
Kinetic vs. Potential Energy Potential Energy is the energy an object possesses by virtue of its position or composition. Kinetic Energy is the energy of motion K.E. ½mv 2 where m mass and v velocity Notes 6.1 2c Initial vs. Final Position In the initial position, ball A has a higher potential energy than ball B.
on work, power and energy]. (iv)Different types of energy (e.g., chemical energy, Mechanical energy, heat energy, electrical energy, nuclear energy, sound energy, light energy). Mechanical energy: potential energy U mgh (derivation included ) gravitational PE, examples; kinetic energy
1. Potential and Kinetic Energy In this video we look at different types of energy and focus specifically on gravitational potential energy and kinetic energy and we also do calculations with the given equations. 2. Mechanical Energy Mechanical energy is the sum of gravitational potential energy and kinetic energy. In this
The amount of kinetic energy in a moving object depends on its speed and its mass. x Kinetic energy can change into other forms of energy. x Potential energy is known as stored energy. x It is energy that could cause changes in the future. x Potential energy often changes into kinetic energy. Exampl
Potential energy can be defined for conservative forces only Examples: gravitational potential energy spring elastic potential energy 6 Connection between energy and force - hint Left side – the kinetic energy has been
Mary Barton A Tale of Manchester Life by Elizabeth Cleghorn Gaskell Styled byLimpidSoft. Contents PREFACE1 CHAPTER I6 CHAPTER II32 CHAPTER III51 CHAPTER IV77 CHAPTER V109 CHAPTER VI166 CHAPTER VII218 i. CHAPTER VIII243 CHAPTER IX291 CHAPTER X341 CHAPTER XI381 CHAPTER XII423 CHAPTER XIII450 CHAPTER XIV479 CHAPTER XV513 CHAPTER XVI551
Potential energy may be released and converted into other forms (such as kinetic energy) Work is done, increasing the potential energy. Potential energy Potential energy difference is the on
Energy is often defined as the ability to do work. Pair up and list as many forms of energy as you can. Electrical. Chemical. Nuclear. Magnetic. Elastic. Sound. Gravitational energy. Kinetic energy (energy of motion). Thermal energy (heat energy). Potential energy. Potential energy
7.6 Summary of Renewable Energy Potentials and Developments 96 8 Renewable Energy Developments and Potential in Viet Nam 99 8.1 Institutional and Policy Framework for Renewable Energy Initiatives 99 8.2 Solar Energy Resources Potential 103 8.3 Wind Energy Resources Potential 105 8.4 Biomass and Biofuel Energy Resources 108
with ASTM D2310, D2992 and D2996. Fittings meeting ASTM D6041 are available upon request. · NATIONAL SANITATION FOUNDATION (NSF) Can be Manufactured to meet ANSI/NSF Standard No. 61 for potable water usage. F-CHEM Piping Systems Smith Fibercast is a World Leader in Composite Piping featuring ISO 9001: 2000 quality assurance at both production facilities. 60-inch cooling water recirculation .