Chapter 7HAPPY BIRTHDAY GEORGE!KalendarENERGYIntroduction to EnergySystemsValid SystemEnvironmentWorkWorking, Working, WorkingWork, cont.Work ExampleMore About WorkUnits of WorkSlide 15Slide 16Work Is An Energy TransferWork Is An Energy Transfer, contSlide 19ShejuleLAST TIMEWORKScalar or DOT Product of Two VectorsScalar Product PropertiesDot Products of Unit VectorsSlide 26Work Done by a Varying ForceSlide 28Work Done By Multiple ForcesHooke’s LawHooke’s Law, cont.Work Done by a SpringSpring with an Applied ForceSlide 34Slide 35Consider the following:Kinetic EnergyWork-Kinetic Energy TheoremNonisolated SystemBREAK POINTStuff HappensInternal EnergyPotential EnergyConservation of EnergySlide 45Slide 46Slide 47Slide 48Slide 49PowerInstantaneous PowerPower GeneralizedUnits of PowerSlide 54BREAKSlide 56Let’s Review with some ProblemsSlide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Potential (Stored) EnergyTypes of Potential EnergySystems with Multiple ParticlesSystem ExampleLet’s drop the book from yb and see what it is doing at ya.Slide 76Gravitational Potential EnergyGravitational Potential Energy, contEnergy ProblemsGravitational Potential Energy, finalConservation of Mechanical EnergySlide 82Let’s look at the more general case.ANY PATHSlide 85Conservation of Mechanical Energy, exampleElastic Potential EnergyElastic Potential Energy, contElastic Potential Energy, finalThe Bindell Conservation of Energy EquationSlide 91Problem Solving Strategy – Conservation of Mechanical EnergyProblem-Solving Strategy, 2Problem-Solving Strategy, 3Problem-Solving Strategy, 4Slide 96Slide 97Slide 98Slide 99Conservation of Energy, (Pendulum)Conservative ForcesNonconservative ForcesSlide 103Nonconservative Forces (Connected Blocks)Connected Blocks, contConservative Forces and Potential EnergySlide 107Conservative Forces and Potential Energy – CheckSlide 109Energy Diagrams and EquilibriumEnergy Diagrams and Stable EquilibriumEnergy Diagrams and Unstable EquilibriumChapter 7Chapter 7EnergyEnergyandandEnergy TransferEnergy TransferFebruary 22, 2006February 22, 2006Subject to much changeHAPPY BIRTHDAY HAPPY BIRTHDAY GEORGE!GEORGE!KalendarToday we start the new TOPIC OF ENERGYNo Quiz on Friday, but there MAY be one on MondayThe BAD NEWS:EXAM #2 will be on March 3 (Friday)ENERGYWe use energy to walk, run or even sleepWe use energy when we lift a weightWe use energy when we drive a carWe even use energy to THINK!BUT …..Introduction to EnergyIntroduction to EnergyThe concept of energy is one of The concept of energy is one of the most important topics in the most important topics in sciencescienceEvery physical process that occurs Every physical process that occurs in the Universe involves energy in the Universe involves energy and energy transfers or and energy transfers or transformationstransformationsEnergy is not easily definedEnergy is not easily definedSystemsA system is a small portion of the UniverseWe identify a number of particles or objects and draw a sphere around themThere are no forces acting on anything inside the sphere from outside the sphereWe will ignore the details outside of the sphere.A critical skill is to identify the systemValid SystemA valid system maybe a single object or particlebe a collection of objects or particlesbe a region of spacevary in size and shapeEnvironmentThere is a system boundary around the systemThe boundary is an imaginary surfaceIt does not necessarily correspond to a physical boundaryThe boundary divides the system from the environmentThe environment is “the rest of the Universe”WorkThe work, W, done on a system by an agent exerting a constant force on the system is the product of the magnitude, F, of the force, the magnitude r of the displacement of the point of application of the force, and cos  where is the angle between the force and the displacement vectorsWorking, Working, WorkingWORK = Component of the applied force x the displacement=Fcos() x rWork, cont.W = F r cos The displacement is that of the point of application of the forceA force does no work on the object if the force does not move through a displacementThe work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of applicationrF -(Later for the dot!)Work ExampleThe normal force, n, and the gravitational force, m g, do no work on the objectcos  = cos 90° = 0The force F does do work on the objectSame amount as in the previous overheadMore About WorkThe system and the environment must be determined when dealing with workThe environment does work on the systemWork by the environment on the systemThe sign of the work depends on the direction of F relative to rWork is positive when projection of F onto r is in the same direction as the displacementWork is negative when the projection is in the opposite directionUnits of WorkWork is a scalar quantityThe unit of work is a joule (J)1 joule = 1 newton . 1 meterJ = N · mA block of mass 2.50 kg is pushed 2.20 m along a frictionless horizontal table by a constant 16.0-N force directed 25.0 below the horizontal. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, and (c) the gravitational force. (d) Determine the total work done on the block.A raindrop of mass 3.35  10–5 kg falls vertically at constant speed under the influence of gravity and air resistance. Model the drop as a particle. As it falls 100 m, what is the work done on the raindrop (a) by the gravitational force and (b) by air resistance?Work Is An Energy TransferThis is important for a system approach to solving a problemIf the work is done on a system and it is positive, energy is transferred to the systemIf the work done on the system is negative, energy is transferred from the systemWork Is An Energy Transfer, contIf a system interacts with its environment, this interaction can be described as a transfer of energy across the system boundaryThis will result in a change in the amount of energy stored in the systemShejuleShejuleContinue to work on energy.Continue to work on energy.Exam on March 3Exam on March 3rdrd..Material … as far as we get by Material … as far as we get by March