Mechanics Chapter 4 Kinetic energy and potential energy

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Mechanics Chapter 4. Kinetic energy and potential energy for a particle 4. 6 Review

Mechanics Chapter 4. Kinetic energy and potential energy for a particle 4. 6 Review and Summary 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 1

4. 6 Review and Summary Absolute motion Kinematics Relative motion Particles Classical mechanics Force-massacceleration

4. 6 Review and Summary Absolute motion Kinematics Relative motion Particles Classical mechanics Force-massacceleration method Dynamics Work-energy method Rigid bodies Impulse momentum method Statics 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 2

4. 6 Review and Summary Work: The product of force and the amount of

4. 6 Review and Summary Work: The product of force and the amount of displacement along the line of action of that force. Energy: The capacity of something to do work Mechanical Energy = Kinetic energy + Potential energy Work of a force: Definition: Calculation: 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 3

4. 6 Review and Summary 1) Rectangular coordinate system 2) Path coordinate system 3)

4. 6 Review and Summary 1) Rectangular coordinate system 2) Path coordinate system 3) Polar coordinate system 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 4

4. 6 Review and Summary Work of some typical forces: Constant force: Weight: Spring

4. 6 Review and Summary Work of some typical forces: Constant force: Weight: Spring force: Gravitational force: 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 5

4. 6 Review and Summary Kinetic energy: Work-kinetic energy principle: work-kinetic energy method 2005年

4. 6 Review and Summary Kinetic energy: Work-kinetic energy principle: work-kinetic energy method 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 6

4. 6 Review and Summary Conservative force: A force is conservative if the work

4. 6 Review and Summary Conservative force: A force is conservative if the work it does on an object moving between two points is independent of the path taken. Examples of conservative forces: force: A = F· r • A constant • Force of gravity: • Spring force: • Gravitational force: 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 7

4. 6 Review and Summary Potential energy: Define: F · dr = -d. V

4. 6 Review and Summary Potential energy: Define: F · dr = -d. V 1) Potential energy of constant force 2) Potential energy of gravity 3) Elastic potential energy: 4)Gravitational potential energy 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 8

4. 6 Review and Summary Mechanical energy: E = EK + V Work-energy principle:

4. 6 Review and Summary Mechanical energy: E = EK + V Work-energy principle: Principle of conservation of mechanical energy If no net non-conservative forces Then, conservation of mechanical energy holds 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 9

6. 7 Review and Summary 2. Work Energy principle • Work done on the

6. 7 Review and Summary 2. Work Energy principle • Work done on the particle system: • Work done by gravity on the system: • The work done by a pair of internal forces depends only on the relative displacement of the two particles. • Principle of work and kinetic energy for a particle system 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 10

6. 7 Review and Summary • Principle of Work and mechanical energy • Principle

6. 7 Review and Summary • Principle of Work and mechanical energy • Principle of conservation of mechanical energy: If Aext =0, (Aint)noncon = 0, then Ek + Ep = Ek 0 + Ep 0 = constant 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 11

6. 7 Review and Summary 6. Impact Direct central impact 2005年 11月17日晚 7: 00

6. 7 Review and Summary 6. Impact Direct central impact 2005年 11月17日晚 7: 00 -9: 00 Oblique central impact 第四章 动能和势能 12

6. 7 Review and Summary • For both direct and oblique impact problems, the

6. 7 Review and Summary • For both direct and oblique impact problems, the following equations apply along the line of v 1 impact (n-dir. ): v 2 t m 2 m 1 of n e Lin act p im v 20 v 10 • For oblique impact problems, the following equations are also required, applied perpendicular to the line of impact (t-dir. ): 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 13

6. 7 Review and Summary 5. Center of mass system A reference frame in

6. 7 Review and Summary 5. Center of mass system A reference frame in which the mass center of a particle system is at rest. q. Work-energy principle: • kinetic energy Konig theorem • Work-kinetic energy principle in CM frame The total work done by the inertial forces is zero • work-mechanical energy principle in CM frame 2005年 11月17日晚 7: 00 -9: 00 第四章 动能和势能 14

Kinetic and Potential Energy Potential Energy Potential energyKinetic and Potential Energy Potential Energy Potential energy
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Rotational Kinetic Energy Kinetic Energy The kinetic energyRotational Kinetic Energy Kinetic Energy The kinetic energy
Kinetic Potential Energy Definitions KINETIC ENERGY Energy ofKinetic Potential Energy Definitions KINETIC ENERGY Energy of
Kinetic Gravitational Potential Energy Mechanical Energy Kinetic EnergyKinetic Gravitational Potential Energy Mechanical Energy Kinetic Energy
Kinetic and Potential Energy Potential Energy Stored energyKinetic and Potential Energy Potential Energy Stored energy
Kinetic and Potential Energy Conservation of Energy KineticKinetic and Potential Energy Conservation of Energy Kinetic
Types of Energy kinetic and potential Energy KineticTypes of Energy kinetic and potential Energy Kinetic
Kinetic Energy and Gravitational Potential Energy Define kineticKinetic Energy and Gravitational Potential Energy Define kinetic
Conservation of Energy Kinetic and Potential Energy KineticConservation of Energy Kinetic and Potential Energy Kinetic
Potential Kinetic energy Kinetic Energy If an objectPotential Kinetic energy Kinetic Energy If an object
Mechanics Kinetic energy and potential energy 4 3Mechanics Kinetic energy and potential energy 4 3
Mechanics Kinetic energy and potential energy 4 2Mechanics Kinetic energy and potential energy 4 2