1. Chapter 3 Work and Energy

2. §3-1 Work §3-2 Kinetic Energy and the Law of Kinetic Energy §3-3 Conservative Force, Potential Energy §3-4 The Work-Energy theorem Conservation of Mechanical Energy §3-5 The Conservation of Energy

3. Work §3-1 Work -- element work or  ab：ab：ab：ab： 1.Work -- variable force Equal to the displacement times the component of force along the displacement.

4. In In Cartesian coordinate system 2.Work done by resultant force If Then The work done by the resultant force = the algebraic sum of the works done by every force.

5. 3. Power The work done per unit time 4.Work done by action-reaction pair of forces

6. 与参考点的选择无关 relative displacement relative displacement

7. Work-kinetic energy theorem §3-2 Work-kinetic energy theorem 1. WKE Theo. of a particle 

8. The total work done on a particle = the increment of its kinetic energy -- Work-kinetic energy theorem Definition -- Kinetic energy ( the Law of kinetic energy)

9. According to above For m 1 ……  +  2. WKE Theo. of particle system For m 2 ……

10. -- Work done by external force -- Work done by internal force Final KE Initial KE

11. The sum of the works done by all external forces and internal forces = the increment of the system’s KE. -- System’s work-kinetic energy theorem Extend this conclusion to the system including n particles

12. [Example] A particle with mass of m is fixed on the end of a cord and moves around a circle in horizontal coarse plane. Suppose the radius of the circle is R. And v o  v o /2 when the particle moves one revolution. Calculate  The work done by friction force.  frictional coefficient.  How many revolutions does the particle move before it rests? · · v R

13.  Opposite to the moving direction We get Solution  According to WKE theo.,

14.  Suppose the P moves n rev. before it rests. According to work-kinetic energy theorem, (rev) We have

15. §3-3 Conservative force Potential energy 1. Conservative force The work done by Cons. force depend only on the initial and final positions and not on the path. The integration of Cons. force along a close path l is equal to zero. The potential energy can be introduced when the work is done by the Cons. Force. Otherwise, non-conservative force

16. (1) PE of weight 2. Potential energy Gravitational force or

17. Definition Definition --PE of weight then the work done by GF = the reduction of PE of weight

18. The point of zero PE of weight is arbitrary PE of weight at point a = the work done by GF moving m from a to zero PE point. then If

19. (2) Elastic PE Elastic force Definition --Elastic PE

20. then The point of zero elastic PE ： relaxed position of spring (x=0) relaxed position of spring (x=0) the work done by EF = the reduction of elastic PE

21. (3) Universal gravitational PE Universal gravitational force

22. Definition when The point of zero UGPE ： the distance of both particles is infinity ( r  the distance of both particles is infinity ( r  ----UGPE then

23.  The PE of a particle at a point is relative and the change of a particle from one point to another point is absolute. Remarks  Only conservative force can we introduce potential energy.  The done by conservative force =  The done by conservative force = the reduction of PE

24.  PE belongs to the system. Gravitational force Elastic force Universal gravitational force Conservative internal force The frictional force between bodies is non-conservative internal force

25. Internal force = Conservative IF + non-Cons.IF §3-4 The work-energy theorem Conservation of Mechanical Energy System’s work-kinetic energy theorem System’s work-kinetic energy theorem

26. Let -- mechanical energy of the system The sum of the work done by the external forces and non-conservative forces equals to the increment of the mechanical energy of the system from initial state to final state. -- the work-energy theorem of a system

27. --Conservation of mechanical energy when We have

28. [Example] Two boards with mass of m 1 ， m 2 (m 2 >m 1 ) connect with a weightless spring.  If the spring can pull m 2 out of the ground after the F is removed, How much the F must be exerted on m 1 at lest?  How is about the result if m 1 ， m 2 change their position? F

29. Solution Suppose the length of the spring is compressed as the F is exerted. And m 2 is pulled out of the ground as the length is just stretched after the F is removed then

30. Chose the point of zero PE : The spring is free length ( no information) The spring is free length ( no information) Its mechanical energy is conservation  Two boards+spring+earth = system We can get  The result do not change if m 1 ， m 2 change their position.

31. §3-5 The Conservation of Energy Friction exists everywhere

32. The frictional force is called as a non- conservative force or a dissipative force which exists everywhere. Its work depends on the path and it is always negative. So if the dissipative forces exist such as the internally frictional force, it is sure that the mechanical energy of the system decreases. According to the work-energy theorem

33. The decrease of mechanical energy The decrease of mechanical energy is transformed into other kinds of energy such as heat energy because of friction. Which leads to the increase of temperature of system so that the internal energy of the system has an increment. In order to simplify this problem, if we suppose W ex =0 We have

34. Re-write above formula The change of internal energy + the change of mechanical energy = conservation So we can get the generalized conservation law of energy as follow Energy may be transformed from one kind to another in an isolated system. But it cannot be created or destroyed. The total energy of the system always remains constant.