复旦大学：《大学物理》课程教学资源（PPT课件，英文）Ch.13 Energy III：Conservation of energy

Ch 13 Energy III Conservation of energy Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy Ch. 13 Energy III: Conservation of energy

Law of conservation of mechanical energy K:+u =ke+u In a system in which only conservative forces do work the total mechanical energy remains constant In this chapter: we consider systems of particles for which the energy can be changed by the work done by external forces(系统外的力) and nonconservative forces Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy In this chapter: we consider systems of particles for which the energy can be changed by the work done by external forces(系统外的力) and nonconservative forces. Ki +Ui = K f +U f Law of conservation of mechanical energy: “In a system in which only conservative forces do work, the total mechanical energy remains constant

13-1 Work done on a system by external forces △K+△U= (13-1) SyS SyS ext Positive external work done by the environment on the system carries energy into the system, thereby increasing its total energy i vice versa The external work represents a transfer of energy between the system and the environment. Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy 13-1 Work done on a system by external forces Positive external work done by the environment on the system carries energy into the system, thereby increasing its total energy; vice versa. The external work represents a transfer of energy between the system and the environment. Ksys + Usys =Wext (13-1)

An example Fig 13-2 Let us consider a block of mass m attached to a vertical spring near the Earths surface 1. system=block. Here the spring force and gravity are external forces, there are no internal forces within the system and thus no potential energy Using Eq(13-1), △K=W+诉 Spring graI Earth Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy Let us consider a block of mass m attached to a vertical spring near the Earth’s surface. 1. system=block. Here the spring force and gravity are external forces; there are no internal forces within the system and thus no potential energy. Using Eq(13-1), K = Wspring +Wgrav Earth Fig 13-2 An example

2. System=block spring. The spring is within the system △K+△U Spring gra 3. System=block Earth Here gravity is an internal force △K+△U gra Spring 4. System=block spring Earth The spring force and gravity are both internal to the system, so △K+△U+△U 0 Spring grav Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy 2. System=block + spring. The spring is within the system. 3. System=block + Earth. Here gravity is an internal Force. 4. System=block + spring + Earth. The spring force and gravity are both internal to the system, so K + Uspring = Wgrav K + U grav = Wspring K + Uspring + Ugrav = 0

13-2 Internal energy(p]ae) in a system of particles 1 Consider an ice skater she starts at rest and then extend her arm to push herself away from the ailing at the edge of a skating rink(溜冰场) + Use work-energy railing relationship to analyze g △+△U=Wgxr F The system chosen Ice only include the skater g →△U=0 Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy 13-2 Internal energy (内能) in a system of particles 1. Consider an ice skater. She starts at rest and then extend her arm to push herself away from the railing at the edge of a skating rink（溜冰场）. •••• ice railin g Use work-energy relationship to analyze: K + U =Wext The system chosen only include the skater Mg N F U = 0

WE=O: W N+MG 0 Wext=0 今△K=0??? in disagreement with our observation that she accelerates away from the railing Where does the skater's kinetic energy come from? Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy WF=0; WN+MG=0; Wext=0 K = 0 ??? in disagreement with our observation that she accelerates away from the railing. Where does the skater’s kinetic energy come from?

The problem comes from The skater can not be regarded as a mass point but a system of particles For a system of particles it can store one kind of energy called"internal energy:△K+△U=Wxt △K+△U+△Emt=Wa(13-2 It is the internal energy that becomes the skater's kinetic energy. Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy For a system of particles, it can store one kind of energy called “internal energy”. The problem comes from: The skater can not be regarded as a mass point, but a system of particles. K + U =Wext It is the internal energy that becomes the skater’s kinetic energy. K + U + Eint = Wext (13-2)

2. What's the nature of internal energy? Int S K+U In Ini Sum of the kinetic energy associated with random motions of the atoms and the potential energy associated with the forces between the atoms Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy 2. What’s the nature of “internal energy”? Sum of the kinetic energy associated with random motions of the atoms and the potential energy associated with the forces between the atoms. Eint = Kint +Uint

Sample problem13-1 a baseball of mass m=0. 143kg falls from h=443m ith v;=0, and its v =42m/s Find the change in the internal energy of the ball and the surrounding air. Solution: system ball air earth F=0=△K+△+△E=0 AU=Ur-U1=0-(mgh)=-621 △K ny 0=126J △E=-△U-△K=495J Ch 13 Energy III: Conservation of energy

Ch.13 Energy III: Conservation of energy Sample problem13-1 A baseball of mass m=0.143kg falls from h=443m with , and its . vi = 0 U U U mgh J  = f − i = 0 − ( ) = −621 K m v J f 0 126 2 1 2  = − = Fext = 0 K + U + Eint = 0 v m s f =4 2 / Find the change in the internal energy of the ball and the surrounding air. Solution: system = ball + air + Earth. E U K 495J  int = − −  =