chap13 conservation of energy

Chapter 13 Energy3: Conservation of energy
Key words:
System environment and system boundary 环境和系统边界 Internal energy Conservation of energy (COE) Center-of-mass energy (COM) 内能 能量守恒 质心能量
* K→the kinetic energy associated with the motion translational or rotational) of the system as a whole or with its macroscopic. * U→the macroscopic potential energy associated with the interaction of macroscopic parts of the system with each other. * Eint→the internal energy of the system, associated with the kinetic energies of the individual particles within each object in the system and the potential energies of their interactions with each other. * Wext→the work done by external forces on the system. Now for the motion of the skater, still with Wext=0 and △U=0, we have △Eint=－△K. The increase in her kinetic energy comes about at the cost of a decrease in her supply of internal energy, which her body obtains from the food she eats.
13-2 Internal energy in a system of particles Since mechanical energy is often not conserved, the importance of energy was not realized until the 19 century, when it was discovered that the disappearance of macroscopic mechanical energy is accompanied by the appearance of thermal energy, usually indicated by an increase in temperature. Consider a ball of putty(灰泥) of mass m is released from rest from a height h above the floor. It falls to the floor. The work done by the floor is zero because the point of application of the force does not move. Thus the total work done on the ball is mgh. Energy is transferred to the ball by the work done on it by gravity. This energy appears as kinetic energy of the ball before it hits the floor and as thermal energy (called internal energy) within the ball after.
2) If the system consists of N particles and the internal forces includes non conservative force, for particle i Wnet,i=Wint,i +Wext,i=Wint,i (conservative)+Wint,i (non conservative)+Wext,i =△Ki W=∑Wnet,i=∑Wint, i (conservative)+∑Wint, i (non conservative)+∑Wext,i = Wint, i (non conservative) –△U+ Wext ∴ Wext+ Wint (non conservative) =∑△Ki + △U= △K + △U or Wext+ Wint non conservative=△K + △U
The ball warms slightly and the energy is eventually transferred to the ball's surroundings as heat. Note that we cannot treat the ball of putty as a particle and apply the workenergy theorem. Although the only work done is by a conservative force, the total mechanical energy of the ball is not conserved. There are situations in which some of a system's internal energy is converted into mechanical energy with no work being done by any outside agent. Consider an ice skater as she pushes herself away from a railing(扶手) at the edge of a skating rink. She starts at rest against the railing, and by extending her arms to push away from the railing she begins to slide across the ice.
1) If the system consists of N particles and the internal forces are conservative, for particle i, Wnet,i= Wint,i +Wext,i=△Ki W=∑Wnet,i= ∑Wint,i + ∑Wext,i= Wint+ Wext=-△U+ Wext ∴ Wext= ∑Wnet,i + △U=∑△Ki + △U= △K + △U (here we assumed that the internal forces are conservative, so Wint= -△U) i.e., △K + △U = Wext Discussion: if Wext>0, then △(K +U)>0; if Wext<0, then △(K +U)<0. Positive external work done on the system increases its total energy,while negative external work done on the system transfers energy out of the system, and thus decreases its total energy.
Define the system to be the skater only. There are three forces on the skater: gravity, normal force and the force exerted by the railing. Clearly, △U=0 (there are no other objects within the system to exerted forces on the skater), gravity and the normal force do no work on the skater, the third force (which is equal and opposite to the force exerted on the railing by the skater) also does no work, because the point of application of the force does not move. Thus Wext=0, from the work-energy theorem→△K=0, in disagreement with the observation that she accelerates away from the railing. The reason is that the system consisting of the skater could not treated neither as a particle nor as a rigid body. Where does the skater’s kinetic energy come from? → It comes from another form of energy (internal energy) stored in the system. So we can extend the work-energy theorem to include this new form of energy: △K +△U+ △Eint =Wext.