西尔斯大学物理Ch4-2WorkandEnergy-2

1、University Physics14-4 Potential EnergyUniversity Physics2 Definition of potential energyPotential energy U is the energy that can be associated with the configuration ( or arrangement ) of a system of objects that exert conservative force on one another.4-4 Potential EnergyThe increment of the pote

2、ntial energy is defined as the negative value of the work done by the relative conservative force. fiifl dfWUUUUniversity Physics34-4 Potential Energy)(ifggyymgWUWeight potential energy:)(2122ifsxxkWUElastic potential energy:)11(ifgravgravrrGmMWUGravitational energy:mgyUg0, 0giUy221kxUs0, 0siUxrmMGU

3、grav0,graviUrUniversity Physics4 Potential energy is the function of position. The choice of the position where the potential energy is zero is discretional. Potential energy is belong to the two particles of interaction. Potential energy is the work done by conservative force from some position to

4、the zero potential energy point.4-4 Potential EnergyNotice:University Physics54-4 Potential EnergybaiymgymgdyrdFWi0Weight potential energy:2021ixxxkxxdxkidxikxWifiElastic potential energy:rmMGdrrmMGrdrrrmMGWirba22Gravitational energy:Evaluating potential energyUniversity Physics64-4 Potential Energy

5、Example 4-3 : The repulsion between two particles can be described as f=k/r3 where k is a known constant, r is the distance between the particles. Find the potential energy function U(r) of the repulsion if we set U()=0.Solution 232)()(rkdrrkWrUUr2222)()(rkrkUrU0)(UUniversity Physics74-4 Potential E

6、nergyExample 4-4 : A uniform chain of mass m and length l is put on a frictionless horizontal surface. The length of hanging down part is 0.2 l ，pull the chain very slowly back to the surface. Find the work done by the pulling force.University Physics84-4 Potential EnergyWork done by avariable force

7、Solution 1xlmThe mass of the hanging downpart5002 . 0mglxdxlmgidxi xlmgl dGWlG50mglWWGFUniversity Physics950)10(551mgllmghmgUcInitial state:4-4 Potential Energythe potential energySolution 20UOn the surface50mglWWGF02UFinal state:50)(12mglUUUWGWork done by mg:Work done by :FUniversity Physics104-5 C

8、onservation of Mechanical EnergyUniversity Physics111. Kinetic energy of a system 12f21f1F2F1m2mA system： m1 and m21F2FExternal forces:12f21fInternal forces:4-5 Conservation of Mechanical EnergyUniversity Physics1212f21f1F2FiV1iV21m2m12f21f1F2F1m2mfV1fV2iffiiffiKKrfFKKrfF2221211121d)(d)(Applying the

9、 law of kinetic energy to m1 & m2, we have 4-5 Conservation of Mechanical EnergyUniversity Physics13Rewrite them asifinexifinexKKWWKKWW22221111ifKKWWintext12f21f1F2F1m2m4-5 Conservation of Mechanical Energy The total work done by all the forces in a system equals the change in the total kinetic ener

10、gy of the systemUniversity Physics14 Work done by a pair of (internal) forces21ff 0fLfW11SfW22AB1f2fABSL)(1SLfW0 The kinetic energy of a system can be changed by the work done by the internal forces4-5 Conservation of Mechanical EnergyDiscussUniversity Physics15ifextKKWWintifcncextKKWWWWWork done by

11、 all external forcesextWWork done by all internal nonconservative forcesncWWork done by all internal conservative forcescW4-5 Conservation of Mechanical Energy2. Conservation of Mechanical EnergyUniversity Physics16 The sum of the potential energy U and the kinetic energy K is defined as the mechani

12、cal energy. ifcncextKKWWWUKWKWWcncextKUEUWc4-5 Conservation of Mechanical EnergyUniversity Physics17iiffUKUK In an isolated system where only conservative forces are acting, the kinetic energy may change, the potential energy may change, but their sum-the mechanical energy of the system, remains con

13、stant.UKWWncext 0 0 extncW,WIf0then UK4-5 Conservation of Mechanical EnergyconstantifEEUniversity Physics18Example 4-5 An asteroid, headed directly toward the Earth, has a speed of 12 km/s when it is at a distance of 10 Earth radii from the Earths center. Neglecting the effects of the Earths atmosph

14、ere on the asteroid, find the asteroids speed vf when it reaches the Earths surface.4-5 Conservation of Mechanical EnergyUniversity Physics194-4 Potential EnergySolution iiffUKUKEiEfRGMmmvRGMmmv10212122skmsmvf/16/106 . 14smRGMmvvEif/10567. 2)1011 (2822University Physics20Example 4-6 A ball of mass m

15、 = 2.60 kg, starting from rest, falls a vertical distance h = 55.0 cm before striking a vertical coiled spring, which then compresses an amount Y = 15.0 cm. Determine the spring constant of the spring. Assume the spring has negligible mass.4-5 Conservation of Mechanical EnergymhhY 1yyh 20yy 3yyY Uni

16、versity Physics21mhhY 1yyh 20yy 3yyY Choose two points 1 and 3 to use the Conservation of Mechanical Energy 211332mgymgyky 212mghmgYkY Solving for k 22()mg hYkY = 1585 N/mSolution4-5 Conservation of Mechanical EnergyUniversity Physics223. Conservation of Energy(能量守恒定律能量守恒定律)4-5 Conservation of Mecha

17、nical Energy The frictional force is called as a nonconservative force or a dissipative force which exists everywhere and its work depends on the path. If there exist dissipative forces (internal) such as the internally frictional force, it is sure that the mechanical energy of the system decreases.

18、 cncextWWWWUniversity Physics23Question: disappears? ncWIt is transformed into other energy such as heat energy which leads to the increase of temperature of system so that their internal energy of system has an increment .intE4-5 Conservation of Mechanical EnergyintEWncUWcKWWWWcncextconstant0intint

19、EEEE0extWIn an isolated non-conservative system,EUKextWEEintUniversity Physics24 对一个孤立系统，各种形式的能量可以相互转对一个孤立系统，各种形式的能量可以相互转化，但无论如何转化，能量既不能产生，也不能消化，但无论如何转化，能量既不能产生，也不能消灭灭, 保持守恒。保持守恒。 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. 4-5 Con