复旦大学《大学物理》课件（英文）-第12章Potential energy(1).pdf

Ch.12 Energy II:Potential energyCh.12 Energy II:Potential energyCh.12 Energy II:Potential energy12-1 Conservative forces(保守力)Potential energy?It is defined only for a certain class of forces called conservative forces.Do spring force,gravitational force,and frictional force et al.belong to conservative forces?Kinetic energyVelocityWhat are conservative forces?Ch.12 Energy II:Potential energy1.The spring forceFig 12-1x00dd-d(a)(b)(c)(d)(e)(2122ifsxxkW=oxRelaxed lengthFig 11-13The total work done by the spin force is zero in the process from(a)to(e)(round trip).00Ch.12 Energy II:Potential energyThe total work done by the gravity is zero during the round trip.2.The force of gravityIf the gravitational force is not constant,is there still such behavior of the work?See See 动画库动画库/力学夹力学夹/2/2-0404功的计功的计算举例算举例(2)(2)Ch.12 Energy II:Potential energy3.The frictional forceThe total work done by frictional force is not zero in a round trip.See See 动画库动画库/力学夹力学夹/2/2-0404功的计功的计算举例算举例(1)(1)Ch.12 Energy II:Potential energyDefinition of conservative force:One particle exerted by a force moves around a closed path and returns to its starting point.If the total work done by the force during the round trip is zero,we call the force a conservative force，such as spring force and gravity.If not,the force is a nonconservative one.Ch.12 Energy II:Potential energyTwo Mathematical statements:aabb1221Fig 12-4(a)(b)If is a conservative force,we have:F0WWba.2ab.1=+0sdFsdFabba=+(12-1)Path1Path2Statement 1=sdFsdFsdFbaabbaPath1Path2Path2(12-3)0=sdFStatement 2=sdFsdFbabaPath1Path2Ch.12 Energy II:Potential energyTo every action,there is an equal and opposite reaction.Newtons third lawNote:(1)Both the action and reaction forces belong to the system.(2)The total work done by action and reaction forces is independent of the reference frame chosen(even in non-inertial frame).Prove point(2):Ch.12 Energy II:Potential energy1f2f1r2rzyxm1m2221121rdfrdfWWW+=+=SIn S frame:In S frame with velocity ofrelative to S frame:ssv rdf rdfWWW221121+=+=)()(2211dtvrdfdtvrdfssss+=dtv)ff(rdfrdfss+=21221121ff=2211rdfrdf+=W=Ch.12 Energy II:Potential energy12-2 Potential energy1.DefinitionWhen work is done in a system(such as ball and earth)by a conservative force,the configuration of its parts changes,and so the potential energy changes from its initial value to its final value .We define the change in potential energy associated with the conservative force as:iUfU=sdFWUUUif(12-4)Ch.12 Energy II:Potential energy2.The potential energy of gravityFor the ball-Earth system,we take upward direction to be y positive direction)()()()(122112yymgdymgyUyUUyy=The physically important quantity is ,Unot or .)(2yU)(1yU0)0(1=yUmgyyU=)(12-9)If We setWe have(the reference zero point of U is at O)y2y1y=sdFWUUUifmg)()()(1212yymgyUyU+=,dependent on)(1yUCh.12 Energy II:Potential energy3.The potential energy of spring force00=u=xkx)dx(FdxU(x)00221)(kxxU=oxRelaxed lengthFig 11-13When the spring is in its relaxed state,and we can declare the potential energy of the system to be zero()(12-8)The reference zero point of potential is at x=0.21Ch.12 Energy II:Potential energyi.The physically important quantity is .Not or .Notes:01xxUUU=1xU0 xUiii.Potential energy belongs to the system(Such asball-Earth)and not of any of the individual objectswithin the system.ii.We are free to choose the reference point at any convenient location for the potential energy.Ch.12 Energy II:Potential energyiv.The inverse of Eq(12-4)allows us to calculate the force from the potential energy (12-7)dxxdUxFx)()(=xxFdxUUU00Eq(12-7)gives us another way of looking at the potential energy:“The potential energy is a function of position whose negative derivative gives the force”Eq(12-4)mgyyU=)(yFmgdyydU=)(221)(kxxU=xFkxkxdxddxdU=)21(2Ch.12 Energy II:Potential energyAn elevator cab of mass m=920 Kg moves from street level to the top of the World Trade Center in New York,a height of h=412 m above ground.What is the change in the gravitational potential energy of the cab-Earth system?Sample problem 12-1.107.34128.99206JmghymgU=Ch.12 Energy II:Potential energy12-3 Conservative of mechanical energy=dxxFWUUUif)(KU=KmvmvWifnetF=222121From the definition of potential energy,we have:K=0=+KU(12-14)0)()(=+ififKKUUffiiUKUK+=+(12-15)Mechanical energyWhen can Eq.(12-15)be satisfied?is a conservative forceFCh.12 Energy II:Potential energyEq(12-15)is the mathematical statement of the law of conservation of mechanical energy:“In a system in which only conservative forces do work,the total mechanical energy of the system remains constant.”Such as the systems of:Ball-Earth system;Block-spring system on frictionless table.Ch.12 Energy II:Potential energyHow to write the formula of conservation of mechanical energy for:Ball-Earth system/m+M system(Mm)?No other forces exerted in the system.2121)(22constMVmvRrU=+m and v are the mass and speed for Ball,respectively.M and V are the mass and speed for Earth,respectively.212constmvmgh=+orWhich one is c