1、Ch.11 Energy I:Work and kinetic energyCh.11 Energy I:Work and kinetic energyCh.11 Energy I:Work and kinetic energy11-1 Work and energyExample:If a person pulls an object uphill.After some time,he becomes tired and stops.We can analyze the forces exerted in this problem based on Newtons Laws,but thos
2、e laws can not explain:why the mans ability to exert a force to move forward becomes used up.For this analysis,we must introduce the new concepts of“Work and Energy”.Ch.11 Energy I:Work and kinetic energyNotes:1)The“physics concept of work”is different from the“work in daily life”;2)The“energy”of a
3、system is a measure of its capacity to do work.Ch.11 Energy I:Work and kinetic energy11-2 Work done by a constant force1.Definition of WorkThe work W done by a constant forcethat moves a body through a displacement in the directions of the force as the product of the magnitudes of the force and the
4、displacement:(11-1)Fs(Here )FsW=F/s11-3 Power Ch.11 Energy I:Work and kinetic energyThe normal forcedoes zerowork;the friction forcedoes negative work,the gravitationalforcedoes positive work which is orNNmghmgs=cos)cos(cosmgsmgs=gmgmfshvFig 11-5fExample:In Fig11-5,a block is sliding down a plane.Ch
5、.11 Energy I:Work and kinetic energy2.Work as a dot productThe work done by a force can be written as(11-2)(1)If ,the work done by the is zero.(2)Unlike mass and volume,work is not an intrinsicproperty of a body.It is related to the external force.(3)Unit of work:Newton-meter(Joule)(4)The value of t
6、he work depends on the inertial reference frame of the observer.FWF s=sFFgmshvCh.11 Energy I:Work and kinetic energyIf a certain force performs work on a body in a time ,the average power due to the force is(11-7)The instantaneous power P is(11-8)If the power is constant in time,then .avWPt=dWPdt=av
7、PP=3.Definition of power:The rate at which work is done.WtCh.11 Energy I:Work and kinetic energy(11-10)Unit of power:joule/second(Watt)dWF d sd sPFF vdtdtdt=If the body moves a displacement in a time dt,sdSee See 动画库动画库/力学夹力学夹/2/2-0303变力的变力的功功A.exe 1A.exe 1Ch.11 Energy I:Work and kinetic energyWork
8、done by a variable force1.One-dimensionalsituationThe smooth curve inFig 11-12 shows an arbitrary force F(x)that acts on a body that moves from to .Fig 11-12ixixfxfxxxF1F2F)(xFx11-511-4Ch.11 Energy I:Work and kinetic energyWe divide the total displacement into a number Nof small intervals of equal w
9、idth .This interval so small that the F(x)is approximately constant.Then in the interval to +dx,the work and similar The total work is or (11-12)11WF x=x22WF x=1x1x=NnnxFW1.2121+=+xFxFWWWCh.11 Energy I:Work and kinetic energyTo make a better approximation,we let go to zero and the number of interval
10、s N go to infinity.Hence the exact result isor x01limNnxnWFx=01lim()fiNxnxxnWFxF x dx=(11-13)(11-14)ixfxNumerically,this quantity is exactly equal to the area between the force curve and the x axis between limits and .Ch.11 Energy I:Work and kinetic energyExample:Work done by the spring forceIn Fig
11、11-13,the spring is in the relaxed state,that is no force applied,and the body is located at x=0.oxRelaxed lengthFig 11-13221()2fixssfixWF dxkxdxk xx=kxFs=Only depend on initial and final positionsCh.11 Energy I:Work and kinetic energyFig 11-16 shows a particle moves along a curve from to f.The elem
12、ent of work The total work done is(11-19)ifFsdxyoidWF d s=cosffiiWF d sFds=()()()fxyifxyiWF iF j dxidy jF dxF dy=+=+Fig 11-162.Two-dimensional situation(11-20)orCh.11 Energy I:Work and kinetic energySample problem 11-5A small object of mass m is suspended from a string of length L.The object is pull
13、ed sideways by a force that is always horizontal,until the string finally makes an angle with the vertical.The displacement is accomplished at a small constantspeed.Find the work done by all the forces that act on the object.ymgmFmdsTFig 11-17FmxCh.11 Energy I:Work and kinetic energy11-6 Kinetic ene
14、rgy and work-energy theoremfor a body of mass m moving with speed v.212Kmv=,F,avRelationship between Work and Energy1.Definition of kinetic energy K:2.The work-energy theorem:221122netFfiWmvmv=(11-24)“The net work done by the forces acting on a body is equal to the change in the kinetic energy of th
15、e body.”Ch.11 Energy I:Work and kinetic energy3.General proof of the work-energy theoremFor 1 D case:represents the net force acting on the FdxdvmvdtdxdxdvmdtdvmmaFxxxxxnet=The work done by isnetFxnetnetxdvWF dxmvdxdx=It is also true for the case in two or three dimensional cases221122xfxivxxxfxivmv
16、 dvmvmv=Ch.11 Energy I:Work and kinetic energy4.Notes of work-energy theorem:221122netFfiWmvmv=The work-energy theorem survives in different inertial reference frames.But the values of the work and kinetic energy in their respective reference frames may be different.Please relate a)point to conservation of momentuma).In different inertial reference frames?b).Limitation of the theoremIt applies only to single mass points.Ch.11 Energy I:Work and kinetic energyCh.11 Energy I:Work and kinetic energy
