虚功原理在竞赛中的妙用

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·◇ζ,,WWi。:W()=Wi()。:———。,,,。:11,5lm,,,,,,。:,。。l,E=-2mgl4-2mg3l4-mgl=-3mgldl,W=-TdlW=dE-Tdl=d(-3mgl)=-3mgdlT=3mg。2AB,A,B,2。B,。:3,,。1yOAθB(x,y)x2yANθCPN2N1φφB(x,y)O3x56·:N1N2=tanφ=dydx%%①:sinθ=x/l%%%②:N2=P%%%③A:N1cosθ+(Plsinθ)/2=N2lsinθ%%④①②③④N1,N2①:dydx=xl21-xlφφ2%姨dylφφ=xl21-xlφφ2%姨dxlφφsinu=x/l,:dylφφ=12sinudu:yl=-12cosu+C%y=-121-xlφφ2%姨+C′x=0y=0,:C′=l2:y=121-1-xlφφ2%姨姨姨,。:,,,,PδyC=0%yC=:yC=y+12l2-x2%姨y+12l2-x2%姨=x=0y=0%,l2。y=121-1-xlφφ2%姨姨姨,。34,l,,P,2a(2a<2l),?φ。:,AP,CPP。F1,Q,。,F4。5。AQ::F4sinφ=F2K:F4cosφasinφ=F3l-asinφφφA::F2cosφ+F3sinφ=F1cosφ:T+F1sinφ+F2sinφ=F3cosφP::2F1cosφ=P5:T=Pa2lsin2φcosφ-tanφφφ:4,T,P,,:xA=lsinφ%δxA=lcosφδφyP=2lcosφ-acotφ%%δyP=-2lsinφδφ+aδφsin2φQKφx2aJCATTlPy4F4QφasinφNKF3F2AF2F3φAφF1TF1φφF1P557·:-2TδxA+PδyP=0δxA,δyP:T=Pa2lsin2φcosφ-tanφ4lmg,2l2mg,6,2%姨l,。:,。:,Bδy%,C2δy,BCδy%,:-TδyB,8mgδy,:-Tδy+8mgδy=0T=mg,,,,。。57,,2n,W,ii+1Ni。:8,k。:α=π4n%β=kπ2n-π4n=(2k-1)π4nx0,:Nk-1cosα+Wcosβ-Nkcosα=0:Nk-Nk-1=cos(2k-1)π4ncosπ4n姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨W:Ni=ik=1∑cos(2k-1)π4n∑∑Wcosπ4n=ik=1∑2coskπ2n-π4nsinπ4n∑∑W2cosπ4nsinπ4n=ik=1∑sinkπ2n-sin(k-1)π2n∑∑∑∑Wsinπ2n=siniπ2nsinπ2n姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨姨W,。:9,OO′R,iC,COL。:NiRcosαdθ=iWd(Lsinθ)=iWLcosθdθ%α=π4n:Ni=iWLcosθRcosαLθK2n2n-17βNkαWxN(k-1)8θOaRO′NiC9AllBCδy2δy658·θ=122iα=iαL:10。imR、2αimL。:imL=2mR2sinαsin(iα)%L=Rsin(iα)isinαN:Ni=iWLcosθRcosα=iWRsin(iα)isinαcos(iα)Rcosα=Wsin(iα)cos(iα)sinαcosα=siniπ2nsinπ2nW,,,。,,。,,,,。611,R1,R2,εrρ,U,。:,,。:λ,rE=λ2πε0rU=%%乙Edr=R1R2乙λ2πε0rdr=λ2πε0lnR1R2C0=λU=2πε0ln(R1/R2)C0′=2πε0εrln(R1/R2)L,x,:C=xC0′(L-x)C0=2πε0[(εr-1)x+L]ln(R1/R2)E=12CU2,F(),Fdx,Fdx=dE=d12CU乙乙2=U22dC=U222πε0(εr-1)dxln(R1/R2)F=U222πε0(εr-1)ln(R1/R2):F=ρhπ(R21-R22)gh=U2ρ(R21-R22)gε0(εr-1)ln(R1/R2),。,。,。,。。11mR(i)imL2a101928,、、、、、、。、,。,。:、、、、。()59

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