物理培训课程

1PhysicsEnhancementProgramme–StudentSelf-learningBooklet(try-outversion)MECHANICSINPHYSICSOLYMPIADChapter1VectorandMechanicalMotionLHYungChapter2ForceandEquilibriumofBodySCNgChapter3Newton’sLawsofMotionandLawofUniversalGravitationSCNgChapter4MomentumandTheoremofMomentumSCNgChapter5Work,MechanicalEnergyandTheoremofKineticSCNgChapter6LawsofConservationinMechanicsSCNgChapter7SimpleHarmonicMotionWYDikChiefEditor:ProfessorYangZhiYu:HongKongPhysicsOlympiadCommittee20072•••••31.1-……-……1.2--BArr-BArr-BrAr()BArr-)(BArr-+Br().ArBrBArr+ArBrBArr+)(BArr-BrAr)(BABArrrr-+=-ArBrArBr-)(BArr-+BArr-41.3---x-oxry-oyr1ArAr(A)1==ooyxrr-Ar2oxxAroyyAr()Ar2-oyoxyAxAArrr+=(1.1)Ax=Acosq,qArx-Ay=Asinq,22yxAAA+=(1.2)-oyoxyAxAArrr+=oyoxyBxBBrrr+=oyyoxxyBAxBABArrsr)()(±+±=±(1.3)xyoxroyrxyoxxAroyyArxyAr51.41.4.1-ArBr()cosABABq•≡××rrrr(1.4),q2-ArBrBrBrArAr.-FrsrWcosWFsFsq≡•=rr(1.5)-(1)ABBArrrr•=•(1.6a)(2))()(BAkBAkrrrr•=•,k(1.6b)(3)CABACBArrrrrrr•+•=+•)((1.6c)(4)ArBr0=+BnAmrrm=n=0(1.6d)(5)ArBr,0=•BArrArBr(1.6e)(6)oyoxyAxAArrr+=oyoxyBxBBrrr+=yyxxBABABA+=•sr,(1.6f)1=•=•ooooyyxxrrrr0=•=•ooooxyyxrrrr(1.6g)ArBrqArBrqqcosBABBA×=•)cos(qrr=qcosBBrArArBrqqcosABABA×=•)cos(qrr=qcosAArBr61.4.2ArBrCrCAB=×rrrCrArBrsinCABq=⋅⋅(1.7).(0BBAA×==×rrrr)ABBA×=-×rrrr.(1.8)(oxroyrozrooozyxrrr=×)1212()AABABAB+×=×+×rrrrrrr;1212()BAABABA×+=×+×rrrrrrr(1.9)()()()kABkABAkB×=×=×rrrrrr,k(1.10)x-y-z000xyz×=rrr,000yzx×=rrr,000zxy×=rrr.(1.11)000xyzAAxAyAz=++rrrr,000xyzBBxByBz=++rrrr000000()()xyzxyzABAxAyAzBxByBz×=++×++rrrrrrrr=…..000xyzxyzxyzABAAABBB×=rrrrr.(1.12)CBArrr•×)(ArBrCrqArBrCrq71.5-x-yP(x,y)-rrOPooyyxxOPrrrr+==(1.13)-z-z-x-y-ooozzyyxxOPrrrrr++==(1.14)Ooxr,oyrozr1.6,-rrΔ.=Δrr-P(x,y)xyP(x,y)xyO(x,y,z)xyzxyz8-ooozzyyxxrrrrrΔ+Δ+Δ=ΔΔx,ΔyΔzx,yz--ΔtoooaveztzytyxtxtrvrrrrrΔΔ+ΔΔ+ΔΔ=ΔΔ=(1.15)-Δt000000zvyvxvzdtdzydtdyxdtdxdtrdvzyxrrrrrrrr++=++==(1.16)-()000000zayaxazdtdvydtdvxdtdvdtvdazyxzyxrrrrrrrr++=++==(1.17)02202202222zdtzdydtydxdtxddtrdarrrrr++=≡(1.18)1.7-u,vxk-Ÿdxdvdxduvudxd±=±)((1.19a)Ÿdxduvdxdvuuvdxd+=)((1.19b)Ÿ2vdxdvudxduvvudxd-=⎟⎠⎞⎜⎝⎛(1.19c)Ÿdxdydyydfyfdxd×=)()(,(1.19d),f(y)y9-Ÿ0=kdxd,k(1.20a)Ÿdxdukkudxd=(0=dxdk)(1.20b)Ÿ1-=nnnxxdxd,n(1.20c)Ÿxxdxdcossin=(1.20d)Ÿxxdxdsincos-=(1.20e)-)213(2kttdtd+k)213(2kttdtd+=)21()3(2ktdtdtdtd+()2213tdtdkdtdt+=())2(21)1(312-+=tkkt+=32213ktts+=ktktdtdsv+==3,vtv(x)kktdtddtdva=+==)3(,ak)sin(trdtdwrw)sin()sin(tdtdrtrdtdww=()dttdttddr)()sin()(×=())cos(trww=101.8()-(CE)atuv+=(1.21a)221atuts+=(1.21b)asuv222=-(1.21c)-()--(x0=y0=0)u(oxr)q--ax=0,vx=()=ux=ucosq.(1.22a)x–x0=uxt(1.22b)-ay=-g(1.22c)gtutauvyyy-=+=qsin(1.22d)22011sin22yyyyutatutgtq-=+=-(1.22e)(x0,y0)t=0(x0,y0)oxroyr-tyx1.9-(r,q)r-q(x,y)yxoygarr-=uqqr11q(rad)-wwrads-1dtdqw=(1.23a)-arads-2aq22dtddtdqwa==(1.23b)1.9.1-w(a=0)qfwq+=t(1.24)ff=0-v-qxy)cos(costrrxwq==(1.25a))sin(sintrrywq==(1.25b)-vrx-y-)sin())sin((trtrdtdxvx=×-==(1.26a))cos()cos(trtrdtdyvy=×==(1.26b)vr()wrvvvyx=+=22,(1.27)-vrrr•=0-arvrt)cos(2trdtdvaxxww-==(1.28a)qr(x,y)12)sin(2trdtdvayyww-==(1.28b)-2wxxra-=and2wyyra-=rarr2w-=(1.28c)1.9.2()-w(a≠0)-tqcosrx=qsinry=qwqqsin)sin(rdtdrvx-=-=qwqqcoscosrdtdrvy==qwqaqqwqwcossincossin2rrdtdrdtdrax--=--=qwqaqqwqwsincos)sin(cos2rrdtdrdtdray-=-+=rCTreaeaereraˆˆˆˆ2+=-=qqwarreˆqeˆq-2wraC-=-araT=-aTvdtdvaT=v1.10SS’OO’SX–Y-Z-S’X’-Y’-Z’OO’rr'rrRrOO’rr'rrRr13urArRrrrrr+='.(2.1)uvdtRddtrddtrdvrrrrrr''+=+==(1.29)''dvdvduaaAdtdtdt≡=+=+rrrrrr(1.30)ur0A=r'aarr=1.11()1.+/-+/-2.+/-3.oxv,oyrozrx,yz-ozoyoxzAyAxAArrrr++=ozoyoxzByBxBBrrrr++=.a.BArr±b.BArr•c.ArandBArr+d.2AAArrr=•e.CBArrr•×)(;)(CBArrr•×;()ABC××rrr;()ABC××rrrABC××rrr4.0yr0xr0zr(a))175(00zyrr-m/s;)51712(000zyxrrr++-m/s(b))51712(000zyxrrr++-m/s;)517(00zyrr+m/s(c))5(0zrm/s;)51712(000zyxrrr++-m/s(d))517(00zyrr+m/s;)512(00zxrr+-m/s(e)017yrm/s;)512(00zxrr+-m/s145.P0342ooorxyz=-+rsrrooozyxarrrr--=32rr(2012rrat=+rrr)6.)sin(tAxw=Aw(Aw)x-t,v-ta-t.ax(7)qq30o60o151.124.1017vy=rr2012vx=rr305vz=rr305vz=rr413vvv=+rrr542vvv=-rrr8.βαcosxvta=21sin2yvtgta=-tanyxb=00sincosggxgybb=--rrr21cos()sin2xvtgtabb=--,(1)21sin()cos2yvtgtabb=--(2).2sin()cosvtgabb-=22xy+11.(0,H)211sin2yHvtgtq=+-,1cosxvtq=(0,0)20y=,22xvt=y1=y2,x1=x22cosvvq=qq210sin2Hvtgtq=+-ttx1x2162.11ÄÄÄÄ2.(1)2)(3)……3.(1(a)(b)G=mgmg(c)(d)(a)(b)(c)Fkx(a(bFsFNsFN(c)FkFNFkFN17(4)221rmmGF=(2.1)G=6.67×10-11Nm12/kg21.234ABBABA5.A.B.C.D.2N2cm10cm10NA.AB.C.vCD.D182.2(1)2121FFFFF+≤≤-(2)qcos2212221FFFFF++=qqfcossinarctan121FFF+=qcos2212221FFFFF++=FFqfsinsin2=22yxFFF+=xyFFarctan=f∑∑==iyiyixixFFFFqqcos,cosFFl=mgsinaF2=mgcosaAB.C.D.E.2121FFFFF+≤≤-192.3?????????????????????????????,????????????????????????????????????????????????????????????O(??????)??Fr???O???????M=rF(2.2)rOFrMrF≡×rrr(2.3)(2.3)(2.2)2.41.2.(1)123...0inFFFFF=+++=∑rrrrr(2.4a)(2)123...0inMMMMM=+++=∑rrrrr(2.4b)3.(1)a.b.()c.d.(2):a.b.FrrOFrrFrrOFrOrrFrOrr20c.d.MFA.B.C.D.GxFGxFGxFGx=FABCDFA.BC.DF2.5A.B.C.D.T=mg21Tsin?Tcos?N+Tsin?=GN=G-Tsin?f=Tcos?cos?fRhRLGFhRRGN+=+=;hRRGN+=hRLGF+=F1F2F3F4F5F3ACDCOACDF1F4F3FlF4F3OBCEF2F5F3F1F2F3F4F5F=3F3=30N30N22a=gsinal1l2l3l4?A.l1l2B.l3l4C.l1l3D.l2=l4DABABOOA2m0coscos2211=-aaTT.()TTT==21,aaa==21