第22届全国部分地区大学生物理竞赛试题

222005.12.411213141516171819100B17110A17181201719120.1222481.mRIK=O0vGO=ω20=t0x0vtetAAxβ−+=)(21β21AA0=t=0a13scmu/200=cm100=λPxPP=cm20=4cmξ/12vPscmπ==A,0=x=0φ3427CDsm/485,D27C56SPV121T27321rrrεεε=minE=maxE8a,I729RBA=ABRCA=ACR103.0mm550nm,=minθrad()2cmS=m.11.902mv121011.9×=1063.6kgme31−−34sm/106sJh⋅×=m45g40m/sm34135213hT41402TR2502TR27η5151R)(tuu=TRPURPPU2101)(tuUV3==εε,24),cos(20202Vt=+=εφωεεRU616.S12'SS'SS1S2S719B17A171817173R32RR21RRQeW818ARl2ABCCBµµ919gG)()(xQyxpdxdy=+:,)()()()(CCdxexQexydxrxPdxxP⎟⎠⎞⎜⎝⎛+∫∫=∫−10222005.12.4100B17110A17181201719120AB1222481.=0vmIG=ωmRI2.00201,vxAxA+==β=0a)2(00vx+−ββ3=A5cm,=0φπ19.04396m/s1584m/s5267.=minEdUrrr313εεε+=maxEdUrrr311εεε+89aIπµ2/20=ABRR65=AcRR241710=minθ410237.2−×rad()S=89.4m.11.0m0221mcv−12mm)108.5(103.776−−××)109.2(107.33332−−××4135213yShgghhS21)'(ρρ=+3,)'()(12ghhSgyhSFy+−−=ρρ3,)'(1yyahhSF+=ρ10)'(12=++yhhgayρρ1h1ρ)'(1hh+ρ0=+yhgay2ghTπ2=(3)114000825327RTTRTRQABννν=×−×=33ln3ln300RTVVTRQBCBCνν=×=2)3ln38(0+=+RTQQQBCABν08RTQQABCDν==23lnln00RTVVRTQADDAνν==2)3ln38(0+=+RTQQQDACDνη%5.193ln383ln811=+−=QQη4151,)()(2Rtutp=1∫∫==TTdtRtuTdttpTP020)(1)(1121022)(1,⎥⎦⎤⎢⎣⎡=⇒==∫TdttuTUPPRUP4221022010)]cos([1⎥⎦⎤⎢⎣⎡++=∫TdttTUφωεε221022202010210)](cos)cos(2[1⎥⎦⎤⎢⎣⎡++++=∫TdtttTφωεφωεεε2102220210)](cos[1⎥⎦⎤⎢⎣⎡++=∫TdttTTφωεε220210212202102121[1εεεε+=⎥⎦⎤⎢⎣⎡+=TTT32V5=2161421QSS∆2PP21QSS∆S1S11111PSLLSBSA+=111111SSOSBSALL=1111PSLLSSO+=PS2S22222222PSLPSLLSSOSBSA−=−=1L2L)()(21212211PSPSLLLLLSSOSSO++−=−=∆212211SSLLSSOSSO−=−)(212121PSPSSSLLL++−=−=∆621SS=+21PSPS321SS17Q3R3043RQURπε=22R3R30432RQUURRπε==21R)111(443210202211RRRQUdrrQURRRR+−=+=∫πεπε3[])111(8)(2132102123RRRQQUUQQUWRRR+−=+−+=πε33180ωθω2220231,,2121mlImrIIIICCPCP=+==ωω0223ωωrll+=θωωRrrrllrvC=+==,32203C222420)3(rlRldtdddrdrdvdtdvaCCC+==ωθθ22222023rlrlraC+=ωω1NfCCmafmaN==2CCaaNf=≥µRlrlRlrrl40,)3(222⇒≥+≥µµ2191ρ2ρtr1334ρπrm=vdt22)(ρπvdtrdm=0'=vdtdmvdtdvmmg+=22211143ρρρvrdtdvg+=1dtdr2212)()4(ρπρπvdtrdrr=2221214,4dtrddtdvdtdrvρρρρ==24211222243ρρgdtdrrdtrd=⎟⎠⎞⎜⎝⎛+34dtdry=drdyydtrd=22312243ρρgyrdrdyy=+2yu=drdudrdyy21=1226ρρgurdrdu=+44uydtdr==⎟⎠⎞⎜⎝⎛22:,261262CCdregeudtdrdrrdrr⎟⎟⎠⎞⎜⎜⎝⎛+∫∫==⎟⎠⎞⎜⎝⎛∫−ρρ612214rCrgdtdr+=⎟⎠⎞⎜⎝⎛ρρt=00r2121256,14tgrrgdtdrρρρρ==tr~2gagtv71,71==47g5