第25届全国部分地区大学生物理竞赛试题

**********************************************************************************************252008.12.141~12131415161718191.xυ=αxα0t=0x00xa=ta=2.1P1N12P2N2P1P2N1N2“”“”“”12BA3.mAmBAB1a0Ba=2B1µ≥mA/mBa0a0B4.mq0123l123lmax=υmax=lll1235.ν0SBSLt=0BBSυuυtBν(t)=t=0tBN(t)=υLBS6.T1=αT2=α2T3=α3T4α1ηmax=T1T2T3T4η=7.R2QR3R1rqT3T2T1T4VPO8.QR1R2R3qrR2rR1U=U=21BA2BA**********************************************************************************************9.1rABR1=13r2ABR2=10.λnoned0=λ11.U2384.51090.7%U23493%1981U1371.5m22cm20.25%400125U238τ=ln2=0.693U238m=kg212.SS'υS'x'y'S'σ0Sσ1=σ0S'x'υSσ2=σ0υO'OSS'xx'y'y41352yyOLaaνaO'ν13.13νaLdO'OOy31yδ2yOδ13y∆l04daa4**********************************************************************************************14.13SσσE=σ/ε0ES=σ/2ε01F=σS·ES∆lA2AS·∆lEFK=σ/ε0ωeωe~ESσESF∆l32ωe~EQREREKSσFKsEKsEKσ515.13x1xxL/2N2Ntx12LL-x22L6**********************************************************************************************16.13R2=7.5cmR1=5cmρQ=5.5103W/(m3·s)Ku=46W/(m·K)KA=8.6110-3W/(m·K)T2=300K1Q2T1ln1.5=0.4053T04R1ρ1R2ρ2γ710B17A1718171917.10Rm1=m232m=mR2RRm1ω0m2ω1ω2Rm1m2RRR2R8**********************************************************************************************18.10ARR/2BKBKtK=dB/dtOO'Nmq0POυ0θPOMNNυ0θθυ0RMOBK~tPO'N919.10lRABBKφ=0φAυA1ABεAB23φ=45˚βυAφBKlBOAυA101.2xα20etxαα2.3.()B0ABa+mgmm+B0BAa+mgmmµ≥4.43l06qmlπε5.0222(1)tvuLtυυυ−+2220()LtLtvuυ+−−6.311α−211α−7.8.01231()4QqQqQqRrRRπε+++−+034QqRπε+9.153209r23r10.oe4()nnλ−11.96.4910×3012.212(1)cυ−−2222(1)(1)ββ+−113.1(1)asina(3)(2)1324yO2(3)4(3)(2)()ayLcvyycLδθλδλδδ=≈=11min(3)a2a(4)1.221.22aa1.22(4)vcLyvcLlyvcdvdcLlvdλθθ=∆==∆===⋅∆=214.2S0202e01(1),,221(3)21(2)(2)(3)AFlESlAESlASlAESlAESlσσσεεωε=∆=∆=∆=∆=⋅∆∆2RRRR220Rd(d)/,4,ddddddd(4)d(d4d4ddssFsEQSSRrAFrEsrEsrQErQAVRrERQErAσσπσσππε=====⋅======∫∫∫∫)222e020R201dd4d8(4)8QrVERrRQERωεππεπε=⋅==σdsdFKREKRdr14315.22(1)12()2212(2)2222MLxLMMgxLgLxLLxxMgPMLxLLLυυυ−=−⇒=−−−==−22000(3)d()dd22d1(22)(3)4(2)121(2)(1)22xtPMgNMgMgLxtLNxxxLxxgLxgLLυυυ=−=−=−−==−==−=0ζ0ζζ0SS2S3()gLLxMMLLLxυυυζυζζζυυυυζ==−⎡⎤=⇒=⎢⎥−⎣⎦0ζ0(3)LxLxυυυζ−−=−400ζ02000000000000d1(22()2()2d221492(3)4txtLxttLxLxxLxtxxLxLxLxLxxLtLxgζυυυζζυζυ−=−=−−−===−−−−−==−∫∫22000CCB4CB2SBC(3)BCSLLxxLxLtυυυ−==**00C0CB22CBCB1492(3)4LLxxLtLxgυυυ=−−−===−−υζ(L–x0)+ζ153Sx0-ζυ0υυ151L/2-xxL/2L/2-xL–x0152SBx0Cυ0516.12232Q1AA(1)5.510(0.05)43.2J(1)(2)ddddTRTRQRrQTKrQrQrQTKrKρπππππ=⋅=×××=⋅⇒==∫∫2A12123A112Quln43.27.5ln300ln624K(3)8.61105(3)dddRRRQTTKRrRTrKrrTππρππρ−=+=+=××⋅⇒=21QQ210uu23Q1201u01d5.510624(0.05)624.07K446624K(3)(4),:TRTrrRKKRTTKTTPPnkTnρρ−=×=+=+×=×⇒≈==∫∫1122()()()()0.481(3)nrTrrTrTTρργρ=⇒====617.111110102111C1110(1)O()()222()(2)(O)3(32)(3NNtNtNtmRmRmRNtRNtRRmRIRmωωωωωωω∆∆−∆=⋅−⋅=−∆⋅−∆⋅=⋅+−C1022222C1122221110222211222)(2)3(1)11,(3)133()57311RINtRIImRImRmRNtRNtRmRNtRmRIIωωωωωωω⋅+∆⋅===+⋅∆⋅−∆⋅=−∆⋅=+=2102211111210201(2)1(2)1136(3)6565IImRmRNtmNtmωωωωωωω=+⋅∆∆=−=−ω0ω1ω2N1NNO1O22RRm2Rm1R17718.A111d()d2()A1d1(2d2rEBErrtRBrRBBErkt=×=−=×+−KKKKKKKKKKKK20O20d1d)(4)d2d2Pd1a(2)4d4sin2/a(1)BBrkrkEttrRqERBEKRmtRυθ′×=×======KKKKKKKٛ22022sin/2a(1)2sin2sin2sincossintan2arctan2(63.4)Rυθθθθθθθθθ==⇒=⇒=⇒==°22000(1)a/sin,sin255(1)4RKqRmυυθθυ==⇒=BK~t()ErKKrK181BK~t1rK2rKOO'0rK182kKEKO′ON2R2Rm,q0aaPO'ON183819.22ABOAAA(1)ABOA11(cos)(sin)sin224d1dcos2d2d(sin)sinBllBlBlttllφφφεφωωυυφωωφΦ=−⋅=−ΦΦ=−=⋅==⇒=ABABOAAABABA22ABAx1cos2sin(1.5)2cos2(2)AB2sinABcos2,2sinBlBlIRRFeBlFFeFIBlRFεευφφεφυφφυφ========−KKKKyABddABdcos,sinABddddddddddddlllFFFlFFeIBlelFPFIBlelmlφφυυυλλ=−=⋅=⋅=⋅=⋅=KKKKKKKKKKKABdFABd0dC0CFABCABCC1d(d)AB1dd:d:llllllPIBemFPPIBemmlmmmPIBelIBeFυλυλλυυυυυυλ=⋅⋅==⋅⋅=⎧⋅=⎨⎩=⋅=⋅=⋅∫∫∫KKKKKKKKKKKKKKBACAAC11cos22sin1(0)2ijφυυυφυυυυυυ⎧==⎪⎪+⎨⎪=−⎪⎩KKK92FxyAA22222FA222222IABA21cos1cos2(sin)2sin2sincos2(6)4sincos2(0.5)4sinPFFFFBlPRBlPIRRφφυυυφυφφφυφφυφ=+=−−=−⇒−===FI222km22k(3)1126dd1d1ddd3d3PPEImltttEmltmltφωωφφφωωβφ−===→+→+==()PIIIkPI2kPdd1cossind22dd450ddd145dddsind32llEmgmgWPtPEEWlEEmlmgφφφφφβφφ⎡⎤−=−=⎢⎥⎣⎦==°==−−=°=−⇒=φ332sin(2)24ggllβφ⇒==φφeKIABCυKIABBυKAυKdlKdFKFKyAφBKCBO19x10