物理学的发展促进了其它自然科学的发展

ABmn=aobonm=vVlL=wWlL=v=rtv=lim=drdtt0→rtv=v=drdtr=→limtt0v=limr=limst=dsdtt0t0→→tv=dxdti+dydtj+dzdtk=vj+vj+vkxyzv=x2vvvyx++22a=vta=limt0→=vtdvdta=dvdti+dvdtj+dvdtk=ai+aj+akxyzxyzaaaaxyz222++x(1.10)a=dvdtxxdv=adtvv0t0∫∫x=vt+12at02v-v=2ax202y-y=vt+12at1002y-(y+h)=vt-12gt2002vt+12at=h+vt-12`gt0202t=2ha+g=22.741.22+9.80=0.705(s)×d=y+h-y=12gt-vt0120=129.80.705-2.440.705=0.720(m)2s=v2t1.12ABst2=h=v2tl=v2t1tthl1=gg=tt=hl=sin11u=vcosv=vsin-gtx0y0⎫⎬⎪⎭⎪x=(vcos)ty=(vsin)t-12gt002⎫⎬⎪⎭⎪y=xtan-12θθgxv2022cosy=(vsin)t-12gt102x=xy=y-12gt20202(vsin)t-12gt=y-12gt0202tan=yx00θv=dsdtv=Rddtθddtθ=ddtθa=limvt=limt+limvt=a+at0t0t0tnt→→→na=lima=limnt0t0→→vtvtntv=v=vnsRa=lim=limlimnt0t0t0→→→=vtvsRtvRvsRtnlimst=vt0→a=vn2Ra=limvt=dvdttt0→a=d(R)dt=Rddt=Rdt2ωωθdt2a=an2+at2=arctanaa(1.28)nta=v,a=dvdtn2tρa=dvdt=vt=20360=0.111(m/s)t2×a=vR=(at)=(0.111120)800=0.222(m/s)n1211222R×a=a=0.222=0.248(m/s)n222++at220111.=arctanaa=arctan0.2220.111=63.4ntdvdtdvdtdudt=+a=dudt=00v=v=10=11.2(m/s)bbc22++vcω225θ=90+arctan510=116.6SESPSESP(1.31(a))()CCP=SEEC=SPSESP(1.31(c))()r=x2+y2v=drdta=drdt22v=dxdta=dxdt22⎛⎝⎜⎞⎠⎟+⎛⎝⎜⎞⎠⎟⎛⎝⎜⎞⎠⎟+⎛⎝⎜⎞⎠⎟22222dydtdydt/122uv⎛⎝⎜⎞⎠⎟(3)t=t2122uvx=0y=vt-12gt(vg)020t=lgF=d(mv)dtFFmai∑FFaa1212=mmaa1221=F=GMmREE2mg=GMEmRE2g=GMREE2f=Nsmaxsxfcos-Nsin=m(-a)yfsinNcos-mg=0sminsθθθθa=sin-coscos+sinminssθμθθμθ⎛⎝⎜⎞⎠⎟ga=sin+coscossinmaxssθμθθμθ-⎛⎝⎜⎞⎠⎟gE=2246060π××F=GMmrE2FGMmr=maE2r=GM3EE2ωr=3GMEEω2112452366710598107310=××××--..(.)xNsin=mvryNcos=mg2ααtan=αvrg2α=arctanvrg=arctan2254009.8=arctan0.0574=3172×f=man=mrn2ωmr2ωTcos-G=0θT-Gcos=0θ(1)a=13g(Mastlin)1591&&aT32=KR=K3T2I=2mvFTmvRR=2πT=2RvF=mv2πRF=mvR=m2RT2π⎛⎝⎜⎞⎠⎟∞==22322211RRTRTRRBEBABABD=2Rssh=h=s22Rh=v222122222RRTRRT=⎛⎝⎜⎞⎠⎟=ππh=22π×××××=×-603500528027321624360039102223..()ft391016141003.×≈-h=12atfmt2212=3.13ACFAFECFD1212AFAEFCDCAECDFCFA=EMDNAECD=()()22EMDNFCFA=()()22FFFCFAAC=()()22FF=GmmRmmR122122M=GMMEacEMrEM2a=GMrcMEM2OfGMmrRGMmrMEMEMEM022=--()=-⎛⎝⎜⎞⎠⎟-⎡⎣⎢⎢⎤⎦⎥⎥-GMmrRrMEMEEM2211n(n-1)2!x2fGMmrRMEME032≈e/(Gmm)=2.3102pe39mec/(eH)71032039&G/G-1/t=-610/a-11g=GM/RRE=6.37106mG=6.6710EE2-11M4r/TGMMP2PS2PS/rPS2,MrTGMMrPPSPSPS4222π=K=rTPS32RTMP32=GM4P2πF=dmvdtdPdt()=Fdt=dp=p-pttpp000∫∫IFdttt0∫E=12mvK2I=dt=p-pI=dt=p-pxxttxx0yyttyy000FF∫∫⎫⎬⎪⎭⎪FF=1t-tFdt0tt0∫FPPtt--00F+f=dPdtF+f=dPdt1122F+F=ddt(p+p)1212F=ddtPiiii∑∑Fp1iii∑∑FdtPPiiittiii∑∑∫∑⎛⎝⎜⎞⎠⎟=-00F=0ii∑p==iiiiP∑∑0Fixi∑=0P==ixii∑∑Pix04.4vFF=01ix∑(m+m)v=mvcos+mv1202211∂v=(m+m)v-mvcos112022αm1=+×-××=()..(/)2005035060866200245msFdt=(m0-mvsin)-(m+m)0=-mvsin=-5060.5=-150(Ns)1221222tt0∫αα0=mv+MVmv=-MVxxmvdt=-MVdtxmvdt=-MVdtx0t∫∫0tX=-mm+MRdv=-udmmdvudmmvMM00∫∫=-v=ulnMM0[(v-u)-v]dmdt=-udmdtF=udmdtvulnN11v-vulnN212vulnNulnNu(lnNN)21212v=uln(NNN)n12n4.7ABCrpsin2=rpsin=rpsin=h=rsin1122ππαα2rpsin=hp=hpαL=rp=rmvL=rpsin=rmvsinααdLdtddtrmvrdmvdtdrdtmv=×=×+×()()dr/dt=vmv=0=Fdrdtdmvdt()dLdt=rFMdldtM=dLdtMM=dLdtxxyzzdldtyM=dLdtzzdLdt=0L=σα=12rrsin=12rrσddttrrtttσσ==×→→limlim0012=12rdrdt=12××rvddtrvσ=12×v=v2389=6.31(km/S)216378439+)12mvmv22(12)mv2Fds∫=12mv2W=Fs=FscossθW=dW=Fdrababab∫∫W=Fdr=(FFF)drFdrFdrFdrabab12nab12n∫∫∫∫∫abababW=Fdr=Ftdr=matdrabababab∫∫∫a=dvdtdrvdttWmvdt=mvdvababvvabdvdtt∫∫12mvE2kE=12mvk2W=E-EabkbkaW(Tmg)drmgdr=mgdrcosabababab∫∫∫θdr=ldθW=mglcosd=mglsin=mghababθθθ∫mglsin=12mv2θv=2glsinθT-mgsin=mv2θlT=mgsinmvl=3mgsin2θθWmv-12mv20212W=Ns=0W=mghNPWmghmvf212W=12mv-mghf2=1221105-21109.83.9-5.410(J)3235W=fscos=-fsfπf=-Ws=1.5410Nf3WFdxi-kxiidx-kxdx=12kx-12kxabxa2b2axxxxxabbab∫∫∫F-GMmre2rdWFdr-GMmredr-GMmrdrcos=GMmrdr2r22θWFdrGMmrdr=GMmr-GMmrab2baabrrab∫∫-FdrFdrFdrFdr-Fdr∫∫∫∫∫LLLLABBAABBAFFdr=LFdr|ABLAB∫∫Fdr0∫∫W=E-E=-EabpapbpE=WFdrpaaa∫E=-GMmrpE=12kxp2f=N=kmgkkμμ-mgx=0+12kx-12kmμmmv2020⎛⎝⎜⎞⎠⎟+⎛⎝⎜⎞⎠⎟μkmmkxmgx=mv02-=×-××××222204380022049802.....v=22gh1mv(m+m)v12v=gh/22v12122mv2mgl+12kl=12k(ll)22212122k=mg/l1v=gh/2=10cm22l1l-20l-300=0222GMmrmvrE22=v=GMrE1212mv-GMmRmv-GMmr12EE2Ev=GM1E21RrE-⎛⎝⎜⎞⎠⎟v=GMR1minEEgGMREE2v=gR1minEv=9.86.3710m/s=7.90km/s1min6××12mv-G022v=2GMR2EE=2gREv11.2km/s22v31232mv-GMsmr=0v=2GMsr3=×××××-267101991014910113011...v3v42.2-29.812.4(km/s)312mv3212mv=12mvmv322232v16.7(km/s)3vv223222112124++..mghmu212yky212v=2GM/Reμk=hsE=-GMmr+r12mdxdt=-kx22ω2=kmdx2dt+=022x=Acos(t+)ωφA=xt=0maxφAφxAcosv=-Asin00φφA=x=arctan-vx0200+⎛⎝⎜⎞⎠⎟⎛⎝⎜⎞⎠⎟v02ωφωv=0(6.5)cos=1=0t0x-Av0=000φφφT=1T=2ωπ=kmT=2=2πωmkAφv=dxdt=-Asin(t+)=Acos(t++2)φφπa=dvdt=-Acos(t)=Acos(t++)22φφ(t)tφt+=0x=Av=0t+=/2x=0v0xt+x-Av0t+=(3/2)x=0vOφφφφφx=Acos(t)x=Acos(t)1122φφ12φφφφφ=(t+)-(t+)=-2121φφφφ2112-)φφφ(12φ),,φ(1)=026.4φ(2)=6.5φ(3)=(-)0xx2121φφφxx()x1x2212φφφφφφπππ=32xx=32-2=-2xxxx2121123222t+=t+1122φφφt=t-t=-(6.11)21φφωφω12-xx0t0ttx21212φφxt1Aφrad/st=0Ax)φφtAx(t+)Axx=Acos(t+)φAφφφt+tTAt2AφAt=0Aφ.xA=4cm=12Hzx=Acos(t+)φ=2=rad/sAt=1sφcos(+)=-12φ+=23=-3+=43=3φφπφφπv=-Asin(t+)φv=-Asin(+)0φ=3φπx=4cos(t)ππ3φt=1sA+=43At=0πφφπ=3x=Acos(t+)ωφφπφ1202x=Acost+2xAcost12ωπω⎛⎝⎜⎞⎠⎟φφφπ=-=122tt-t12--=-φωπππ2224/Tx=Acos(t+)ωφE=12kx=12kAcos(t)p222ωφv=-Asin(t)φE=12mv=12mAsin(t)k2222ωωφ2=k/m((6.7))cos22(t+)sin(t+)φωφE=E+E=12mA=12kApk222ωf=-v=-rdxdtmdxdt-kx-22dxdt=km2=m02ωγω0dxdtdxdt2202+2+x=0ωxAecos(t)0-tβφ0=02ωβ-2A(6