大学物理-力学中的功和能1

1.51.5WorkandEnergy)WorkandEnergy)1WorkθFvrv∆rFnFrFWvv∆⋅=θcosrFWv∆==rFrv∆,π2π≤θ0,2π0≤Wθ0,2π==Wθ0W∫=bLasF)(dcosθab(L)FvrvdθrFWvvdd⋅=a→bA∫⋅=bLarFW)(dvv∫=bLarF)(cosdθvkFjFiFFzyxvvvv++=kzjyixrvdddd++=∫⋅=bLarFW)(dvv()∫++=bLazyxzFyFxF)(dddvvvabnFFFvLvv,,21Fv∫⋅=bLaabrFW)(dvv∫⋅+++=bLanrFFF)(21d)(vvLvv∫∫∫⋅++⋅+⋅=bLanbLabLarFrFrF)()(2)(1dddvvLvvvvnababab=L21(Power)1.PtWP∆∆=W2.PtWtWPtddlim0=∆∆=→∆trFtWPddddvv⋅==VFvv⋅=θcosFV=abbarrrr⋅=⋅abbarrrr×−=×rr)()()(cabcbabacrrrrrrrrr⋅−⋅=××2aaa=⋅rraa×=0)()()(acbcbabacrrrrrrrrr×⋅=×⋅=×⋅bdtaddtbdabadtdrrrrrr⋅+⋅=⋅)(bdtaddtbdabadtdrrrrrr×+×=×)(m(ms–1):0T,ttt23)(2+=vtpFdd=)23(dddd2tttmtm+==v)26(+=tm∫⋅=rFWvvd∫=xFd∫∫==tFttxFddddv∫++=Tttttm02d)23)(26(∫++=Tttttm023d)299(2)4129(2234TTTm++=mRABµk,ABOfvrdvmgNfkkµµ==rFWvvdd⋅=rFvd−=∫−=BArFWvd∫−=BAsFd∫−=BAksmgdµRmgkπµ−=mgskµ−=RmgWk2µ−=x2=4y4y=x+6abab(N)42jiyFvvv+=:a21),b39/4()∫∫+=⋅=bayxbayFxFrFWdddrrO2−314y=x+62.25abyx2=4y∫∫+=2121d4d21yyxxyxyW∫∫+=−491322d4d2yxxx10.8J∫+=bayxyFxFW)dd(2∫∫+=2121d4d2yyxxyxy∫∫++=−49132d4d)6(21yxxO2−314y=x+62.25abyx2=4y21.25Jx#mechwe12.(02RA.F0R2B.2F0R2C.3F0R2D.4F0R2xyRO)(0jyixFFrrr+=B2222121ABKAKBABmmEEWvv−=−=(AB)ABFvrvdrFvrFWvvdd⋅=rFrvd=rtmvdddv=trmdddvv=vvdm=∫=BAABWWd∫=BAmvvd222121ABmmvv−=KAKBEE−=θ0vvfvvv0vvfvv2210)(vmsNpf−=⋅++vvvvNvpvkfvsθθ0=⋅sNvv)2πcos(θ+=⋅mgsspvvsmgsfθµcosk−=⋅vv20k21sincosvmsmgsmg−=−−θθµ202fk2121cos2vvmmsmg−=−θµhpvNvkfvθv=0N=mgcosθf=µkmgcosθ20k21sincosvmsmgsmg−=−−θθµ202fk2121cos2vvmmsmg−=−θµθsin4220gsfvv+=0vvsvθhv=0θsinsh=gf4220vv+=PlθFvFvpvTvrvd=−=−0cos0sinpTTFθθθtanpF=rFWvvdd⋅=θθθdcostanlp=∫=θθθ0dsinplW)cos1(θ−=pl∫⋅=θ0drPWpvv∫−=θθθ0dsinlp)cos1(θ−−=plW−=θθsFdcosθ=∫+=θθ0d)2πcos(spFvθpvTvrvdFv0d)(=−=⋅++∫KAKBEErFpTvvvv∫∫⋅−=⋅sFspvvvvddA1B11AVv1BVv(L1)A2B22AVv2BVv1Fv(L2)2Fv1fv2fvm1m2211211111112121dd:1111ABBABAVmVmrfrFm−=⋅+⋅∫∫vvvv222222222222121dd:2222ABBABAVmVmrfrFm−=⋅+⋅∫∫vvvv)dd()dd(2211221122112211∫∫∫∫⋅+⋅+⋅+⋅BABABABArfrfrFrFvvvvvvvvWW)2121(222211BBVmVm+=)2121(222211AAVmVm+−EKBEKAKAKBEEWW−=+,Q1Q2KAKBEEWW−=+1/4RMmv12RMmhmgrmgWdcosdd==ϕvmgRW=mgϕdhrvd0=+MVmvMmVv−=MmVv−=222121vmMVWW+=+mN221vmmgRWN=+MN’222221MmMVWNv==′MNVvmN’mgRmWN−=221vR*KCK22k2121EEmmEiciiii−=−=′∑∑vv∑∑∑∑+−=−=′iciiciiiiiiciimmmmE222k2121)(21vvvvvv∑icim2v12vvvrrr−=2121mmmm+=µ2k21vµ=′E21mm2m≈µKAKBEEWW−=+