Manual de Física 10 e 11 Classe
October 11, 2022 | Author: Anonymous | Category: N/A
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BCOWC@ AG FÂUMEC [C^C FD^ FD^BCÌÅ BCÌÅD D BÍAMC QÍEOME QÍE OME C
3;.ª g 33.ª E@CUUGU
3
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BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC
ÂOAMEG [ ............................................................................................................................ 3- Edoegmtds Motrdaut Motrdautõrmds õrmds ............................................................................................ ...................................... 3.3- Motrdauìå Motrdauìådd ........................................................................................................ ........................................ 3.> - Lrcoagzcs âsmecs .......................................................................................... ............................. 3.5 ― Umstgbc ag Womacags .................................................................................. ............................ 3.1 - Odì÷gs Nãsmecs ac Qrmldodb Qrmldodbgtrmc gtrmc .........................................................
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[ 39 Bgeîomec .............................................................. ............................................................................................................... ................................................. Womacag 3- Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` ................................................. .................................................
>7 >6
3.3 - [dotd Bctgrmc` .......................................................................................................... ................................................. 3.3.3 - ^g`ctmvmac ^g`ctmvmacag ag ad bdvmbgotd ................................................................. ....
>6 ><
3.> - Qrcig Qrcigetõrmc etõrmc.................................................................................................................. .................................................. 3.5 - Ags`decbgotd ........................................................................................................... .................................................. 3.5.3- Drmlgb ads Gspcìds.................................................................................. ........................... 3.1 - Vg`demacag .................................................................................................................. ................................................... 3.1.3 - Vg`demacag Bíamc ...................................................................................... ............................ 3.1.> - Vg`demacag Mostcotîogc .......................................................................... ................. 3.7 - Bdvmbgotd ^getm`âogd g Womfdrbg................................................................... ....... 3.7.3- Ceg`grcìå Ceg`grcìådd ..................................................................................................... .......................................... 3.6-Bdvmbgotdd rgetm`âogd .............................................................................................. 3.6-Bdvmbgot ...............................
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3.6.3- Bdvmbgotd rgetm`âogd uomfdrbgbgotg vcrmcad........................ vcrmcad............................. ..... 3.6.> - Sugac ag ub Edrpd ................................................................................. .................. 3.6.5 - Csegosåd ag ub Edrpd ........................................................................... ................. 3.< - Bdvmbgotd emreu`cr................................................................................................ ......................................... 3. 73 75 76 7< 7=
Womacag > - Motgrceì÷gs gotrg Edrpds ............................................................................ ..................
6>
6> 6=
>.3- Fdrì Fdrìcc ........................................................................................................................... ................................................................. >.> - @gms ag Ogwtdo.................... Ogwtdo.................................................................................... ..................................................................................... .....................
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BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC
ÂOAMEG
>.>.3 - @gm ac Moíremc .............................................................................................. ............................... >.>> - @gm Fuoacbgotc` ac Amoîbmec ............................................................
6= .>.5 - @gm ac Ceìåd g ^gceìåd ........................................................................... ................... >.5 - Mbpu`sd g qucotmacag ag bdvmbgotd…… bdvmbgotd…………………………........... ……………………........................ >.5.3- Mbpu`sd ag ubc Fdrì Fdrìcc ............................................................................. .....................
=6 =:
[ >9 Fgoõbgods Qírbmeds…………………………………………... .................. Womacag 3- Gogrlmc Qírbmec ................................................................................................ ................................
3;3 3;>
3.3 Qgbpgrctur gbpgrcturcc ................................................................................................................ ...................................................... 3.3.3 Gsec`cs Qgrbdbítrmecs ............................................................................. .................... 3.3.> -^g`cì÷gs gotrg cs Gsec`cs Qgrbdbítrmecs ......................................
3;> 3;5 3;1
3.> - Am`ctcìåd ads Uõ`mads Uõ`mads............................................................................................. ............................................................................................. 3.>.3 -Am`ctcìåd @mogcr ......................................................................................... .................................. 3.>.> - Am`ctcìåd Uupgrmemc` Uupgrmemc`................................................................................ ................................................................................ 3.>.5 -Am`ctcìåd Vd`ubítrmec.............................................................................. ........................ 3.5 - Qrco Qrcosbmssåd sbmssåd ag Ec`dr ............................................................................................ .................................... 3.1 - Ecpcemacag Ec`drâmec ............................................................................................ ..................................... 3.7 - Gqum`ânrmd Qírbmed.................................................................................................. ......................................
3;< 3;< 33; 333 33> 331 33:
Womacag > - Gqucìåd ag Gstcad ag ub Lãs [grfgmtd ...............................................
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>.3 - @gms ads Lcsgs………………………… Lcsgs……………………………………………………. …………………………. ................................
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC
ÂOAMEG
>.> - [rdegssd Msdtírbmed9 @gm ag Ndy`g ― Bcrmdttg ............................................ >.5 - [rdegssd Msdnãrmed9 (Lcy-@u (Lcy-@ussce) ssce) .................................................................... ..............
3>1 3>6
>.1 - [rdegssd Msdeõrmed 9 @gm ag Icequgs Ejcr`gs .............................................. >.7 - Eã`eu`d Emoítmed ac [rgssåd ................................................................................ .......................... >.6 - Motgrprgtc Motgrprgtcìåd ìåd Emoítmec ac Qgbpgrctur gbpgrcturcc ........................................................ >.< - Am`ctcìåd ads Lcsgs................................................................................................ ...................................... >.= 35> 355 35< 35<
>. - Qrcnc Qrcnc`jd `jd ^gc`mzcad pg`d Lãs .......................................................................... ............... >.: - Gxpgrméoemc ag Idu`g .............................................................................................. ......................................
31; 313
Womacag 5 - Qgrbdamoîbmec ........................................................... ................................................................................................. ......................................
311
5.3 - [rmbgmrc @gm ac Qgrbdamoîbmec ....................................................................... ............... 5.3.3 -Qrcos Qrcosfdrbcìåd fdrbcìåd Msdtírbmec ..................................................................... .............. 5.3.> - Qrcosf Qrcosfdrbcìåd drbcìåd Msdnãrmec....................................................................... .............. 5.3.5 - Qrcosf Qrcosfdrbcìåd drbcìåd Msdeõrmec du Msdbítrmec ......................................... 5.3.1 - Qrcos Qrcosfdrbcìåd fdrbcìåd Camcnãtmec.................................................................... .... 5.3.7 - Qrcos Qrcosfdrbcì÷gs fdrbcì÷gs Eâe`mecs ........................................................................ ............... 5.> - C Ugluoac @gm ac Qgrbdamoîbmec ................................................................... .... 5.>.3 - Qrcos Qrcosfdrbcì÷gs fdrbcì÷gs ^gvg ^gvgrsâvgms rsâvgms ................................................................ .... 5.>.> - Qrcosfdrbcì÷gs Mrrgvgrsâvgms Mrrgvgrsâvgms.............................................................. .............................................................. 5.5 - Bãqumocs Qírbmecs ................................................................................................ ........................................
311 311 317 316 316 31: 373 37> 37> 371
5.5.3 - ^goambgotd ag ubc Bãqumoc Qírbmec ........................................... 5.5.> - D Eme`d ag Ecrodt....................................................................................... ............................ 5.1 - C Edosgrvcìåd ac Gogrlmc ................................................................................... ............................ 5.7 - C Gogrlmc Qírbmec9 Wbc Gogrlmc ‐Aglrcacac ‐Aglrcacac‒‒ ..........................................
377 376 37: 37=
[ 59 G`getrdstãtmec g Edrrgotg G`íetrmec edotâouc ...................... Womacag 3- Motgrceìåd G`getrdstãtmec.............................................................................. ..............................................................................
65 361
3.3- Edoegmtd ag Ecrlcs (@gm ac Edosgrvcìåd ac Ecrlc) ..................................
361
3.> -@gm ag Edu`dbn - [grbmtmvmacag G`ítrmec ad Bgmd .....................................
366
7
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC
ÂOAMEG
3.5 - Ecbpd G`getrdstãt G`getrdstãtmed med ............................................................................................ ............................... 3.1 - Qrcnc` Qrcnc`jd jd ad Ecbpd G`íetrmed ............................................................................ ....................
36: 3
3.7 - [dtgoemc` G`íetrmed .................................................................................................. ........................................... 3.6 - Ecpcemacag G`íetrmec ............................................................................................. ................................. 3.6.3 - Edoagoscadr Edoagoscadrgs gs (Ecpcemtdr (Ecpcemtdrgs) gs) ............................................................. 3.6.> - Gogrlmc ad edoagoscadr ecrrglcad.................................................. 3.6.5 - Gogrlmc ad edoagoscadr ecrrglcad..................................................
3 3:5
>.> - ^gsmstéoe ^gsmstéoemc mc ag ub Edoautdr G`íetrmed (^gsmstm (^gsmstmvmacag) vmacag) ........................ >.5 - @gm ag Djb pcrc Uglbgotd ag ub Emreumtd ................................................. >.1 - Qrcnc Qrcnc`jd `jd g [dtéoemc G`íetrmec ............................................................................ ............ >.7 - Gogrlmc amssmpcac oub Edoautdr9 Gfgmtd Idu`g .......................................... >.6 - Fdrì Fdrìcc G`getrdbdt G`getrdbdtrmz rmz (f.g.b. g^gsmsté g^gsmstéoemc oemc Motgroc) .................................... >.: - @gms ag Hmrejjdff ..................................................................................................... ...............................................
3:6 3:= 3=> 3=5 3=1 >;1
N ............................................................ ........................................................................................................................... ................................................................
>37
6
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
[rgfãemd Od qucard ac ^gfdrbc Gauectmvc oc ^gpùn`mec ag Cold`c, d Bmomstírmd ac Gauecìåd ctrcvís ad MOMAG, prdpñs c g`cndrcìåd ag bcoucms amaãetmeds pcrc d Uunsmstgbc ad Gosmod Qíeomed [rdmssmdoc` gb Cold`c c mb ag ed`bctcr c fc`tc ag bgmds amaãetmeds ag gosmod pcrc edrrgspdoagr ës gxmléoemcs g dnigetmvds ag ub gosmod sgluoad odrbcs uomvgrscms. Ícssmbqugublrupdagprdfgssdrgscold`codsedb`crlcgxpgrméoemcodgosmodagFâsmec,iuotdu gsfdrìds pcrc g`cndrcr g`cndrcr d prgsgotg bcouc` qug, pdr egrtd, vcm edotrmnumr od cpgrfgmìdcbgot cpgrfgmìdcbgotdd g bg`jdrmc ad gosmod ac Fâsmec g rglu`cr ds prdegambgotds amaãetmeds ag cedrad edb ds dnigetmvds supgrmdrbgotg prgedomzcads pg`d Gstcad Cold`cod ctrcvís ads prdlrcbcs eurrmeu`crgs. C Fâsmec í ubc acs eméoemcs qug iuotd edb c Suâbmec g c Bctgbãtmec, edostmtum d oùe`gd g supdrtg fuoacbgotc` pcrc qug ds futurds prdmssmdocms ods bcms amvgrsds adbâomds ac moaùstrmc gstcng`gegb g crtmeu`cb ds sgus edojgembgotds tíeomeds emgotâmeds edb c prãtmec qudtmamcoc. Cssmb c Fâsmec pcrc c Fdrbcìåd Qíeomec Qíeomec [rdmssmdoc` pgrbmtg qug ds c`uods edostrucb ds fuoacbgotds ads sgus edojgembgotds edojgembgotds oubc ncsg sõ`mac pcrc c agsermìåd ads fcetds du fgoõbgods octurcms ngb edbd oc motgrprgtcìåd acs bcms amvgrscs `gms qug rglgb c octurgzc, pgrbmtmoad-`jgs, agstg bdad, cetucrgb edb rcemdoc`msbd g rmldr emgotâmed oc nusec ag sd`uì÷gs pcrc c rgsd`uìåd ads bcms vcrmcads prdn`gbcs ad odssd qudtmamcod. C fgejcr pdagbds cssglurcr qug gstg bcouc` edostmtuâ ub motgrcetmvd amoîbmed oc cndraclgb tgbãtmecads adsfuturds edoegmtds g `gms d quggb edofgrg ubc `crlc cngrturc prclbãtmec g gspgeâmec oc fdrbcìåd prdmssmdocms Cold`c.
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BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
3. Edoegmtds Motrdautõrmds 3.3. Motrdauìåd C moe`usåd ad gstuad ag c`luos edoegmtds, od momemd agstg bcouc`, tgb edbd dnigetmvd ermcr ub supdrtg bctgbãtmed g c`línrmed pcrc bg`jdr edbprggosåd g motgrprgtcìå m otgrprgtcìådd gb tgrbds ambgosmdocms ads fgoõbgods âsmeds ngb edbd sucs `gms. Edbd í odtõrmd sgb d gstuad ac bctgbãtmec g suc vmoeu`cìåd amc`íetmec cd gstuad ads fgoõbgods Fâsmeds sgrmc amâem` gstcng`gegr c rg`cìåd gotrg c `gm g d fgoõbgod, gb tgrbds ag lrcoagzc g ambgosåd. Iã Lc`m`gu rgedojgegr rgedojgegrcc c mbpdrtîoemc ag qug sg rgvgstg c bctgbãtmec od edotgxtd ad gstuad ads fgoõbgods âsmeds, qucoad edosmagrdu c bctgbãtmec edbd `moluclgb octurc` ac Fâsmec. Mstd sõ pdr sm vgb edofgrmr bcmdr qudtc c mbpdrtîoemc cd gstuad prívmd ag c`lubcs fuoì÷gs g dpgrcì÷gs bctgbãtmecs cotgs sg gstuacr edoergtcbgot edoergtcbgotg g ds cspgetds bctgbãtmeds emreuosergvgb tcmsag fgoõbgods âsmeds ag ubc fdrbc lgrc` g gbc`línrmeds pcrtmeu`crgads fgoõbgodsqug bgeîomeds. Cssmb gstcrgbds gb edoamì÷gs ag ermcr cs ncsgs edoegptucms pcrc d gstuad qucotmtctmvd ad bdvmbgotd bgeîomed, fdrbu`coad ag fdrbc g`gbgotcr cs ncsgs bctgbãtmecs sustgotcadrcs.
3.>. Lrcoagzcs Fâsmecs Lrcoagzc fâsmec í tdac prdprmgacag du ecrcetgrâstmec ag ub fgoõbgod qug í susegptâvg` ag sgr bgamac g ag sg ctrmnumr ub vc`dr oubírmed. Gxgbp`ds 9 Vg`demacag, ags`decbgotd, fdrìc, tgbpd, bcssc, gte...
[dr suc vgz cs lrcoagzcs âsmecs såd e`cssmmecb-sg gb adms lrupds qug såd9 lrcoagzcs gsec`crgs g vgetdrmcms.
Lrcoagzcs Gsec`crgs Uåd cqug`cs qug pdagb sgr agtgrbmocacs sdbgotg pg`d sgu vc`dr oubírmed g pg`c suc uomacag. Gxgbp`d9 C bcssc, d gspcìd, d tgbpd, gte.
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BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
Lrcoagzcs Vgetdrmcms Uåd qugg pcrc sgrgb agtgrbmocacs í ogegssãrmd edojgegr c amrgeìåd, sgotmad, vc`drcqug`cs, oubírmed uomacag. Gxgbp`d9 ags`decbgot ags`decbgotd, d, vg`demacag, ceg`grcìåd, gte.
Agmog-sg ub vgetdr, edbd ub sglbgotd ag rgetc amrmlmad. Ecrcetgrâstmec ag ub vgetdr9 • Drmlgb8 • @mojc ag ceìåd8 • Ugotmad8 • Vc`dr oubírmed8 Odrbc`bgotg, ds vgetdrgs såd rgprgsgotcads lrcmecbgotg pdr ub sglbgotd ag rgetc tgrbmocac oubc sgtc.
C
N
Fml. 3 ― ^gprgsgotcìåd lrãec ag ub vgetdr
Dpgrcì÷gs edb Vgetdrgs Edbd iã couoemcbds prgvmcbgotg, í pdssâvg` sdbcrbds du suntrcmrbds vgetdrgs. vgetdrgs. ^glrc lgrc` sg ds vgetdrgs gstmvgrgb c`gctdrmcbgotg ed`decads d vgetdr rgsu`tcotg dntíb-sg sglumoad ds sglumotgs pcssds9 Gsed`jg-sg ub pdotd crnmtrãrmd od gspcìd du p`cod. • Fcìc edmoemamr c drmlgb ad vgetdr edb d pdotd gsed`jmad. • [crc d sgluoad vgetdr, c suc drmlgb agvg edmoemamr edb c gxtrgbmacag ad prmbgmrd vgetdr. • Fmoc`bgotg c rgsu`tcotg agvg sgr trcìcac edmoemamoad suc drmlgb edb c drmlgb ad prmbgmrd g suc gxtrgbmaca gxtrgbmacagg edb c ad sgluoad.
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BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
Gb ecsd ag vgetdrgs drtdodrbcads, (fdrbcb ub îolu`d gotrg sm), d bõau`d ad vgetdr rgsu`tcotg,, sgu bõau`d dntíb-sg cp`mecoad c `gm ads edssgods du pg`d bítdad ad pcrcrgsu`tcotg `g`dlrcbd. Ug d îolu`d fdr mluc` c =;» d tgrbd >cnedsγ >cnedsγ sg cou`c, g cssmb tgbds c rglrc rglrc ag [mtãldrcs. • Sucoad adms vgetdrgs téb c bgsbc amrgeìåd g d bgsbd sgotmad (γ 2 ;), d vgetdr rgsu`tcotg sgrã9 Motgosmacag9
x 3
x 2 x3 + x >
Amrgeìåd9 bgsbc ag x 3 g x >
x >
Ugotmad9 bgsbd ag x 3 g x >
x 3
x >
x
• Sucoad adms vgetdrgs tmvgrgb c bgsbc amrgeìåd amrgeìå d g ds sgotmads dpdstds (γ 2 3:;¹), d vgetdr rgsu`tcotg sgrã9
Motgosmacag9
x 3
x
2
x3
∞
x >
Amrgeìåd9 bgsbc ag x 3 g x >
x >
x
Ugotmad9 bgsbd sgotmad ad vgetdr ag bcmdr motgosmacagg motgosmaca
x
3
>
x
Udbc ag Adms Vgetdrgs Acads ds vgetdrgs x 3 g x > . D vgetdr sdbc ag adms vgetdrg vgetdrgss pdag sgr dntmad ag aucs bcogmrcs.
3ª
3;
Qrcosp÷g-sg pcrc`g`cbgotg c sm prõprmds cbnds vgetdrgs ag bdad qug cs sucs drmlgos edmoemacb8 d vgetdr rgsu`tcotg ac sdbc sgrã c amcldoc` ad pcrc`g`dlrcbd qug sg dntíb edb ncsg ods adms vgetdrgs momemcms (rglrc ag pcrc`g`dlrcbd).
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
N
x >
(vgetdr sdbc) x (vgetdr
D
x 3
C
Fml. > ― Udbc ag vgetdrgs ― rglrc ad pcrc`g`dlrcbd
>ª Ds vgetdrgs såd trcospdstds c sm prõprmds, ag bdad qug, c gxtrgbmacag ag ub sgic c drmlgb ad dutrd8 d vgetdr rgsu`tcotg ac sdbc ads adms, sgrã d trcìcad gotrg c drmlgb ad prmbgmrd g c gxtrgbmacag ad sgluoad. (bítdad ad trmcolu`d)
x3 + x >
(vgetdr sdbc)
x >
x 3 Fml. 5 ― Udbc ag vgetdrgs ― rglrc ad trmîolu`d
Coc`mtmecbgotg, d vgetdr sdbc í acad pdr9 Motgosmacag (bõau`d) x 2 x3> + x >> + >x3 x > edsγ
Gstc gxprgssåd í dntmac pg`c `gm ads edssgods9 [crc d trmîolu`d DCE ac mlurc >, vc`g9 > DE
2
> DC
> +
CE
∞
> .DC. CE . eds ξ
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BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
DC 2 x
3
CE 2DN 2 x >
Bcs9
DE 2 x
ξ 23:;»∞γ eds ξ 2 ∞ eds γ
Uunstmtumoad-sg oc @gm ag Edssgods, dntíb-sg c gxprgssåd ac motgosmacag ad vgetd vgetdrr sdbc (rgsu`tcotg) x 2
x3> + x>> + >x3 x > eds γ
Amrgeìåd9 d vgetdr rgsu`tcotg tgb c amrgeìåd acac pg`c rgetc DE. Ugotmad9 d vgetdr rgsu`tcotg tgb d sgotmad ag D pcrc E.
[crc d ecsd pcrtmeu`cr ag adms vgetdr vgetdrgs gs drtdldocms gotrg sm, ncstc cp`mecr d tgdrgbc ag [mtãldrcs9
x >
x
x > 2 x3> + x >> x 2
x 3 Fml. 1 ― Vgetdrgs drtdldocms
3>
x3> + x >>
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
Gxgreâemds Gxgr eâemds ag cp`mecìåd [3 ― Agtgrbmog d bõau`d ag vgetdr sdbc ag adms vgetdrgs qug fdrbcb gotrg sm ub îolu`d 5;¹ g euids bõau`ds såd
Eã`eu`d ad bõau`d ag x
x
x 3
>
2
x
x
2
<
x
2
1= + 36 + 76.; , :6
x
2
335,36
x
2 3;, 6b
3 >
+
>
x
x
>
+ >x
3
x .eds γ >
>
+ 1 + >. ― Agtgrbmog c motgosmacag ad vgetdr sdbc ag adms vgetdr vgetdrgs gs pgrpgoameu`crgs gotrg sm g euids bõau`ds såd 5b g 1b.
⎬
x3 2 5b Acads x 2 1b ⎪⎭ γ>2 =;» Eã`eu`d ad bõau`d ag x
^gsd`uìåd
x >
x
>
2
x
x
2
5 + 1 + >.5. 1. ed eds =;»
x
2
= + 36 + >1.;
x
2
= + 36
x
2
>7
x
2 7b
3
>
+
>
x
x
>
+ >x
3
x
>
eds γ
>
x 3
35
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
Amfgrgoìc gotrg adms Vgetdrgs
Acads ds vgetdrgs x 3 g x > . D vgetdr amfgrgoìc í acad pdr
x
2
x
2
x
>
∞
x
3
(N;) ( C;) ∞
N
x (vgetdr amfgrgoìc)
x > D
C
x 3 Fml. 7 ― Amfgrgoìc ag vgetdrgs
Coc`mtmecbgotg, d vgetdr amfgrgoìc í acad pg`c `gm ads edssgods pcrc trmîolu`d DCN9 Motgosmacag9 x
>
2
x3
>
+
x>
∞
>x
3
x > eds γ
Amrgeìåd9 ac rgetc CN
Ugotmad9 ag C pcrc N
Gxgreâemds Gxgr eâemds ag cp`mecìåd [3 ― Suc` d bõau`d ad vgetdr amfgrgoìc gotrg adms vgetdrgs qug fdrbcb ub îolu`d ag 5;¹ gotrg sm g euids bõau`ds såd 5b g :b4
⎬ x3 2 5b Acads ⎪ x> 2 :b ⎭ γ 2 5;»
31
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
^gsd`uìåd
Eã`eu`d ad bõau`d x
>
2
x
x
2
5 + : ∞ >.5. :.e ds 5;»
x
2
= + 61 ∞ 6.:.;, :
x
2
51 , 6
x
≇ 7,:b
3
+
>
x
x
>
∞ > x
3
x >
eds γ
x 3
x 5;»
x >
>
>
x
2
― Agtgrbmog d bõau`d ad vgetdr x ∞ x ads vgetdrgs cncmxd9 ⎬ x3 2 7b 357» Acads ⎪ x> 2 >b x ⎭ eds 357» 2 ―;,< 3
>
3
x >
^gsd`uìåd
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357»
x 3
x >
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x
x
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37
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
[rdautd ag ub oùbgrd pdr ub vgetdr
D prdautd ag ub oùbgrd c pdr ub vgetdr x 3 , rgsu`tcrã gb ub dutrd vgetdr x > , acad pdr9 Motgosmacag9 x > 2 c. x x 3 Amrgeìåd9 c bgsbc ag x 3
Ugotmad9 sg c ? d ↞ bgsbd ag x 3
sg c ? d ↞ edotrãrmd cd ag x 3
Gxgreâemd Gxgr eâemd ag cp`mecìåd [3 ― Acad d vgetdr x edofdrbg edofdrbg moamec c mlurc, dntgr ds vgetdrgs > x g ― x
― x | | 2 >b
|―b
[> ― Acads ds vgetdrgs c , n g e edofdrbg moamecb cs mlurcs, dntgr cs motgosmacags ag
sucs prdigeì÷gs od gmxd jdrmzdotc` x
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BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
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Agedbpdsmìåd aub Vgetdr sdnrg adms Gmxds Drtdldocms Acad ub vgetdr x 3 g ub smstgbc ag adms gmxds drtdldocms x g g y
[''
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x γ x x
x y
D
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x
Fml. < ― Agedbpdsmìåd aub Vgetdr Vgetdr sdnrg ds gmxds x g y
[rdigetcoad-sg drtdldoc`bgotg cs gxtrgbmacags ad vgetdr x ods ods gmxds x g g y dntgbds dntgbds edbpdogotgs rgetcolu`c rgetcolu`crgs rgs x x g y x .
Coc`mtmecbgotg tgbds9 d trmîolu`d D[±[ í rgetîolu`d rgetîolu`d,, pdrtcotd9
eds γ
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2
x
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x
e eds γ γ
2
x y
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x x
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2
xsgo goγ
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
Gxgreâemd Gxgr eâemd ag cp`mecìåd [3 ― Agtgrbmog d bõau`d acs edbpdogotgs rgetcolu`crgs ad vgetdr x ag bõau`d 3;
bgtrds, edofdrbg c mlurc.
x
5;»
^gsd`uìåd [g`d pdotd ag drmlgb ad vgetdr x , edosmagrgbds ub smstgbc ag gmxds eddragocads x g y , edbd bdstrc c mlurc.
y x y 5;»
x
x x
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x
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x
x
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5
x y 2 3;.
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5b
>
x y 2 7b
[> ― Agtgrbmog cs edbpdogotgs ag ub vgetdr x ag bõau`d 1 bgtrds, qug fdrbc ub
îolu`d ag 5;¹ edb c vgrtmec`.
^gsd`uìåd [rdigetcoad d vgetdr x ods ods gmxds x g g y tgbds9 tgbds9
Acads9 x 2 1b γ26;»
3=
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
Edbpdogotg sgluoad x x
x
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2 >.3, ). Womacag ag vd`ubg ― c suc gqucìåd ag agmomìåd í8 V 2 E@J, fczgoad E2@2J2 3b,
edoe`um-sg qug c uomacag ag vd`ubg í d bgtrd eùnmed (b 5) Womacag ag vg`dem vg`demacag acag ― c suc gqucìåd ag agmomìåd agmom ìåd í8
s
v
2 , fczgoad U 2 3b g t 2 3s, t
edoe`um-sg qug c uomacag ac vg`demacag í d bgtrd pdr sgluoad (b/s).
>;
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
>) Umstgbc E. L. U Cs uomacags fuoacbgotcms såd d egotâbgtrd (uomacag ag edbprmbgotd), d lrcbc (uomacag ag bcssc) g d sgluoad (uomacag ag tgbpd). Womacags agrmvcacs ― dntéb-sg c pcrtmr acs gqucì÷gs ag agmomìåd, edbd sg fgz pcrc d smstgbc bítrmed ― lrcvmtct lrcvmtctõrmd. õrmd. Womacag ag supgrâemg ― í d egotâbgtrd qucarcad (eb>) Womacag ag vd`ubg ― í d egotâbgtrd eùnmed (eb5) Womacag ag vg`demacag ― í d egotâbgtrd pdr sgluoad (eb/s)
D smstgbc B.H.U motglrc-sg cbp`cbgotg od smstgbc motgrocemdoc` (UM), qug cadptc bcms quctrd uomacags fuoacbgotcms9 d Cbpêrg (C) ― uomacag ag motgosmacag ag edrrgotg g`íetrmec8 d Hg`vmo (H) ― uomacag ag tgbpgrcturc tgrbdamoîbmec8 c ecoag`c (ea) ― uomacag ac motgosmacag `ubmodsc8 d bd`g (bd`) ― uomacag ag qucotmacag ag sunstîoemc.
3.1. Odì÷gs Nãsmecs ac Qrmldodbgtrmc Emreuofgréoemc trmldodbítrmec Ac mlurc : (emreuofg (emreuofgréoemc réoemc trmldodbítrmec), pdag - sg agauzmr cs rg`cì÷gs fuoacbgotcms ac trmldodbgtrmc. sgod, ed-sgod, tcolgotg g ed-tcolgotg. C fuoìåd sgod vgb ac rg`cìåd gotrg d edbpdogotg eddragocad eddragocad y g g d rcmd ^, du sgic gotrg d ectgtd dpdstd ^y g c Jmpdtgousc ^, cd pcssd qug c fuoìåd ed-sgod í c rg`cìåd gotrg d edbpdogotg eddragocad eddragocad gb x g d rcmd du sgic ectgtd caicegotg ^ x g c jmpdtgousc. ^23 sgoγ
y 2
y
y
x ^ y sgoγ
eds γ
tlγ
2
^ x
2
2
2
2
^ eds γ ds γ ds x ed
edt lγ
2
y γ x
x
2
y
sgoγ Fml. : ― Emreuofgréoemc trmldodbítrmec
>3
BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
sgoγ
y
eds γ
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BCOWC@ AG FÂUMEC FÂUME C [C^C FD^BCÌÅD BÍAMC QÍEOMEC EDOEGMQDU MOQ^DAWQÕ^MDU
Vc`drgs ag sgod, edssgod, tcolgotg g ed-tcolgotg ag c`luos îolu`ds
Îolu`d
sgod
eds
tl
edtl
;¹ (; rca)
;
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Bgeîomec WOMACAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACAG > ― Motgrceì÷gs gotrg gotrg Edrpds WOMACAG 5 ― Qrcnc`jd g Gogrlmc
M G Q ^ C >7
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
[C^QG 39 BGEÎOMEC B GEÎOMEC Gstc prmbgmrc pcrtg ad bcouc` trctc ac coã`msg ads bdvmbgotds, cs vcrmcì÷gs ag gogrlmc g cs fdrìcs qug cetucb sdnrg ub edrpd.
Womacag 3
BdvmBgotd ag uBc [crtâeu`c Bctgrmc` D dnigetmvd agstc uomacag í ag agsergvgr cs fdrbcs nãsmecs ad bdvmbgotd bgeîomed g cs `gms qug c rglgb. C pc`cvrc bdvmbgotd gstã `mlcac ë vmac g tgb vãrmcs fdrbcs ag sg bcomfgstcr, ubc agsscs fdrbcs í d bdvmbgotd bgeîomed qug agsergvg c buacoìc ag pdsmìåd ads edrpds od tgbpd. C emogbãtmec í c pcrtg ac Bgeîomec qug sg deupc ad gstuad ad bdvmbgotd, sucs fdrbcs g sucs `gms sgb tgr gb edotc cs ecuscs qug ds drmlmocb.
3.3. [dotd Bctgrmc` C Fâsmec rgedrrg ë ubc `moluclgb prõprmc pcrc ecrcetgrmzcr c`luos edrpds. Od gstuad ad bdvmbgotd bgeîomed, edosmagrc-sg
pdotd pdo td bctgr bctgrmc` mc` , ub edrpd euics ambgos÷gs pdagb sgr agsprgzc-
acs, od gstuad ag ub agtgrbmocad fgoõbgod, gb rg`cìåd c ub agtgrbmocad rgfgrgoemc`. [dotd bctgrmc` í ub edrpd qug pdssum ubc qucotmacag ag bcssc, bcs sucs ambgos÷gs såd agsprgzã agsprgzãvgms vgms qucoad edbpcrcacs ës amstîoemcs govd`vmacs od prdn`gbc. Gxgbp`d9 c) D bdvmbgotd ag trcos`cìåd ac Qgrrc gb tdrod ad sd`, pdag sgr edosmagrcad edbd bdvmbgotd ag ub pdotd bctgrmc`, goqucotd ag rdtcìåd ac tgrrc gb tdrod ad sgu gmxddiãbdvmbgotd oåd.
>6
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
n) Wb cutdecrrd oubc vmclgb ag Ecxmtd c Bcqug`c ad Ydbnd, gb edbpcrcìåd ë gstrcac, tgb sgu tcbcojd agsprgzâvg`, gotåd, pdag sgr edosmagrcad ub pdotd bctgrmc`8 bcs qucoad gstg bgsbd cutdecrrd fcz bcodnrcs gb ub gstcemdocbgotd sgu tcbcojd agmxc ag sgr agsprgzâvg`.
3.3.3. ^g`ctmvmacag ad Bdvmbgotd Bdvmbgotd D bdvmbgotd ag ub edrpd tgb sgbprg ub smlommecad rg`ctmvd. [dr gxgbp`d, ubc pgssdc sgotcac oub edbndmd gstã gb rgpdusd, rg`ctmvcbgotg cd smstgbc bctgrmc` qug edostmtum d edbndmd, bcs gstã gb bdvmbgotd rg`ctmvcbgotg c quc`qugr smstgbc bctgrmc` edosmagrcad od gxtgrmdr ad edbndmd (gstcìåd ad ecbmojd ag fgrrd, crvdrgs gte). G quc`qugr agstgs smstgbcs ag rgfgréoemc gstã gb rgpdusd rg`ctmvcbgotg c dutrds. D edoegmtd ag bdvmbgotd du rgpdusd í rg`ctmvd sgbprg c agtgrbmocads edrpds.
Fml. 3.3 ― Vu`d`c dnsgrvcoad d bdvmbgotd ad edbndmd
Amrgbds cssmb, qug ub pdotd bctgrmc` gstã gb bdvmbgotd rg`ctmvcbgotg c ub rgfgrgoemc` du smstgbc ag rgfgréoemc, qucoad c suc pdsmìåd gb rg`cìåd c gstg rgfgrgoemc`, vcrmc od agedrrgr ad tgbpd.
3.>. Qrcigetõrmc Agodbmoc-sg trcigetõrmc cd ecbmojd pgredrrmad pdr ub bõvg` gb rg`cìåd c ub rgfgrgoemc` cadptcad. cadptcad.
yb
x hb
Fml. 3.> ― Qrcigetõrmc ac gsfgrc gsfgr c gb bdvmbgotd
><
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
C trcigetõrmc pdag sgr9 ― ^getm`âogc ― Eurvm`âogc Mbclmogbds ub jg`meõptgrd vdcoad edb ubc vg`demacag edostcotg. Ug, oub agtgrbmocad mostcotg g`g `crlcr ub sced ag crrdz, gstg ecmrã sgluoad ubc trcigetõrmc vgrtmec` gb rg`cìåd cd pm`dtd ad jg`meõptgrd. Bcs, pcrc ub dnsgrvcadr mxd oc Qgrrc, c trcigetõrmc ad sced sgrã pcrcnõ`mec.
3.5. Ags`decbgo Ags`decbgotd td 3.5.3. Drmlgb ads Gspcìds U5 U> U3 [3 ;
Drmlgb ads Gspcìds
[> [ 5
Agmog-sg drmlgb ads gspcìds d pdotd D (mxcad crnmtrcrmcbgotg) gb rg`cìåd cd quc` såd bgamads ds gspcìds, du sgic9 ― od pdotd [3 c amstîoemc ad bõvg` ë drmlgb í s3 ― od pdotd [> c amstîoemc ad bõvg` ë drmlgb í s> ― od pdotd [> c amstîoemc ad bõvg` ë drmlgb í s>
>:
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Ugic ub bõvg` agsergvgoad ubc trcigetõrmc quc`qugr drmgotcac deupcoad cs pdsmì÷gs [ ;3, [33, [> ... gte.
; [;
[> [3
t 2 d (drmlgb ads tgbpds)
[dag-sg agmomr tcbníb c drmlgb ads tgbpds edbd sgoad d mostcotg gb qug edbgìc c sgr edotcad d tgbpd (t 2 ;) pdagoad sgr mxcad gb quc`qugr pdsmìåd ad bõvg`. [dr gxgbp`d, qucoad d bõvg` oc pdsmìåd [;. Gspcìd Momemc` sd Agmog-sg edbd gspcìd momemc` (s;) c amstîoemc ad bõvg` ë drmlgb ads gspcìds od moâemd ac edotclgb ads tgbpds (t 2 ;). Ug ub bõvg` sg bdvmbgotc gb `mojc rgetc, c suc pdsmìåd buac gb ecac mostcotg g od moc` ad bdvmbgotd, c suc pdsmìåd sgrã amfgrgotg ac pdsmìåd momemc`. C vcrmcìåd ag pdsmìåd ad bõvg` ogstg motgrvc`d ag tgbpd í agsmlocac ags`decbgotd.
3.1. Vg`demacag C vg`demacag í c rg`cìåd gotrg c vcrmcìåd ac pdsmìåd od gspcìd gb agtgrbmocad motgrvc`d ag tgbpd, du sgic. Í ubc lrcoagzc vgetdrmc`, du sgic pdssum amrgeìåd, sgotmad g bõau`d. Od Umstgbc Motgrocemdoc` (U.M.), c uomacag ac vg`demacag í d b/s. Qcbníb Qcbníb utm`mzc-sg d hb/j edbd uomacag ac vg`demacag. C edovgrsåd gotrg d hb/j g d b/s, qug í acac pg`c sglumotg rg`cìåd9 3hb 3j
3;;;b
2
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[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
C pcrtmr agstc rg`cìåd, í pdssâvg` gxtrcmr d sglumotg fcetdr ag edovgrsåd9 b s
.5, 6 2
hb j
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g
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t 3 x3
t > x>
D U>
Ugic tcbníb9 x
2x
>
― x
3
vcrmcìåd ag pdsmìåd Xgspcìd (ecbmojd) pgredr rmadR
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>
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3
v b
x 2
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t
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∞
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x
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3
t
3
C vg`demacag bíamc, moamec d ags`decbgotd qug gb bíamc d edrpd gfgetuc pdr uomacag ad tgbpd. C vg`demacag bíamc tdtc` oåd í sgbprg mluc` c bíamc crmtbítmec acs vg`demacags. Agbdostrgbds mssd c`lgnrmecbgotg.
5;
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Ecsd gb qug cs amstîoemcs såd mlucms, bcs ds tgbpds amfgrgotgs
v b
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[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
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^gsd`uìåd v
b
2
s
⇞ v 22 bb
t
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⇞v
b
2 355, 5hb / j
[crc sg dntgr c vg`demacag bíamc gb b/s, í prgemsd edovgrtgr hb gb b g jdrc gb sgluoad,
Acads s 2 >;; hb t 2 2 3j5; bmo 2 3,7j
v b
3;;;b
2 355, 5 .
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⇞
v
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5>
^gsd`uìåd [g`c fõrbu`c 3.>, tgbds >v v b
3
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+ v
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v
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2
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2
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[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Gxgreâemds prdpdstds [3 ― Wb cutdbõvg` bdvgu-sg ë vg`demacag ag 1; hb/j aurcotg c prmbgmrc bgtcag ad tgbpd g ë vg`demacag ag >; hb/j aurcotg c sgluoac bgtcag. Cejcr c vg`demacag bíamc ad cutdbõvg`.
^9 v 2 5; hb/j
>
[> ― Wb cutdbõvg` pgredrrg ag ub pgreursd edb vg`d5 emacag ag 6; hb/j g d rgstcotg edb vg`demacag ag =; hb/j. Agtgrbmog c vg`demacag gsec`cr bíamc ad cutdbõvg`, aurcotg d pgreursd.
^9 6 jdrcs, od trdìd sglumotg, suc vg`demacag pcssdu pcrc . Vg` Vg`demacag demacag Mostcotîogc Qdbcoad edbd rgfgréoemc d ecsd cotgrmdr ag vg`demacag bíamc vgrmmecbds qug, ë bgamac qug sg ambmoum d motgrvc`d ag tgbpd gotrg ds mostcotgs t 3 g t > du sgic, Αt tgoad pcrc zgrd, c vg`demacag bíamc tgoag pcrc c vg`demacag mostcotîogc. mostcotîogc. Mstd í, c vg`demacag mostcotîogc í d `mbmtg pcrc d quc` tgoag c vg`demacag bíamc, qucoad d motgrvc`d ag tgbpd Αt tgoag c zgrd.
v
2
`mb v
t ↞;
b
2
`mb
s
(3.1)
t ↞;
t
55
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
3.7. Bdvmbgotd ^getm`âogd g Womfdrbg Wb ads bdvmbgotds bcms smbp`gs qug c emogbãtmec gstuac, í d bdvmbgotd rgetm`âogd uomfdrbg. Gssg bdvmbgotd rcrcbgotg cpcrgeg oc vmac prãtmec. Gotrgtcotd, d sgu gstuad sgrvg ag ncsg pcrc c edbprggosåd ag bdvmbgotds bcms edbp`gxds edbd9 • D bdvmbgotd í rgetm`âogd pdrqug c pcrtâeu`c pgredrrg ubc trcigetõrmc gb `mojc rgetc. • D bdvmbgotd í uomfdrbg pdrqug oåd jã vcrmcìåd ac vg`demacag. Bdvmbgotd rgetm`âogd g uomfdrbg í ub bdvmbgotd gb qug c Fml. 3.5 ― Bdvmbgotd rgetm`âogd g uomfdrbg
pcrtâeu`c agsergvg du gfgetuc ags`decbgotds/gspcìds mlucmsbctgrmc` gb motgrvc`ds ag tgbpds mlucms. [crc agtgrbmocr d ags`decbgotd aubc pcrtâeu`c bctgrmc` gb bdvmbgotd rgetm`âogd g uomfdrbg, aurcotg ub egrtd motgrvc`d ag tgbpd Α t prgemscbds scngr d ags`decbgotd ac pcrtâeu`c aurcotg cqug`g motgrvc`d ag tgbpd. C rg`cìåd gotrg c vcrmcìåd ad ags`decbgotd g d motgrvc`d ag tgbpd, ejcbc-sg vg`demacag.
v
2
s
Doag Α s 2 s f ― s; Gb qug
g
t
(3.7)
Α t 2 t f ― t ;
s ― pdsmìåd moc` s; ― pdsmìåd momemc` t ― ― tgbpd moc` t ; ― tgbpd momemc`
Qgoad gb edotc qug od momemd ac edotclgb ad bdvmbgotd d mostcotg momemc` í sgbprg mluc` c zgrd t ; 2 ;, vgb9 v
51
2
s t
edbd Α s 2 s ― s;
g
s 2 s; + v t
Α t 2 t ― t ; rgsu`tc9 (3.6)
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Gxgreâemds Gxgr eâemds ag cp`mecìåd ^gsd`uìåd c) s v 2 t
hb ⇞ v 22 :; ⇞ v 2 1;hb / j
>j
n) s 2 v .t ⇞ s 2 1;hb / j.7j ⇞ s 2 >;;hb
[3 ― Wb cutdbõvg` qug sg ags`dec edb bdvmbgotd uomfdrbg, pgredrrg :;hb gb >jdrcs. Ec`eu`g9 c) C vg`demacag ad cutdbõvg`. n) C amstîoemc pgredrrmac pg`d cutdbõvg`, gb 7jdrcs. Acads
s 2 :; hb t 2 2 >j
Gxgreâemds prdpdstds [3 ― Wb edbndmd pgredrrgu, gb bdvmbgotd uomfdrbg, 7; hb/j
n) C amstîoemc pgredrrmac pg`d edbndmd gb ;,7j.
n)
^9 s 2 3>7 hb
c) Uuc pdsmìåd momemc`.
c)
^9 s; 2 5; b
n) Uuc vg`demacag.
n)
^9 v 2 ―7b/s
e) Uuc pdsmìåd od mostcotg 5 sgluoads.
e)
^9 s5 2 37 b
a) D ags`decbgotd od mb ag 6 sgluoads.
a)
^9 s6 2 ―5; b
g) D mostcotg gb qug d bõvg` pcssc pg`c pdsmìåd >;b.
g)
^9 s>; 2 >s
[> ― Wb pdotd bctgrmc` bdvmbgotc-sg sgluoad c gqucìåd jdrãrmc s 2 5; ― 7t (s gb b g t gb s)
g) Gsqugbctmzg d bdvmbgotd oub gmxd drmgotcad.
57
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Gxgreâemds prdpdstds [5 ― Wb bõvg` ags`dec -sg sdnrg ubc rgetc g tgb sucs pdsmì÷gs gb fuoìåd ad tgbpd rgprgsgotcacs pg`c gqucìåd s 2 5+ 7t ( (s gb b)
^9 v b 2 7b/s pcrc ds ds adms adms motgrvc`d motgrvc`dss
^9 v 2 67 hb/j
^9 =;; hb
Agtgrbmog c vg`demacag bíamc ad bõvg` ods motgrvc`ds (; c 6) s g (> c 33) s.
[1 ― Wb cutdecrrd bdvg edb bdvmbgotd uomfdrbg ë vg`demacag ag 6; hb/j. Edb qug vg`demacag agvgrã sglumr dutrd cutdbõvg` qug pcrtg 37 bmoutds agpdms, pcrc c`ecoìcr d agpdms ag >3; hb. [7 ― Wb cvmåd pcssc sdnrg ubc emacag edb c vg`demacag ag 1;; hb/j, qug bcotíb aurcotg d rgstd ad pgreursd. Agpdms ag 17 bmoutds pcssc ub dutrd cvmåd sglumoad c bgsbc rdtc ad prmbgmrd edb vg`demacag ag 6;; hb/j. C qug amstîoemc ac rgfgrmac emacag d sgluoad cvmåd u`trcpcsscrã d prmbgmrd.
Lrãmeds ad bdvmbgotd rgetm`âogd uomfdrbg [crc d bdvmbgotd agsermtd ogstg ecpâtu`d pdagbds trcìcr ds lrãmeds • Ags`decbgotd ― tgbpd
D ags`decbgotd g d tgbpd såd lrcoagzcs amrgetcbgotg prdpdremdocms. D lrãmed í ubc `mojc rgetc moe`mocac gb rg`cìåd cd gmxd acs cnemsscs. s
; 56
s
t
;
t
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
• Vg`demacag ― tgbpd
Ugoad c vg`demacag c bgsbc gb quc`qugr mostcotg, pdagbds amzgr qug d lrãmed ac vg`demacag gb fuoìåd ag tgbpd í ubc `mojc rgetc. D vc`dr ac vg`demacag bcotíb-sg edostcotg. D lrãmed í ubc `mojc pcrc`g`c cd gmxd acs cnemsscs. v
v
t t Bdvmbgotd prdlrgssmvd
Bdvmbgotd rglrgssmvd
Gxgreâemds Gxgr eâemds ag cp`mecìåd ^gsd`uìåd t
s
;
1
3
<
[3 ― Wb bõvg` bdvmbgotc-sg sgluoad c gqucìåd9 s 2 1 + 5t (UM) (UM) Edostruc d lrãmed ag s 2 f (t )
s (b) < 1
;
3
t (s)
5<
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Gxgreâemds prdpdstds [3 ― Wb pdotd bctgrmc` bdvmbgotc sg gb ubc trcigetõrmc rgetm`âogc g tgb sucs pdsmì÷gs, gb fuoìåd ad tgbpd acacs pg`d lrãmed.
n)
^9 D pdotd bctgrmc` pcrtmoad ac pdsmìåd 6b, ctmolg c pdsmìåd 76b gb `;s (bdvmbgotd prdlrgssmvd) oc quc` pãrc aurcotg :s. Gb sglumac rgtdbc ë drmlgb (; b) gb :s (bdvmbgotd rgtrõlrcad). Ejglcoad ë drmlgb, pcrtg odvcbgotg edb bdvmbgotd prdlrgssmvd.
76
s (b)
6 1
t (s) 3;
3:
>6
5; 5;
c) Edostrumr d lrãmed v 2 2 f ( (t ) ag tdads ds trgejds8 n) Motgrprgtcr d bdvmbgotd8
e)
^9 1b
e) Suc` d ags`decbgotd ad pdotd bctgrmc` gotrg >6s g 5;s4
[> ― Adms bõvgms C g N pgredrrgb ubc rgetc edb BW g téb sucs pdsmì÷gs, gb fuoìåd ad tgbpd, acacs pg`d lrãmed9 s(b)
N
C
= 7 >
Agtgrbmog9
-5
c)
^9 1s
c) D Mostcotg ad goedotrd8
n)
^9 35b
n) C pdsmìåd od mostcotg ad goedotrd.
5:
t(s)
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
3.7.3. Ceg`grcìåd Cmrbcbds sgbprg qug ub cutdbõvg` gstã c ceg`grcr qucoad d vc`dr ac suc vg`demacag gstã c cubgotcr edb d agedrrgr ad tgbpd. D edoegmtd ag ceg`grcìåd gb Fâsmec í, pdríb, bcms lgrc`. Cssmb, amzgbds qug ub bõvg` gstã c ceg`grcr qucoad c suc vg`demacag vcrmc, edb d agedrrgr ad tgbpd. [dagbds agmomr c ceg`grcìåd edbd sgoad c rcpmagz edb qug vcrmc c vg`demacag od agedrrgr ad tgbpd
Fml. 3.1 ― Cutdbõvg` Cutdbõvg` ceg`grcoad
3.7.3.3 Ceg`grcìåd Bíamc Sucoad ubc pcrtâeu`c bctgrmc` vcrmc c suc vg`demacag ag v ; c v aurcotg aurcotg d motgrvc`d ag tgbpd t ; c t , c ceg`grcìåd bíamc pdag
sgr agmomac edbd sgoad c rg`cìåd gotrg c rcpmagz edb qug vcrmc c vg`demacag g d tgbpd gb qug dedrrgu gssc vcrmcìåd. c
doag Α v 2 v ― v ;
g
2
v t
(3.) ELU9 egotâbgtrd pdr sgluoad cd qucarcad (eb/s>)
5=
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Gxgreâemds Gxgr eâemds ag cp`mecìåd [3 ― C vg`demacag ag ub cutdbõvg` vcrmc ag 7 b/s pcrc 37 b/s aurcotg 1 sgluoads, agtgrbmog c ceg`grcìåd edb qug sg bdvg d cutdbõvg`.
^gsd`uìåd v c
2
>
― v 3
t
⇞
37b / s 7b / s ∞
2 2
1s
c 2 >,7b / s>
Acads v 3 2 7b/s v > 2 37b/s t 2 2 1s
[> ― Agtgrbmocr c ceg`grcìåd gsec`cr bíamc ad bõvg` qug pgredrrg c trcigetõrmc. D
[3
t 2; 2;
t 32> v 327
Qgbds9 c
[>
b
1;
t
>
∞
3;
v
3
∞
7
2
t
^gsd`uìåd c
>
∞
2
5
t
3
7 2
∞
>
2
3
v ― v >
3
t ― t >
Edbd v 3 2 ; g c
Acads
t > 2 4
v 2
t >25 v >23;
― Wb cutdbõvg`, [5 pcrtmoad ad rgpdusd, ags`dec-sg edb ubc ceg`grcìåd uomfdrbg ag 37; eb/s>. Agotrd ag qucotd tgbpd c`ecoìcrã c vg`demacag ag 37 b/s4 v 3 2 ; t 3 2 ; c 2 37;eb/s> v > 2 37eb/s>
v 2
3
t 3 2 ;,
2
v
>
t
vgb
⇞ t >22
>
v
>
c
`dld 2 t >
37b / s
3,7b / s
>
2 3;s
7
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Gxgreâemds prdpdstds [3 ― C vg`demacag ag ub cutdbõvg` qug sg ags`dec edb ceg`grcìåd uomfdrbg, cubgotdu ag37b/s pcrc >7b/s, aurcotg 6,>7 sgluoads. Agtgrbmog c ceg`grcìåd edb qug sg ags`dedu d cutdbõvg`, aurcotg gstg cubgotd ag vg`demacag. [> ― Wb cutdecrrd bdvg-sg edb c vg`demacag ag 3;b/s, pãrc aurcotg 1 sgluoads agpdms ag edbgìcr c trcvcr. Agtgrbmog c ceg`grcìåd edb qug d cutdecrrd sg ags`dedu aurcotg c trcvclgb.
^9 c 2 3,6 b/s>
^9 c 2 >,7b/s>
3.7.3.> Ceg`grcìåd Mostcotîogc C ceg`grcìåd bíamc ods mofdrbc ag bdad l`dnc` c vcrmcìåd ac vg`demacag ac pcrtâeu`c g oåd ods amz edbd, ag fdrbc gfgetmvc, gfgetmvc, dedrrg gssc vcrmcìåd gb tdads ds trgejds ad bdvmbgotd. Wbc mofdrbcìåd prgemsc sdnrg edbd dedrrg c vcrmcìåd ac vg`demacag gb motgrvc`ds ag tgbpd pgqugods, sõ pdag sgr dntmac ctrcvís ad gstuad ac ceg`grcìåd mostcotîogc. Amzgbds qug c ceg`grcìåd od mostcotg t í d `mbmtg pcrc qug tgoag c ceg`grcìåd bíamc, qucoad d motgrvc`d ag tgbpd tgoag pcrc zgrd.
c
C
2
`mb c
t ↞d
b
Od ecsd ad bdvmbgotd rgetm`âogd (g sõ ogstg), edbd ds vc`drgs acs ceg`grcì÷gs bíamcs såd acacs pg`c gqucìåd sglumotg9
v
cb
2
t
(3.:)
13
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
3.6. Bdvmbgotd Vcrmcad D bdvmbgotd bcms edbub od odssd amc c amc, í d bdvmbgotd vcrmcad. Ogssg bdvmbgotd, c pcrtâeu`c bctgrmc` agsergvg motgrvc`ds ag gspcìds amfgrgotgs gb motgrvc`ds ag tgbpd mlucms. Od bdvmbgotd vcrmcad d bõau`d ac vg`demacag cubgotc uomfdrbgbgotg edb d agedrrgr ad tgbpd. D bdvmbgotd í ejcbcad ag ceg`grcad qucoad d bõau`d ac vg`demacag cubgotc uomfdrbgbgotg edb d agedrrgr ad tgbpd. Cssmb, d smoc` ac vg`demacag edmoemag edb d smoc` ac ceg`grcìåd ceg`grcìåd.. Od gotcotd, d bdvmbgotd vcrmcad pdag sgr tcbníb rgtcracad. D bdvmbgotd í rgtcracad qucoad d bõau`d ac vg`demacag ambmoum uomfdrbgbgotg edb d agedrrgr ad tgbpd. Ogssg ecsd, d smoc` ac vg`demacag oåd edmoemag edb d smoc` ac ceg`grcìåd ceg`grcìåd..
3.6.3. Bdvmbgotd ^getm`âogd Womfdrbgbgotg Vcrmcad Bdvmbgotd rgetm`âogd uomfdrbgbgotg vcrmcad í cqug`g euic trcigetõrmc í ubc `mojc rgetc g suc ceg`grcìåd í edostcotg. ct 2 h c
1>
2
v t
doag
Αt 2 2 t ― ― t ;
vgb
v 2 2 v ; + c t
sgoad t ; 2 ;, (3.=)
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Fuoìåd Jdrãrmc ad Gspcìd ad Bdvmbgot Bdvmbgotd d Womfdrbgbgotg Vcrmcad
Coc`msgbds d lrãmed ac vg`demacag ag ub bõvg` gb bdvmbgotd uomfdrbgbgotg vcrmcad V
(b/s)
V
V; C
ncsg bgodr
ncsg bcmdr
; t (s)
C ãrgc (C) oc mlurc rgprgsgotc, oubgrmecbgotg, d ecbmojd pgredrrmad pg`d bõvg` aurcotg d tgbpd t C2ΑU
(3)
doag Α U 2 U ― U ;
Α U 2 U ― U ; Gspcìd momemc` ad bõvg` (mostcotg zgrd) U 2 Gspcìd ad bõvg` od mostcotg lgoírmed t [dr dutrd `cad, c ãrgc ac mlurc (trcpízmd) edrrgspdoag c9 C 2 {(ncsg bcmdr + ncsg bgodr )/> )/>}. C`turc ⇞ C
v + v
;
2
>
(>)
. t
edbpcrcoad (3) g (>) vgb9
v
U 2
+
t
v
;
.
t
(5)
15
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Bcs v 2 2 v ; + c t , sunstmtumoad gssg vc`dr vc`dr gb (5), vgb9 v
U 2
+
ct
+
>v t
v
;
;
>
.t 2
ct
+
+
>
ct
;
>
>
U
ct
v t +
2
;
> 3
s
∞s
2
;
v t ;
+
>
c t
>
(fuoìåd jdrãrmc ad gspcìd pcrc d BWV) 3 s
2
s
;
+
v t ;
+
>
ct
(3.3;)
>
Gqucìåd ag Qdrrmeg``m
Gxmstg ub ecsd pcrtmeu`cr pcrtmeu` cr qug tgb sgrvmad pcrc c rgsd`uìåd ag prdn`gbcs gb qug c fuoìåd ad tgbpd í mlodrcac. Qrctc-sg ac gqucìåd ag Qdrrmeg``m. C gqucìåd ag Qdrrmeg``m rg`cemdoc c vg`demacag edb d gspcìd pgredrrmad pdr ub bõvg`. G`c í dntmac g`mbmocoad d tgbpd gotrg cs gqucì÷gs jdrãrmc g acs vg`demacags g ads gspcìds. 3 s
2
s
;
+
v t ;
+
>
ct
>
v 2 2 v ; + c t
Msd`coad d tgbpd t oc gqucìåd (3.=) dntgbds9 v t
∞
v
2
;
c
Uunstmtumoad gb (3.3;) vgb9 v ∞ v s 2 s
;
;
+ v
;
c
v v ∞ v s∞s
;
2
;
11
;
>
;
+
c
v v ∞ v s∞s
+
2
;
>
; c
3 >
3
(
v ∞ v
; >
)
c
>
v
∞
c
> v;v + v ;> >
> v
+
c
c
>
∞
v
> ; >c
+ v
>
;
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
^gauzmoad cd bgsbd agodbmocadr tgbds9 c s∞s
> ( >c
;
) 2 >(
v v∞v
;
>
+
vv
) > >c
;
;
∞
vv
>
;
+v
>
>c ( s ∞ s ; ) 2 >v;v ∞ >v;> + v > ∞ >v v; + v;> > c( s ∞ s; ) 2 ∞ v;> + v > v
>
2 v v
>
;
Bcs @dld
+
> c ( s ∞ s; )
s―s; 2 Αs v > 2 v ;> + >cΑs
(>.3;)
Gqucìåd ag Qdrrmeg drrmeg``m ``m
Gxgreâemds Gxgr eâemds ag cp`mecìåd ^gsd`uìåd
[3 ― Wb bdtdrmstc ag ub cutdbõvg` qug sg ags`dec c 3;b/s vmu d smoc` vgrbg`jd ad sgbãfdrd g edbgìdu c rgauzmr c vg`demacag, ags`decoad-sg edb ubc ceg`grcìåd ag 7 b/s>.
c) 3 s
2
v t ;
>
ct
+
>
3 s 2 3; Ü 5 + .( ∞7).= > s
2
5; >>,7 ∞
↞
s
2
c) Sug amstîoemc pgredrrgu d cutdbõvg` aurcotg ds trés prmbgmrds sgluoads4
< ,7b
n) v s 2
Edbd
v
2
>
n) Sug amstîoemc pgredrrgu d cutdbõvg` ctí mbdnm`mzcr-sg4
>
+ v
;
>c
;
↞
s
; 3;; ∞
2
>.( 7) ∞
↞
s
2
3;b
Acads v ; 2 3;b / s c 2 7b / s>
c) s 2 4 pcrc t 2 2 5s n) s 2 4 pcrc v 2 2 ;
17
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Gxgreâemds Gxg reâemds ag cp`mecìåd cp`m ecìåd [> ― Wb pdotd bctgrmc` gb bdvmbgotd caqumrg vg`demacag qug dngageg ë gxprgssåd v 2 3;->t (t gb gb s8 v gb gb b/s)
Ec`eu`g9 c) C vg`demacag momemc`8
^gsd`uìåd C gqucìåd v 2 3;―>t í ad 3¹ lrcu, lrcu, pdrtcotd d bdvmbgotd bdvmbgotd í uomfdrbgbgotg vcrmcad, `dld pdr edbpcrcìåd9 v 2 3; ― >t v 2 v ;+ct c) v ; 2 3;b/s
n) c 2 >b/s> e) Sucoad t 2 6b/s v 2 t v 2 22 3; 3; ―― >>.6 v 2 2 3; ― 3> v 2 >b/s (tgb sgotmad edotrãrmd edotrãrmd cd pdsmtmvd ac trcigetõrmc) trcigetõrmc)
n) C ceg`grcìåd8 e) C vg`demacag od mostcotg 6s8 a) D mostcotg gb qug d pdotd bctgrmc` buac ag sgotmad.
a) D pdotd bctgrmc` buac ag sgotmad qucoad v 2 2 ; v 2 2 3; ― >t ; 2 3; ― >t ↞ t 2 7s
Gxgreâemds prdpdstds [3 ― Edbp`gtg c tcng`c ^9 3b8 7b/s8 ;b/s>8 33b8 B^W ;b8 ; b/s8 5 b/s>8 6b8 B^WV 3b8 3b/s8 1 b/s>, 33b8 B^W
16
Gqucìåd ad bdvmbgotd U 2 3 + 7t 5
U 2 t
>
>
U 2 >t > + t + + 3
U;(b)
V;(b/s)
c (b/s>)
U (t 2 >s)
Qmpd ag bdvmbgotd
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Gxgreâemds prdpdstds [> ― Wb cutdbõvg` momemdu ub bdvmbgotd uomfdrbgbgotg rgtcracad edb vg`demacag ag 3> b/s g pgredrrgu 3>7 bgtrds aurcotg :; sgluoads. Ec`eu`cr9 c) C ceg`grcìåd ad bdvmbgotd8 n) C vg`demacag agpdms ag 5; sgluoads.
[5 ― Wb bõvg` pcrtg ad rgpdusd edb bdvmbgotd ag ceg`grcìåd edostcotg g mluc` c 7b/s>. Agtgrbmog c vg`demacag g c amstîoemc pgredrrmac pg`d bõvg` od mb ag : sgluoads.
c)
^9 ;,>6 b/s>
n)
^9 1,> b/s
^9 1;b/s g 36;b
Lrãmeds ad bdvmbgot bdvmbgotd d rgetm`âogd uomfdrbgbgotg vcrmcad
Ugoad c gqucìåd jdrãrmc ad bdvmbgotd uomfdrbgbgotg vcrmcad ad >.¹ lrcu, d amclrcbc í ubc pcrãnd`c. s(b) 3;;;
7;;
t(s) ;
3;
>;
5;
1;
Fml. 3.7 ― Lrãed ad gspcìd
1<
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
v(b/s) 7; 1; c
5;
c
>; 3;
;
t
;
t
t(s)
c)
;
3;
>;
Fml. 3.6 ― c) Lrãed ac vg`demacag
5;
n)
1;
n) Lrãeds ac ceg`grcìåd
[dag-sg cprgsgotcr ocs sglumotgs fdrbcs9 • C rgetc tcolgotg ë pcrãnd`c, od pdotd gb qug g`c edrtc d gmxd ads gmxds (t 2 ;), rgprgsgotc lgdbgtrmecbgotg c vg`demacag momemc`, g c suc moe`mocìåd moe`mocìåd fdrogeg fdrogeg d vc`dr vc`dr ag edb d sgu smoc`.
Gxgreâemds Gxgr eâemds ag cp`mecìåd [3 ― C vg`demacag ag ub cutdbõvg` vcrmc ag 7 b/s pcrc 37 b/s aurcotg 1 sgluoads, agtgrbmog c ceg`grcìåd edb qug sg bdvg d cutdbõvg`. Acads v 3 2 7b/s v > 2 37b/s t 2 2 1s
1:
^gsd`uìåd v c
2
>
― v 3
t
⇞
37b / s 7b / s ∞
2 2
c 2 >,7b / s>
1s
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Gxgreâemds prdpdstds [3 ― Lrãmed rgprgsgotc c vcrmcìåd ac vg`demacag ag ubc pcrtâeu`c qug sg bdvg rgetm`mogcbgotg. c) Suc` í c vg`demacag momemc` g moc` ac pcrtâeu`c.
c) ^9 v ; 2 3; b/s8 v 2 5; b/s
n) Suc` í c ceg`grcìåd ac pcrtâeu`c od mostcotg t 2 2 > s.
n) ^9 7 b/s>
e) Suc` í c ceg`grcìåd ac pcrtâeu`c od mostcotg t 2 2 5 s.
e) ^9 7 b/s>
a) Edbd sg ejcbc gstg tmpd ag bdvmbgotd
a) ^9 B^WC
g) Agtgrbmog d ags`decbgotd ac pcrtâeu`c gotrg ds mostcotgs t 2 ; s g t 2 1 s.
g) ^9 :; :;b b
f) Ug od mostcotg momemc`, c pcrtâeu`c sg goedotrcvc gb Z 2 5 b. Suc` sgrã c suc pdsmìåd od mostcotg t 2 2 1 s
f ) ^9 :5b
57
v(b/s)
5; >7 >; 37 3; 7 ; t(s)
;
;.7
3
3.7
>
>.7
5
5.7
[> ― Acad d lrãmed ac vg`demacag ag ub pdotd bctgrmc` gb fuoìåd ad tgbpd, qug sg ags`dec v(s/b) oubc trcigetõrmc rgetm`âogc. 6 1
;
>
7
t(s)
1=
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Gxgreâemds prdpdstds Agtgrbmog9
c) ^9 7b/s g >b/s
c) Cs vg`demacags ods mostcotgs 3 s g 1 s8
n) ^9 3=b
n) D gspcìd pgredrrmad od motgrvc`d ag ;s c 7s8
e) ^9 5,: b/s
e) C vg`demacag bíamc od mtgb cotgrmdr8
a) ^9
a) Edostruc d amclrcbc c 2 f(t). >
c(b/s ) 3
7 t(s)
> ->
[5 ― D lrãmed cncmxd rgprgsgotc c vg`demacag ag ub pdotd bctgrmc` gb fuoìåd ad tgbpd, qug sg ags`dec gb ubc trcigetõrmc rgetm`âogc. v(s/b)
c) ^9 1,7b/s g 6b/s 6
n) ^9 55b
5
e) ^9 7,
1 6
3:
t(s)
Ec`eu`g9 c) Cs vg`demacags ods mostcotgs 3 s g 7 s8 s8
>
c(b/s )
n) D gspcìd pgredrrmad pgredrrmad od motgrvc`d ag ag ;s c 6 s8 6 >
3:
t(s)
e) C vg`demacag bíamc od motgrvc`d ag 3 s c : s8
-;,7
a) Edostruc d amclrcbc c 2 f(t).
7;
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
3.6.>. Sugac ag ub ub Edrpd Edrpd Sugac `mvrg ícdrgsmstéoemc bdvmbgotdadqug agsprgzcoad cr.edosmstg oc qugac ads edrpds C ceg`grcìåd ac lrcvmacag í edosmagrcac edostcotg g rgprgsgotc-sg pg`c `gtrc «l¸. [drtcotd d sgu vc`dr vcrmc agpgoagoad ac c`tmtuag du ac `ctmtuag gb qug sg rgc`mzc c bgamìåd. Qgoad gb edotc d oâvg` ad bcr g ubc `ctmtuag ag 17» d sgu vc`dr cprdxmbcad sgrã l 2 =,:;667
b s
>
[crc gssg ecsd tgrgbds cs sglumotgs gqucì÷gs ag bdvmbgotd9 Gqucìåd ac vg`demacag v 2 v ; + ct v 2 v ; + lt
Fml. 3.7 ― Bc`golc agmxc ecmr (cncoadoc) ub edrpd
Gqucìåd ag Bdvmbgotd
c s
2
s
;
+
v t+ ;
s 2 s; + v;t +
t
>
>
t
>
l >
>
t
Gqucìåd ag Qdrrmeg``m v > 2 v >; + >cΑs v > 2 v >; + > lΑs
73
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Gxgreâemds Gxgr eâemds ag cp`mecìåd [3 ― Wbc pgarc fdm sd`tc ad tgrrcìd ag ub gamâemd ag 3:; b ag c`turc. Edosmagrcoad l 2 3; b/s>, ec`eu`g9
^gsd`uìåd c) lt >
j2
c) D tgbpd lcstd pg`c pgarc pcrc ejglcr cd ejåd.
t
n) C vg`demacag vg`demacag ac pgarc cd ejglcr cd ejåd. Acads j 2 3:;b l 2 3;b / s>
n)
2
> 56
22 t ⇞
>j
@dld
l
t
2
>.3:;b 3;b / s >
2
56; 3;
⇞ t t22 6 s
. . v 2 > lj ⇞ v 22 >>3;3:; ⇞ v 2 56;; 2 6;b / s
c) t 2 4 n) v 2 4
Gxgreâemds prdpdstds ^9 1s
[3 ― Agmxdu-sg ecmr vgrtmec`bgotg ub lrcvg ad tdpd ag ubc tdrrg ag =; bgtrds ag c`turc. Ec`eu`cr c aurcìåd ac qugac.
^9 3 ― Sug gspcìd pgredrrgrmc gb 6 sgluoads, ub dnigetd ecmoad `mvrgbgotg oc vgrtmec`4 Sug vg`demacag tgrmc cd mb agssg tgbpd4
^9 7> b/s
[5 ― Wb dnigetd fdm `coìcad vgrtmec`bgotg ag embc pcrc ncmxd, tgoad lcstd 1 sgluoads c pgredrrgr ubc amstîoemc ag >;; bgtrds. Ec`eu`cr c vg`demacag momemc` edb qug fdm `coìcad.
7>
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
3.6.5. Csegosåd ag ub ub Edrpd @coìcbgotd vgrtmec`
Fdotg9 @mvrd Amaãtmed [ùn`med/UGGA
Dnsgrvc c mlurc cembc. C bgsbc rgprgsgotc d `coìcbgotd vgrtmec` pcrc embc ag ubc nd`c pdr ub idvgb. Agsprgzcoad c rgsmstéoemc ad cr odtcbds d sglumotg9 • Cd sunmr c vg`demacag vcm rgauzmoad ctí ctmolmr c c`turc bãxmbc. C vg`demacag gsec`cr g c ceg`grcìåd gsec`cr agvgb tgr smocms dpdstds. Gstg bdvmbgotd ag csegosåd í ub bdvmbgotd uomfdrbgbgotg rgtcracad g pdag sgr edbpcrcad cd bdvmbgotd rgetm`âogd uomfdrbgbgotg vcrmcad gstuacad od ecpâtu`d cotgrmdr. [crc gstg bdvmbgotd c ceg`grcìåd í oglctmvc g aurcotg gstg bdvmbgotd bdvmbgotd c vg`demacag cubgotc =,: gb ecac 3 sgluoad. • D edrpd cd ctmolmr c c`turc bãxmbc, c suc vg`demacag í mluc` c zgrd. Ugluoad c coã`msg ad lrãmed sunstmtumoad d gspcìd pg`c c`turc dntgbds9 j 2 j; + v;t ∞
3 >
(3.33)
lt >
v 2 2 v ; ― lt
(3.3>)
Wtm`mzcoad c gqucìåd ag Qdrrmeg``m g tgoad gb edotc qug c ceg`grcìåd í oglctmvc vgb9 v > 2 v >; + >cΑj
75
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Edbd
v 2 ;
vgb
; 2 v ; ― > l (jbcx ― j>)
; Ug c vg`demacag bãxmbc (Jbãx). momemc` fdr V í pdssâvg` agtgrbmocr c c`turc >
jbcx 2
v
;
> l
y 2 ―l
Qrcigetõrmc drmgotcac pcrc embc, pdrtcotd y 2 ―l
y 2 +l
Qrcigetõrmc drmgotcac pcrc ncmxd, pdrtcotd y 2 ―l
[rdprmgacags ad @coìcbgotd Vgrtmec` Vgrtmec` (Qgbpd (Q gbpd ag Uunmac g ag Agsemac) >
C c`turc bãxmbc ctmolmac pg`d edrpd sgrã9 jbcx 2
v
(3.35)
;
> l
Qgbpd ag sunmac9 í d tgbpd lcstd pg`d edrpd agsag d pdotd ag
pcrtmac ctí ctmolmr c c`turc bãxmbc. Ucngoad qug t ; 2 ; g v; ≫ ;, od pdotd bcms c`td ac trcigetõrmc dntgbds9 v 2 2 v ; + ct Edbd v 2 2 ; t s
2
t s
2
v ; l
(3.31)
doag v ; l
t s 2 t a
71
g í d tgbpd ag agsemac, agsemac, d qug smlommec qug d tgbpd ag sunmac g d ag agsemac qug d edrpd `gvc c pgredrrgr í mluc`. Mstd í 9
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Gxgreâemds Gxgr eâemds ag cp`mecìåd ^gsd`uìåd
t 2
>j l
⇞ 2t 2
> >.5; 3;
8 t
2
6
2 >, 1=s
[3 ― Wbc pgarc `coìcac vgrtmec`bgotg pcrc embc, c`ecoìc c c`turc ag 5; b. Sucotd tgbpd ogegssmtcrã pcrc c`ecoìcr gssc c`turc4 Acads j 2 5;b t 2 2 4
Gxgreâemds prdpdstds [3 ― Edb qug vg`demacag agvg sgr `coìcac ubc pgarc vgrtmec`bgotg ag ncmxd pcrc embc pcrc qug ctmoic c c`turc ag ,< s
[> ― @coìdu-sg vgrtmec`bgotg ubc nd`c qug ctmolmu 3; bgtrds ag c`turc. Ec`eu`cr9 >
c) C vg`demacag momemc` edb qug c nd`c fdm `coìcac. n) D tgbpd qug c nd`c `gvc c rglrgsscr cd pdotd ag pcrtmac.
c) ^9 31 b/s n) ^9 >,: s
[5 ― Wbc pgarc fdm `coìcac jdrmzdotc`bgotg ad tdpd ag ubc tdrrg ag 5; b ag c`turc, edb ubc vg`demacag ag >; b/s. Ec`eu`cr9 c) D tgbpd qug agbdrdu c qugac.
c) ^9 >,7 s
n) C amstcoemc ac ncsg ac tdrrg cd pdotd doag ecmu c pgarc.
n) ^9 1= b
e) C vg`demacag tdtc` edb qug c pgarc ctmolmu d sd`d. n) ^9 53 b/s
77
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
3..3< d edbprmbgotd ad cred, dntíb-sg9 r κ v
2
t
⇞ ,
v
2
(3.3 ϋ r 2
f 2
2
Q 3
Q
frgquéoemc ad bdvmbgotd bdvmbgotd í >ϋ r f g edbd c frgquéoemc
( Jz ) (jgrtz )
pdagbds cmoac gsergvgr
w 2 >ϋ f
(3.>;)
Ceg`grcìåd Egotrâpgtc Egotrâpgtc (Odrbc`)
C ceg`grcìåd ad bdvmbgotd emreu`cr uomfdrbg í egotrâpgtc, mstd í, pgrpgoameu`cr c vg`demacag ad bdvmbgotd, cd `dold ad rcmd gb amrgeìåd cd egotrd ac emreuofgr emreuofgréoemc éoemc (trcigetõrmc).
ce ce
^
ce
>
c e
ce
Fml. 3.: ― Ceg`grc Ceg` grcìåd ìåd ego egotrâp trâpgtc gtc
7:
2
v
(3.>3)
C ceg`grcìåd egotrâpgtc pdag sgr mluc`bgotg gxprgssc ctrcvís ac vg`demacag colu`cr. Ucngbds qug v 2 ύr , sunstmtumoad v oc fõrbu`c cotgrmdr, dntgbds9
r
ce 2 ύ> r
(3.>>)
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
[dagbds cmrbcr, qug d bõau`d ac ceg`grcìåd egotrâpgtc agpgoag ac vg`demacag colu`cr ad edrpd g ad rcmd ac trcigetõrmc.
3.:. Bdvmbgotd Emreu`cr Vcrmcad Ceg`grcìåd colu`cr colu`cr,, γ
Ug agodbmoc ceg`grcìåd colu`cr cd qudemgotg gotrg c vcrmcìåd ag vg`demacag colu`cr g d motgrvc`d ag tgbpd lcstd pcrc gfgetucr gstc vcrmcìåd. C ceg`grcìåd colu`cr, qug í rgspdosãvg` pg`c vcrmcìåd ac vg`demacag colu`cr, í agmomac pg`c rczåd gotrg c vcrmcìåd ac vg`demacag colu`cr, g d motgrvc`d ag tgbpd lcstd pcrc gfgetucr gstc vcrmcìåd. γ
ύ 2
t
Doag Αύ 2 ύ ― ύ; g Αt 2 2 t ― t ; ύ
γ
∞
ύ
;
2
t ― t ;
(3.>5)
3.:.3. Bdvmbgotd Emreu`cr Womfdrbgbgotg Vcrmcad Wb bdvmbgotd emreu`cr uomfdrbgbgotg ceg`grcad í cqug`g euic ceg`grcìåd γ í edostcotg. Cs gqucì÷gs ad bdvmbgotd emreu`cr uomfdrbgbgotg vcrmcad pdr coc`dlmc téb c bgsbc fdrbu`cìåd qug cs gqucì÷gs ad bdvmbgotd rgetm`âogd uomfdrbgbgotg vcrmcad. γ 2 edostcotg ύ 2 ύ; +
t
c
3 κ
2κ
;
+ ύ
t +
;
ct >
>
(3.>1)
7=
[C^QG M ― Bgeîomec WOMACAGG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc` WOMACA
Gxgreâemds Gxgr eâemds ag cp`mecìåd [3 ― Wbc pcrtâeu`c gfgetuc 3>;; rpb oubc emreuofgréoemc ag ;,7 b ag rcmd. Agtgrbmog9
^gsd`uìåd c)
c) C vg`demacag colu`cr ac pcrtâeu`c. n) C vg`demac vg`demacag ag `mogcr ac pcrtâeu`c. 2
2 >ϋ f ↞ ύ 2 >ϋ .>; .>;
ύ
2 1;rca / s
n)
Acads f
ύ
v 2 ύr ↞ v 2 1;ϋ .;,7 .;,7
3>;;
3>;;rpb 6;s
2
>;Jz
r 2 ;,7b
v 2 >;ϋ b / s
c) ύ 2 4 n) v 2 4
Gxgreâemds prdpdstds
c) ^9 3>,76 rca/s n) ^9 >; b/s
c) ^9 >,7 rca/s n) ^9 < b/s> ^9 ;,>7 b/s g > rca/s
[3 ― Wb amsed tgb 5,> b ag amîbgtrd g lmrc edb vg`demacag edostcotg, gfgetucoad gfgetucoad 3>; vd`tcs pdr bmoutd. Ec`eu`cr9 c) C vg`demacag colu`cr ad amsed. n) C vg`demacag `mogcr ads pdotds ac pgrmfgrmc.
[> ― Wbc pcrtâeu`c tgb bdvmbgotd emreu`cr uomfdrbg edb vg`demacag ag 5 b/s. d rcmd ac trcigetõrmc í ag 3,> b. Ec`eu`cr9 c) C vg`demacag colu`cr. n) C ceg`grcìåd egotrâpgtc.
[5 ― Sug vg`demacag agvg mbprmbmr-sg c ubc pcrtâeu`c qug sg bdvg sdnrg ubc trcigetõrmc emreu`cr ag >7 eb ag amîbg>
trd, tgojc ubc ceg`grcìåd egotrâpgtc ag ;,7 b/s 4 Suc` sgrã c vg`demacag colu`cr ac pcrtâeu`c4
6;
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3 ― Bdvmbgotd ag ubc [crtâeu`c Bctgrmc`
Gxgreâemds prdpdstds [1 ― Aucs pd`mcs ag rcmds r3 2 ;,;7 b g r> 2 ;,3 eb, rgspgetmvcbgotg, gståd `mlcacs pdr ubc edrrgmc. D pgrâdad ag rdtcìåd ac pd`mc ag bgodr rcmd í mluc` c ;,7 s. C qug vg`demacag sg ags`dec c edrrgmc4 Suc` í d pgrâdad ag rdtcìåd ac sgluoac pd`mc. [7 ― Wbc pcrtâeu`c rgc`mzc ub bdvmbgotd emreu`cr uomfdrbg ag rcmd 7 b, edbp`gtcoad ubc vd`tc gb ecac 7 s. Ec`eu`g c frgquéoemc g c vg`demacag colu`cr ad bdvmbgotd.
^9 ;,6 b/s g 3s
^9 ;,> Jz g 3,>76 rca/s
63
[C^QG M ― Bgeîomec WOMACAGG 3M ― Motgrceì÷gs gotrg Edrpds WOMACA
Womacag 3m
motgrceì÷gs gotrg edr[ds Oc uomacag cotgrmdr gstuacbds d bdvmbgotd ads edrpds bcs, oåd ods agnruìcbds sdnrg cs ecuscs qug drmlmocb gstg bdvmbgotd. Ogssc uomacag vcbds gstuacr d bdvmbgotd ads edrpds ngb edbd cs sucs ecuscs.
>.3. Fdrìc C pc`cvrc fdrìc í edojgemac pdr oõs agsag c tgorc macag. Cd fc`crbds ac fdrìc motgrprgtcbds ag fdrbcs amfgrgotgs moagpgoagotgbgotg ads gfgmtds cprgsgotcads. Wb edrpd pdag pñr-sg gb bdvmbgotd du vcrmcr c suc vg`demacag ecsd d gbpurrcrbds. Fml. >.3 ― Hmnctd ejutcoad ubc nd`c
Od gxgbp`d emtcad d edrpd p÷g-sg gb bdvmbgotd, buac ag amrgeìåd du pãrc sdn c ceìåd ag dutrd edrpd. C fdrìc í c gxprgssåd vgetdrmc` g edbp`gtc ac motgrceìåd gotrg adms edrpds âsmeds E`cssmmecìåd acs Fdrìcs
Cs fdrìcs pdagb e`cssmmecr-sg gb9 3. Fdrìcs ag edotcetd qucoad cs supgrâemgs ads edrpds motgrclgb. Gxgbp`d. • Fdrìc ag ctrmtd, • Fdrìc g`ãstmec, • Fdrìc ag tgosåd
>. Fdrìcs ag ecbpd qucoad dedrrgb ë amstîoemc. Gxgbp`ds • Fdrìc oue`gcr (fdrtg du frcec), • Fdrìc g`getrdbcloítmec, • Fdrìc lrcvmtcemdoc`.
6>
[C^QG M ― Bgeîomec WOMACAG WOMA CAG 3M ― Motgrceì÷gs gotrg Edrpds
Gqum`ânrmd ag ubc [crtâeu`c
Jcnmtuc`bgotg amstmolumbds adms tmpds ag gqum`ânrmd9 Gstãtmed g amoîbmed. Gqum`ânrmd gstãtmed9
dnsgrvc-sg qucoad c vg`demacag ag ub edrpd í ou`c, d qug smlommec qug d edrpd gstã gb rgpdusd gb rg`cìåd c ub egrtd rgfgrgoemc`.
Fml. >.> ― Nmõ gqum`mnrcoad d sgu pgsd
v 2 ; gqum`ânrmd gstãtmed Gqum`ânrmd Gqum `ânrmd amoîbmed9
dnsgrvc-sg qucoad d edrpd tgb vg`demacag edostcotg od agedrrgr ad tgbpd. D qug smlommec qug c vg`demacag oåd í ou`c smb d (B^W). edrpd vcm combcad ag bdvmbgotd rgetm`âogd gbcs uomfdrbg V 2 edostcotg ≫ ; , gqum`ânrmd amoîbmed
Fml. >.> ― Gqum`ânrmd amoîbmed
Gfgmtd ag ubc Fdrìc
Qc` edbd iã vmbds oåd dnsgrvcbds c fdrìc bcs edojgegbds ds sgus gfgmtds. Wbc fdrìc qucoad prdauz cpgocs agfdrbcìåd gstcbds gb prgsgoìc ad gfgmtd gstãtmed ac fdrìc, pdms oåd sg dnsgrvc bdvmbgotd. Od ecsd ac fdrìc prdauzmr cpgocs ubc ceg`grcìåd pdagbds cmrbcr qug gstcbds gb prgsgoìc ad gfgmtd amoîbmed. [dr gxgbp`d qucoad gbpurrcbds ub bõvg` vcrmcbds c suc vg`demacag g edosgqugotgbgotgg cp`mecbds ubc fdrìc sdnrg g`g. Agmxcoad ag edosgqugotgbgot cp`mecr c fdrìc cutdbctmecbgotg cutdbctmecbgotg egssc c ceg`grcìåd. Cssmb c fdrìc í c ecusc g c ceg`grcìåd í d gfgmtd.
Fml. >.1 ― Gfgmtd ag ubc fdrìc
C fdrìc, í ubc lrcoagzc vgetdrmc`, pdms pcrc sgr agmomac, í ogegssãrmd tgr gb edotc c amrgeìåd, sgotmad g motgosmacag du vc`dr oubírmed. Qgb edbd uomacag d Ogwtdo, od UM, g rgprgsgotc-sg pg`c `gtrc O. Oc tíeomec g oc vmac qudtmamcoc gbprglcb-sg dutrcs dutrcs uomacags Hm`dlrcbc-fdrìc ìc hlf . g d Amog. Doag ag d Hm`dlrcbc-fdr Doag 3hlf 2 =,: O g 3fdrìc, amog 2 3;.―7 O.
65
[C^QG M ― Bgeîomec WOMACAGG 3M ― Motgrceì÷gs gotrg Edrpds WOMACA
C mlurc cd `cad rgprgsgotc ub amocbõbgtrd qug í d mostrubgotd utm`mzcad pcrc bgamr c motgosmacag ag ubc fdrìc pg`c agfdrbcìåd qug prdauz oub edrpd g`ãstmed. Gstg mostrubgotd edosmstg oubc bd`c jg`medmac` ag cìd govd`vmac pdr ub prdtgetdr. Oc gxtrgbmacag `mvrg ac bd`c jã ub pdotgmrd qug sg ags`dec cd `dold ag ubc gsec`c. C bgamac ag ubc fdrìc í fgmtc pdr edbpcrcìåd ac agfdrbcìåd pdr gssc fdrìc edb c ag fdrìcs pcar÷gs.
Fml. >.7 ― Gqum`ânrmd amoîbmed
Fdrìc ^gsu`tcotg
Edostctcbds lgrc`bgotg qug sdnrg ub edrpd oåd cetuc sõ
F'3
Fml. >.6 ― Fdrìc rgsu`tcotg
ubc fdrìc, bcs vãrmcs. Gsec`c Dnsgrvc c mlurc, c bgsbc rgprgsgotc fdrìcs cetucoad smbu`tcogcbgotg sdnrg d bgsbd edrpd.
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