Modul Mekanika Gerak Kendaraan OTO226-03

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    ludoMedoK

    .KGM OTO 2 62 - 30

    YNUkinkeTsatlukaFf itomotOkinkeTnakididnePnasur uJ

    NAMEREGNEPKITSIRETKARAKITNEHREBKARAJNAD NAARADNEK

    :nusuyneP

    .T .M ,.d P .M ,i bu t r aM

    f itomotOk ink eTnak ididnePnasuruJK INK ETSATLUK AF

    ATR AK AYGOYIR EGENSATISR EVINU4002

    Y

    R a X

    h a nisW R d h g/a.W

    R f r B F b h d l1 R rr Al2

    W f socW WL W r

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    2

    R ATNAGNEPATAK

    nagnedludoM 622OTO.K GM nagned30 ludu j k itsiretk araK

    nameregneP itnehreBk araJnad naudna piaga besnak anugidini malad

    :utiay,isnete pmok utashalask utne bmemk utnuhailuk nataigek nadimahameM

    mta pad ayagnak utnenemmaladnamer egne pak inak em pesnok nak anuggne

    .naar adnek aynitnehr e bk ar a jnadnamer egne pisneisif e,namer egne p iniludoM

    esk utnunak anugidta pad Mhailuk atr ese paum naar adneK k ar eGak inak e id

    Ir etsemes V satisr evinUk ink eTsatluk aFf itomotOk ink eTidutSmar gor Pada p.atr ak aygoYir ege N

    nak i jasidiniludomadaP pesnok - r asad pesnok r adnek namer egne pgnatnet a na ,

    hotnoc - eyne patr ese blaoshotnoc aynnaiasel , nahital - nahital setnadsagut/

    isaulaveatr esf itamr of aynulr e pes k utnu em isnete pmok ia pacn .nak par ahidgnay

    satair idr etiniludoM agit .r a jale bnataigek r a jale bnataigeK 1 :gnatnetsaha bmem

    igeK ,gna pmune pnaar adnek namer egne pk itsir etk ar aK r a jale bnata 2 saha bmem

    namer egne pk itsir etk ar aK :gnatnet r ot car t - r el iar t ime s r a jale bnataigeK nad, 3

    .namer egne pk ar a jnadisneisif E:gnatnetsaha bmemawsisahammak par ahid,hadumnagnediniludomir a jale pmemasi bk utnU

    ik ilimemhalet nauhategne p sisilana pesnok amatur et,ihunememgnaylawa

    .adne bnagna bmitesek ir oetagu jnadnemom pesnok ,k ar eggnatnetsitametam

    .

    ,atr ak aygoY iluJ 4002

    nusuyneP

    .T.M,.dP.M,i butr aM

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    namalaH

    :2r a jaleBnataigeK .2 namer egnePk itsir etk ar aKr ot car T - r el iar t imeS ............................ ......... ....... . 22

    r a jale bnataigek nau juT.a 2 ......................................... ......... ........... 22

    ir etamnaiar U. b 2 .................................. ........ ......... 22...........................

    namuk gnaR .c 2 ...................................................... ......... .................. 27

    saguT.d 2 ............................................... ......... ................................... 28

    .e f itamr of seT 2 .............................................. ........ .......................... . 29

    f itamr of set bawa jicnuK .f 2 ............................................. ......... ....... 29

    :3r a jaleBnataigeK .3 eisif E sn i namer egnePnar adneK itnehr eBk ar aJnad .......... ........... ........ 29

    ............3r a jale bnataigek nau juT.a .......... ........................................ 29

    ......3ir etamnaiar U. b ................................. ........ ............................... 03

    .................................................3namuk gnaR .c ......... ....................... 43

    ..........................................................3saguT.d ......... .. 3...................... 6

    .................................................3f itamr of seT.e ........ 3........................ 6

    ....................................2f itamr of set bawa jicnuK .f ...... ................ 36

    ISAULAVE.III ..... ...................................................................... ...... .......... 37

    .........................................................................naaynatr eP.A ........... ....... 37

    .........................na bawaJicnuK .B ......................................... ......... ......... 38

    ...................................nasululeK air etir K .C ........ ................ . .................... 39

    PUTUNEP.VI .......................................................... ...... ....... .. ...................... 04

    AK ATSUPR ATFAD ................................................... ....... ........................ 14

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    5

    /NAHALITSIR EP Y R A S S O LG

    nel avi uk eassamr ot k aF k utnunak hutu bidgnaynar ase bhau beshau beshalada:

    em .k ar egr e bgnadesgnayassamutaus padahr etnagna bmiesek tau bm

    si mani d or e Anat abma H na pednaiga bada pa jr ek e bgnaynignanata bmahhalada:

    .)naar adnek (li bom

    r abwar d nat abma H gnak ale bnaiga bada pa jr ek e bgnaynignanata bmahhalada:.)naar adnek (li bom

    H t ni o phct i ar atnanagnu bmasta pmetk itithalada: r ot car t nagned r el iar t ime s .

    i sehd anei si f eo K nata bmahaynadanak k u jnunemgnaynar ase bhau beshalada:

    .nala jnaak umr e pnagnedli bomna br atatnair anemk ir atayagta bik a

    e pol S la jnagnir imek tudushalada: .tualr ianaak umr e pnak gnidna bidna

    esabl eehW gnak ale bador u bmusnagnedna pedador u bmusar atnak ar a jhalada:

    .sur ulisiso pada pli bomhau bes

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    6

    BAB I

    NAULUHADNEP

    ispirk seD.A

    ludu jr e bgnayludoM ar ad ne K namer e g ne P k i t si r et k ar a K na ini

    naanacner e pmetsisnagnedtiak r etgnayr asad pesnok a par e be bsaha bmem

    maladir a jale pidgnayir etamna puk acnu padA.naar adnek k ar eggne paganet

    nad,gna pmune pnaar adnek namer egne pk itsir etk ar aK )1(:itu pileminiludom

    namer egne pk itsir etk ar aK )2( r ot car t - r el iar t ime s isneisif E)3(nad,

    .naar adnek aynitnehr e bk ar a jnadnamer egne p

    satair idr etiniludoM saha bmem1r a jale bnataigeK .r a jale bnataigek agit

    2r a jale bnataigeK ,gna pmune pnaar adnek namer egne pk itsir etk ar aK :gnatnet

    saha bmem namer egne pk itsir etk ar aK :gnatnet r ot car t - r el iar t ime s nad,

    .namer egne pk ar a jnadisneisif E:gnatnetsaha bmem3r a jale bnataigeK adaP

    nadlaoshotnocnagnedi pak gnelidulalesr a jale bnataigek paites

    nahitalatr ese baynnasaha bme p - amr of set,sagut/nahital isaulavenadf it

    gnayisnete pmok ia pacnemmaladawsisahamutna bmemk utnuaynulr e pes

    .nak par ahid

    awsisahamnahur ulesek ar acesiniludomir a jale pmemiaseleshaleteS

    nak par ahid ak inak em pesnok nak anuggnemta padnadimahameM

    maladnamer egne p nadnamer egne pisneisif e,namer egne payagnak utnenem

    .naar adnek aynitnehr e bk ar a j

    taraysarP.B

    nak ididnePnasur uJawsisahamiga blawaludomnak a pur eminiludoM

    ir etamisir e bgnay,3Dnu puam1Sgna jneJf itomotOk ink eT - gna jnune pir etam

    / hailuk atamir adnaayagne p - gnayf itomotognadi bidnailhaek hailuk atam

    hailuk atamhaladaamatur etaynmule besir a jale pidhadusaynsur ahes

    iladnegnePmetsiS .

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    ir etamnaik imednagneD - nak ainiludomisinagnedtiak r etgnayir etam

    nak a pur em ia pacnemak gnar maladgnitne ptagnasgnaygnuk udne p

    k aditaynsutatsnu pik sem,iniludommaladnak par ahidgnayisnete pmok .ayntar aysar piaga besimser ar aces

    ludoMnaanuggnePk u jnuteP.C

    awsisahaMigabk u jnuteP.1

    yr a jale blisahhelor e pidr agA nak anuggnemmaladak am,lamisk amgna

    nak anask alidnad,nak itahr e pidulr e pgnayr udesor pa par e be badainiludom

    :nialar atna

    pesnok naiar uamask esnagnedimahaf nadhalacaB.a - gnaysitir oet pesnok

    na par ene palu pimahaf naidumek ,iniludomada pnak i jasid pesnok -

    hotnocmaladtu besr et pesnok - .aynnaiaseleyne par acatr ese blaoshotnoc

    asi bmule bnadsale jgnar uk gnayir etamadahisamask a pr etaliB

    nesodada pek nak aynanemta padawsisahamar a pk ia bnagnedimahaf id

    .nahailuk r e pnataigek u pmagnemgnay

    r ek a boC. b inilah,ir idnamar aces)nahitallaos(sagut paitesnak a j

    haletgnaynamahame pr ase ba par e besiuhategnemk utnunak dusk amid

    ir etam padahr etawsisaham paitesik ilimid - ada psaha bidgnayir etam

    .r a jale bnataigek paites

    bawsisahamaynnaataynek maladali ba pA.c ada pir etamiasaugnemmule

    igalnak a jr egnemnadaca bmemigalignalua boc,nak par ahidgnaylevel

    nahital - gnaynesodada pek halaynatr e bulr e pualak nadaynnahital

    gnayir etamualaK .natuk gnasr e bgnaynahailuk r e pnataigek u pmagnem

    ame pnak ulr ememnatuk gnasr e b nak nik ayak am)tar aysar p(lawanamah

    r ane bdusk amidgnaytar aysar pawha b - .ihune pidhadusr ane b

    nesoDigabk u jnuteP.2

    :k utnunar e pnadsagutiaynu pmemnesod,nahailuk r e p paitesmalaD

    a. .r a jale bsesor pnak anacner emmaladawsisahamutna bmeM

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    b. sagutiulalemawsisahamgni bmi bmeM - nahitaluatasagut - gnaynahital

    .r a jale b bahatmaladnak sale jidc. bawa jnemnadur a b pesnok imahamemmaladawsisahamutna bmeM

    .nak ulr e pidali ba paawsisahamnaaynatr e p

    d. ynialr a jale br e bmussesk agnemk utnuawsisahamutna bmeM gna

    .nak ulr e pid

    e. .nak ulr e pidak i jk o pmolek r a jale bnataigek r isinagr ogneM

    f. .nak ulr e pidak i jgni pmadne pnesod/ilhagnar oesnak anacner eM

    g. gnayawsisahamisnete pmok naia pacne p padahr etisaulavenak adagneM

    .nak utnetidhalet

    rihk Anau juT.D

    haleteS iniludommaladr a jale bnataigek ir etamhur ulesir a jale pmem

    :nak par ahidawsisaham

    .1 gna pmune pnaar adnek namer egne pnar utanadtaf is, pesnok nak anuggneM

    .halasamnahaceme pmalad

    namer egne pnar utanadtaf is, pesnok nak anuggneM.2 r ot car t - r el iar t ime s

    malad halasamnahaceme p

    namer egne pk ar a jnadisneisif f eir adnar utanadtaf is, pesnok nak anuggneM.3

    .halasamnahaceme pmalad

    isnetepmoK .E

    622OTO.K GMludoM - k utne bmemak gnar maladnususidini30

    isnete pmok snok nak anuggnemta padnadimahameM ak inak em pe

    nadnamer egne pisneisif e,namer egne payagnak utnenemmaladnamer egne p

    naar adnek aynitnehr e bk ar a j hi belr et,tu besr etisnete pmok ia pacnemk utnU.

    busia pacidta padsur ahuluhad - ayna jr ek k u jnuair etir k atr ese bisnete pmok bus

    ale b puk gniliulalem :tuk ir e biaga besnar a jale bme pk ok o pir etamnagnedr a j

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    buSisnetepmoK

    airetirKa jreK k u jnU

    puk gniLra jaleB

    nara jalebmePk ok oPiretaM

    pak iS nauhategneP nalipmarteK

    imahameM ta padnadanuggnem -

    pesnok nak ak inak em

    mer egne p - na malad

    nak utnenem payag egne -

    ,namer isneisif e

    namer egne p k ar a jnad

    aynitnehr e b.naar adnek

    asr e p pesnoK .1 -egne pnaam -adnek namer -

    mune pnaar - imahaf idgna p

    r ane bnagned .ir oetiauseslamr onna beB.2

    sor o pada p naar adnek

    gna pmune pegne pamales -

    gnutihidnamer r ane bnagned

    uses .ir oetiaegne payaG.3 -

    k amnamer -adnek mumis -

    mune pnaar - gnutihidgna p r ane bnagned

    .ir oetiauses .namer egne p

    latotisr o por P.4egne payag -

    ada pnamer sor o p paites

    naar adnek gna pmune p

    nagnedgnutihid iausesr ane b

    .ir oetak em pesnoK .6 -

    egne pak in -mer na r ot car t -

    r el iar t ime s nagnedimahaf id

    iausesr ane b.ir oet

    lamr onna beB.7 paitesada p

    sor o p r ot car t -r el iar t ime s

    egne pamales gnutihidnamer

    r ane bnagnedir oetiauses

    ayaG.8 namer egne p

    mumisk amr ot car t - ime s r el iar t gnutihid

    r ane bnagnedtiauses .ir oe

    pesnoK .1 naamasr e p

    namer egne p naar adnek

    .gna pmune p

    lamr onna beB.2 sor o pada p

    naar adnek gna pmune p

    amales .namer egne p

    e payaG.3 -

    namer egn mumisk am naar adnek

    .gna pmune p

    latotisr o por P.4 ayag

    namer egne p paitesada p

    sor o p naar adnek

    mune p .gna p

    pesnoK .6 ak inak em

    namer egne p

    r ot car t -r el iar t ime s .

    lamr onna beB.7 paitesada p

    sor o p r ot car t -r el iar t ime s

    amales namer egne p

    ayaG.8 namer egne p

    mumisk amr ot car t -

    r el iar t ime s

    ,sitir K naditilet

    tamr ec malad

    silunem gna bmal

    alemnad -uk r e pnak -

    .nagnutih

    pesnoK .1 naamasr e p

    namer egne p naar adnek

    .gna pmune p

    lamr onna beB.2 sor o pada p

    naar adnek gna pmune p

    e pamales - .namer egn

    e payaG.3 -

    namer egn mumisk am naar adnek

    .gna pmune p

    latotisr o por P.4 ayag

    mer egne p - na paitesada p

    sor o p naar adnek

    .gna pmune p

    pesnoK .6 ak inak em

    mer egne p - na

    r ot car t -r el iar t ime s .

    na beB.7 ada plamr on sor o p paites

    r ot car t - ime sr el iar t

    e pamales -namer egn

    e payaG.8 - namer egn

    mumisk amr ot car t -

    r el iar t ime s

    gnutihgneM nagned

    nadr udesor p gnaylisah

    r ane b

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    01

    naupmameK k eC.F

    cadnatnagnedhalisi,ini622OTO.K GMludoMir a jale pmemmule beS k e ( paitesheloik ilimidhaletgnayisnete pmok nak k u jnunemgnaynaaynatr e p)

    :nak bawa jgnuggnatr e pidta padnadr u ju jnagnedawsisaham

    buSisnetepmoK naaynatreP

    nabawaJ aYnabawaJaliBnak a jreK aY k adiT

    imahameM ta padnadanuggnem - pesnok nak

    ak inak em mer egne p - na malad

    nak utnenemegne payag -

    ,namer isneisif e

    namer egne p k ar a jnad

    aynitnehr e b.naar adnek

    1. k imahamemayaS pesno naamasr e p.gna pmune pnaar adnek namer egne p

    1f itamr oFseT

    .2 gnutihgnemta padayaS ada plamr onna be br o p naar adnek namer egne pamalesso

    gna pmune p1f itamr oFseT

    .3 gnutihgnemta padayaS namer egne payag gna pmune pnaar adnek mumisk am 1f itamr oFseT

    .4 gnutihgnemta padayaS ayaglatotisr o por p naar adnek sor o p paitesada pnamer egne p

    ne p gna pmu1f itamr oFseT

    .5 nak utnenemta padayaS anamadoruluditnehr e bgnay

    1f itamr oFseT

    6. k imahamemayaS pesno ak inak emada pnamer egne p r ot car t - r el iar t ime s .

    2f itamr oFseT

    .7 gnutihgnemta padayaS na be b lamr onsor o p paitesada p r ot car t - r el iar t ime s

    .namer egne pamales2f itamr oFseT

    .8 gnutihgnemta padayaS egne payag -mumisk amnamer r ot car t - .r el iar t ime s

    2f itamr oFseT

    .9 pesnok imahamemayaS isneisif e.namer egne p

    3f itamr oFseT

    .01 gnutihgnemta padayaS latotk ar a j.naar adnek aynitnehr e b

    3f itamr oFseT

    bawa jnemawsisahamali ba pA k adiT iniludomir a jale pak am

    bawa jidgnayir etamiauseS k adiT .tu besr e

    buSisnetepmoK

    airetirKa jreK k u jnU

    puk gniLra jaleB

    nara jalebmePk ok oPiretaM

    pak iS nauhategneP nalipmarteK

    imahameM ta padnadanuggnem - nak

    pesnok ak inak em

    namer egne p nenemmalad

    ayagnak ut ,namer egne p

    k ar a jnad aynitnehr e b

    naar adnek .

    noK .9 isneisif e pes namer egne p

    imahaf idta pad r ane bnagned

    .ir oetiauseslatotk ar aJ.01

    aynitnehr e b ta padnaar adnek nagnedgnutihid

    iausesr ane b.ir oet

    pesnoK .9 isneisif e

    namer egne p

    latotk ar aJ.01namer egne p

    itilet,sitir K tamr ecnad

    maladnem silu

    gna bmalalemnad -r e pnak uk -.nagnutih

    pesnoK .9 isneisif emer egne p - na

    latotk ar aJ.01mer egne p - na

    gnutihgneM nagned

    nadr udesor p gnaylisah

    r ane b

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    BAB II

    NAR AJALEBMEP

    awsisahaMra jaleBanacneR .A

    nadinihawa bidle batisignemnagnedr a jale bnataigek anacner haltauB

    .iaselesr a jale bnataigek haletesnesodada pek itk u bhalatnim

    nataigeK sineJ laggnaT utk aW tapmeT ra jaleBnasalA

    nahaburePf araPnesoD

    ak inak em pesnoK .1 naar adnek namer egne p

    gna pmune pada plamr onna beB.2

    naar adnek sor o p amalesgna pmune p

    namer egne p namer egne payaG.3

    naar adnek mumisk am.gna pmune p

    egne payagisr o por P.4 - naar adnek ada pnamer

    nadgna pmune p ador uluditnehr e bgnay

    ak inak em pesnoK .5 namer egne p r ot car t -

    r el iar t ime s ada plamr onna beB.6

    sor o p r ot car t - r el iar t ime s namer egne pamales

    ayagnak utneneM.7 mumisk amnamer egne p

    ada p r ot car t - r el iar t ime s

    e pisneisif E.8 namer egn

    namer egne pk ar aJ.9

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    21

    .ra jaleBnataigeK .B

    :1ra jaleBnataigeK .1 nameregnePk itsiretk araK gnapmunePnaaradneK

    :1ra jaleBnataigeK nau juT.a

    )1 . lamr onna be bnak utneneM ada p sor o p naar adnek gna pmune p

    ales am sesor p namer egne p .

    )2 . nak utneneM mumisk amnamer egne payag naar adnek .gna pmune p

    )3 . nak utneneM namer egne payagisr o por p latot gna pmune pnaar adnek .

    :1iretaMnaiarU.b

    .)1 nauluhadneP

    ignar uk id,nak iladnek idta padnaar adnek u jalr aganima jnemk utnU

    ,taas paitesada pilak esamasnak itnehr e bidnak ha buataaynnata pecek

    ta padgnaymer metsisgnasa pidulr e pnaar adnek paitesada pak am

    k ak amhalutik utnU.aynitsemanamiaga besa jr ek e b nau pmame

    gnaynai jak utashalasnak a pur emsur ahnaar adnek namer egne p

    maladnatamalesek nadnanamaek ia pacidnigniak i jgnitne p puk uc

    hi beL.ar adnek r e b - nala jidsatnilulalnatada pek tahilemali bhi bel

    r ihk autk awada payar - atok idamatur et,inir ihk a - tok ada pigala paa

    nala j - r ihk ahalutianer ak helO.satnilulalu pmalr atik esidnala j - r ihk a

    aynadaf itomotoir tsudnik ayna bhelonak lanek idhaletagu jini

    sagmer ,k ilor dihmer aynlasim,mer metsise pitnadmacamiaga br e b

    sine jnadgnau b - .nialgnaysine j

    utimer metsisanamiaga bsaha bidnak ak aditini ba badaP

    ,aynsaha bmemgnayir idnesr ethailuk atamadahadusaner ak ,a jr ek e b

    k utnuair etir k utashalaS.iladnegnePmetsiShailuk atamutiay

    k itsir etk ar ak haladamer a jr ek nau pmamek isaulavegnem ,namer egne p

    ayagaynadair adua jnitidamatur et - ada pa jr ek e bgnayr aulayag

    .naar adnek

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    ayaG - naar adnek ta bmahgnema jr ek e bgnayamatur aulayag

    nak k u jnutid)gna pmune pnaar adnek (sor o paudnaar adnek sine jk utnu

    nihawa bid1r a bmaGada p :i

    )2 . ak inak eM P :nameregne

    ayagak iteK namer egne p adar e b hawa bid sata b isehda ar atna

    :haladanamer egne payagaynr ase bak amnala jnadna bM b .I na

    F b = ------------------r

    M b = nemom namer egne p

    F b = (namer egne payag ecr o f g nik ar b )

    =I nata bmalr e pamalesnar atu paisr eni

    na = r alugnanata bmalr e p

    =r .na b)gnidnileg(r atu psuidar

    heloihur agne pidagu jnamer egne payagutigni pmasiD

    ,k imanidor eananahat,na bgnidnilegnanahatitr e pesr otk af a par e be b

    tnanahatnadisimsar tnanahat k a jna ek k utnu(na gnaynaar adn

    .)k iannala jr e b (latotta bmahayagnaik imednagneD r ayagnatluse

    ta bmah :tuk ir e biaga besgnutihidta pad)

    R a

    g/a.Wh a nisW R d

    ah

    R f r B F f b h dl1

    l2 R rr A rbF

    socW WW f L W r

    1r a bmaG

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    F ser F= b f + r socW R + a R + t nisW

    :nagnar eteK

    f r nahatneisif eok = na gnidnileg ador

    naar adnek tar e b=W

    tudus= e pol s nala j

    R a k imanidor eananahat=

    R t isimsnar tnanahat=

    nisW (adnatir e bid + .k iannaar adnek ak i j)malaD naadaek ,lamr on t nanaha ,licek tagnasisimsnar t aggnihes

    d .nak ia baidta pa

    )3 . :nameregnePamaleSsoroPadaplamroNnabeB

    sor o pir adna be br ef snar thalida jr etnamer egne psesor pamaleS

    k na pedsor o pek gnak ale b nemommaamasr e ptur uneM.naar adne id

    ak am,gnak ale bnu puamna pedidk ia bnala jnagnedna bk atnok k itit

    W(na pedsor o pada plamr onna be baynr ase b f lamr onna be bnad)

    W(gnak ale bsor o pada p r nagnedgnutihidta pad) :naamasr e p

    1 WW f = ---- lW{ 2 (h+ ---- a R a nisW })

    gL

    W1W r = ---- lW{ 1 (h ---- a R a nisW })

    gL

    e pmalaD ,sataidnaamasr a .nata bmalr e phalada

    nisWak amk iannala jr e bnaar adnek ak iteK (adnatr e b .),naar adnek tar e btasu pada pa jr ek e bk imanidor eananahat paggnaiD

    na be badak aditanasidnad r abwar d R ( d)

    tur unemayntu jnaleS ayagnaamasr e p - latnosir ohhar amaladayag

    :helor e pid)naar adnek gna jnamemu bmushar aes(

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    WF b f + r F=W f b F+ r b f + r W = --- a aR nisW

    g

    Fsataidnaamasr e pmalaD f b Fnad br tur utr e b - ayaghaladatur ut

    .gnak ale bnadna pedsor o pada pnamer egne p

    Wmaladek tu besr etnaamasr e pnak isutits busnemnagneD f Wnad r

    agr ahta padidnak a - sor o pada plamr onna be bagr ah - amalessor o p

    sesor p :namer egne p

    1:na peDsor oPlamr o Nna beB W f = ---- lW{ 2 F(h+ b f + r })W

    L

    1:gnak aleBsor oPlamr o Nna beB W r = --- lW{ 1 F(h b f + r })W

    L

    mumisk aMnameregnePayaG.)4

    gnaysor o paudnaar adnek ada pmumisk amnamer egne payaG

    idta pad helonak utnetidnala jnagnedna baynk atnok helognuk ud

    namer egne payagak iJ.)(nala jisehdaneisif eok nadlamr onna be b

    gnisamgnak ale bnadna pedsor o pk utnumumisk am - gnisam

    Fnagnednak ataynid f b sk am Fnad br sk am gnisamaynr ase bak am - gnisam

    ihidta pad :tuk ir e biaga bessumur nagnedgnut

    F f b sk am W.= f Fnad br sk am W.= r

    Wak iJ f Wnad r :helor e pidinisumur maladek nak isutits busid

    W l{ 2 (h+ f + r })F sk amf b = ---------------------------

    L

    W l{ 1 (h + f r })F sk amrb = ---------------------------

    L

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    .)5 atoTayaGisroporP nameregnePl :

    nu puamna pedsor o pada platotnamer egne payagisr o por P nak gnidna bmemnagnednak utnetidta padnaar adnek gnak ale bsor o p

    :utiay,mumisk aMnamer egnePayaGaudek

    K f b F sk amf b l2 (h+ f + r )----- = ---------- = ------------------

    K rb F sk amrb l 1 (h f + r )

    K :natataC f b K + br 1=%001=

    eS k utnuayntu jnal uatana pedador hak a panak utnenem

    ulr e pak am,uluhadhi bel)mer egnem(icnuk r etnak agnaygnak ale b

    ir adagr ahiuhatek id ak gna )sor o p(ador audek ada pnata bmalr e p

    .)isatif ar g(gnautasmaladnak ataynidgnay

    a l2 / K +L f b f . r --- = ---------- - -----------

    f g K f b h / L

    a l1 / K +L .rb f r --- = --------------------

    rg K rb + h / L

    :ak i juluhadhi bel)itnehr e b(icnugnemnak ana pedadoR

    aa--- < ----

    g r gf

    :ak i juluhadhi bel)itnehr e b(icnugnemnak agnak ale badoR

    aa--- < ----

    f gr g

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    laoshotnoC :

    iaynu pmem)sor o paud(gna pmune pnaar adnek hau beS e sabl eehw = nadna pedsor o pgnak ale bidmc09adar e bayntar e btasu p,mc002

    Nk 21=naar adnek tar eB.r atadnala jnaak umr e psataidmc06

    0=gnidnilegnanahatneisif eok nagned nala jisehdaneisif eok nad5,

    nala jsataidnala jr e bgnadestu besr etnaar adneK .7,0=na bnagned

    a bitutausesaner ak i patet,utnetr etnata pecek nagnedr atad - a bit

    :halnak utneT.itnehr e bia pmasnamer egne pnak uk alid

    paitesada pmumisk amnamer egne payaG.)a .naar adnek sor o p

    amalesnaar adnek sor o p paitesheloatir edidgnayna beB.) b

    .namer egne psesor p

    .naar adnek sor o p paitesidlatotnamer egne payagisr o por P.)c

    .uluhadhi belicnugnemgnayanamadoR .)d

    naiaseleyneP :

    hatek iD iu sataidnala jr e bgnadesgna pmune pnaar adnek hau beS:

    a bitr atadnala j - .itnehr e bia pmasmer ida bit

    =L mc002 Nk 21=W

    l1 lmc09= 2 L= l 1 002= mc011=09

    f mc06=h r nad5,0= = 7,0iD nak aynat F.)a: f b sk am Fnad br sk am

    b .) W f Wnad r namer egne pamales

    K .)c f b K nad br

    .uluditnehr e bgnayanamadoR .)d

    bawaJ : l{W 2 (h+ f + r })

    F.)a sk amf b = --------- -- ------------------L

    21.7,0 { 5,0+7,0(06+011 )}= --- ---- ----------------- --------- ---

    002

    = 7 446, Nk

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    l{W 1 (h f + r })F br sk am = --------- -- ------------------

    L

    21.7,0 { 09 5,0+7,0(06 )}= - ---- ----------------- --------- --- = ,0 657 Nk

    002

    .) b W f = F sk amf b / = 7,0/446,7 Nk 29,01=

    W r = F br sk am / = 657,0 7,0/ Nk 80,1=

    K f b F sk amf b Nk 446,7.)c ----- = --------- - = ------------ = 11,01

    K r b F sk amr b Nk 657,0

    K f b .11,01= K br K f b 1= K f b

    K f b 1(.11,01= K f b 11,01=) .11,01 K f b

    K f b .11,01+ K f b 11,01=

    11,11 K f b 11,01=

    11,01K f b = -------- = 19,0 K rb 1= =19,0 90,0

    11,11

    uata K f b = 19 % nad K f b = %9

    a l2 / K +L f b f . r .)d --- = ---------------------

    K f g f b h / L

    .7,0 011 / 002 + 19,0 5,0.. = ------------- -- ---- ------- = 2,1

    19,0 06.7,0 / 002

    a l1 / K +L .r b f r --- = ------------- - -------

    K r g r b + h / L

    .7,0 09 / 002 + 90,0 . 5,0= ----------------- ---------- - -- 2,1=

    90,0 + .7,0 06 / 002

    aaaner aK --- = ---- ador audek ak am

    amasr e bitnehr e br gf g

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    .c namuk gnaR :1

    halashaladasor o paudnaar adnek uatagna pmune pnaar adneK .)1 utas

    ta padsur ahaynu jalak am,nak anugidk ayna bgnaynaar adnek sine j

    .k ia ba jr ek e bgnaymer metsisaynadaulr e paggnihesnak iladnek id

    haladamer a jr ek nau pmamek isaulavegnemk utnuair etir k utashalaS.)2

    ua jnitidamatur et,namer egne pk itsir etk ar ak ayagaynadair ad - ayag

    .naar adnek ada pa jr ek e bgnayr aul

    R .)3 ta bmahayagnatluse idnala jr e bgnaygna pmune pnaar adnek ada p

    e polsnagnednala jsata gnutihidta pad sumur nagned :

    F ser F= b f + r socW R + a R + t nisW

    B.)4 W(na pedsor o pada plamr onna be baynr ase f nad) W(gnak ale b r )

    namer egne pamales nagnedgnutihidta pad :sumur

    1:na peDsor oPadaP W f = ---- { lW 2 F(h+ b f + r })W

    L

    1:gnak aleBsor oPadaP W r = --- lW{ 1 F(h b f + r })W

    L

    gnisamgnak ale bnadna pedsor o pada pmumisk amnamer egne payaG.)5 -

    :tuk ir e biaga bessumur nagnedgnutihidta padgnisam

    F f b sk am W.= f nad F rb sk am W.= r

    uatA W l{ 2 (h+ f + r })

    F sk amf b = ---------------------------L

    W l{ 1 (h + f r })F sk amrb = ---------------------------

    L

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    sor o pnu puamna pedsor o pada platotnamer egne payagisr o por P.)6

    audek nak gnidna bmemnagnednak utnetidta padnaar adnek gnak ale b:utiay,mumisk amnamer egne payag

    K f b F f b sk am l2 (h+ f + r )----- = ---------- = ------------------

    K rb F sk amrb l 1 (h f + r )

    K :natataC f b K + br 1=%001=

    k a panak utnenemk utnU.)7 nak agnaygnak ale buatana pedador ha

    ir adagr ahiuhatek idulr e pak am,uluhadhi bel)mer egnem(icnuk r et

    ak gna maladnak ataynidgnay)sor o p(ador audek ada pnata bmalr e p

    .)isatif ar g(gnautas

    a l2 / K +L f b f . r --- = --------------- - ------

    f g K f b h / L

    a l1 / K +L .rb f r --- = --------------- - -----

    rg K rb + h / L

    edadoR :ak i juluhadhi bel)itnehr e b(icnugnemnak ana p

    aa--- < ----

    gf g r

    :ak i juluhadhi bel)itnehr e b(icnugnemnak agnak ale badoR

    aa--- < ----

    f gr g

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    .d saguT 1 :

    S iaynu pmem)sor o paud(gna pmune pnaar adnek hau be e sabl eehw =

    nadgnak ale bsor o pna pedidmc011adar e bayntar e btasu p,mc012 nagned Nk 51=naar adnek tar eB.r atadnala jnaak umr e psataidmc05

    ala jisehdaneisif eok nad2,0=gnidnilegnanahatneisif eok na bnagnedn

    nagnedr atadnala jsataidnala jr e bgnadestu besr etnaar adneK .57,0=

    a bitutausesaner ak i patet,utnetr etnata pecek - namer egne pnak uk alida bit

    :halnak utneT.itnehr e bia pmas

    .naar adnek sor o p paitesada pmumisk amnamer egne payaG.)1

    na beB.)2 amalesnaar adnek sor o p paitesheloatir edidgnay

    .namer egne psesor p

    .naar adnek sor o p paitesidlatotnamer egne payagisr o por P.)3

    .uluhadhi belicnugnemgnayanamadoR .)4

    .e f itamrof seT :1

    a pmune pli bomhau beS iaynu pmem)sor o paud(gn e sabl eehw =

    nadgnak ale bsor o pna pedidmc521adar e bayntar e btasu p,mc042

    nagned Nk 22=naar adnek tar eB.r atadnala jnaak umr e psataidmc55

    na bnagnednala jisehdaneisif eok nad2,0=gnidnilegnanahatneisif eok

    .7,0= nagnedr atadnala jsataidnala jr e bgnadestu besr etnaar adneK

    a bitutausesaner ak i patet,utnetr etnata pecek - namer egne pnak uk alida bit

    .ted/m18,9=isatif ar gnata pecr e pak iJ.itnehr e bia pmas 2 :halnak utnet,

    a pedsor o pada pmumisk amnamer egne payaG.)1 .n

    gnak ale bsor o pada pmumisk amnamer egne payaG.)2

    .namer egne pamalesna pedsor o pada plamr onna beB.)3

    .namer egne pamalesgnak ale bsor o pada plamr onna beB.)4

    .na pedsor o pada platotnamer egne payagisr o por P.)5

    ada platotnamer egne payagisr o por P.)6 .gnak ale bsor o p

    .uluhadhi belicnugnemgnayanamadoR .)7

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    R 2a W ih W 2

    d 2 h 1a W 2 ag/a.

    R 1a d 1 W 1

    F ih h 2 h 1a

    h 3

    l 1 F f b F rb F sb L 1

    L 2 W f W r W s

    .2r a bmaG

    .f icnuK J bawa FseT f itamro :1

    F.)1 f b sk am = K .)5 Nk 02,11 f b 37,0=

    F.)2 r b sk am .)6 Nk 02,4= K r b 72,0=W.)3 f na peDadoR .)7 Nk 61=

    W.)4 r Nk 6=

    :2ra jaleBnataigeK .2 nameregnePk itsiretk araK r ot car T - r el i ar t i mes

    :2ra jaleBnataigeK nau juT.a

    sor o pada plamr onna be bnak utneneM.)1 r ot car t - r el l iar t ime s amales

    .namer egne psesor p

    ada pmumisk amnamer egne payagnak utneneM.)2 r ot car t - r el l iar t ime s

    :2iretaMnaiarU.b

    .)1 nauluhadneP

    ada pnamer egne pk itsir etk ar aK r ot car t - r el iar t ime s hi bel

    k utnU.gna pmune pnaar adnek nagnedgnidna bidsk el pmok r ot car t -

    r el iar t ime s gni pmasidnamer egne pamalesna be bnahadnime p

    e payaggnutnagr etagu jnata bmalr e pnata pecek gnutnagr et namer egn

    ir ad r el iar t .ayn

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    nameregnePak inak eM.)2

    ayagnak k u jnunem2r a bmaG - ada pa jr ek e bgnayamatuayag

    r ot car t r el iar t ime s .namer egne pamales maladnak hadumemk utnUR (k imanidor eananahatak am,aynsisilanagnem a nanahatnad)

    R (gnidnileg r .aynhur agne pnak ia baid)

    namer egne psesor pada puk alr e bgnayna be bnaamasr eP r ot car t

    r el iar t ime s :halada

    a .) k utnU r ot car t :

    W f W=r W+ 1 W+ ih

    C f W f r Wr C+ = g

    a W 1 F+ ih

    g

    a W 1h1 F+ ih h3 W+ 1 L( 1 l 1 d 1 d.r W+) 1 W= f l( 1 d 1 )

    .) b k utnU r el iar t ime s :

    W ih =sW+ W 2

    F ih =sW.sC+ g

    a W 2

    W 2 d2 F+ ih =3h. g a W 2 h2 L.sW+ 2

    .)c isani bmok k utnU r ot car t - r el iar t ime s :

    W f W=sW+r W+ 1 W+ 2

    C .f W f =sW.sC+r W.r C+ g

    a W( 1 W+ 2 )

    g

    aW .1 h1 +

    g

    a W .2 h2 L.r W+ 1 L(sW+ 1- d 1 L+ 2 W=) l l 1 W+ 2 L( 1 - d 1 d+ 2)

    naamasr e pmalad :sataidnaamasr e p

    W ih ada plak itr evna be b= t nio phct ih

    F ih ada platnosir ohna be b= t nio phct ih

    naar adnek nata bmalr e p=a

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    Cf C, r Cnad, s tur utr e b - namer egne payagoisar haladatur ut

    na pedsor o pada plamr onna be b padahr et r ot car t sor o p,

    gnak ale b r ot car t sor o pnad, .r el iar t ime s

    lamroNnabeB.)3

    naamasr e pir aD - gnisamk utnulamr onna be bak am,sataidnaamasr e p -

    :tuk ir e biaga besnak utnetidta padsor o pgnisam

    na pedsor o pk utnU.)a r ot car t :

    W1 L{ 1 l 1 h)g/a(+ 1 C(+ r h)g/a 3}

    W f = ----------------- ---------------------------- +L1 C(+ r C f h) 3

    W2 L{ 2 d 2 C(+ s h)g/a 3 h)g/a(+ 2 d(} 1 C+ r h3)----------------------------------------------------------

    L( 2 C+ sh3 L{) 1 C(+ r C f h) 3}

    gnak ale bsor o pk utnU.) b r ot car t :

    W1 l{ 1 h)g/a( 1 g/a(+ C f h) 3}W r = ------------------------------------------- +

    L1 (+ C r C f h) 3

    W2 L({ 2 d 2 C(+) s h)g/a 3 h)g/a(+ 2 L({} 1 d 1 ) C f h3}- --------------------------------------------------------------------- -

    L( 2 C+ sh3 L{) 1 C(+ r C f ) h3}

    sor o pk utnU.)c r el iar t ime s :

    W2 d{ 2 h(+ 3 h 2 }g/a)W s = ------------------------------

    Cs h3 L+ 2

    naamasr e pir aD - nak utnenemk utnuawha bk a pmatsataidnaamasr e p

    be b ada pnamer egne payagneisif eok nadak gnaataynr etlamr onna

    sor o p r el iar t ime s .nak utnetiduluhadhi belr etsur ahsC

    sor o pada pnamer egne payagnadnata bmalr e pak gnaak iJ

    r el iar t ime s sor o pada plamr onna be bak am,iuhatek id l iar t ime s r e ta pad

    gnutihid nadlatnozir ohna be bagu jutige b,sataidsWsumur nagned

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    ada plak itr ev t nio phct ih naamasr e pnagnedgnutihidta pad - naamasr e p

    nagneD.) br omon)2 ba b bus36namalahada pnak silutidhaletgnay

    agr ah - Wagr ah ih Fnad ih aynr ase bgnutihidagu jta padtu besr et na be b gnak ale bnadna pedsor o pada plamr on r ot car t naamasr e piulalem -

    .)ar omon)2 ba b bus36namalahada pnaamasr e p

    mumit pognaynamer egne pisidnok helor e pidr agaayntu jnaleS

    agr ahia pacnemta padsor o paumesidnamer egne payaganamid

    mumisk am itak ednemsur ahgnautasmaladnata bmalr e pak gnaak am,

    nala jisehdaneisif eok nagned)amas( C, f C= r C= s a= =g .sor o pada plamr onna beB - ta padnamer egne pamalestu besr etsor o p

    :ida jnemnak anahr edesid

    W 1 L( 1 l 1 + h 1) W 2 L( 2 d 2 + h 2 d() 1 + h 3)W f = - ---------------------- + ---------------------------------------

    L 1 L 1 L( 2 + h. 3 )`

    W 1 l( 1 - h. 1 ) W 2 L( 2 d 2 h.+ 2 L() 1 - d 1 - h. 3)W r = -------------------- + ---------------------------------------------

    L 1 L 1 L( 2 h.+ 3)

    W 2 d{ 2 .+ h( 3 h 2 })W s = -----------------------------h. 3 L+ 2

    :mumisk amnameregnepayaG.)4

    gnaynamer egne pisidnok ada plamr onna be bnaamasr e pir aD

    agu jnak utnetidta padak amr ihk ar ettu besr etmumit po ayagir adagr ah

    Futiay,mumisk amnamer egne p sk am b W.= :aggnihes

    F f b sk am W.= f

    F rb sk am W.= r

    F sb sk am W.= s

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    laoshotnoC :

    naar adnek hau beS r ot car t - r el iar t ime s tar e b:iaynu pmem r ot car t , Nk 76

    tar e b r el iar t ime s , Nk 762 r ot car t e sabl eehw sor o p,mc183=r el ir at ime s gnak ale bidmc117adar e b r ot car t , t nio phct ih adar e b

    sor o pna pedidmc16 gnak ale b r ot car t .nala jsataidmc261nad

    isatif ar gtasuP r ot car t na pedsor o pgnak ale bidmc302adar e b r ot car t

    isatif ar gtasu pgnades,nala jsataidmc79nad r el iar t ime s adar e b

    sor o pna pedidmc033 r el iar t ime s .nala jnaak umr e psataidmc871nad

    i patet,r atadgnaynala jsataidnala jr e bgnadestu besr etnaar adneK

    a bitutausesaner ak - nak utnetidak iJ.itnehr e bia pmasmer ida bit

    :halnak utneT.8,0=nala jnagnedna bisehdaneisif eok

    sor o pada plamr onna beB.)a - ani bmok naar adnek sor o p tu besr etis

    .namer egne psesor pamales

    naar adnek sor o p paitesada pmumisk amnamer egne payaG.) b

    :naiaseleyneP

    iuhatek iD isani bmok naar adnek hau beS: r ot car t - r el ir t ime s

    W 1 l Nk 76= 1 mc302=

    W 2 h Nk 762= 1 mc79=

    L 1 hmc183= 2 mc871=

    L2 d1 Lmc117= 2 d2 mc033=

    d1 hmc16= 3 mc261=

    8,0=

    nak aynatiD W.)a f W, r Wnad s

    F.) b k amf b F, k amr b F, sk ams b

    bawaJ L: 2 d+117= 1 mc277=16+117=

    d 2 L= 2 277=033 =033 mc244

    W. 1 L( 1 l 1 + h1 W) 2 L( 2 d 2 + h2 d() 1 + h3)W.)a f = - ---------------------- + ---------------------------------------

    L1 L1 L( 2 + h. 3 )

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    183(76 79.8,0+302 ) 277(762 16()871.8,0+244 )261.8,0+W f = -------------------------- + --------------------------------------------

    )261.8,0+277(183183

    = 59,06+59,44 09,501= Nk

    W 1 l( 1 h. 1 W) 2 L( 2 d 2 h.+ 2 L() 1 d1 h. 3)W r = -------------- ------ + ---------------------------------------------

    L 1 L1 L( 2 h.+ 3)

    76 302( 79.8,0 277(762) 183()871.8,0+244 16 )261.8,0W r = - -------------------- + -----------------------------------------------------

    183 )261.8,0+277(183

    = 19,96+50,22 Nk 69,19=

    W2 d{ 2 (.+ h 3 h 2 })W s = -----------------------------

    h. 3 L+ 2

    762 { 244 + 8,0 ( 261 871 })W s = ------------------------------- = Nk 01,721

    8,0 . 261 + 277

    F.) b f b sk am W= f sk am =8,0.09,501=. Nk 27,48

    F r b sk am W= r sk am =8,0.69,19=. Nk 75,37

    F s b sk am W= s sk am . = 8,0.01,721 Nk 86,101=

    .c namuk gnaR :2

    ada pnamer egne pk itsir etk ar aK .)1 r ot car t - r el iar t ime s sk el pmok hi bel

    ayaganer ak sor o paudnaar adnek nagnedgnidna bid - amatuayag

    a jr ek e bgnay ada p r ot car t r el iar t ime s hi belnamer egne pamales

    ak am,aynsisilanagnemmaladnak hadumemk utnunuman,k ayna b

    nak ia baid)r R (gnidnilegnanahatnad)aR (k imanidor eananahat

    .aynnialnanahatgnidna bidaynitr alicek tagnasaner ak aynhur agne p

    na beB.)2 sor o pada pnahatidgnaylamr on - sor o p r ot car t r el iar t ime s

    :sumur nagnedgnutihidta padnamer egne pamales

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    W 1 L( 1 l 1 + h 1 W 2 L( 2 d 2 + h 2 d() 1 + h 3)W

    f = - -------------------- + ----------------- ---------------------

    L 1 L 1 L( 2 + h. 3 )`

    W 1 l( 1 - h. 1 W) 2 L( 2 d 2 h.+ 2 L() 1 - d 1 - h. 3)W r = ------------------- + ------------- --------------------------------

    L 1 L 1 L( 2 h.+ 3)

    W 2 d{ 2 h(.+ 3 h 2 })W s = -----------------------------

    h. 3 L+ 2

    .)4 :sumur nagnedgnutihidaynsor o p paitesmumisk amnamer egne payaG

    F f b sk am W.= f

    F rb sk am W.= r

    F sb sk am W.= s

    .d 2saguT :

    r adnek hau beS naa r ot car t - r el iar t ime s tar e b:iaynu pmem r ot car t 06

    tar e b, Nk r el iar t ime s , Nk 042 r ot car t e sabl eehw sor o p,mc073=

    r el ir at ime s gnak ale bidmc007adar e b r ot car t , t nio phct ih 55adar e b

    gnak ale bsor o pna pedidmc r ot car t .nala jsataidmc021nad tasuP

    isatif ar g r ot car t na pedsor o pgnak ale bidmc091adar e b r ot car t nad

    isatif ar gtasu pgnades,nala jsataidmc001 r el iar t ime s mc003adar e b

    sor o pna pedid r el iar t ime s .nala jnaak umr e psataidmc561nad

    sataidnala jr e bgnadestu besr etnaar adneK nagnedr atadgnaynala j

    a bitutausesaner ak i patet,ma j/mk 09nata pecek - ia pmasmer ida bit

    .8,0=nala jnagnedna bisehdaneisif eok nak utnetidak iJ.itnehr e b:halnak utneT

    sor o pada plamr onna beB.)1 - tu besr etisani bmok naar adnek sor o p

    ales .namer egne psesor pam

    naar adnek sor o p paitesada pmumisk amnamer egne payaG.)2

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    .e f itamrof seT :2

    naar adnek hau beS r ot car t - r el iar t ime s tar e b:iaynu pmem r ot car t , Nk 05

    tar e b r el iar t ime s , Nk 042 r ot car t e sabl eehw ,mc053= sor o p r el ir at ime s

    gnak ale bsor o pgnak ale bidmc096adar e b r ot car t , t nio phct ih

    gnak ale bsor o pna pedidmc25adar e b r ot car t .nala jsataidmc041nad

    isatif ar gtasuP r ot car t na pedsor o pgnak ale bidmc081adar e b r ot car t

    a jsataidmc59nad isatif ar gtasu pgnades,nal r el iar t ime s 013adar e b

    sor o pna pedidmc r el iar t ime s .nala jnaak umr e psataidmc061nad

    aner ak i patet,r atadgnaynala jsataidnala jr e bgnadestu besr etnaar adneK

    a bitutauses - isif eok nak utnetidak iJ.itnehr e bia pmasmer ida bit isehdane:halnak utneT.6,0=nala jnagnedna b

    sor o pada plamr onna beB.)1 - tu besr etisani bmok naar adnek sor o p

    .namer egne psesor pamales

    .naar adnek sor o p paitesada pmumisk amnamer egne payaG.)2

    .f awaJicnuK f itamroFseTb :2 .

    W.)1 f = Nk 72,87

    W r = Nk 03,38 W s = 30,221 Nk

    F.)2 f b sk am = Nk 69,64

    F r b sk am = Nk 89,94

    F s b sk am = Nk 22,37

    :3ra jaleBnataigeK .3 isneisif E k araJnad nameregneP

    :3ra jaleBnataigeK nau juT.a)1 . eM pesnok imaham namer egne pisneisif e

    )2 . egne pk ar a jnak utneneM namer .laminimnamer egne pk ar a j/

    )3 . namer egne pk ar a jnak utneneM .naha bmat

    )4 . namer egne pk ar a jnak utneneM .latot

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    :3iretaMnaiarU.b

    .)1 nameregnePisneisif E

    eayngnitne ptagnastagnigneM iga bmer metsisisgnuf nadk ef ak imanidgnatnethua jhi beli jak idulr e pak am,naar adnek utaus

    lahiuhategnemnagnedaner aK .namer egne p - hisamnik gnumgnaylah

    aynak imanidalagesnagnednamer egne pmetsisnagnedtiak r et

    naar adnek naanacner e pmaladnak par ahid gnaylisahhelor e pidta pad

    gnaynadnali batsek ,nanamaynek ihunememta padaynitr a,lamisk am

    .tu besr etnaar adnek ar adnegne pnatamalesek nima jnemta padamatu

    utausnamer egne pk itsir etk ar ak gnatnetiuhategnemhi belk utnU

    naar adnek namer egne pisneisif ehalasamir a jale pidagu julr e pak am,

    r otk af haladainilahmaladk usamr et,icnir ar acesnaar adnek - r otk af

    .aynihur agne pmemgnay

    utausiaga besnak isinif edidta padnamer egne pisneisif E

    ak gnaar atnanagnidna br e p ta padgnaymumisk amnata bmalr e p

    .nala jisehdaneisif eok nagneditnehr e bnaar adnek mule besia pacid

    :tuk r e biaga bessilutidta padnamer egne pisneisif esitametamar aceS

    g/a b = ---- ---

    nata bmalr e pak gna=a

    imu bisatif ar gnata pecek =g

    nala jisehdaneisif eok =

    aak i jawha bk a pmatsataidnasumur ir aD --- < ak am b 1