ludoM edoK

.KGM OTO 2 62 - 10

YNU kinkeT satlukaF fitomotO kinkeT nakididneP nasuruJ

IRTEMOEG GNIREETS NAARADNEK

naped

a b θ

B ro r i

θ O

c d T X

: nusuyneP

.T.M ,.dP.M ,ibutraM

fitomotO kinkeT nakididneP nasuruJ KINKET SATLUKAF

ATRAKAYGOY IREGEN SATISREVINU 4002

2

RATNAGNEP ATAK

luduj nagned ludoM irtemoeG gnireetS naaradneK iagabes nakanugid ini

uk nataigek malad naudnap :utiay ,isnetepmok utas halas kutnebmem kutnu hail

pesnok nakanuggnem tapad nad imahameM “ irtemoeg gnireets malad

.“ tapme ador naaradnek koleb suidar nad koleb tudus gnutihgnem ini ludoM

M hailuk atresep aumes kutnu nakanugid tapad aaradneK kareG akinake n id

I retsemes V satisrevinU kinkeT satlukaF fitomotO kinkeT idutS margorP adap

.atrakaygoY iregeN

nakijasid ini ludom adaP pesnok - rasad pesnok gnatnet irtemoeg gnireets gnay

itupilem : tihrep nu ag n p tapme ador naaradnek koleb suidar nad koleb tudus ada

aynmumu emsinakem atres gnireets aparebeb nad namrekcA epit

ludoM .fitomoto irtsudni id nakanugid kaynab ini asawed gnay aynnahalasamrep

sata iridret ini aud gnatnet sahabmem 1 rajaleb nataigeK .rajaleb nataigek : tuduS

naaradneK koleB suidaR nad koleB nad ,tapmE adoR K 2 rajaleb nataige

gnatnet sahabmem : emsinakeM gnireetS .namrekcA epit

nakparahid awsisaham hadum nagned ini ludom irajalepmem tapad kutnU

akitametaM gnatnet amaturet ,ayngnukudnep rasad nauhategnep iaynupmem halet

P metsiS aguj nad irajalepid halet aynitsem gnay naaradneK iladnegne adap

aynmulebes retsemes .

.

,atrakaygoY iluJ 4002

nusuyneP

.T.M ,.dP.M ,ibutraM

3

LUDOM ISI RATFAD

namalaH

LUPMAS NAMALAH ....................................... ..................................... ...... 1

RATNAGNEP ATAK ............................................................................ ........ 2

ISI RATFAD ......................................................................................... ... ..... . 3

YRASSOLG / NAHALITSIREP ............................................................. ..... . 5

NAULUHADNEP . I ................................................................................ ....... . 6

.................... luduJ ispirkseD .A .......................................................... ........... . 6

........................................................................................ taraysarP .B ............ 6

............................. ludoM naanuggneP kujnuteP .C ............................ ............ 7

......................................................... awsisaham igab kujnuteP .1 ............. 7

..................................................... ............ nesod igab kujnuteP .2 .... ........ 7

................................................................................. rihkA naujuT .D ........... 8

................................................................................... isnetepmoK .E ............ 8

.F ........................................................................... naupmameK keC ............. 9

NARAJALEBMEP .II ............................................................................ ........ . 11

..... awsisahaM rajaleB anacneR .A .................................................. ............. . 11

........................................................................... rajaleB nataigeK .B ............. 11

: 1 rajaleB nataigeK .1 naaradneK koleB suidaR nad tuduS ...... . .............. 11

................................................... 1 rajaleb nataigek naujuT .a ............. 11

..................................................................... 1 iretam naiarU .b ............. 12

.................. 1 namukgnaR .c .................................................... ............. . 51

................................................................................ 1 saguT .d ............. . 61

.......................................................... 1 fitamrof seT .e ............. ............ . 61

.f ................................................. ... 1 fitamrof set bawaj icnuK .......... . 61

4

namalaH

: 2 rajaleB nataigeK .2 emsinakeM gnireetS namrekcA epiT ........ ........... . 71

rajaleb nataigek naujuT .a 2 .. ............ .................................................. 71

iretam naiarU .b 2 ................................ ........... ...................................... 71

namukgnaR .c 2 ................... ........................... ........... .......................... 82

saguT .d 2 .................................................................. ........... ................ 92

fitamrof seT .e 2 ............................................................. ...... .......... ...... 92

fitamrof set bawaj icnuK .f 2 ............................................... ... ........... 29

ISAULAVE .III ................................................................................. ..... ... .... 30

........................................................................... naaynatreP .A ............. ..... 30

........................................................................ nabawaJ icnuK .B ............ ... 03

.C .................................................................. nasululeK airetirK ............ ..... 13

PUTUNEP .VI ................................................................................... ......... .... 23

AKATSUP RATFAD ..... ...... ... ...................................................................... 33

5

/ NAHALITSIREP YRASSOLG

maeB ador nagned irik ador nakgnubuhgnem gnay upmut sorop/gnatab halada :

.libom haubes nanak

xob raeG gnay katok haubes halada : kareg surenep nad haburep emsinakem isireb

reseg kareg idajnem idumek ador ratop mra namtip .

gnildnaH .naaradnek nailadnegnep metsis halada :

mra elkcunK nagnorod/nakirat surenep nagnel/gnatab haubes halada : dor eit

bes naped ador ratup kareg idajnem .libom hau

mra namtiP kareg idajnem idumek ador ratup kareg haburep nagnel halada :

.libom naped ador koleb

gnireetS .naaradnek naidumegnep metsis halada :

koleb tuduS adap libom naped ador ubmus aratna kutnebid gnay tudus halada :

us nagned koleb isisop .surul isisop adap tubesret ador ubm

dor eiT ratup kareg surenep gnatab halada : mra namtip /gnorodnem kiranem

.koleb idajnem aggnihes libom naped ador

kcarT nagned nanak halebes libom ador naped ek ubmus aratna karaj halada :

libom ador naped ek ubmus .irik halebes

esab leehW gnakaleb ador ubmus nagned naped ador ubmus aratna karaj halada :

.surul isisop adap libom haubes

6

BAB I

NAULUHADNEP

ispirkseD .A

622 OTO.KGM ludoM – rasad pesnok aparebeb sahabmem ini 10

gnireetS ( irtemoeg dnah gnil gnay ,)libom( tapme ador naaradnek adap )

hailukatam adap iretam irad naayagnep/gnajnunep nakapurem - hailukatam

iladnegneP metsiS hailukatam utiay amaturet ,aynnial fitomoto gnadib

upilem ini ludom malad irajalepid gnay iretam napukac nupadA .naaradneK : it

emsinakeM .)2( nad ,naaradnek koleb suidar nad koleb tuduS )1( gnireets epit

.namrekcA

sahabmem 1 rajaleb nataigeK : rajaleb nataigek aud sata iridret ini ludoM

2 rajaleb nataigeK ,naaradnek koleb suidar nad koleb tuduS :gnatnet

ahabmem emsinakeM : gnatnet s gnireets nataigek paites adaP .namrekcA epit

atreseb aynnasahabmep nad laos hotnoc nagned ipakgnelid ulales rajaleb

nahital/sagut - kutnu aynulrepes isaulave atres fitamrof set nad nahital

y isnetepmok iapacnem malad awsisaham utnabmem .nakparahid gna

awsisaham nahurulesek araces ini ludom irajalepmem iaseles haleteS

pesnok nakanuggnem tapad nad imahameM “ nakparahid irtemoeg gnireets

.“ tapme ador naaradnek koleb suidar nad koleb tudus gnutihgnem malad

taraysarP .B

nakididneP nasuruJ awsisaham igab lawa ludom nakapurem ini ludoM

iretam isireb gnay ,3D nupuam 1S gnajneJ fitomotO kinkeT - iretam

hailukatam irad naayagnep/gnajnunep - fitomoto gnadib id nailhaek hailukatam

halada amaturet ,irajalepid aynsurahes gnay nagneD .iladnegneP metsiS

iretam naikimed - hailukatam malad iretam - tiakret gnay tubesret hailukatam

gnitnep tagnas gnay gnukudnep iretam nakapurem naka ini ludom isi nagned

,ini ludom malad nakparahid gnay isnetepmok iapacnem akgnar malad

nsutats nupiksem .ayntaraysarp iagabes imser araces kadit ay

7

ludoM naanuggneP kujnuteP .C

awsisahaM igab kujnuteP .1

malad akam ,lamiskam gnay rajaleb lisah helorepid ragA

nad ,nakitahrepid ulrep gnay rudesorp aparebeb ada ini ludom nakanuggnem

askalid : nial aratna nakan

pesnok naiaru amaskes nagned imahaf nad halacaB .a - gnay sitiroet pesnok

pesnok naparenep alup imahaf naidumek ,ini ludom adap nakijasid -

hotnoc malad tubesret pesnok - .aynnaiaseleynep arac atreseb laos hotnoc

tam ada hisam askapret aliB asib muleb nad salej gnaruk gnay ire

nesod adapek nakaynanem tapad awsisaham arap kiab nagned imahafid

.nahailukrep nataigek upmagnem gnay

ini lah ,iridnam araces )nahital laos( sagut paites nakajrek aboC .b

mep raseb aparebes iuhategnem kutnu nakduskamid halet gnay namaha

iretam padahret awsisaham paites ikilimid - adap sahabid gnay iretam

.rajaleb nataigek paites

adap iretam iasaugnem muleb awsisaham aynnaataynek malad alibapA .c

igal nakajregnem nad acabmem igal ignalu aboc ,nakparahid gnay level

nahital -l gnay nesod adapek halaynatreb ulrep ualak nad aynnahita

gnay iretam ualaK .natukgnasreb gnay nahailukrep nataigek upmagnem

naknikay akam )taraysarp( lawa namahamep nakulremem natukgnasreb

raneb duskamid gnay taraysarp awhab - .ihunepid hadus raneb

2 nesoD igab kujnuteP .

: kutnu narep nad sagut iaynupmem nesod ,nahailukrep paites malaD

a. .rajaleb sesorp nakanacnerem malad awsisaham utnabmeM

b. sagut iulalem awsisaham gnibmibmeM - nahital uata sagut - gnay nahital

.rajaleb bahat malad naksalejid

c. nabmeM bawajnem nad urab pesnok imahamem malad awsisaham ut

.nakulrepid alibapa awsisaham naaynatrep

8

d. gnay nial rajaleb rebmus seskagnem kutnu awsisaham utnabmeM

.nakulrepid

e. .nakulrepid akij kopmolek rajaleb nataigek risinagrogneM

f. p nesod/ilha gnaroes nakanacnereM .nakulrepid akij gnipmadne

g. gnay awsisaham isnetepmok naiapacnep padahret isaulave nakadagneM

.nakutnetid halet

rihkA naujuT .D

ini ludom malad rajaleb nataigek iretam hurules irajalepmem haleteS

: nakparahid awsisaham

1 . k imahameM naruta nad pesno irtemoeg gnireets malad

halasam nahacemep gnildnah naaradnek .

raga tapme ador naaradnek koleb tudus aynraseb nakutnenem tapaD .2

kefe helorepid gnireets .anrupmes gnay

aynraseb nakutnenem tapaD .3 raga tapme ador naaradnek koleb suidar

kefe helorepid gnireets .anrupmes gnay

.4 emsinakem imahameM gnireets .namrekcA epit

.5 adap malad naigab ador koleb tudus aynraseb nakutnenem tapaD

emsinakem nakanuggnem gnay tapme ador naaradnek gnireets epit

kcA .namre

.6 naaradnek adap raul naigab ador koleb tudus aynraseb nakutnenem tapaD

emsinakem nakanuggnem gnay tapme ador gnireets .namrekcA epit

isnetepmoK .E

622 OTO.KGM ludoM – kutnebmem akgnar malad nususid ini 10

nad imahameM “ isnetepmok pesnok nakanuggnem tapad irtemoeg gnireets

.“ tapme ador naaradnek koleb suidar nad koleb tudus gnutihgnem malad

bus iapacid tapad surah uluhad hibelret ,tubesret isnetepmok iapacnem kutnU -

pukgnil iulalem aynajrek kujnu airetirk atreseb isnetepmok bus nagned rajaleb

: tukireb iagabes narajalebmep kokop iretam

9

naupmameK keC .F

622 OTO.KGM ludoM irajalepmem mulebeS – adnat nagned halisi ,ini 10

( kec ikilimid halet gnay isnetepmok nakkujnunem gnay naaynatrep ) helo

: nakbawajgnuggnatrepid tapad nad rujuj nagned awsisaham paites

buSisnetepmoK

airetirK ajreK kujnU

pukgniLrajaleB

narajalebmeP kokoP iretaM

pakiS nauhategneP nalipmarteK

imahameM

tapad nad anuggnem -

pesnok nak gnireets irtemoeg

malad gnutihgnem

udus koleb t suidar nad

koleb naaradnek.tapme ador

pesnoK .1 eets -

irtemoeg gnir imahafid

raneb nagned.iroet iauses

tudus aynraseB .2

gnutihid koleb raneb nagned

.iroet iauses aynraseB .3

koleb suidar gnutihid

raneb nagned .iroet iauses

emsinakeM .4

gnireets epit namrekcA

imahafid raneb nagned

.iroet iauses tudus raseB .5

malad koleb adap raul nad

emsinakemgnireets epyt

namrekcA gnutihid

raneb nagnediroet iauses .

pesnoK .1

gnireets irtemoeg

naaradnektapme ador

leb tuduS .2 ko

naaradnek.tapme ador

koleb suidaR .3

naaradnek.tapme ador

emsinakeM .4

gnireets epit.namrekcA

nagnutihreP .5

koleb tudus raul nad malad

adap emsinakem

gnireets epit.namrekcA

itilet ,sitirK

tamrec nad malad

silunem gnabmal

nad alem -rep nakuk -.nagnutih

pesnoK .1

gnireets irtemoeg

naaradnektapme ador

koleb tuduS .2

naaradnek.tapme ador

koleb suidaR .3

naaradnek.tapme ador

emsinakeM .4

gnireets epit.namrekcA

nagnutihreP .5

koleb tudus nad malad

adap raul emsinakem

gnireets epit.namrekcA

gnutihgneM

nagned nad rudesorp

gnay lisahraneb

01

buS

isnetepmoK naaynatreP

nabawaJ “aY“ nabawaJ aliB

nakajreK aY kadiT

imahameM

tapad nad anuggnem -

pesnok nak gnireets irtemoeg

maladihgnem - gnut

koleb tudus suidar nad

koleb naaradnektapme ador

imahamem ayaS .1 pesnok gnireets

irtemoeg . tapme ador naaradnek adap

1 fitamroF seT

.2 gnutihgnem tapad ayaS aynraseb koleb tudus . tapme ador naaradnek

1 fitamroF seT

.3 em tapad ayaS gnutihgn aynraseb

koleb suidar . tapme ador naaradnek

1 fitamroF seT

.4 imahamem ayaS emsinakeM gnireets namrekcA epyt

2 fitamroF seT

.5 gnutihgnem tapad ayaS aynraseb

emsinakem adap koleb tudus gnireets namrekcA epyt .

2 fitamroF seT

.6 imahamem ayaS koleb tudus nagnubuh

emsinakem adap raul nad malad gnireets namrekcA

2 fitamroF seT

bawajnem awsisaham alibapA kadiT ini ludom irajalep akam

wajid gnay iretam iauses ba kadiT .tubesret

11

BAB II

NARAJALEBMEP

awsisahaM rajaleB anacneR .A

nad ini hawab id lebat isignem nagned rajaleb nataigek anacner haltauB

.iaseles rajaleb nataigek haletes nesod adapek itkub halatnim

nataigeK sineJ gnaT lag utkaW tapmeTrajaleB

nasalAnahabureP

faraPnesoD

koleb tudus naitregneP .1 koleb suidar nad

.tapme ador naaradnek

malad naigab koleb tuduS .2.tapme ador naaradnek .

raul naigab koleb tuduS .3.tapme ador naaradnek

oleb suidaR .4 naaradnek k.tapme ador

emsinakem pesnoK .5gnireets .namrekcA epit

.6 malad naigab koleb tuduS nagned naaradnek

gnireets .namrekcA epit

.7 raul naigab koleb tuduS nagned naaradnek

gnireets .namrekcA epit

.rajaleB nataigeK .B

rajaleB nataigeK .1 : 1 naaradneK koleB suidaR nad koleB tuduS

: 1 rajaleB nataigeK naujuT .a

koleb suidar nad koleb tudus naitregnep naksalejneM .)1

.naaradnek

me ador naaradnek malad naigab koleb tudus nakutneneM .)2 .tap

.)3 nakutneneM .tapme ador naaradnek raul naigab koleb tudus

.naaradnek koleb suidar nakutneneM .)4

21

napeD adoR koleB suidaR nad koleB tuduS : 1 iretaM naiarU .b

K naaradne tapmE adoR .

halada )libom( tapme ador naaradnek utaus isakifiseps utas halaS

iaynupmem naped ador koleb tuduS .naped ador koleb tudus

nugnabmem akgnar malad gnitnep pukuc gnay nanarep

aaradnek idumek metsis naanrupmesek ini laH . natukgnasreb gnay n

sorop helo ihuragnep id idumek ador nakareg awhab tagnignem

ador ) katelret ( takelem aynadap gnay naped ador - ragA .naped ador

metsis gnireets isis ador sorop akam ,anrupmes hibel tapad ) idumek (

alad koleb tudus iaynupmem surah kolebmem uti libom alibapa m

.raul naigab ador koleb tudus adapirad raseb hibel gnay

naped

θ

ro ri

O 1 rabmaG

gnasapret gnakaleb ador nagnasap awhab kapmat 1 rabmaG iraD

kitit padahret amas gnay koleb suidar kutnebmem ulales aggnihes patet

am naped ador kutnu ipatet ,O tasup gnis - suidar kutnebmem gnisam

laH .O kitit utiay tasup utas adap umetreb tapad raga adebreb gnay ratup

kutnebid gnay koleb tudus ,kolebreb libom utkaw adap awhab itrareb ini

.adebreb uti naped ador audek helo

nalaj isatnilem surah raul halebes adoR suidar nagned suidar nagned

( licek hibel koleb tudus nad raseb hibel gnay naped ador gnades )

licek hibel suidar nagned nalaj nasatnil kutnebmem malad halebes

( raseb hibel gnay koleb tudus nagned θ idaJ .) θ .

31

)1 utihreP . napeD adoR koleB tuduS nagn :

: ini tukireb 2 rabmaG nakitahreP

naped

a b θ

r B o ri 2 rabmaG

θ O d c

X T

: awhab kapmat 2 rabmag iraD

dc = ba ( B = ca esab leehw )

Oc( = ba – )Od T + X = Oc

B ca gt = ---- = -------------

T + X Oc

T + X 1 1 X T ---- = ------- -- - -- = - -- + ---- ... )1( ..……..

gt B gt B B

nakitahrep ayntujnaleS : Odb

db

gt θ = ------ X = Od nad B= db anamid Od

)2(............... idaj

B X 1 gt = ---- uata ---- = ----

X gt B

41

esret )2( nad )1( sumuR gnisam tub – kutnu sumur halada gnisam

.malad nad raul isis naped ador koleb tudus nakutnenem

)1( naamasrep ek nakkusamid )2( naamasrep akij gnarakeS

: helorepid naka akam

= T ini lah malaD kcart

= B esab leehw

.)2 gnutihgneM J ira – iraj B kole M mumiska :

nakmutnacid asaib aguj gnay idumek mitsis malad nial narukU

iraj :halada naaradnek isakifiseps iagabes – .mumiskam koleb iraj

nek halada )sitkarp( kiab gnay naaradneK iaynupmem gnay naarad

iraj – iraj nupadA .licek gnay mumiskam koleb iraj – koleb iraj

tahil( : tukireb iagabes arac nagned gnutihid tapad mumiskam

iraJ .)2 rabmag – sata id naadaek adap mumiskam gnay koleb iraj

r gnajnap helo nakujnutid o iraj ( - iraj ) raul isis ador koleb B

adaP nis :Oca = -- -- -- ro

B iraj idaJ - : aynmumiskam koleb iraj ro = --- -- --

nis

: laos hotnoC

iaynnupmem iuhatekid libom haubeS kcart nad mc 571 =

esab leehw aynmalad naigab naped ador uti libom akij .mc 023=

02 tudus nagned ratupid naped ador koleb tudus halgnutih akam ,

guj nad raul naigab kefe helorepid raga aynmumiskam koleb suidar a

gnireets ! raneb gnay

1 T 1 T 1 1 ----- = ----- + ---- uata --- = ---- – ----

gt gt B gt gt gT θ =

51

naiaseleyneP 3 rabmaG tahiL :

naped a b

02 = θ 0

mc 023 ro ri rabmaG 3

θ O d c

mc 571 X

023 023 023 B

gt = ----- = ------ = X ------- = - ------- 91,978 = gt X X 02 gt 0

B 023 gt = ------ = -------- -- -------- 5303,0 =

571 + 91,978 T+X

61 = ’35

= raul naigab naped ador koleb tudus helorepid idaJ 61 ’35

iraJ - r = mumiskam koleb iraj o

023 023 B

ro = ------- = ------- = -------- nis 61 nis 4092,0 35

idaJ r o mc 48,1011 =

.c namukgnaR : 1

.)1 d gnay tudus : halada koleb tuduS naped ador ubmus helo kutnebi

.kolebmem isisop nagned surul isisop adap tapme ador naaradnek

2 .) rukuid naped ador koleb narakgnil irad suidar :halada koleb suidaR

.gnakaleb ador ubmus nagnajnaprep padahret aynnagnotoprep irad

61

b ador koleb tuduS .)3 malad naiga ( tapad tapme ador naaradnek )

: naamasrep nagned nakutnetid B

gt = ---- X

.)4 raul naigab ador koleb tuduS ( naamasrep nagned nakutnetid tapad )

5 .) koleb suidaR ( ro nagned gnutihid tapad tapme ador naaradnek )

sumur nakanuggnem :

B ro = -- ---- --

s ni

.d 1 saguT :

iaynnupmem iuhatekid libom haubeS kcart naped ador akiJ .m 4,1 =

aynnanak naigab koleb tudus aggnihes nanak ek nakkolebid uti libom

03 rasebes ik gnay naigab nakgnades 22 rasebes tudus kutnebmem ir 0 .

halgnutiH esab leehw raga uti libom mumiskam koleb suidar nad

kefe helorepid gnireets ! raneb gnay

.e fitamrof seT : 1

iaynupmem iuhatekid libom haubeS kcart nad mc 081 esab leehw

om naped ador akiJ .mc 043 22 tudus nagned irik ek nakkolebid uti lib ,

: halgnutih akam

.nanak naigab naped ador koleb tudus .)1

kefe raga aynmumiskam koleb suidar .)2 gnireets ! raneb gnay

.f icnuK J bawa F seT fitamro : 1

.)1 11,91 =

.)2 ro = mm 9301

1 1 T T 1 1 ----- = ----- + ---- uata --- = ---- – ----

gt gt B gt gt gT θ =

71

2 rajaleB nataigeK . 2 : emsinakeM gnireetS namrekcA epiT

rajaleB nataigeK naujuT .a 2 :

naksalejneM .)1 emsinakem gnireets .namrekcA epit

2 nakutneneM .) naigab koleb tudus malad naaradnek nagned gnireets

.namrekcA epit

3 nagned naaradnek raul naigab koleb tudus nakutneneM .) gnireets epit

.namrekcA

emsinakeM : 2 iretaM naiarU .b gnireetS namrekcA epiT

emsinakeM gnireets fitomoto irtsudni helo nakanugid kaynab

emsinakem halada ini asawed gnireets sitameks araceS .namrekcA epiT

kem adap nakanugid gnay amatu nenopmok emsina gnireets ini epyt

.ini hawab id 4 rabmaG adap tahilid tapad

nareteK rabmaG nag :

= BA maeb = EA elkcunk nanak ador

= DE eit - dor nanak ador = FB elkcunk irik ador

FD = eit - dor irik ador = P xob raeg

= DC mra namtip Q idumek ador =

emsinakem ajrek arac takgnis araceS gnireets tapad namrekcA epyt

: tukireb iagabes naksalejid

Q

nanaK P iriK

A B C

D E F

napeD

4 rabmaG

81

akam ratupid idumek ador alibapA naaratnarep nagned xob raeg

,P mra namtip ,idumek ador naratup nagned haraes karegreb naka DC

ayntujnales mra namtip gnorodnem naka eit - dor aggnihes elkcunk

tubesret ador aggnihes naaradnek ador audek reseggnem nad resegreb

.kolebreb

1) malaD naigaB napeD adoR koleB tuduS nagnutihreP . :

namrekcA epyt idumek metsis emsinakem nakitahrepid ualaK

awhab kapmat tubesret elkcunk - aggnihes tuduynem taubid ayn

kitit irad iridret gnay muisepart nugnab kutnebmem - )lesgne( ratup kitit

elkcunk mra kitit nad - gnuju ktit eit - dor raga taubid ajagnes ini laH .

gnay koleb tudus idajret tapad kolebmem naaradnek taas adap

.nanak nad irik ador aratna adebreb

naka akam nakanahredesid sata id idumek metsis akiJ kapmat

G itrepes rabma 5 tukireb ini :

nagnareteK :

L1 karaj = AO = nip gnik padahret nanak mra namtip

L2 karaj = BO = nip gnik padahret irik mra namtip

L3 gnajnap = eit - dor nanak ador

L4 gnajnap = eit - dor irik ador

p gnajnap = mra namtip

gnajnap = R lkcunk e mra

nad tudus = mra elkcunk

2L 1L A B O

R p R

3L 4L

D C P

d nape 5 rabmaG

91

( lamron naadaek adaP surul isisop tudus ) tudus = tapad gnay

L( 1 L + 2 ) – L( 3 L + 4)

: sumur nagned gnutihid soc soc = ------------------ -- ------- R 2

eS ,hara utas halas ek nakkolebid naaradnek akij ayntujnal

akam nanak ek aynlasim mra namtip ek resegreb naka nanak

tudus nagned , nad eit - dor gnorodnem nad nanak ek resegret aguj

koleb tudus kutnebmem nanak ador aggnihes mra elkcunk nad

tudus kutnebmem irik ador ador koleb tudus ini naidajek adaP .

tapad aynraseb gnay malad naigab koleb tudus tubesid nanak

agned gnutihid : sumur n = o –

( malad naigab koleb tudus aynraseB gnutnagret )

tudus aynraseb mra elkcunk ( koleb isisop akitek .)o

tudus nakitahrepid ualaK elkcunk ( agit ada aynraseb )o

ek ador naratumep aynlicek raseb gnutnagret nanikgnumek ,idum

: utiay

.)a 09 < o 0 ) picnal (

)b 09 = o 0 ( ukis - ukis )

)c 09 > o 0 ( lupmut )

A o

o R

φ

D D ’ X X X

6 rabmaG

02

)a : I nanikgnumeK . 09 < o 0 ) picnal (

: awhab iuhatekid tapad sata id rabmag iraD

X = nis p

c = a – X

L( 1 L + 2 ) – L( 3 L + 4) a = ------------------ -- -------

2

(L1 L + 2 ) – L( 3 L + 4) = c akaM ------------------ -- ------ - – nis p

2

(L1 L + 2 ) – L( 3 L + 4) – 2 nis p = c -------------- -- ---- -- --- ------------ --- -

2

nakitahrep gnarakeS : MDA

a MA

soc = ------ = ----- R DA

L( 1 L + 2 ) – L( 3 L + 4) soc = ------------------ -- -------

2 R

a c

L M N A 1 O

o

pL3

’D D P X X

7 rabmaG

12

nakitahrep ayntujnaleS N’DA

c NA

soc o = ------ = ----- ’DA R

(L1 L + 2 ) – L( 3 L + 4) – 2 nis p soc o = -------------- -- ---- -- --- ------------ --- -

2 R

agrah helorep id ini sumur iraD o agrah ayntujnales ,

sumur ek nakisutitsbusid ini = o – akam

agrah halhelorepid .

: II nanikgnumeK .)b o 09 = 0 ( ukis - ukis )

: awhab iuhatekid tapad sata id rabmag iraD

a = C – X 0 = c itrareb X = a anerak

= o –

aneraK awhab iuhatekid hadus o = 09 0 akam asib gnusgnal

tudus aynraseb gnutihid : utiay , 09 = 0 –

a

L A 1 O

o

pL3

P D ’D X X

8 rabmaG

22

c .) : III nanikgnumeK o 09 ) lupmut (

: awhab iuhatekid tapad sata id rabmag iraD

X = nis p

c = X – a

(L1 L + 2 ) – L( 3 L + 4) = c akaM nis p – ------------------ -- ------ -

2

2 nis p – (L1 L + 2 ) + L( 3 L + 4) = c -------------- -- ---- -- --- ------------ --- -

2

akutnenem malad hadumrepmem kutnU adap udus raseb n

akam ini naidajek utiay ,naigab aud idajnem igabid 1 nad 2

gnisam gnay - : naamasrep nagned gnutihid tapad gnisam

( a L1 L + 2 ) – L( 3 L + 4)

gt 1 = ------ = --- --------------------- -- p2 p

nis p 2 c (L1 L + 2 ) + L( 3 L + 4)

gt 2 = ------ = --- ------------------- --------------- -- p2 p

akiJ 1 nad 2 halet itrareb helorepid anerak ,gnutihret aguj

awhab kapmat rabmag irad = 1 + 2

a c

L A 1 O

o p R

2 1 pL3 ’P

P D X X ’D

9 rabmaG

32

umek agitek iraD agrah nanikgn o gnisam tubesret - gnisam

agrah naklisahgnem naka kutnu ayntujnaleS .adebreb gnay

gnutnagret hisam )tarays ihunemem( raneb gnay anam nakutnenem

( aynraul naiugab koleb tudus garah .)

2 .) napeD adoR koleB tuduS nagnutihreP rauL naigaB

gnay anam iagabes nanakek idumek ador naratumep adaP

ador adap akam )nanak ador adap( uluhadret awitsirep adap idajret

koleb utiay ,amas gnay kefe idajret naka aguj nupirik halebes

burep irik halebes ador kutnu ,aynnaadebreP .nanakek tudus naha o

utiay nanik gnumek utas ada aynah 09 .) picnal ulales (

:ini tukireb 01 rabmaG nakitahreP

lo nakkujnutid raul naigab koleb tuduS reseg tudus he elkcunk ador

rasebes utiay ,irik : tukireb iagabes gnutihid tapad gnay

= – o

a + c tudus nupadA o soc :sumur nagned nakutnetid o = ----------

R nis p = X ; X = c aneraK :akam ,aynmulebes uhat hadus a nad

L( 1 L + 2 ) – L( 3 L + 4 nis p2 + )

soc o = ----------------------------------- -------- R 2

a c

O L2 B o

p ’C RL4

P ’P C X X

01 rabmaG

42

3 .) ( rauL tuduS nagnubuH ( malaD tuduS nagned ) ) :

kefe naktapadnem kutnU gnireets aynsurahes akam ,raneb gnay

seb nagned malad koleb tudus raseb ,adebreb raul koleb tudus ra

.iracid ulrep aynaudek nagnubuh uti kutnu

A O B =

R1

081 O-

’C C ’P ’D P D X X X

11 rabmaG

naresegrep paggnaid akam hadum idajnem nagnutihrep ragA eit - dor

utas nakapurem .latnosiroh sirag

iraD 1 rabmaG : awhab kapmat sata id 1

’DD = ’CC = X nad R = DB = CA

lamron isisop adaP =

tahiL : ’CCA

R12 R = 2 X + 2 – soc X R 2

R1 = R2 X + 2 – soc X R 2

tahiL : ’DDB

R22 R = 2 X + 2 – 081( soc X R 2 O – )

nerak 081( soc a O – = ) – soc : akam

R22 = R2 X + 2 soc X R 2 +

R2 = R2 X+ 2 soc X R 2 +

R2 R2 X + 2 soc X R 2 + = 1 irad hibel R1 R2 X + 2 – soc X R 2

ayntubeynep nad gnalibmep kutneb nakitahrep ( )

52

R2 anerak ---- 1 m aka R2 R1

R1

: ukalreb akam , sunis sumur turuneM

R X 1 X adaP ‘ CCA : ----- = ------ nis = -- --- nis

nis nis R1

2R X adap : ‘ DDB --------- = ------------------

nis 081 ( nis o - )

X 081 ( nis aneraK o- nis = ) nis akam = ---- nis

R2

nis akij gnarakeS nis nad : nakgnidnabid

nis R/X( 1 ) nis . nis R2 ------- = ------------------- -------- = ---- nis R/X( 2 ) nis . nis R1

R2 nis

aneraK ------ akam 1 ------- 1 R1 nis

nis idaj nis uata

koleb tudus aynraseb awhab naklupmisid tapad aynrihkA

koleb tudus adap irad raseb hibel malad naigab naped ador

ab itrareb ini laH .raul naigab naped ador emsinakem awh

gnireets kefe nimajnem tapad naka namrekcA epyt gnireets

.) .raneb ( anrupmes gnay

)4 . idumek ador naratup gnutihgneM

iuhatekid alibapA mra namtip tudus nagned resegreb o ,

: kaynabes ratupreb tubesret mra namtip itrareb akaM

o = -------- 063 = naratup utas ( naratup o )

063 o

62

yntujnaleS n = igig ador nagnidnabrep iuhatekid akij a g 1 :

naratup 1 : itrareb gnay mra namtip n = g idumek ador naratup

n ( idumek ador naratup aynkaynab idaJ kr akij ) mra namtip

tudus nagned resegreb o : halada

o n kr = -------- n . g naratup

063 o

laoS hotnoC :

emsinakem nakanuggnem libom haubeS gnireets namrekcA epyt

iaynupem naruku - gnajnap : naruku mra namtip iraj ,mc 22 : - iraj

elkcunk gnajnap ,mc 52 : maeb gnajnap ,mc 57 : nanak maeb : irik

gnajnap ,mc 55 dor eit gnajnap ,mc 17 : nanak dor eit ,mc 15 : irik

adap igig nagnidnabrep nad xob raeg idumek ador akiJ . 1 : 42 =

akam nanakek ratupid tubesret libom mra namtip nagned resegret

02 = tudus 0 : halnakutneT .

(1 .) tuduS elkcunk .surul isisop adap

(2 .) .irik naigab ador koleb tuduS

(3 .) .nanak naigab ador koleb tuduS

(4 .) .idumek ador naratumep aynkaynaB

: naiaseleyneP

iuhatekiD : S emsinakem nagned libom haube gnireets namrekcA epyt

L ; mc 52 = R ; mc 22 = P 1 ; mc 57 = L2 ; mc 55 =

L3 L ; mc 17 = 4 ratupid idumek adoR ;mc 15 =

, nanakek 02 = 0 n ; g 1 : 42 = 1 :

nakaynatiD .)1( : uata

.)2(

.)3(

n .)4( kr .

72

: bawaJ

L( 1 L + 2 ) – L( 3 L + 4 )55 + 57( ) – )15 + 17( soc .)1( soc = = -------------------------- = --------------------------

52. 2 R2 0061,0 = helorepid = 97,08 = 0

.)2( = – o

L ( 1 L + 2 ) – L ( 3 L + 4 nis p2 + )

soc o = -----------------------------------------

R2

57 ( ) 55 + – 15 + 17 ( 02 nis 22.2 + ) 0

= --------------------------------------- ------ -- 52.2

= 0164,0 o 55,26 = 0

helorepid aggniheS 97,08 = – 55,26 0 = 42,81 0

:nanak ador koleb tuduS .)3( θ = o – nanikgnumek 3 ada

aynraseb o

: I nanikgnumek * o 09 0

L( 1 L + 2 ) – L( 3 L + 4 ) – nis p2

soc o = ---------------------------------------- = R 2

57 ( ) 55 + – 15 + 17 ( ) – 02 nis 22.2 0

= --------------------------------------- ------ -- 52.2

= – 0141 ,0 sunisoC anerak( nikgnum kadit

)fitisop ulales picnal tudus

: II nanikgnumek * o 09 = o θ 09 = o – 97 ,08 o 12,9 = o

aynsurahes ,tarays ihunemem kadit ( θ > )

: III nanikgnumek * o > 09 o θ = θ1 + θ2

(L 1 L + 2 ) – L( 3 – L4) )55 + 57( – )15 + 17 ( gt θ1 = ------------------------- = --------------------------

p2 22.2

gt θ1 helorepid 8181,0 = θ 1 03,01 = 0

82

nis p2 – L( 1 L + 2 L( + ) 3 L + 4 )

gt θ 2 = --------------------------------------- p2

02 nis 22.2 0 – 57 ( 15 + 17 ( + ) 55 + )

= ---- ----------------------- - ------------ ------ -- 22.2

gt θ2 2061,0 = helorepid θ 2 01,9 = o

idaJ θ 03,01 = o 01,9 + o = 04,91 o anerak ,ihunemem ( θ > )

o 02 n .)4( kr = -------- n . g = ------ 42 . = 33,1 naratup

063 o 063 o

.c namukgnaR : 2

1 .) emsinakeM gnireets emsinakem halada namrekcA epyt gnireets gnay

d fitomoto irtsudni id nakgnabmekid kaynab nenopmoK .ini asawe

,idumek sorop ,idumek adoR : sata iridret ini emsinakem amatu raeg

eit ,xob - mra namtip ,dor nad .mra elkcunk

2 .) tuduS elkcunk emsinakem gnireets surul isisop adap namrekcA epyt

: sumur nagned gnutihid tapad

(L1 L + 2 ) – L( 3 L + 4) soc soc = = ---------------------------

R 2

malad naigab ador koleb tuduS .)3 ( θ emsinakem adap ) gnireets epyt

netid tapad namrekcA : sumur nagned nakut

θ = o –

malad naigab ador koleb tuduS .)4 ( emsinakem adap ) gnireets epyt

: sumur nagned nakutnetid tapad namrekcA

= – o

idumek ador naratup aynkaynaB .)5 (n kr ed gnutihid ) : sumur nagn o

n kr = -------- n . g naratup 063 o

92

.d saguT 2 :

emsinakem nakanuggnem libom haubeS gnireets namrekcA epyt

naruku iaynupmem – gnajnap : naruku mra namtip iraj ,mc 02 : - iraj

gnajnap ,mc 42 : elkunk maeb gnajnap ,mc 46 : nanak maeb ,mc 44 : irik

gnajnap dor eit gnajnap ,mc 95 : nanak dor eit nad mc 93 : irik

adap igig nagnidnabrep xob raeg uti libom idumek ador akiJ .1 : 63 =

akam irik ek ratupid mra namtip 51 = tudus nagned resegret o .

tuduS .)1 : halnakutneT elkcunk .surul isisop adap

.nanak naigab ador koleb tuduS .)2

rik naigab ador koleb tuduS .)3 .i

.idumek ador naratumep aynkaynaB .)4

.e fitamrof seT : 2

emsinakem nakanuggnem libom haubeS gnireets namrekcA epyt

naruku iaynupmem – gnajnap : naruku mra namtip iraj ,mc 91 : - iraj

gnajnap ,mc 02 : elkunk maeb 07 : nanak gnajnap ,mc maeb ,mc 04 : irik

gnajnap dor eit gnajnap ,mc 76 : nanak dor eit nad mc 73 : irik

adap igig nagnidnabrep xob raeg uti libom idumek ador akiJ .1 : 84 =

akam irik ek ratupid mra namtip 21 = tudus nagned resegret o .

duS .)1 : halnakutneT tu elkcunk .surul isisop adap

.nanak naigab ador koleb tuduS .)2

.irik naigab ador koleb tuduS .)3

.idumek ador naratumep aynkaynaB .)4

.f icnuK J bawa F seT fitamro : 2

tuduS .)1 elkcunk : surul isisop adap = 8 = 1, 73 0

: nanak naigab ador koleb tuduS .)2 = 11, 17

: irik naigab ador koleb tuduS .)3 θ = 11, 48 o

: idumek ador naratumep aynkaynaB .)4 n kr = ,1 6 naratup

03

BAB III E ISAULAV

.A naaynatreP

.1 iaynupmem libom haubeS leehw esab mc 072 : nad kcart .mc 061 :

51 tudus nagned nanak ek nakkolebid uti libom naped ador akiJ akam ,

: halgnutih

.irik naigab naped ador koleb tudus .a

kefe raga aynmumiskam koleb suidar .b gnireets - ! raneb ayn

emsinakem nakanuggnem libom haubeS .2 gnireets namrekcA epyt

naruku iaynupmem – : naruku gnajnap maeb gnajnap ,mc 77 : nanak maeb

gnajnap ,mc 75 : irik dor eit gnajnap ,mc 27 : nanak or eit d mc 25 : irik

gnajnap mra namtip iraj ,mc 02 : - nagnidnabrep nad ,mc 42 : elkunk iraj

adap igig xob raeg nanak ek ratupid uti libom idumek ador akiJ .1 : 23 =

aggnihes mra namtip 81 = tudus nagned resegret o ! halgnutih ,

tuduS .a elkcunk .surul isisop adap

.irik naigab ador koleb tuduS .b

kefe helorepid raga nanak naigab ador koleb tuduS .c gnireets

.anrupmes gnay

.idumek ador naratumep aynkaynaB .d

nabawaJ icnuK .B

.a .1 1 = 3, 20

.b ro = 119 64,8 mm

tuduS .a .2 elkcunk : surul isisop adap = 89,77 = 0

b k naigab ador koleb tuduS . iri : 47,51 = o

c k naigab ador koleb tuduS . nana : θ 14,71 = o

d n : idumek ador naratumep aynkaynaB . kr naratup 6,1 =

13

.C nasululeK airetirK

airetirK rokS 1( – )01 toboB ialiN nagnareteK

( fitingoK 1 romon laos ) 2 nad 5

sulul tarayS laminim ialin

65

isaton silunem naitileteK 1

rudesorp natapeteK 2

nabawaj alumrof natapeteK 1

utkaw natapeteK 1

RIHKA IALIN

23

BAB VI

PUTUNEP

622 OTO.KGM ludum halnaikimeD – luduj nagned 10 irtemoeG gnireetS

naaradneK set ,sagut/nahital aparebeb ipakgnelid nagned nususid iaseles halet ini

ludom nautnab nagneD .aynnabawaj icnuk atreseb rihka isaulave nupuam fitamrof

kparahid ini nagnabmekrep iridnes uatnamem tapad awsisaham arap na

raneb halet akerem hakapa ,aynisnetepmok - isnetepmok ikilimem raneb

rajaleb nataigek paites adap nakparahid gnay naujut adap nimrecret anamiagabes

.muleb uata

cnem halet gnay awsisaham arap igaB akam laminim nasululek tarays iapa

.ini hailukatam adap aynrajaleb nataigek nakitnehgnem tapad hadus akerem

surah akerem akam ,laminim nasululek ihunemem tapad muleb akij aynkilabeS

iretam naigab adap amaturet aynrajaleb ilabmek gnalugnem - muleb gnay iretam

huggnus hibel surah akerem aynkiabes nad )sulul muleb( ayniasaukid - huggnus

irad nautnab kusamret ada gnay satilisaf naktaafnamem nagned rajaleb malad

.ini hailukatam rotatilisaf iagabes nesod

33

AKATSUP RATFAD

.0791 .noipmahC & dlonrA ecneicS dna noitaluclaC elciheV rotoM :hciwroN ..dtL ,snoS dna rehctelF yb niatirB taerG

.1791 ..E.D ,eloC .scimanyD elciheV yratnemelE lacinahceM fo tnemetrapeD.I.M ,robrA nnA nagihciM fo ytisrevinU gnireenignE

.7791 .nitraM italuclaC dna ecneicS snoicinhceT selciheV rotoM rof no : nodnoL .dtL sserP ytisrevinU hsilgnE ehT

.1002 .namojN ,artnatuS aynisakilpA nad iroeT fitomotO igolonkeT : ayabaruS ..aydiW anuG tibreneP

.8791 .Y.J ,gnoW .selciheV dnuorG fo yroehT .snoS & yeliW nhoJ :kroY weN