MI1JlAH O PACnOnOBI111 bull JOBAH fT WETPAJYI111 6PAHVlCJlAB UBETKOBJ111 bull )lPAfOJbYE fTEllAHAU

)lPArOJbY6 M~JAfl(1n

-----

)

ltP11311KA 36l1PKA 3A)lATAKA CA JlADOPATOPyenJCKI1M BJDKEAMA

3A OeMyen PA3PE)l OCHOBHE WKOJTE ~

~ ~bull

3ABOA 3A Y1)6EHII1KE 111 HACTABHA CPEQCTBA II1CT04HO CAPAJEBO

YOYTCTBO 3A PJElliABM-bE 3AUATAKA 11 113B013Ef-hE JTA60PATOPl1JCKYIX BJE)KEH

Pjewa133Hgte 3anaTaK3je npHJ~I1Ka na ce TeopHjcKO 3Hal-bC nOHOBIi YTBpn~l npo shyJly6H II npoBjepl1

[1pe~1a canp)j(ajy H Hall1HY pjell13Bal-ba 3anaUI1 Y QJI13HUI1 Mory JIa 6YJIY 3acJashy

~u - IlUmafba (K6WlIImamU8HII 30dauu) paIYHCKIi 3aOG~u (J60flIl1UIIWmU6HII 3adGu

eKcnepu~efllnOJHII 3aeJauu

J anallll - llHTaaa To cy TaKBH 3anaUI1 ltmje pjell1aBal-be He 3axTlljeBa paltI)HCKe unepaulfje [10 npaBIUly y canp)I(ajy TI1X 3anaTaKa He nocToje 6pojHl-I nonaUl1 npH pjewaBal-bY 3anaTKa-mlTal-ba no npaBlUry He nOCToje npopallYHI1 (MaTeMaTI1YKe onepaUl1je) To o~loryhyje ycpencpel)HBal-be naK]-be Ha centlIl3HIK) cYWTlfHY np06Jle shy~ta

PaqyJfCKH (KBaHTHTaTUBHU) 3aaaIDI Y OBHM 331Iaumla ouroBop Ha nOCTaBJbeshyHO nl1Tal-be He MO)l(e ce Q06~ITH 6e3 olIpel)eHux paI)HCKI1X onepaUHja rTPI1 pjell1a shyBal-bY TaKBllX 3anaTaKa KBaJlIITaTHBHa (CYlliTHHCKa) aHaJll13a j e TaKol)e HeonXOlIHa aiIII ce OHa uonYl-baBa jow H KBaHTHTaTl1BHOM (paYYHCKml) aH3J11130 ea npopayyshyHOM OJIpelleHIIJ( 6POjHlfX KapaKTepl1CTllKa npoueca 11)111 nojaBe

PjelIlaBathe KBaHTInaTl1 BH I1X (paYYHCKJiX) 3aJIaTaKa nOnpa3~H1jeBa n a gtKlb 11 so tIT1t al-be QgtopMYJlaul1je 3anaTKa H ~13pauy CKHIle 3a pjell1aBal-be 3ltUaTKa

II3)KJbHBO ltJ1fTalbe $oPMYJlaIlHje (I10CTaBKe) 3an3TKa no l1oTpe611 11 HeKOJIIIKO ny-ra HeorrxollHo je )Ia 61--1 ce eXBanUla eYWTllHa np06JleMa y uaTO 3arraTKY Pa3shyMjerl1 3auaTaK - 3Hayrl cxsanlTl1 npo611eM 0 Kojel je pl1je-l Qgt1311JKY nojaBY U 3amiddot KOH KOjH o)Ipel]yje l-beH TOK Te npeKo n03HaTHX BeJIIlqHHa Koje KapaKTepIHuy na shyry nojaoy Inpa311TI1 Hen03HaTe BPHje)IHOCTI1 Be1lWmiddotHlHa

CKHUOM 33 pje1ll3Balhe 331laTKa rpynl1ruy ce n03HaTI1 II Hen03HaTl middotV1aHOBI OuHOCHO qH13JJIKe BeJTIflI1l-le 360r JeJIHOeTaSHOCTl1 YOyaBal-ba oQI-Qca JUMel)y noshyjeuI1HI1 X Qgt113J111KJ1X BeJlHLJI1Ha Kop~lcTe ce upTe)IUi w eMe CKHue rpacPHUH

Tpe6a 06paTI1TI1 lla)l(l-bY Ha pe3J1HOCT pe3YJlTaTa (onrOBopa) n06Hjellor npH pjell1asal-bY 3auaTKa HeonXOlIHO je IlpouHjeH~rrH pe3ymaTe (onr030pe) He ca~w ca MaTeMaTHYKOr Hero ca QgtH311yKor r1leuHWTa lIa 611 ce YO~II1Jla 1-b11XOBa eseHryaJl Ha al1CYPllHOCT (He06HYHoCT HepeaJIHOcT)

H anaMo ceonparH ytleHHIlH na heTe yyehl1 QgtH3I1KY pjell1aBal-beM 3auaTaKa 11 113Bot)el-beM eKCl1epHMeHaTa 11 Jla60paTopHjCJlt11X Bje)(611 bull u0)JU1BjeTl1 11 ocjeTHTH 6ap nlfO ou OHor y36yljel-ba Ii panoCTH 11 60p6e JbynCKor YMa WTO I1X uOgtK11BJbaBa Qgt11middot 31Nap HacTojel1l1 na lllTO 60Jbe pa3YMHje 3aKOHHTOCTl1 npHpone

BeJJJ1Kli cPHJ1030Qgt 11 HaIIDIK npeBHe fplKe UeMOKpI1T (460-370 npHje HOBe epe) roBOP HO je BuUJe 6ux 80JUO ga oiIiKpujeMjeqai 3aKOH upupoqe He~o ga t7ociIiashyHeM KPCllb n epcuie

1 KUHeMaUlUKa u ~y=---____qUHaMU~ I bull

1 K yrJllwa ceo y TOKY onpel)eHor BpeMeHa Kpehe paBHoMjepHo no XOPH30HTaJI HOJ nOJlII03H a 3aTI1M HaCTaSJba KpeTaJ-be HIB KOCH )l(JHlje6 Y KojHM TaqKaM je Gp3HHa KyrJlJ1ue HajBena

2 KyrrUlU3 ceoY TOI-) onpel)eHor BpeMeHa Kpehe pasHoMjepHo no XOPH30HT3J1 HOj n0ILl10311 3an1M HaCTaBJba KpeTal-be )3 KOCH )I(lll1je6 11 Ha Kpajy OOHOBO J1(

XOpIBOlTa1Hwj paSHI Y KOj ll- TaYKaMa je 6p311Ha KYTJIHue HajMal-ba

3 AKO ce TpajeKTop~lje 1lsa Tl1jeJla clljeKY ua lUI MO)l(eMO nOY3uaHO TSPJOITH )l

cy ce OHa cyuapilla

4 KaKBo je KpeTalbe y KO~le je cpeJItha 6p311Ha Y CBaKOM TpeHYTKY je)IHaKa Tpe H)fHoj 6p3HH~I

5 MO)Ke J111 Tlljelo na nOBehaBa 6p3HHY aKO -y ce y6p3al-be cMalbyje

v[E ] 6 Ha rpaQgtIIKyje 3a nBa nrjela npl1Ka3aHa S

38SlfCHOCT 6p3JtHe ou npeMeHa Koje je Tl1jeJlo TOKOM BpeMeHa 10 11MaJlO seliy cpeul-b) 6p31H~Y A

to tr 7 B03 ce Kpele ll)l lep~iJIljaHa npeM3 cjeshy

BepHOM nOIIY Koje np3Bue II cMjepoBe Kperal-ba Ie HMao mUlOT aB10Ha aKO je Ha cJbe)IehJi HaYlllI onHcHsao KpeTIUhe B03a a) B03 ce H3J1a311 y CTal-bY MHpOBal-ba

6) B03 ce lltpe1le npeMa j))KHOM noJT)

8 ~aJla ce yeTpeMH Ha )(pTBY K06pl1Ha maBa ce MO)(e KpernTl1 y6p3al-beM HHTeH 311Tera 50 ms2 K31la 6H ayroM06HJ1 Moshyrao 110CTI1hl1 TO y6p3al-be KOJ1I1KO 6H MY BpeMeHa Tpe6aJlo 1la nOCTl-ITHe 6P3J-IHY 100 kmh aKO npeTI10CTaBIDlO ua ce ayshy ~

TOM06HJ1 Kpehe npaBOJ1I1Hl1jCKJ1 H na noshy1Ia311 113 CTal-ba Ml1pOBaHgta

YOYTCTBO 3A PJElliABM-bE 3AUATAKA 11 113B013Ef-hE JTA60PATOPl1JCKYIX BJE)KEH

Pjewa133Hgte 3anaTaK3je npHJ~I1Ka na ce TeopHjcKO 3Hal-bC nOHOBIi YTBpn~l npo shyJly6H II npoBjepl1

[1pe~1a canp)j(ajy H Hall1HY pjell13Bal-ba 3anaUI1 Y QJI13HUI1 Mory JIa 6YJIY 3acJashy

~u - IlUmafba (K6WlIImamU8HII 30dauu) paIYHCKIi 3aOG~u (J60flIl1UIIWmU6HII 3adGu

eKcnepu~efllnOJHII 3aeJauu

J anallll - llHTaaa To cy TaKBH 3anaUI1 ltmje pjell1aBal-be He 3axTlljeBa paltI)HCKe unepaulfje [10 npaBIUly y canp)I(ajy TI1X 3anaTaKa He nocToje 6pojHl-I nonaUl1 npH pjewaBal-bY 3anaTKa-mlTal-ba no npaBlUry He nOCToje npopallYHI1 (MaTeMaTI1YKe onepaUl1je) To o~loryhyje ycpencpel)HBal-be naK]-be Ha centlIl3HIK) cYWTlfHY np06Jle shy~ta

PaqyJfCKH (KBaHTHTaTUBHU) 3aaaIDI Y OBHM 331Iaumla ouroBop Ha nOCTaBJbeshyHO nl1Tal-be He MO)l(e ce Q06~ITH 6e3 olIpel)eHux paI)HCKI1X onepaUHja rTPI1 pjell1a shyBal-bY TaKBllX 3anaTaKa KBaJlIITaTHBHa (CYlliTHHCKa) aHaJll13a j e TaKol)e HeonXOlIHa aiIII ce OHa uonYl-baBa jow H KBaHTHTaTl1BHOM (paYYHCKml) aH3J11130 ea npopayyshyHOM OJIpelleHIIJ( 6POjHlfX KapaKTepl1CTllKa npoueca 11)111 nojaBe

PjelIlaBathe KBaHTInaTl1 BH I1X (paYYHCKJiX) 3aJIaTaKa nOnpa3~H1jeBa n a gtKlb 11 so tIT1t al-be QgtopMYJlaul1je 3anaTKa H ~13pauy CKHIle 3a pjell1aBal-be 3ltUaTKa

II3)KJbHBO ltJ1fTalbe $oPMYJlaIlHje (I10CTaBKe) 3an3TKa no l1oTpe611 11 HeKOJIIIKO ny-ra HeorrxollHo je )Ia 61--1 ce eXBanUla eYWTllHa np06JleMa y uaTO 3arraTKY Pa3shyMjerl1 3auaTaK - 3Hayrl cxsanlTl1 npo611eM 0 Kojel je pl1je-l Qgt1311JKY nojaBY U 3amiddot KOH KOjH o)Ipel]yje l-beH TOK Te npeKo n03HaTHX BeJIIlqHHa Koje KapaKTepIHuy na shyry nojaoy Inpa311TI1 Hen03HaTe BPHje)IHOCTI1 Be1lWmiddotHlHa

CKHUOM 33 pje1ll3Balhe 331laTKa rpynl1ruy ce n03HaTI1 II Hen03HaTl middotV1aHOBI OuHOCHO qH13JJIKe BeJTIflI1l-le 360r JeJIHOeTaSHOCTl1 YOyaBal-ba oQI-Qca JUMel)y noshyjeuI1HI1 X Qgt113J111KJ1X BeJlHLJI1Ha Kop~lcTe ce upTe)IUi w eMe CKHue rpacPHUH

Tpe6a 06paTI1TI1 lla)l(l-bY Ha pe3J1HOCT pe3YJlTaTa (onrOBopa) n06Hjellor npH pjell1asal-bY 3auaTKa HeonXOlIHO je IlpouHjeH~rrH pe3ymaTe (onr030pe) He ca~w ca MaTeMaTHYKOr Hero ca QgtH311yKor r1leuHWTa lIa 611 ce YO~II1Jla 1-b11XOBa eseHryaJl Ha al1CYPllHOCT (He06HYHoCT HepeaJIHOcT)

H anaMo ceonparH ytleHHIlH na heTe yyehl1 QgtH3I1KY pjell1aBal-beM 3auaTaKa 11 113Bot)el-beM eKCl1epHMeHaTa 11 Jla60paTopHjCJlt11X Bje)(611 bull u0)JU1BjeTl1 11 ocjeTHTH 6ap nlfO ou OHor y36yljel-ba Ii panoCTH 11 60p6e JbynCKor YMa WTO I1X uOgtK11BJbaBa Qgt11middot 31Nap HacTojel1l1 na lllTO 60Jbe pa3YMHje 3aKOHHTOCTl1 npHpone

BeJJJ1Kli cPHJ1030Qgt 11 HaIIDIK npeBHe fplKe UeMOKpI1T (460-370 npHje HOBe epe) roBOP HO je BuUJe 6ux 80JUO ga oiIiKpujeMjeqai 3aKOH upupoqe He~o ga t7ociIiashyHeM KPCllb n epcuie

1 KUHeMaUlUKa u ~y=---____qUHaMU~ I bull

1 K yrJllwa ceo y TOKY onpel)eHor BpeMeHa Kpehe paBHoMjepHo no XOPH30HTaJI HOJ nOJlII03H a 3aTI1M HaCTaSJba KpeTaJ-be HIB KOCH )l(JHlje6 Y KojHM TaqKaM je Gp3HHa KyrJlJ1ue HajBena

2 KyrrUlU3 ceoY TOI-) onpel)eHor BpeMeHa Kpehe pasHoMjepHo no XOPH30HT3J1 HOj n0ILl10311 3an1M HaCTaBJba KpeTal-be )3 KOCH )I(lll1je6 11 Ha Kpajy OOHOBO J1(

XOpIBOlTa1Hwj paSHI Y KOj ll- TaYKaMa je 6p311Ha KYTJIHue HajMal-ba

3 AKO ce TpajeKTop~lje 1lsa Tl1jeJla clljeKY ua lUI MO)l(eMO nOY3uaHO TSPJOITH )l

cy ce OHa cyuapilla

4 KaKBo je KpeTalbe y KO~le je cpeJItha 6p311Ha Y CBaKOM TpeHYTKY je)IHaKa Tpe H)fHoj 6p3HH~I

5 MO)Ke J111 Tlljelo na nOBehaBa 6p3HHY aKO -y ce y6p3al-be cMalbyje

v[E ] 6 Ha rpaQgtIIKyje 3a nBa nrjela npl1Ka3aHa S

38SlfCHOCT 6p3JtHe ou npeMeHa Koje je Tl1jeJlo TOKOM BpeMeHa 10 11MaJlO seliy cpeul-b) 6p31H~Y A

to tr 7 B03 ce Kpele ll)l lep~iJIljaHa npeM3 cjeshy

BepHOM nOIIY Koje np3Bue II cMjepoBe Kperal-ba Ie HMao mUlOT aB10Ha aKO je Ha cJbe)IehJi HaYlllI onHcHsao KpeTIUhe B03a a) B03 ce H3J1a311 y CTal-bY MHpOBal-ba

6) B03 ce lltpe1le npeMa j))KHOM noJT)

8 ~aJla ce yeTpeMH Ha )(pTBY K06pl1Ha maBa ce MO)(e KpernTl1 y6p3al-beM HHTeH 311Tera 50 ms2 K31la 6H ayroM06HJ1 Moshyrao 110CTI1hl1 TO y6p3al-be KOJ1I1KO 6H MY BpeMeHa Tpe6aJlo 1la nOCTl-ITHe 6P3J-IHY 100 kmh aKO npeTI10CTaBIDlO ua ce ayshy ~

TOM06HJ1 Kpehe npaBOJ1I1Hl1jCKJ1 H na noshy1Ia311 113 CTal-ba Ml1pOBaHgta

J9AyrOM0611J1 ce Kpehe paBHoMjep Ho y6p3aHO y6p3aJ-be J12 ms~ Y HeKO1 TpeHyrK) I-beroshyBa 6p311Ha Je 96 ms a) K omlKtt je 611J1il 6pJIIHa aYTo10611J1a 25 s

pal-JJtje)

6) KO_1ItKil he 6uTlI 6p3IJHa ilToM051IJ1a noshyC11IIJe 25 s

v~ aBllje ceKYlille l-JaKOIl n OleTKa TpKe 6p3l1Ha IOT~lluJ(JJllcTe je 5 ms A KO npernocTaBI1MO na ce JOTOUJ1KJlJlCTa Kpene paBHoMJepHo yfip3aHO KOJlHKa fie 611T11 l-berOBa fiP3IIH3 Ha Kpajy lleceTe ceK)Hne KpeTal-ba)

Jll AyrOMOfiILl DaBHo~ljepHo lloBefia 6p311HY ca 25 kmh Ha 55 kmh TOKOM nOJla

IIIJfyra 110K fillUUKJlIlCTa Kojl1 n011a311 113 CTalha 1I1pOBalha noclIije 30 s paBshy

HOJjepHo y6p3aHor KpeTal-ba I1Ma fip311HY 30 kmh vbpallYHajTe II ynopellllTe y6p3al-ba aYToI06~lJIa I 6IJUl1K1HcTe

BeMllpCKIi 6poll ce Kpehe paRHOjepHo y6pshy3aHO y6p3aHe1 98 ms2

a) AKO npCrnocTaSIIto la lBeJ1lpCKIf 6po)]

nOlaJIJ 113 CTal-ba JJlpORltHha KOJlIl(OO he

J) BpefeHa 6l1TII nOTpe6Ho aOK He no-

CTlJrHe 6p311H leCeT IJTa al-b) 011 6p311He CBjCTJlOCTlI (Iip311Ha cnjeTJloshyeTlJ je c = 300000 kms)

6) KOlIIKIJ nn npebe cnClIpCKIi fiPOll 3a TO Bpllje(e

13 Ita fill nOJJeTiIO 60VlHr 747 fO pa na 110CTllrHe 6p311HY 360 kmh 360r ry_ -KRe Ha aepOJlpOIY aBIlOH tapa lla Y3leTlJ 3a lOs AKO npernocTaBIIMo 1Ia aBHshy

01-1 nOJla3I1 I lJ CTal-ba 1I1poBalmiddottgta II na ce Kpehe paBHo(j epHo y6p38HO li3pallYshyHajTe

a) yup3aJ-be aRlfOHa

6) Hajtal-h) TIYiKI1HY nrlCTe ca Koje aBlfOH fOgtKe (ie35jenHO Ja nOJlen

14 n YUI4aHo WHO HClnywTa 18 m l~D ullj eB 10B3CIKC nYWKC 6f)lHIIOM 360 ms

AKo Kpe-rltJI-Jgte nYIUllaHor 3PHI JOgtKCIO Cl3Tpn fJ raBIIOljepHo y6p3aHllf 113pa4)11lt-lrfC

a) cpenHgtY Bpl1jellHocT 6p31lHe 3pHa TOshyII

KOI HgterOllor KpeTal-ba KPO] U1ljes

6) Bpl1jeMc Koje je npOTeK10 on n04eTshy

Ka KpeTafta 3pHa no J-beroaor 11311ashyCKa H3 UlljeBI1

B) y6p3alhe 3pHa TOKOM KpeTal-bCl Kp03 IlHjeB

( I ~jHa Kpajy npyre ceK)Hlle paBHoMjepHo ycnopeHor KpeTa~b3 fip311Ha 6JfUlJKJlI1shy

J V CTe je 8 ms a Ha Kpajy CeTBpTe ceKYH1Ie 6p3HHa je 5 ms KOJlHKI1 j e 11HTeH 3HTeT y6p3al-ba 6f1IlHKJlJ1CTe

BehHHa ayroMofiwta I1Ma MaKCHMaJIHO ycnopelhe 6 ms2 Halj~ITe Tpar KOfeshyV J6 J-ba Tj nyr KOjl1 ayroM06HJI npel)e no 3aYCTaBJbaHgta aKO je l-berOBa 6p3l1Ha

n puje K04elh3 6Hlla 12 ms

B03 411ja n04eTHa 6p3HHa je 30 ms yKOfJof 3a 2 min AKa npemOCTaBHMO naJ17 ce B03 KpeTao paBHoMjepHo ycnopeHO 01lpellHTe

a) ycrropeJ-be B03a

fi ) nyr KOjI-l B03 npel)e TOKOM KOl eJ-ba

18 Y TpeHyrKY Kana cy TOLlKOBI1 aBHOHa n011HpHyJlH nHcry l-berOBa 6p31llia je 611shy

Jla 40 ms ao JaYCTaBJbaJ-ba aBHOH je npewao nyr on 1200 m AKo 3HaTe Aa ce aBIIOH KpeTao paBHoMjepHo YClIopeHo OllpellHTe

a) cpenI-bY BpHjeJIHOCT 6p3HHe aBI10Ha TO KOM KOlIefha

6) BplfjeMe Koje je fiUJlO nOTpefiHo aB~10l-ry 11a ce 3aYCT3BH

B) nyr KOjl1 j e aBHOH npewao TOKOM rrpBHX 15 S KpeTaHgta

19 B03a-l je no Y04aBal-bY nOJJl1Ul1jcKor ayro)I06Hlla CMaligtHO 6P3l1RY ca 75 kmb Ha 45 kmh TOKOM KOllelha ayroM0611J1 ie npewao rryr all 88 m AKa npemoshyCTaRIf MO 11a ce ayrmI06~fJ1 KpeTao pal3HoMjepHo ycnopeHO onpenHTe

a) Bpl-ljeMe Koje je npOTeKJIO TOKOM KO1elha

6) y6p3al-be ayro f0511J1a

zoo aBHje CTaHllue non3eMHe gtKeJbe3Hl1lle Y11aJheHe cy I km B03 JCpebe ea rrpBe

CT3HJ1ue II paBHmJjepHo y6p3aHo npeJla311 npBy nOJlOBIrnY rryra y6p3aaeM

I ms2 Ha npyraj nOJlOBl1HH nyra B03 ce Kpehe paBHoMjepHo yenopeHo y6p3ashy

lheM -I ms2 O llpenllTe

a) Bplljele 3a Koje B03 CTllTHe on jenHe no 1Ipyre CTaHl1Ue 6) MaKCHIam-ry 6p3HHY B03a TOKOM KpeTaJ-ba

B) cpenI-bY BpHjenHOCT 6p31IHe B03a

21middot Y TpeHYfKY Kalla ce Ha ce)lacentopy ynaJI~UIO 3eJleHO cBjeTJlO

ayrOMofil1Jl je n04eo lla ce Kpetie paBHoMjepHo y6p3aHo

y6p3aJ-beJ 2 ms~ y ~ICTOM rpeHyrKY KaMliOH KOjH ce Kpeshy

he paBHorljepHo 6P311HOM 10 ms npeTeKao je ayro~106IiJl

AKO ce B031Lla Kpeny paBHoljepHo npaBoJlI1Hl1jCK11 OllpeshyllIiTe

a) nocJII1je KOJlHKO BpeMel-la he ayro)w611J1 npeTetm Kashy

MHOH

6) nyr KOjl1 he TaJla B03HJ1a npehH 3a TO BpJfjeMe

22 B03 ee Kpene KOHCTaHTHOM 6P3HHOM 30 kmlh Y jeJIHOM TpeHyrKY ce OTKa41 nOCJbe11lhl( sarOH KOjll ce 3aTH~f Kpene paBHoMjepHo ycnopeHO 11 3aYCTaBH C( npewaBWH nyr on 200 m fioCJIlfje OTKalIHBaHgta BaraHa B03 HaCTaBJha na CI

Kpehe Henpo~lIIjel-beHoM 6p3HHOM KOJlHKO je pacTojaJ-be H3MelJY B03a H Bara Ha lOs noWTO ce BaraH oTKallHo

23 AyrOM061Ul ce Kpehe paBHoMjepHo npaBOJllnmjCK11 fiP3H HOM 90 kmh Y TPe HyrK) Kana je 803a-l npHMHjerno na ce Ha nyry Ha ynaJbeHOCTII 50 m HaJIa31 naco OH j e npliTliCHYO KOlfHJfi(j H ayro~106Hll je nOlleo na ycnopaBa Xon e JI]o

B03a-l ycnjeTH na H36jeme cynap Y6p3aligte ayroMo6HJ1a je KOHCTaHTH O H H3 HOCI1 75 ms2

24 B03 ce Kpehe Kp03 PYAHl11lt yrJba BaroHl1 OD KOjl1X ce B03 caCTojH nyr11 cy 12 m PyDap Ha Kpajy CBaKe ceKYHDe y6auYje no j eDH JIonaTY yrJba y OTBopeHe BaroshyHe a) AKo ce B03 KpeJie paBHoMjepHo 6P31iHOM 10 kInh 1-1 aKO npna JIonaTa

yrJba nanHe Ha caM nOIeTaK BarOHa KOJII1KO JIonaTa yrJba he PYDap ycnjeshyTH na y6alll1 y Taj BaroH

6) KOJlI1KO JlOnaTa yrJba lie PYDap ycnjeTH na y6aml Y BarOH aKO y TpeffYTKY Kana npBa JlOnaTa yrJba nanHe Ha nOlleraK BarOHa B03 nOlJHe na ce Kpehe

113 CTaHgta Ml1pOBaHa paBHo~ljepHo y6p3aHo y6p3al-beM 05 ms2

25 B03 Kpehe 1i3 CT3Hgta Ml1pOBaHa 113 )f(eJbe3HI1lKe CTaHliue T OKOM npBa nBa ~1l1-

H)Ta B03 ce Kpehe pasHoMjepHo y6p3aHo y6p3aHgteM 05 mfs~ 3aTI1M Onp)laBa

KOHCTaHTHY 6p311JiY Y HapeJlHI1X JleCeT ~U1HyTa 11 KOHalJHO ce 3aYCTaBJba YHashypenHa Jlsa MI1Hyra Kpehyhl l ce paBHoMjepHo ycnopeHO KOJHIKI1 nyr npelJe B03 TOKOM KpeTal-ha

J _26 Ha CJlHllli je npIIKa3aH rpacentliK 6p3HHe OJlpe- v[rns]V JlHTI1

a) 6p3~fHY Y TpeH)TKY Kana je THjeJIO n04eno 20 ycnopasal-be 10

6) y6p3al-be rslB) n pel)eHIl nyr

[ms]27 Ha cmillH je npl1Ka3aH rpacentIlK 6pJIIHe HIshy

jelJa y 3aBHCHOCTIf on BpeMeHa a ) KOJlI1KH nyr je npelllJlo TlljeJIo

6) KOJlI1Kaie cpeJlHa BpI1jeDHOCT 6pJHHe ~L -u0 l-berOBor KpeTaHgta

2 4 6 8 10 12 (rs12 -( H a CJJI1UI1 je npHKa3aH rpacentI1K 3aBIICHOCTl1 6pshy

~ 3~1He TpKalJa OJl BpeMeHa KOJlHKII nyr npel)e TpshyJ KaY3a l6 s

4 8 12 16 I[s] v [rns]

29 K opHcTelll1 rpacentlfK 3aBI1CHOCTJ1 6p311He B03a 011 BpeMeHa CKJ-luupajTe rpacentllK 3aBI1CHOCTI1 y6p3aHgta on BpeMeHa ~~11zL- ~ - -

[0 20 30 ([s]

30 H a CJUtUIi je DaT rpacentIiK 3aBHCHOCTI1 y6p3aJ-ba aymiddot a [ms2 ]

TOM0611JJa OJl BpeMeHa AKo je nOleTHa 6p3HHa ayshyTOM06MJIa 611JJa 72 kmh CKl1Ul1pajTe rpacentHK 3aBHshyCHOCTl1 6p3HHe OD BpeMeHa K OnlllG1 je IIyr aYTOshy 2--- M0611JJ npelllao 3a 20 s

4r _

3J K aua ce TI1jeJlO Kpehe no HHepuHjli

Hashy32 npliJlHKOM KOletba ayr06yca nyrHHUI1 nocphy npHjeu KOjl1M 3aKOH01 ce TO 06jawHgtaBa

33 K oja BeJll1llllla KapaKTepHwe IIHepTHocT THj ClJa

illTa he ce necIHH ca KOJl1fUHMa Male Mace npl1Ka3aHUM 34 [fa CJIHilli Kana ce npecHjele KOHau KOjl1M je ca611jeHa

onpyra

35 )ljelaK je KYTlHO aKBapHjYM ca pll6uuaMa H YKpuao ce Y rpaucI01 ayT06yc Ha nojeuliHI1M llHjeJloBIiMa nyra HI1BO BOlle y aKBapl1j~IY IiMao je jenaH OD TpH

06)HIKa opHKa3aHa Ha CJlHUI1 HaBeJlH BpCTe MeXaHI14KOr KpeTaHgta ayr06yca y

CJlytlajeBIiMa npIIKa3aHI1M Ha CJlHUH

36 MO)le10 Jl1 nona3enH oa Inpa3a m = F a TBPJlIITII 11a ~aca H1jeT13 3aBHCH on

CHJle Koja Ha I-bera njelyje II on HgteroBor y6p3aHgta

37 KaKO O)leo ltPoPYlHCaTII npBl1 f-byrHOB 3aKOH npeKo nojMa CIIJle

38 KaKo ce OllHoce Iace Y3ajaMHo njelJyjyhm TIljeJa ca Hgt11)OBIIM y6p3al-buMa

39 no leMY ce pa3JlIIKyjy CIIJIe aKW1je II peaKUl1je

40 KaKo ne ce KpeTaT11 KOJ1Hlla npll IfCTHllaHgtY Boshyae 113 nocyne Koja ce Ha tbl1Ma HaJJa311 aKO

npeTnOCTaBI1MO lla Komma HeMajy BeJTl1kJ lashycy

41 Y CBm -IYBeHm1 njeJJY QJUJIIKO cTaporplKU cent11l030ltp APIICTOTeJI Y3aKOHliToshyCTl1 KpeTal-ha y6paja 11 cJbellehy 6p3HHa KpeTaHgta cpa3MjepHa je nOKperaqKoj

CMJIH npOKOMeHTaPl1llHITe osy APHCTOTeJ10BY TBpalhYmiddot

42 VlTaJllljaHcKII YMjen-lI1K II HaylHI1K JTeoHapllo lla BIIHYJ1 I1CKa3ao je TBpnlhY AK0 CWla 3a DaTOspl1jeMe nOMjepH TI1jeJ10 Ha ollpel)eHo pacrojaHgte MCTa Ta CHJla nOJlOBI1HY Tora HljeJIa noJtjepl1 Ha HCTO paCTojaHgte 3a n0J10Bl1H) Tora

peMeHa lla JIll j e IICnlHHTa OBa TBpnl-ba

43 TOKOM nOJlI1jeTal-ba aSl~O~13 Mace lO t ~l-berOSH MOTOP pa3BI1JaJY peaKTI1BHY CHJIY HHTeH311Tera 40 kN OupenIiTI1

y6p3afbe aBIiOHa

it Ha TaKMI1~leI-bY aBl10MOlleJJapa no611jellllO je TaICMI14ap - KOHCTpYKTOp paKeTe Koja je nOCTHrJJa y6p3aJ-be 50 msl KonHKa je Maca paKeTe aKO J-beH MOTOD pa3BHja CHJIY I1IHeH31ITeTlt1 5 N

4- I OllpellllTe CHJlY BYLle KOjy pa3JHlja e11eKmiddotV ~114Ha 110KOMOTllBa Mace 20 I aKO BYlJe Tepenrn BarOH lace 5 1 Y6p3aJ-be B03a je 1m52bull

TepeTHII ayroM0611TT Mace 15 t nOml311 In CTaHgta JJ1pOBafhll II Y TOKY 8 s noshy

CTJt)e 6P311Hy 20 ms KOl11 KI1 ie HHTeH311TeT BYlHe CHJJe IOTOpa aKO ce aYTGshy106M) KpeTao paSHOljepHo y6p3atfO

47 KalIlOH Iace 2160 kg nOYIIHgte KpeT3J-be C

y6p3aHgteM Koje y TO- 30 S oCTaje HCIJPoshy ir- l~rl ~ llijeJ-beHo 3a TO BpljeMe KalllllOH je npe -- ~ wao nn OJ] 500 m KOHfKIl je IIHTeH31fshy

TeT CIile Koja lljelyje ~ TOK Tor RpeleHa bullIJ bull - bull 0Ha KalJIOH

48 Ha KOll1ua ca rpaheBIIHCK111 laTepl1ja]IO laCe 100 kg JljeJTyje clUJa IIHTeH311shy

L TeTa 100 N ) TOK 10 S KO_1IIIC) 6p311H) lOCTHrJ-IY KOlfua II KOlIlKIf nyr npeshyby 3a TO Bplljele ClaTpaTll lla KOIIIUa nOIIIHgtY KpeTaJ-be 113 CTal-ba iponashyJ-ba

~ H ocopor lace I t npl 6pJIIHI Oll 15 ms Yllapa y llPSO nOKYwasajyhl1 lla ra

oBopn AI(o ce Hocopor JayeTaBII nOCJe 05 s OllpellllTe CI1Ty KOjoM je HOCoshypar lljeJlOBaO Ha Jlpso

(50 CalllYK ~face 350 kg Hana311 ce Ha 33lHbeM ll1jeJlY K3MUOHa Kojl ce Kpche P3BHo-ljepHo npaBo111HlljcKlI 6p31mol J20 killh B03a1 nOIIHhe J13 1(0Il1 II

TOKOI J7 s 6p311Ha KaMIlOHa ce CralmiddotMI HB 62 kmh KO_lIIKa CHJa njelyje Ha caHllYK TOKOl OBor Bpe(eHa npeTnOCTCIBllTe lla K3-IIIOH paBHoMjepHo ycnoshypaBa II lla caHn~ I( lie IOlln flO K31110HY

51 C~ HLlaHa JaXTa jc CBellIpCI(1 GpOll ca ne1J1KIIM jellpo Iwjll nOKpene cYl-IlJeshy

Ba cnjeTJlOcT AKO je II11TeH311TeT clwe koj3 nje_lYje Ha cBe-lIlpCKI 6POll 20 N a J-beroB3 Iaea 900 kg OllpellliTe

a) y6p3albe enelI1pCKOr 6polla

6) aKO CBeIllHpCK[J 6poJ] nOTl3JII In CTaJ-ba HlpOnal-ba KOJlJl1U1 he nyr npellH 3a je1l3H llaH

52 IIrmje ujenojltllue 411je cy lace 40 kg II 50 kg cTOje Ha KJlJ13aJbK3Ma Ha )teshy1lYmiddot DpBa lljeBoj~rHua ce oTl1cKyje Oll llpyre njeBojlJKUe CIUJOM OJ] 10 N KoshyJJI1KO y6p3aJ-be llo6l1jajy njeBojYHue t

10

53 JljelaK Mace 40 kg H caHKe Mace 84 kg HaIla3e ce Ha pacTojal-bY 15 m Ha TJlaTshyltoj nOBpwHHH CJIei)eHor je3epa DjelJaK BYCle KOHooau KOjH je Be3aH 3a caHKe IIje11yjyliH Ha HgtI1X CIUJOM l1HTeH3men 52 N

a) KOJHIKO je y6p3aHgte cal-llU1

6) KomtKO je y6p3alhe nje4aKa

B) KOJl]tKO je Oll nOlJeTHOr nO)Jo)l(ashya njelJaKa YllaJbeHO ~ljecTo Ha KOshy

Me he ce lIie4aK Ii caHKe cycpeshy

CTM

54 TeAl1CKa JIOnTMua Y1lapa Y 3Hll npH 6p3HHI1 011 10 ms Ii 01l6nja ce OIl 3~Illa 6pshy31HOM HCTor I1HTeH311TeTa AKo je cYllap JIOnTl1ue ca 3HllOM rpajao 05 S 11 aKO je Maca nomHUe 50 g OllpellHTe KOJlHKOM CHlOM je rrOTITllIIa rUeJJoBaIla Ha 311ll

TOKOM cYllapa

55 KOJrnIU1 yrao 3aKJIanajy npaBau 6p3HHe II npaBau cl1JJe KOll paBHoMjepHor KPYshy)KHor KpeTal-ba

56 KaKo he ce KpeTanl mjeJlo Koje lBB01UI KP))KHO KpeTalhe Kalla ce npeKllHe KoshyH3U 3a KOjH je Tl1jeJJO Re3aHo

57 CnplIHTep TpY H 6P311110l IIHTeH3I1TCTltl 92 m s llY)K 3T1eTCKe CTa3e KpYgtKHor 06J111Ka

a) AKO je UeHTpllneTaflHo y6p3a~be cnpHHTcpa 38 ms- H3paYYHajTe n011yshynpeLIHl1K 1I11y)t(IIHY aTlleTCKe CTa3e

6) KOH1KO BpeleH3 he cnpHHTcpy 6flTll nOTpe6Ho na JJPcl)e aTJIeTCKY cTa3Y

58 vt3pa4YHltljTe ueHTplineTarJl-IO y6pJltll--bc TIIje_1a Hltl 3CLbltHOM eKBaTOPY Koje nOTIfLIe 011 POT31lHje 3c~ube KOJll1KO II3HOCII UCHTplmCTaJlHO y6p3albe Ha reoshyrpacentcKoj IUIIPI1H~1 01l45 nO_TlynpeLIHI IK 1eLbcjc 6400 km

59 M3TcpIIJa) 0-1 Kojer je 1131lIJ-bIHa CBelllpCKltI COHD3 KOjOM ce ynpaBJba ca 3eshyUbe lO)Ke 113 113llP)K11 UeHTpllnera1HO yGp33l--bC 01 200 In so KOJJIIKO H3HOCH MHHI1MaJJHl1 nOJlYllpe4HHK Kpyra llY)K Kora COHll3 IO)(C lla ce Kpetie 3lla He lloIJe 110 l--beHOr oWTet1elba J1 HTeH3HTeT 6pJII He COHle je KOHCTatlTaH 11 H3HOCl1 30000 km s

60 LlHjcTe cjeml -Ra CTOJllIUII BawapCKe BprewKe Koja ce neT nyTa o6pHe OKO cBoje Oce Y TOKY jeilllOl MI1HYT3 AKo je pltlCTojaHgte CTOJlI1Ue 011 oce BpTeWKe 10 M H3paLIYHajTe 6p3~IHY II ueHTplmeTaJlHO y6p3al--bc 1lieTeTa npeTIlOCTaBJbajynl1 ll3 ic KperaHgte paBHoMjepHO

61 UIIPKYCKH apTHCTa B0311 6111111KJ1 JIY)K YHYTpawl-ber 3~Illa Jll1MeHOr 6ypeTa KpeTaJ-be ce OllBJlja y BepTJIKaJlHoj paBHI1 AKo je pallHjyc 6ypeTa 27 m Ollpeshy

llI1Te MHHIIMaIlHY 6P311HY apnlCTe npl1 Kojoj he OH OCTant Y KOHTaKT) C nollshyJloroM YHajBHwoj TaYKJ1 cBoje nyraJ-be

I

62middot AyrOto6~fJl Mace 1600 kg YJla3H y KPl1BlfilY nOJlynpelfHIiKa 190 m K OnJ-tKO Mopa na 113HOCII MHHHM8JlHa BplljenHocT KoeqmulljeHTa Tpel-ba H3MeJjy ryMltI II accp8JlTa Jl3 ayrot10611J1 He 611 CJ1eTHO C nYTu 6P31HIa ayroMo6liJla je KOHCT3H shyT3 Ii IHHOCI1 20 In ~

63 A yroM061U1 ce nel-be Ha 6PIlO K30 WTO je Ilpl1Ka3aHO Ha CJIHUI1 Kom1Ka je

MaKCJMaJlHa 6p3HHa KOjOt1 ayro106J1J1 MO)Ke Jla ce Kpehe a Ila OCTaHe Y KOHshyTaKTY C nOuIOrOl y Haj Bllwoj TaIKJ1 cBoje nyral-be

I

FpaeuwauuOJ-LO ilOfbe

1 lla 111 ce Tlljeta IOI IUO10BC1T11 Oil nej crB3 rvaBllTashy

UUOHe cltJle

2 Kalla 611 TIIjelo yll3Jo YTYHe KOjJI cnaja It1mje Kpaj shy

Ibe raLIKe 3CIJbIlHOr npclHIIK3 rDje 611 ce OHO 3ayshy

CT3SJ1J10

3 Kalla TIIjela Hlfey nomnpTa Will o6jeweH3 raje ee CII shy

iey npanUII no KojUla OHa naIlajv HU 1e~Lb

4 160r Iera y6p3al-be rpaBIITawloHe CILle He 3UBI1CI I Ol

Iace nljela

5 Ha Tepa31lJata je ycnocTuBbeH3 p3sHure+a Kal3 ce

Ha jenHo1 Tac) H31a3JI Tlljeno a H3 1pyro)1 orosupa shy

jyhll TeroB~1 lla rill 611 OBe Tepa311je 61l1IC ~ paSHoreshy

gt1-11 I H3 Mjeeeuy

6 y 6eCTe+IIHCKO~1 CTaHgt~ KyrlIIU3 je o6jeweHa 0 KClHau WTa ne ce )leCrUH ea

kyr111UO1 aKo je II3BeneIO In paBHOTegtKHOr no10)l(aja

1 aWTCl ce Ha Behll1 HallIOpCKIIM BIICIIH31a noshy

CTll)KY 60Jbl1 pe3Y_lTaTl1 y CKO yn31gt

8 AKo ce y lien Ta4K~ rpaBIITaUIfOHor nOJ1a YHeshyce Tlljelo lfenpl1 ny-a Hehe Iace KaKO he ce

npOljeHITII IIIITeH31ITCT rpalHITaUIIOHOr nOb3

~ nlJ raLIKIt

9 n ocrojll JUJ pa3J1IIKa 113Mel)y re)l(llHe mje1a II 3e~LbI1He Te)l(e (rpaBWraUl-lOHe

ellJIe) Koja llj eJlyje Ha TO Hlj eJlO

10 M Hjel-ba ~Il ce ie)KHHa HljeJla aKO ce OlIO agt O pelle y6p3aHo y XOPH30 HTaJlHm npaRUYJ

11 3awTo je IIHTell3l1Ter 3 eMJbllHe Te)(e Benl1

Ha nOllY Hero Ha eKBaTOPY

12 lla JlH npTlrulaHa CHJIa 3eMJbe Ha THj enO I1WIe3aBa npl1 npenacKY rnjena Y6ecshy

TegtKlIHCKO CTafhe

13 Lla JTH ce MO)f(e H3MjepIITH Maca 111jeJ1a nOMony Bar e -lHj11 j e oneer MaJ-bH on Mashy

ce Tl1j ena O fipa3JlO)l(HTe OllrOBop

14 lloBjeK CTOjl1 Ha BarH y JlI1qny YnopellliTe nOKltl311BaJ-be Ka3aJbKe H3 Bani Y

ClbelletulM C~ITYal(l1jaMa a) JTllqgtT ce H3Jla311 y CTaJ-bY f-1IJpOBaJ-ba 5) Jll1qn ce Kpene paBHoMjepHo y6p3aHo ca y5p33-beM YCl-ljepeHII l OepTIshy

KMHO HaHIDKe B) JlHltpT ce Kpene paBHoMj epHo y6p3allo ca y6p3albeM YCMjepe Jll~l epTII-

KaJIHO HaBHwe r ) 360r lGlnaJ-ba Ka6JIa JlHqJT CJI060nHO nana n) JII1ltpT ce Kpeoe KOHCTaHTIlOM 6p3HHOM

11=0

a=O altg I agtO a ~ g 1=con51

0 1 11o ~ I

7Jbullfmiddot I ~I

~ ) 6) B) JJ)

15 APIICTOTe~ HaBOllJl TllPllI-bY OllHOClI Te)I(JIHa (118a TlljeJ1 a Koja CJ106011HO nashyllajy) cy ofipanlO cpa HljepHII HpeleHY naua AKO TIIjello ollpebeHe Te)(11He nashyJ3 ca lleKe BlCIIHe 33 HeKO npllje1e Tllje10 llBOCTPYKO Behe TegtKIIHe nalla ca IICTe llllCllHe 3a ynma Kpahe BpIIJele lla 111 je ApJlcToTef1 y npawl

16 Ca IICTe BHCI1He IICTonpe~leHO je 6a 1 leHo jenHo TIljelo Y XOP1l301lshy

TalJHO 1 np3BUY a lpyro je Icnyshy middot0 -

WTeHO na CJl060nHO nan3 Koje

THjeJIO tle npllje nocnjenl Ha xashyPl110llTaJlHY nOl11ory

17 113 Jill K011 Kocor XII ua OplIJIlH- 1d-1Ha Ko~mOHelfld 6p3lIHe MOshy gtKe na 6yne jellHaKa HYJlII

I ij Kana KOCO XJlTH ~TO TlljeJlo 110shy

CTHgtKe ilaKCHMaIJHY BI1CliHY

19 H a CJlllllll cy npI1Ka3aHe nYTal-bc pll CPyn6aJICKe JlOrne Koje je TOshy

KOM rpeHI1Hra I1era)f(ltpao r OJl laH YnopenMTe Bplljete Koje cy OBe JIOnTe npOBeJle y Ba3llYXY Kao II XOPJ130HTaJIHe KOMnOHeH Te nO-leTHe 6p311He

r )

J4

20 lla JIM je npBa KOCMH4Ka fip3HHa jenHaKa 3a esa He6eCKa ntj eJ1a

21 4 eKHn IIcnYWTeH ca CKene Ha rpanl1JlHWT) Yllapa y Tl0 6P311HOM 24 ms AKO npernOCTaBtlMO na yeK11h CJ1060l1HO nalla OnpenliTe a) llplljeMe Tpajaloa CJl060nHOr nana 6) BI1CIH) ca Koje je I eKHO nao

22 JIoma I1cnYWTeHa ca Bpxa Kocor TopJ-ba y nll3l1 CTIDKe Ha Tno 3a 33 s Onpel1I1TH a) 6p]1l Hy JlOfiTe npt ynapy 0 TJlO

6) BI1CIIHY Kocor ropJ-ba y nM31i

23 TujeJlo cn060llHo lIalla 11 y jeJlHOi1 r peHYTKY Hla 6P31tmiddot 11) ) 2 ms KOlIlKa je 6p3l1Ha mjeJla nOCJlllje npBe ceshy

KYH11e y onllocy Ha Taj TpeHyraK

24 Ha Mjeceuy Tltjelo Koje c1060l1110 naJla ca BIiCIlHe 5 m CTl1Ke Ha nOLlory 3a 25 s OnpenllTe jatlllHY rpaBIITa UIiOHor nOJba Ha nOBplUIIHII Mjeceua

25 JanaHcKl1 ryplfcTa KOjll CTOJU Ha BpXY Ajcpelolle 1lt1middot1e ItCnYCTl qoToanapaT AKO je IlIICIIHltt AjltpeJ1ORe KYJle 300 m nocll1je KO1I1KO BpeleHa he cpOToan3paT CTllhll

H8 TlO

26 WTan 3a neual-be KOjll je ca Bpxa Mocr a BllCOKor 45 m 11CnyCTIIO pIl601JOBau ynaua ~ llaMau KOjl1 ce Kpehe no je3epy KOHCTaHTHOJl 6P3 ItHO 1 Y rpeH)TKY IIcnYWTamiddot Iha WTana lfaMau je 6110 ~ nCLbeH 12 m OA JjecTa Ha K( Me je WTan ynao y 13 taU KOlIlKa je 6pJIIHa yaUa

27 Tllje~o je c106onHo nanal0 6 s KO1HKH Je npebeHI1 nYT TlIjela y nOCbeAJ-boj CeIlt11-l111l KpeTal-ba

28middot vh XeJ1l1KOnTepa KOjM ce Kpehe lleTPIIKCL1HO HaHIDKe 6rshy31lHmi 14 ms llCf) WTell je naKer Oca1 ceKYHll1 no llCnYWTatty naKeT CTlLgtKe H3 TJlO Ha Kojoj RIICI1HI1 C

C7~~HLla]11O xell KOnTep) TpeH)TKY IlcnYIUTal-ba nflleTa)

29 CTpfljela OllaneTa 13 JlYKltI BepTHKarlHO J-IaBHwe noshyCHt)le BltCI1HY 1225 m OnpenIlTe j

a) Rpl1je-le Koje je 61lIJO norpe6Ho cTplIjem Ia nol)e no Hajllllwe Ta4Ke cnoje n)T3I-be ~-shy

6) 6P31lHY cTpl1jeae nplt l-beHOi1 ynapy 0 nOMory B) 6p311HY cTpHjeJle Ha Kpajy leTBpTe ceKYHlle KpeTa shy I

Ha I 30 nal106paH3U llCKa 4e 113 aDHOHa H c]1060nHO Dalla 50 111

no OTllapatty nallo6paH3 nano6paHau ce Kpehe paBHashyMjepHo ycnopeHO y6p3a~beM 2 ms2 AKo n3Qo6paHalJ aTepl1pa 6P3HHOM 3 mis OJlpeIII1Te KOJlMKO je spel eHa

pOBeo y Da3D))y

31 JIonTa je 6a4eH3 oepTTiKaJIHO HaBI1We ca 3rpa)Je BHCO)(e 134 m n04eTHOM 6pshy3J1HOM 25 ms AKo J]onT3 npH nauy npOM3WH 3rpa)ly H nanHe JJJipeKTIlO Ha 3eMJbY O)JpeQJ1Te KOJlI-fKO BpeMeHaie JlOnTa npoBeJ3 Y B33nyxy

32 KowapKaw KOjJ1 ce HaJla3J1 Y 6J1II3HH II Kowa CK3 l le

76 cm BepTl1KaJlHO HaOHwe )Ja 611 Ylpa6110 nonTYmiddot 011shypeUHTe

3) YKYnHO BpMjeMe Koje KowapKaw npOBene Y Ba311YXY

6) Bpl-fjeMe Koje KowapKaw npOBelle Ha BHCHHII Behoj

OU 60 cm

33 Uje4aK Mace 60 kg HaJla311 ce y JlI1CPry OllpenHTI1 Te)(l1shy

HY Jlje4aKa aKO ce

a) JlHCPT Kpene paBHoljepHo np3BonHHHjclGI 6P31fHOM

10 ms 6) J1HQJT Kpehe paB~JOMjepHo y6p3aHo y6p3aJ-beM IIHshy

TeH311TeT3 2ms1 YCMjepeHI1M Sepl1KaJlHO HaHI1)1e

34 3a KpOB lmlnltl 33KaleHa je HellCTerJbHBa HIH Ha KOjOj BHCII MeTaJlHa KyrIHua Mace 100 g I1HTeH3HTeT MaKCI1 shy1311He C Hle laTC31HIX1 KOjy H 1fT MO)Ke 11a ~1311p)K Hje 15 N Lla 1 If he CC HilT npeKliHYTl1 aKO

i1 ) 111cpTCl06oJHO nana

ll) 1I1jJT ce Kpeflc paBHoMjeplio y6p33HO y6p3aJ-bel IIH shyTeH3HHTa 7 In YCMjcpeHHM Bepnl Kai HO HaBI1We

~

L-1

35 C Tpem1Ua 33 mIKana 6alJeH a je OplnOHTaJJHO ~ rrpaBUY ueJlTpa teTe P nOlJeTHa 6p3ltHa c-rpeJJlme II1HOCI1 J0 m gt CrpeJJlUa Ylapa y leTY YTalJKII Q Koja ce HaJla311 113 J-beHO1 o6ony

a) KOJlIIKO I13HOltI pacTojal-bc PQ aKO je CTpell1ua ynaplIJla Y MeTY 019 S H3shyKOH WTO je 5aclcHa

6) KOJIJ1KO je 011 ~CTe 6110 YJJalbCH IIrpaLI nl1Kana v TpeH YTKY KMa je 6aUll0 cTpeJ111 uy~

36 J10nTa le JOTpbd 11 ItBItUII OpIIJOHTarll-lOr crOJa BICOKOr 1 M JIonTa LOIlII shypyje no1l Y TalJKIt lJllje pacTojaJ-be (y XOPl130HTaJlIIOM np3Buy) on I1ll1iue CTOla II1HOClI l2 ~1

a) KOJJJfKO Bpe MeHajc ~onTa npOBCla y B331lYXY

6) KOTJIIKI1 je 6110 11HTeH311TeT 6p3JlHe JlOnTe HenOCpe1lHO npuje Hcro WTO je OH a 1l01lllpHYJJa nOJLlOry

37 I1rpa l 6ej36oJJa 6aua Jlomy y XOPl130HT3JlHOM npaBUY Ka 18 m YllaJbeHOM XBashy

TallY n OlJeTHa 6p311Ha JlOnTe je 150 km h

a) KOJJI1KO BpeMeHa rle 6HTI1 nOTpefiHO nOnTI1 )Ja npel)e npsy nOJlOBHHY pashycTojaJ-ba no XBaTalJa

6) AKO je JJOTlTll 1136alJeHa ca BIICItHe Oll 2 m Ha KOjy BI1CI IHY xnaTIl-J Tpe6a na nOCTaBH PYK3BI1J() lla 61i je yxaaTllO

16

38 nywKa je YCMjepeH3 XOPH30HTaJ1HO K3 30 m YllaJbeHoj Menl MeTaK Y)Japa Meshyl) 2 em IIcnon UI11baHe TaLTKe

a) KOlI1KO speMell3 je MeTaK npOBeo y aa3JIYXY 6) K OJl It Ka je 6JIlla nOleTHa 5p311Ha MeITa

39 11jelaK SPTll KaMell rrpltCIBpwheH 3a HIlT ll))I(I1He 15 m K allieH ee Kpehe Y xoshypl130 HTalHoj paSHII Ha BlICHHlt 2 m Oll nO)Ll0re 1l0MeT KaMeHa HaKOH WTO ce

HilT npeKIlHe InHOClt 10 m Onpe)JI1T1 ueHTpltneT3JlHO y6p3al-be Koje je Kashy

MeH IIao npllje npeKlInaJ-b8 HI1TH

40~ Vfrop je JOC~OHaYT Ha PYCKOj CflC~lllpCKOj CTaHIIUII VlCTOK If Koja KpY)l(Y1 OKO

3CMbe Ha BIICIIHI I Oll 520 kill 6P311HOM Oll 76 kllls 3 HajyfH1 ll3 je I1ropoBa

Maca 79 kg lupallYHanl ueHTpuneTaJlHo y6p3aJ-be KOc~wHaYTa Kao Ii 11HTeH311shy

TeT rpaBlnaUllOHe CIl e KOJOl 3eMba J]jc1Yje Ha J-beHa nonynpelHl1K 3eMJbe

je 6400 km

17

3 Pa6HOUl eJICHa CUlafbG ulujew ~~----------------~

l MO)f(e nM nrjeno 6l1Tl1 y paBHOTe)l(f aKO Ha Imiddotbera lIj eJlyje caMO j euHa cHJIa

2 Ha THjeJlo njenyjy JlJ3I1je Cl1JIe KOjH je YCJlOB ua THjeJIO 6yue J CTaHgtY paBHashyTe)f(e

3 Kojl1 yrao 6n Tpe6ano ua 3aKJIanajy npaBUl1 uBl1jy clwa KOJlCTaHTHlfA HHTeH3I1shyTeT3 TaKO na pe3YJlTaHTa HMa MaKCHM3JlaH I1HTeH3uTeT

KaKo ce 11eqlllHllwe llpynl I-bYTHOB 3aKOH aKO Ha THjeno lIjeJlyje setlll upoj

CIIJla

5 Ou 4era JaBIICIl KoeqH1Ul1jeHT Tpel-ba H3Meoy mjeJla

II nOllJlore

6 311 ce CTaBJbaj) ~aHU1 H3 TOltJKOBe ano~106ILla

3awTO

7 Ha CrlHUH je npIIKa3aH JieYaK ca _1YKO1 II CTplljeshy IO~J Koje lIecentopwlcaHo Tltjelo 113331IBa CIIJI) elashyCTlItIHOCTII

8 3awTo fiUUHJlKJlllCTa Y TOKY TpKe nosllja TIIjeno 11

cnYWTa rJlasy

9 360r Jera ce KJllllHe Kami H CHgte)(He naXYlbllue

Kp03 anlOccentepy Kpelw paollOljepHo npaBOJIIIHujshyCKIf

Q w f ~ gti

I I gt gti

~ ~ (~ I ~ I I~t ~ ~ I bull bullbull bull bullbull bull t bull bull I

bull bullbull I tl I 11 ~

middot11

1O TIOn~1OpHHla ce Kpebe paBHo~ljepHo npaBOJlIIHl1jcK~1 Kp03 BOlIeHY cpelIlIHY K oje CBe CJwe njeJTYjy Ha nou~lOpHJ1JO

18

1t K aKo ee Mlijel-ba 6p3HHa a KaKO eMa omopa Ba3uyxa Kalla nauo6paHau OTBOPH nauofipaH

12 K JIliKep ce Hana311 Ha JlH) nOCYlle HanyHgteHe BOllOM Koje CBe c~lJle njenyjy Ha KJlIfKep

13 3alllTO oco6a ca centOTOrpacentl1je He IIp)Kll lJeKlh Ha cpenHH~1

JlpWKe

14 ApXlIlIeu je peKao LlajTe J1I1 OCJloJ-lau 11 ja hy n011I1 shynil 3eMJbYmiddot 0 6jacHIITe OBY ApXI1MellOBY ~llIcao

15 3awTo 6paBa Ha BpaTHMa Hllje yYBpwlieHa Ha Cpeu11 shyiiI span 11Jl1l ~IO)l(Jla 6Jl11)f(e wapKaMa

16 non Koju~1 VCJlOBI~la Jljelo Kpehe TpaHCJ1aTOpshy

HO

17 nPI npaBOJlIIH ljCKOl KpeTaHgtY Ha T1je~ 2 gt

MO)f(e ua nje~yje CIl~a IICTor II HTeH3lfTeTa F r5 N Ha yeTllpll Ior)lia HaYIIHa Kao Ha CJlII shy F

liIl Y 1lt01 CJlY4ajy je CIUla Tpelba HajBeher

IHTeH3HTeTa I ~ 18 HaBeUme npJ1jepe aJJaTa (opyoa) Y~lja C ~f- ~~~~~~riV(~~~X111~1~

ynoTpe6a 3aCHIIBa Ha nplHllllrry nolyre

19 Ha TI1jeno njeJlyjy uBl1je CliJle noJl ~TJIOM 90deg OupelllTe pe3YJlshyTaHTY OBHX CILla (rpaqHIYKIM J1 paqyHcKli n)fel) aKO jellHoM

nonjeibK) ouronapa 11HTeH311TeT CIIJle OJl 1 N

20 lIBllje CJLlle IfHTeH31fTeTa 12 N II 8 N ujenyjy Ha TIIjelo Mo~e Jll L11 HTeH3HTeT pe3YJlTaHTe II MaTI Bpl1jellHOCT

a)4N B)JN 6) 20N I) 16 )

21 lIna KOl-b3 BYKY HaToaapeHu tlaMau Kp03 YCKJf KaHal KOI-bH ce J-I3Jla3e

Ha cynpOTHIiM 06anaMa KaHana I

CBaKH Byye KOHonau CffJlOM HHTeHshymTera 1800 N _ AKo KOHonUl1 3ashy1lt1anajy yrao OJl 60deg Ha1)me ( rpashy

CPH4KJ1 II paYYHCKH) pe3YJITaHTHY Clury Koja njenyje Ha LlaMau

19

~2 Ha CJTHLUf cy npHKa3aHe CHlla KOjOM rMCep Byqe CKH jawa no pHjellH H rpaflHTaUHOHa cJ1JIa Koja J]jeJTYje Ha CKl1jawa Hal)HTe pe3YJlTaHT) 0lH1X nB~tjy CIUla aKO l-btfXOBH npaBUI1 3aKJIanajy yrao 120middot JenHoM

noLIjeJbKY Ha CJlI1UI1 onrOBapa yIHTeH31ner CI1Jle OD 100 N

~3 PanH1-flC Byqe CaHDYK no centgta6pl1~KOM noJlY l-la callmiddot

DYJlt J]jenyje 1 cl1JIa rpeJ-ba Ha CJlI1U11 je npH~a3aHa

pe3YJlTaHTa OBliX DBl1jy cJ1JIa (061)be)f(eHa ca R ) Kao ~ It 1Ii CHlla Byqe (06l1Jbe)l(eHa ca F) rpacpMYKIIM nyTeM

onpelUlTe CHJIy rpeJ-ba ~~ ~4middot H a CJlHUI1 j e npl1Ka3aHa CIiJla it KOjOM PaDHIiK rypa

MOTOPHY KOCI1JlJillY no TpaBl-baKY Kao H BepTI1KaJlHa KOMnOHeHTa OBe C1HIe F AKO je yrao 1i3Mel)y npashyBaua OBJ1X llBHjy CI113 60 a jenHoM noJ]jeJbKY Ha ~c-+R F CJTI1Ut-I ol1roBapa IIHTeH3HTeT CILle 01120 N rpacentHYshyKJ1M II paYYHcKI1M nyreM Ol1pellITe HHTCH311TeT xo shy

n301ITaQHC KOMnOHeHTe

25 I-hpayYHajTe HHTeH311TeT C~Ule Tpel-ba KJlIt3aJ-ba 113MeIJy canyHa 11 XOpI130HTaT]

Hor DHa Ka11e T e)KJ1H3 canyHa je 1 N a Koecp llulljeHT rpel-ba j e 005

26 CILla Byqe J10KOMOTHBe je 150 kN a cWla rpel-ba ~13Meby TOYKOBa ~I WHHa npH

KpeTal-bY je 130 kN KOJ1l1Kl1 j e IIHTeH31neT pe3YJITaHTe II KaKBO je KpeTal-be

Ko~m0311 uuje

27 HaTOBapeHe caHKe 1I~lajy Te)lnlHY 5 kN K omlKH HHTeH3HTeT cJ1Jle Byqe Tpe6a

a 6yue ua 611 ce c3HKe KpeTaJle CTaTJHOM 6P3HHOll no XOpIBOHTaTHoj 11eDeHoj

nOBplilliHIf Koecentgtl1LlHjeHT Tpel-b3 je 002

28 iljelaK By~e 3aBe)I(Jbaj KI-bHra Mace 20 kg no XOPU30HTaJJHOj nOllpWUHl1 CTOl1a AKo

Je HHTeH3UTer CllllC Byye 80 N 11 JltI-bHfe CC

Kpehy paBHoMjepHo npaBOJHlHlljc KII onpemiddot

D1lTe KoeqmuHjeHT Tpel-ba B3Meby KIMtra II nODJlore

29 AKO Ha opMaH nyH Herna rrjeJlyjeMo CHJlOM 11HTeH3HTeTa 100 N 01-1 ce Kpehe

paBHoMjepHo npaHOJlHHJfjCJltl1 no XOpJ130HTaTJHOj nODJl0311 AKo 113 opMaHa 113shy

BallHMO Bern OH he ce y CTal-bY llRHaM I-lyKe p a13HOTC)j(e HahH aKO Ha I-bera Djeshy

nyje10 CJ1JIOM Ml-ITeH3HTeTa 80 N A KO cy npaBUH nOMeH)THX cJ1JIa napaJIeJlI-I11

ca nOIDIorOM ODpeDHTe Macy Berna KOjl1 ce HaTJa3ll0 Y opMaHY Koecp1Ul1jeHT Tpel-ba 113Mel)y o pMaHa 11 n Olla je 04

]0

30 M~lJIaH B1Je caHKe no XOPH30HTaJlHOj 110nplllllHJ1 33J1el)eHe YJll1Ue CJ1JIOM HHmiddot TeH311TeTa 5 N KOlJfKli je I1HTeH3HTeT ByqHe cJ1JIe KOjy fiH MaJlaH Mopao ua ynoTpllje6H aKO Ha caHKe cje11He I-beroaa Ulal)a ceCTpa JJparaHa YJ1ja Te)j(HH3 je 300 N K oecentgtl1uujeHT rpel-b3 113Meby CaHKJ1 H J1eDa jc 01 CMarpaTH 11a ce

caHKe y 06a cll1Jaja Kpehy paBHoMjepHo npallOJlHHl1jcKII

31 B03ay HCKJbY-lyje MOTOP ayroM0611J13 U HarJ10 3aKOQH npu 6P3HHH ayrm-106~lJIa 72 kmh KOflHKO he speMeHa npohll uo 3aYCTaBJbal-ba ayroMo61middotUla aKO j e KOshy

ectHIUHjeHT rpel-b3 m = 0 60

32 3u11ap pa111 Ha KPOBY lHjll 06JUiK je npIIKa3aH Ha CJlHUI1 AKo j e ~Iaca 311n3shy

pa 80 kg ollpe11HTe 5mi~ a) HHTeH3HTeT CHJle 3erMbHHe Te JKe KGshy

ja DjeJJYje Ha 311Dapa ~ +- 1Lm

6) llY)(J1HY KpOlla IJ l IIHTeH3JITeT 3KT1IFlHe JltOMnOHeHTe

3eMI1IlHe Temiddot)j(e

r ) IIHTeH311TeT HOpMalJHe KOMnOHeHTe

3eUbl1He Te)j(e

33 AKo Hit3 KpOIJ H3 npeTXOllHor 3anaTKa paBHoMjepHo npaBOJlllHlljcKl1 KJIIIJH

laYKa KOJllIKlI je KOecentlIll1iJeHT TpeJ-ba 113MelW TIljeJla MaIKe H Kpoaa)

34 UlljeTe KUI3I1 paBHoMjepl-lo npalloTJIIHlljcKII HII3 ToooraH BI1Cl1He 3 m 11 nYJKl1shy

He 5 m AKO je laCa )ljeTeTa 15 kg 0l1penl1T11 IIHTeH3HTer CJlTJe Tpel-ba Koja Djeshy

lyje Ha lllljeTe nplUlllKml l-beroBor KpeTal-ba lin T06oraH

35 TlljeJlO Te)l(I1He 200 N Kpehe ce Y3 CTpMy pashy

BaH craTJHOM 6p3IlHO~1 CI1JI3 Tpel-ba H3MeQY

TIljeJ1a If CTplle paBm1 je 50 N AKO je BMCH

Ha crpMe paBHH 4 H)Ta Mal-ba on l-beHe lIYAOIshy

He Ol1pellllTe HHTeliJIITeT BY4He cllJle

a

36 iljeBojlJUUa lace 40 kg cnYWTa ce HI13 6a3eHcKH T060raH AKO je T060raH y

Oll1I0CY Ha XOPH30HTaJlHY nOlVlOry HarHyr non yrJ10M 30deg 11 Koecpl1UHjeHT rpeshyI-ba I13HOCII 05 ODpe11HTe

a) aKH1BHY Ko~mOHeHTY clme Te)f(e Koja njenyje Ha nlljeTe

6) HOPMaTJlfY KOMnoHelrry CUJle Te)f(e Koja DjeJlyje Ha nHjeTe B) c~ury rpel-ba Koja ce antlpe rrjeTeTOBOM KpeTal-bY

r) KaKO ce l1~ljeTe Jltpehe

37 vf3paf)HajTe y6p3al-be mjeJIa Koje KJI113H no CrpMOj paBHII aKO je l-beHa BHCIImiddot

Ha jenHaKa l))KHHH OCHone a KoecentgtHul1jelfT Tpel-ba Ha CTPlIOj paBHI je 020

38 gtKeHa Ha paMeHY HOCH J1aKH lllTan Ha ql1jeM j e 3aDl-beM Kpajy 06jeUJeHo BeDpO Ca MJmjeKoM Te)KI1He 100 N PacTojalbe 011 3anl-ber Kpaja WTaITa no )f(eHI1HOr paMeHa j e 15 cm KOJHlKI1 MOMeHT cJ1Jle J]jenyje Ha WTan

21

II

39 P060T Y centa6pHUli ayrmro6HJla MeX8HHlIKOil PYKOM APgtK11 KapocepHjy TC)f01lie I KN AKo je MOMeHT CHJle KOjOM KapocepHja ayroM06HJla njenyje Ha po6oTa 1500 Nm KOJTHKa je 1(y)I01Ha MexaHl1 IKe pYKe

40 ilje4aK Te)(J1He 300 N II J-berOB TaTa Te)f(1He 800 N HaJla3e ce Ha KJlaUKashy

JlHUIi npHKa3aHoj Ha Cll1lU1i AKO je pashycTojaJ-be 0U Ta4Ke OCJlOHUa KJlaUKarH1shy

ue AO TaTe 15 m OllpelUITe paCTojatbe Oll TallKe OCJlOHua KJlaUKaJlHue AO Lljemiddot 4aKa

41 Ha KpajeBliMa rpelle (KJlaUKan uue) lJY)KH He 4 m (xoMoreHor cacTaBa ) cjene

OTau 1 MajKa Gnu liMa Macy 70 kg lajKa 60 kg foje Tpe6a lla cjellHe tbllXOB CItH na lla 6yIlY y paSHOTe)lH ellH 11la Iacy 20 kg

42 Ha ClJI1UH je npIIKa3aHa AlteHa Koja nOllll)le Koshy

mlua ca n11jecKo~l 4Hja yKynHa 1aca 113HOC1 50 kg KOJIllKO1 CIlllOM )l(eHa ~Iopa njeloBam

a KOJTI1ua lla 611 nOlllfrJTa ollal TepeT PaCTojashyJ-be OA TallKe OCJlOHua KOYllua AO pYKOXBaTa H3shy

HOCH I m nOK Je ueHTap laCe KOll1ua Oll Tal[shy

e OCJJOHUa YllabCH 60 cm

43 Ha OCHOIlY nOllaTaKa Ha upTe)f(Y onpellirre KOHshyKII IIHTeH3HTeT CILlJe opa ua pa3B11le I II will

PYKe lla 61 oup)Kao paBHOTe)KY Tepel) Q = 80 N allKa C j e Tal[Ka OCJJOHua a Ta4K3 A je HanauHa

TaIKa Te)I(J1He Tepe-ra Ta4Ka B je HanaAHa Ta4Ka

Mll wHna pYKe

44 lla 611 ce opax CJlO1gt1I10 nOTpeoHo je ua Ha J-beshy

ra ojeJJYje C11JJa I1HTeH3~1TeTa 40 N ca 06je cTpashy

He (nouaml Ha CJlI1UII) KO1HIKII je IIHTeH31neT Clele F KOjol je nOTpe6Ho njelJOSaTIl H3 KpUKCIshyHIIUY 11a 611 ce opax CJIOMIIO

45 llpBeHH WTan je uyr I m f oje y 0n110CY Ha

uetrrap WTana MopaMo ua nOCT3BI1MO OCnOHau na na Tepem Te)HHe 5 N 11 15 N KOjl1 Bllce Ha

KpajeBI1Ma WTana 6YllY y paBHOTe)ltlI

46 XOMoreHl1 UlTan ny)KJiHe 100 cm BIICII Iia KOHllY KOjl1 je Be3aH 3a ueHTap J-beroBe Mace TlijeJlo Teshy

)I(ffiIe 2 N o6jeweHo je Ha paCTojaJ-bY J0 cm on JllijeBor Kpaja WTana uOK TIljeno Te)I(JIHe 3 N IlJ1Cll Ha paCTojaJ-bY 20 cm Oll Ta4Ke BjeWaHgta npshyBor TepeTa KomlKa je Te)(l1Ha Tera KojH MopashyMO o6jeCMTl1 Ha paCTojalhY 70 COl ou Jll1jellor Kpaja WTlma na ua WTan oyue y paBHOTe)lH

)

a=4p

~ p

Paq eHepiuja u cHaia

1 HaBenl1 npHMjep pana np lle~IY CIVla MlljeJ-b3 06Jl11K

THjeJlYmiddot

2 Koja CllJIa SPWI1 pall llOK TI1j eno CJl060UHO nana

3 Y KOl CJJYTajy ce MO)e ynoTPHje61ITII centop~IYJla A = Fs 3a 113paryHaBal-be ~leXaHIll[KOr paua

4 IIp)Kehl y PYUlI l)a4Ky Top6y Mace 55 kg YlIeHI1 K ~HIPshyHO CTOjl H8 ayr06ycKoj CTaH HUI I leKajyhl1 npeB03

25 min KomlKII pan IlPWII YleHII K

5 Ha CY11U11 je npIIKa3aHO TlIje)1O Koje ce Kpehe c1llljesa ) leCHO YCHIIM HaBeneHwI c1)llajeslfla Ha HljelO njeshy

T)je CIUla HCTor IIHTeH11HeTa Y CBa yeTHplI cl)Iaja Y Kojel 011 HaBelleHllX c1)LfajeBa je pall CI1JJe HeraTllIlaH

I IF~ I ~ I Flo -~ ~ - _ I ~ _ _

~ ~~ ~ ~ ~ ~~ -~-- ~~~-~- - ~ - ~ ~ ~~ - ~ ~~-~- ~

6 Ha CJlI1U1I je npl1Ka3aHO TlljeJlo OKa4eHO Ha

eJlaCTlfYHY onpyry TlfjeJlo ce Kpehe BepTII Ka~HCl HaHU)Ke a 3aTltl In HajHIDKer nonDshy)Iaj a Kpehe ce HaBllwe OllfOBOpllTe

a) Y Km1 cTI)-rajy C11Jl a eJJaCTlf-IHOCTH llPWli

n03HTlmau pan a Y KOM HeranlBaH

6) Y KOM CJlY4ajy je pall 3eMJb~IHe Te)le noshy

3HTl1BaH a Y KOt HefaTHBaH

MpaB nonI1)1e MPBHUY XJbc6a Ha BPX MpaBHshyJ-baKa KYIlaCTOr 06J1I1llta Kao Ha CJlJ111H Ynoshypeulrre pan KOjH Mpall 113BPWH npH cnl1panshy110M nel-batby y3 MpaB11J-baK ca panOM KOjH OH H3BPWH npH npaBoJll1mljcKoM neHgtatby Ha BpX

23

20 _ 4~ -shy

- ~-~-~~~~~~~ ~

a gt ~ ~ Fbull ~ F

I)

L---

~

Fg

~ K OJll1KIi paJ] npH KpeTal-bY K)TJTl1ue no XOP ~I-

30HTaJlHOj paBml BPWl1 3 eMJbUHa Te)J(a

9 bll6mloTeKapK3 nOUl)(e Kl-bllre Cll HII)J(e Hltl BIIWY 1l0Jl1IUY na J1I I pltla KOj l OHll BPW l np l -~ ~ ~ ~- ~~-~~~~~~ ~middot~~f ~ 1I0J]H3a1-bY j eaHe Kl-bllre 3alll1CII OJl

a) I ace KI-bUre

6) TeJKHHe Kl-bll re

ll) BICllHe ropl-be nOlllue y OlIlIOCY 113 lIOHY

r) BpCMCHa 3a KOJe 6116J1IIOTeKarK3 nO1llrHe

KHllIl)

IL l nyr3lbe n o KOjOj 6I1fi-1I10TeKapK3 1l0111iKe

K I-bll ry

0 nPCTIIOCT3SIIO l3 ce 3eLba Krehe OKO C YH ua IT)Tal-bOM Koja je ILleLLlaH Kpyr lla 11 rpamiddot

BIlTaUllOHa CIL13 KOjOl C) Hue ~e1YJe Iia 3emiddot IbY npWI1 paJl npll TO KpeTal-bY

1 aUlTo ce a)Tolo6lLlll H3 Y36PllIIUII Blue tryshyrO1 6p31IHOI a He Tpeho)1 ILlII ICTl-lPTO1 Kao

Hlt1 IIpaBol nYTY

1 3aulTo j J-oetPl1UltjeHT KOpICHLlr lelcn~a Iamiddot

WIIHe ) Bllje lal-bll 0)1 J

3 KaKo ce llIjel-b3 Joeq)llulljeHT KOplIClIOr llejmiddot CTBa laWlIHC npil nOJl1331IBal-bymiddot1

4 KaKo ce llIjel-ba KIIHenlrKa eHeprllj a Tlljela

3KO elLla Koja JjeIYje Ha TO TnjCJ10 BpWJ a) n0311TIIB3H ran

6 ) HerltlTl IB3H pall

5 Mlljelba 111 ce Ki lHeTJlLIKa eHepr llja TlljeJla npl1 IOljeHl1 c tjepa l-herose 6p]ll shylie

6 T 1tje lo ce Kpehc HII3 CTPl) paB3H 6eJ Tpel-ba Koj a CWla n p l TO~IC BPWI pan 331111CII ~Il PM n1 u) AltIIHe CTPIC pallHlt

7 K alo ce MHjel-ba nOTellulljLLTJII3 cHeprllja TlljeJIa npil -beroao t KpeT3l-bY BepTI Klt11HO YBlle ( H31l 1I we)

8 M lIjelba IH1 ce nOTcHUllja1Ha eHeprllja npll KpeT3lhY TIIjeJ1a napaneJ1 HO nORp WlIHI13eIJbe

9 IhlaMo llBHje elaCTlI lJ HC onpyre jenHltlKe Tnpnone JellHa 011 I-bI IX j e ca611je1l3 33 5 cm a npyra IIcTerHyra Ja 5 em lla nl l ce pa3Jl ll Kyjy I-b I1XOBe nOTeHuujaJ1shyHe eHep n l je

]4

20 J1Y-1 KJI panHI1K nY4e CaHll)K no nollY MarashyUI1Ha CHJlOM I1HTeH3I1TeTa 250 N flpaBau cline KOjOM p aJ]HHK DjeJIyje H3 CaHJ]YK namiddot paJleJIaH j e XOPl130HTaJlHOj n0)l110311 Kao H3 CJH1UI1 I-bpalJYH3TI1 KOJ1)ITH je pan panmiddot HHKa n pH nOMjep al-bY caHnYKa 3lt1 32 m

21 KO11l ll0 1 je pan Cl1JIe KOjoM ltloBjeK Djeflyj e cMjepa

n peJla31l _- Ha BarOH Y cMjepy cynpOTl-lO on JpeTal-ba BarOHa aKO je CIUla KOjOM )ljcJlyj e Ha BarOH 100 N a BarOH

nyr OJl 2 m ~~~1-~~IJ~Jf$f~t~~Ok~J~~~tit~~

22 UlljeTc B)-re HrpatlKY no noJlY co6c nO~lOny KaHana njerryjyt1l1 1-Ia f-her a ClUlOM KOHCT3HTHor 11HTeH3tITeTa 080 N I1rpalJKa npeJ1a311 nyr YKynHe n )KHHe 2 m Urll lJeMY Je H3 n pBoj nO10BIlHlf n)Ta KaHan napailelaH ca AOPI130HTaJIHO~ nOD-loro 3 Ha Jlpyroj nOJlOBIfHII nyra KaHan 3aKJIana )Tao 30 ca XOPI130HTashy

1O( KOlIKII je pall JllljeTeTltI H3 ulljeJlol nyry

23 KOIIIIJI paJl ce It3BPWII nplf n01l1nal-bY TepeTa TegtKIIHC 800 N Ha BIICI1

H 01 J 2 mt 2~ b~ rapc Ilt I tllJal Te roBa KOJI I jc l)CBOjIlO 3-JaTH~ tC1ahY

111 O_1I1tllllJCKIII ItrpaILI ~ CJllllej ~ lOOO rotIIHe 060shy

pllll jl (lljcnKll peKopJ ) KO11IKII je plW (i~ rapCKor cnOpTIICTl npll nOll3al-b~

fcrona TegtK1I He 2500 Ha mICIlH~ 03 2 m 0) KOllllJl pan npll nOJlnal-b) TeroB3 II3BPWII 3eshy

LbIlH3 TCf(a

B) K OTJllKH je piU t1I0PTlICTe 10K Je IIIPHO 1pf(ao r e roAe

ltJHart cBoje r]clBemiddot)

25 K ynmltl XpaMa CBeTor Cu~e ~ 6corpaI) Mace J 50001110shyLlIrHYTa je J 99 roJlIIHC HH BIICIIH~ 01 50 Ill KOIII II pltu je I13BpWI11a CI1I3 npllTllCKa 1Iltl clltIl XIl] pa~ J114He

lHI33Jlll ue KoillM ic nOJlllrH~Ta KynO~ta

26 A)T0106Il~ lace 800 kg pehe ce paDIIOjepHo ~ (ipJaHO

y6p3al-beM 2 ms~ KOJ1lIKI I je pall BY11He CIUlC MOTopa

IlOK ayro~106W1 n pebe nyT on 50 m

27 TlljeJ10 Mace 102 kg Kpene ce P3BHOMjcPHO npaBolHHllj shyCKH 6p3JtHOM 53 ms H a THjeno nOlJHe aa ujeryje CHJTa

YCThell ltlera ce OHO naJbecne 110 3ayeTaBJb3l-ba Kpene paBshyHojepHo ycnop cHO y6p3al-be~1 I1HTeH3HTeTa 2 ms~

a) K OJII1KH j e IIHTeH3HTeT CltHe Koj a je njeJTOBana H3 TIt middot

jeJ1o

6) KOJllKH nyr Tl1jeJlO npel]e 011 nOlJeTKa njeJlOBaHa Clt shyJle n o 3aYCTaBlhalDa

B) K oJI1UQ1 pan H3BPWH CHJla

25

28 eMa MOTopa 6poncKe nJI3~UHl ue npl1 nO)]1I3ashy-by cl1npa ca llHa pl-ljeKe II3BPWII pan 30 kJ AKo nOillnal-be cllnpa Tpaj e I min OJlpeJlIITe cHary MOTopa

29 EneKTpOlIOTOP c06H or BeHTILlaTopa liMa clIashyry 40 W OupeniITH pall C1IJ1e eneKTpOMOTOpa

yTOKY Ih

30 KOlll1KII je pall XllnpOlleliTpaJle Y TOKY jenHe (1ronllHe aKO je Cpenl-b3 CHara l-beHOr rCHep3shyTopa 25 MW

--c31 AKo je ulljeHa CJIeKTP f1e eJleprllje 004 KM no KIIJlOBaT-I3CY KOJ1l KO he Hac KO WTaTII ynOTpe6a ClljarHlue CHare 250 W TOKO~1 12 h

32 CKII-THlcj)T nOllllJ(1 11130j1lUY cKlljaWlt1 Maca CBHKor cKujawa JajeJHO cn onpeOf je 75 Kf BIIClfHcKa pa11I1t-a 01 IIO IHOgtKja 10 npxa CTa shy3C je 150 1 a 10 Bpxa ce CTlIA( 13 2 mIll KOH shynaIlTHO1 6P311HO1 KOHna je CH 1rLl nOTpe6 shyHn C KII-lllcpTY

B lllCln y XOTel) 1113 lacy -l500 kg II lO)feua 1I0CII TepeT -II1ja ~faca lie npegtlashylII 1800 kg MaKClnIltLlHO HaTOBapeHl1 111cpT Kpelle ce BepnlKrulHO HaBI1We 6pshy311HO1 38 ms KOlI1Ka je CHara nOTpe6Ha lllqn-y

34 ACTpoHayr ca nYHOM onpeIO 1113 -lacy 1J0 kg Jla 6n ce noneo Y1 6pno BIICOKO 73 rn 3a 72 s aCTpol-laY-ry j e nOTpe6Ha CHara 100 W na 111 1 ce aCTpoHayr llala311 lIa 3e~lhll

35 KaMlloH Mace 2000 kg Kpelle ce no XOpIl30HTaJIshyHOM ny-ry 6P3I1HOl1 72 kmh C IL13 omopa KpeshyTalmiddotM je 005 l-berOBe Te)Kl llle OJpeilltTe cHary

KOJY pa3BI1ja npll TOle MOTOp KltIllIOHa

36 J1 0KoMOTI1Ba BY4e B03 MHee 100 t 6p311HO~1 10 ms KOJIlIKa je CHara nOTpe6H3 nOKOlt OTliBl1 aKO je Kcr ecentHUlljer-rr Tpel-ba 1l3eljy WIiHa 11 TOIK08a 803a 005gt

37 YtltyTllia CHara plHf~e Ha WTClll-baKY je 1000 W KOpl1CHa CHara Koja ce ynoTpllje611 1a 3arpl1jashyBaHC BOne Y JlOHIlY je 800 W K Olll1KU je CTeneH KopHcHor uejclBa wTe)]l-baKagt EJ

]6

38 VlHTcH311TeT BlHe CHlle Koja njenyje Ha TpaKY ay shyilIiOKaCeTe je I N Eip3l1Ha KOjOM ce TpaKa Kpehe je 25 ems 3a nOKpeT3l-be TpaKe eJleKTpO~IOTOp KaceshyTOcjJOH3 YJlCUKe cHary 2 W KOJll-IKH j e KoeclmuHjeHT KopllcHor llejCTB3 IOTopa

39 ilpBeHa H rB03neHa KyrJla jeJlHaKlLX npeIHllKa HMa1e ce Ha I1CTOj BHCI1HI1 113shy

lIall Tlla Lla 1 11 OBe llBllje cyfJle H~lajy jenH3Ke rpaBIlTaUIIOHe nOreHUl1jMHe eHeprllje

40 AKO ce 6P3JiH3 TIIjella nOBeha 4 nYTa KaKO ce npOIHjeHll l-berOBa KJlHeTi-I-IKa eHepnlja

41 Lla 1r1 ce npl cl106011l-lo1 nalIal-bY TIjeJla llljel-b3 l-beroBa YKynHa MeXaHWUlta

eHepntja

42 4eMY je j ellHaKa npoMjeHa MexaH1PIKe eHepruj e

43 KaKo ce Mlljel-ba MexaHH4K3 eHeprltja TlIje1u aKO llHO KPWI1 paD

44 vl3paIYHajTe KI1HeTll4Ke eHeprllje a) KOJIlIua Mace 25 kg Koja ce Kpeh~ 6p311HO1 3 I11 S 6) eTKa Mace 3 g KOjl1 ce Kpefie 6P311HOl 400 01 5

) an leTllyapa Mace 60 kg KOjl1 TpYI 6P311HOl 9 ms

45 ~ l3par)llajTe 6p3Hlle a) jJltebe3HtJL1KOr BaroHa ~l ace I t 1~lja je KllHenlLIKa eHepfllja 4500 J 6) njeHoj411ue Mace 45 kg Koja K03JI 61lUlIK1 ~lace 15 kg YKynHa K1IHeTltllKa eHepmja njesoj411ue JI 611U1lKJ1a je 2430 J

46 A)TLl106ILl Mace 1000 kg Kpehe ce 6P111HOl 60 kmh no npaBOM XOPI130HTaJIshy110 n)1) 360r K04el-ba KltHeTliYKa eHeprllja aYTo106ILla ce C~lal-bll 3a 50 kJ KOJIIIKa j e 6pJIIHa ayro~06111a HaKOH K04el-ba

47 UIlP-)CKJI c10H lIP)101 ) CBOjOj CYP11l1 6a~BaH I ace 100 kg Ha BICIIHI1 3 m 0)) nOlla v13pa4)HajTe f paSIITaUiIOHy nOTeHul ljaJJHY eHeprltjy 6rulBaHa y ODHOCY

Ha UlIPKVCKlI nOll

48 Kl-bllfa 1e)l11 Ha nomlUlI Koja ce Ha1aJII Iia IlI ICHIII 075 In Oil HIIBoa CTOJ1a CTO cc HltlIilJll H3 (Um In Oll1lwoa 1101(1 Maca t-l-blll ell U) I

a) KO111K3 je rpanilTaWlOHa nOTeHulljaclH3 eHepruja KHlIre y OllHOCY Ha H 1 fiO CTOW

6) K o1IIKajc rpllBIITaUlfOHltl nOTellulljal shyHa eHepnlja Kl-bl1re Y OlIHOCY Ha HIIBO nona

49 nltjeTe Mace 40 kg HaJJa311 ce Ha npxy T060rashyHa l)rraIKOr 4 rn Yrao nou Kojml jc T060ralmiddot HafHYT y ODHOCY Ha XOPl130HTrulHY pasaH jc 30deg OnpemtTM rpaBI1Ta UHoHY nOTeHIlHjaJJHY eHepnljy njeTeTa y OID-lOey Ha XOP1130HTrulHY nO)lJ1ory

27

50 YlfeHI1K je CJJyqajHo ryPHYO caKclljy ca 6HJbKOM ca np030pa Kojl1 ce Hana311 Ha BI1CI1HI1 5 m Y OllHOCY Ha TpOToap KOJlllKa he 6HTII 6P311Ha caKcMje npll YllashyPY 0 TpoToap

51 JIjeqaK 6aua YElIC )JonTY 6p311HO1 5 ms KoplicTehll JaKOH OllpiK8l-ba eHeprll j e 01lpell~ITe Ha K0111KY he ce BllCHHY Y OnHOCY Ha Mj ecTo 1136aLJaja nOneTII )JonTa aKO je 6aleHa BepTI1KHJ1HO HaBllwe

52 Jaje je BCnaJIO 113 rHllje3na Koje ce 1I)Ja311 Ha RpXy llPseTa BI1COKOr 3 m Koshynl1Ka ne 611TII 6P3 111U jajeTa Ha BIICI IHII 05 m Oll nOll10re

53 B03l1n Y YHa nap) Kpetle 113 CTatb8 MllpOBal-ba nyral-bOM npllKa3aHO~1 Ha CJJIIUI1 OllpelllITl1 6p311He B0311ha Y TaIKa la A B 1 C aKO ~1O)f(e~1O na 3aHeshy~tanHMO Tpel-be

lo A

c

54 LJelI14Ha K)rJlllua Iace 50 g IICnaJbeHa je BepTIIKaTlHO HaHIDKe In lljelJlljer [1

w j Oba ca BlICllHe 1 IT) nOLreTHOM 6p311HO~1 3 ms a) OnpellllTe leXaHIIlKY eHeprlljy K)Tluue

6) KomlKa ne 611Tli 6p311Ha )Tmlue nplf Yllapy 0 nolUlory Il) Lla je K)Tll1ua IICnabeHa ca IICTe B~ICIIHe 6P3lfHOM IICTor IIHTeH3IITeTa

3-111 BepTlIKalHO HaBlIwe aD Koje 611 ce BIlCIIHe y OllHOCY Ha nOllnory noshynella

55 lljelaK KOjl1 ce HaHa311 Ha 3eIh1l IOiKe lla CKOlII HajBllwe 50 cm BepTllK3-lshyo YElle Llo Koje BIICIlHe 611 lOrao ila CKOllH oBaj IICTII nje4aK Ha JymlTepy

aKO je rpaBIITaUiIOHO y6p3albe Ha JynUTePY 22 ms2

56 HllJantpllHII 1l0ilOnallll C) llllCOKII 53 Ill HI13 I3Oilonalle ce tllaKe CekYHile cpyshylIt 6000 l BOlle AKO 6JC1O CBy eHeprlljy IOLll na TPaHCcentOpM11we~10 y KOPl1shynaH pall KOJIIIKY 611C 1O CHary llo6WIII

] 8

OCLUJlallruje u ZuaJlaCU

1 KaKo ce Ha3JIBa Bplljele Ja Koje ce lI3BPWil jellHa oCu11JlaUlija

1 Kalw ce 30BY oCUlL~aUlje lfllja ce aMIlJIIIT)lla cMal-byje y TOry 13peMeHa

3 Y KojllM TalJKa la nYTal-be mjeJo npll4Bpwhemiddot HO 3a eTaJlHY onpyry npl1 OCUIIJlOBaI-bY II ta

a) 6p3~IHY jeDHaKY HYJI11 6) y6p1al-be paRHO HY qll ~ ~4 )la 111 jelHO UCTO MaTeMaTlllKO K-13THO 1113

r1CTII nep11011 OcuI110IJal-ba lla 3eWbil l Ha [ -Mjeeeuy)

5 Kalla 6HCTe Y4eCTBOBanH Y nplloj eKcnem1UlljH Koja ca 3e~Llbe nyryje Ha Mape IH 111 6J1CTe nOHHjell1 JaCOBHlIK ca KJJaTHOM IL11l ca eJlaCTIIIHOM onpyroM

6 KaKo ce ~llIjel-ba aMrlJIlIT)lla Cij060llHIIX oculLlaullja ~ TOKY BpeMeHa (O CIIHshyHITOP He ry611 eHepmjy YCbell Tpel-ba omopa Ba3rryxa II npeTBapalha l-beroBe eHeprnj e Y llpyre 06RHKe eHepmj e)

7 KaKBe ecpeKTe 3poKyje ClL1a Tpel-ba KOll OCUlLlaTOpHOr KpeTal-ba TlljeJa

8 Koja CI1i1a y3pOK)je OCUI110BaHgta laTerantlKOr KlaTHa

9 Lla JI ll ncpllOn OCUJLtlOBal-ba MaTeMaTIl Ltmiddot

Kor K1aTlla ca MaJllI a~llLlltTYnala 3almmiddot ell OLI ace II a~mrtllTYlle KlaTHa t

10 Koja K-1aTHa ca CJJlIKe lOry OIlTll Y pe3oshyIlaHUlljl1

11 360r ~Iera ollpen BojHHKa npeKo MOCTa B YBI1jeK npeJla311 CTr06OllHff1 ( RO)bHO ) KopaKoM

12 LlaTI1 je KpeTal-be 3 eMJbe OKO CYHua nepHon11IHO KpeTal-be lla Jlli je aBO Kpemiddot Tal-be H OCUI-uraTopHO

13 Kojl1 TanaCI1 HacTajy Kana 4eCTllUe cpellllHe oCUlUlyjy Hop~lanHO Ha npaBau

KpeTaJha TaJlaca

] 4 llITa je TaJIaCHa 1y)KJ1Ha

29

A

D

c

r - - -- -~ ~ bull bull J O O O O O O O O~~ lleJJ JloHrwrylll1HanHOr Tanaca BCD E F KO]JIKO TanaCHIiX ll)I(IIHa 113shy

Hoce paCTojaHgta AB Ac AE

16 LIa JIB ce 3BYIHH TaJlaCII Mory npelfOCllTIl Kp03 B3KYY~I

17 Mory ~ 11 KOCIOHaYTH Ollp)l(aBaTII Be]y -Ieoy cneSIIpshy

CKHf 6pOllOBmia ]nYYHIIIoI Talacmf3l

18 On Iera ]aRI1CII 6p311H3 3nYKa Y 1l0llH

19 YTspl)eHo je na 3BY IHI1 TalaCIl 1I1je cy q)peKBeHullje Mal-be on 20 Hz KOIl Jbyshy

Ill I Il3a]lIllan ocjeTlaj HelarOllHOCTII KaKo ce Ha3111lajy OBI1 ]BYYHII TaJIaC11

20 360r yera ce TOKO o~1yje npao RlllllI ~IYHgta

a 3aTB1 1yje rpL1gtaBIIHa

Z1 (1)pekBellul-lja OCUIlIOnal-bltt ILleTa eek

TpYHO1 anapaT) ]a 6plljal-be je 120 Hz a) KO1JlKII je neplIOll OCWIJ10llai ba 6) KO1IlKO OCUlLlaUllja lIaYI1Hl1 )KILleT 3ll

5 s

22 KT11Iua o6jeweHa 0 onpyry HaIIIHII 5 OCUlllaul1ja ]a I s KO1J1KII je neplIOll a

fOlI1Ka cPpeKIlCHUflja OCUl1lOBal-ba

23 Kyr1J1ua lace 5 g nplILJBpwheHa je 3a eJlashy

CTIIIH) leTalHY onpyry DplI npo1acKY

P03 paBHOTe)(HII nolo)(aj 6p3JtHa KyrJ1l1shy

ue je 5 ms KOJlHKa je faKCrLI3J1Ha nOTeHshy

ulljalHa eHepnlja ltjLlllue TaKOM KpeTashy

Ina

24 najall ce HaJa]H ) Tlljll nplI1BpwheH 3a

e]JacTI1YH) onpyry KoecentuUlljeHTa eJJacnlYshy

HOCTl 500 Nm Kalla je )Tllja 3aTaopeHa

onpyra ie 5 em Kpaha y () 1110C) H3 HeICshy

centop~nlcaHo CTal-be KomlKo he 61fT11 y6p3ashy

I-be najaLla IIcnocpellHO no oTBapal-bY K)TII shy

j e Maca najaua je 100 g

25 Kalla je onpyra )eI11jcKe OJ10llKe laKCIIlaJ1 shy

HO ca6l1jcHa nOTellllllja1Ha eHepnlja litHe

je 2 J KOJIII-a he 611TII 6p3HHa MIlHe npi l

pOJlaeKY KPO] paBHOTe)f(HlI nOJlOiKai aKO je l-beHa Maca 5 g

-aw26 KOJlIIKI1 je nepHOll OCUlVlOraquoUHgta MUTeManIYshy

Kor KJlaTHa ll))I(IIHe 1 111

30

27 MaTeMaTHYKO KJlaTHO HalHHI1 24 OClUiJlallHje s LJeMY je jellHaK nepl10D 11

cI1peKBeHUHja l-berOBor OClIIUlOBal-ba

28 AKO MaTelltanllKO KJlaTH O HayHHH 72 OCUllJ13ultje 3a J80 S KOJlI1Ka je l-berOBa lIY)l(IHa]

29 najf)bIiRI1~1 Ijepefhe 1 crylleHT cI1H311Ke yTUpJlIlO je llU jc neplIOll OCUIIJ10BaHgta lalelaTIlIKor KJlaTHa 24 75 s llYAltIlHa ~~aTHa II3HOCIl 1518 em K OJJl1KO j e

6p3aHgte 3elJbllle Te)l(e y ~a6opaToplljl1 rnje je Mepel-be BpweHo

30 0JaTHo llY)KI1He L oCUllJ1yje Ha Ha411H np~I Ka3aH Ha CJ1II shy

Ull Ca A je 061IJbe)KeH eKcep II OH je 3aKyuaH Ha panojashy

I-b) 12 01l TaLIKe Iljewafha Kao Ha Cm1U11 OIlpellHTl1 nepll shy

on IalllX OCUlLlaUllja 33 onaj CIICTell

31 lIlJeTe ce urpa H3 b)lbaWUI1 ]aHeMapblllle lacelllljeTe Ct

3a byba TaKO 11a ce by1baWK3 Hana311 Ha BHCIIHII I m y Ollshy

HOC) Ha paBHOTe)KHH II0JlO)f(aj KOTJIfKa he

611TII 6p311Hltl lIjeTeTa npI1 npo1aeKY KpOJ paBshy

HOTeJKHII nO_1O)I(aj

32 OpJIIHa npocmpaHgtU TltLlaCa je 240 ms Ao je TltLHlCHa ilYiIJIHa 32 m KOJllIKII ey

a) cppeKBellulIja

6) neplloil Talaca

33 PI16ap je npllll1jenloIa (iplljer TaJ1aCa npOJa311 nopM Kple theroBe Jlal)e CBashy

KII 6 0 OH je ~TBPllI10 la paCTojafhe I31el)) ana cycjenHa 6pujera Taflaca 113shy

OCII 20 m KOH1Ka je 5p31lHa T3TJaca

34 JbY_bal-bel yalua )]je4aK npaB~1 nOBpwlIHcKe BOlleHe Tanace Ha je3epy 1lieQaK

YOlaBa 11a lalau HaQIlHII 12 oCUILlaUl1ja 3a 20 s CllaKa OCUHJJauHja CTBapa no

jeJIaH 6plljer BoneHor Tanaca lll1ja BIlCIIHa y onHOCY Ha HIIBO Ilolle Y MHPHOM

je3epy 113HOCII 15 cm opljer T31aCa CTIf)Ke no o6ale YlIaJbeHe 12 m 3a 6 s ODshy

penliTe

a) neplIOll Talaca

6) 6p311HY Taflaca

B) TaJ1aCHY 1l))f1I HY

r) aln_l IlTYllY Ta1aca

35 3aTerH)Ta )I(11ua Ha nlTapu nyra je 065 m Kalla 1)31shy

lap OKIIHe lillY 10331t no ltpopMllpal-ba cTojeher Tashy

]laca Lmja cPpeKBeHUl1ja je 440 Hz AKo je TaJlaCHa nyshy

)I(IlHa cTojeher Tanaca 3a 13 MaHgta Oll 11)0KIIHe )K11Jle

OIlpellllTe 6PjIIHY npOCTJlparba Tanaca

36 OIlpellllre TalacHy JlY)f(11HY LJOBjeKoBor L1aca Koje~1 onshy

rOBapa ltppeKBeHullja

a) 80 Hz

6) 1400 Hz

31

aJ Y bVJUJ

6 ) Y Ba3llYxy

EP311H3 3HYKa y BU3LlYXY jc 340 ms a YAOllU 1460 ms

38 HajMalla TalaCHa )])iKIIHU TL1Lca KOjl1 cnlfjenlf 1-IIW IOillte Ila e~lIlTyje IUHOCII 33 mm KOjlllKLl 113HOCII tPPCI--neHullju

ODor TaTJaca Jla 111 lonjeK lOgtKe Ila r a penICTp)je

39 npernocTuHIIMO Ila ce ala31lTe Ha liel1IKO1 KOHllepTY Ha pacTojal-bY 300 01

OIl 1B)nlHIIKa KOHuepT ce TaKol)e npeHOCU II npeKO CaTeJ1I1T3 IlO cIJ)IUJaoua Koshy

jlf je 5000 km YIl3fIgteH OJ ~ljecTa rnje ce KOHuepT OllpAltalla Ko npBJI Iyje MY

31IK) BJI IIHII YIl3TbeHIf cIYWaJ1au

~Omiddot LLBa ne1aOua HLla3e ce 11lt1 $)lI6aICKO1 CT(LllI1OH~ Kana je 13BelleH c-T06ushylall Ylapau npBl rlanalaulyje Jlt1 JC Ionnl YllapeH3 023 s nOIJ)TO je BlIlllIO 1a je Yllapau 113Be)1CII a npYl1I Hlt1lOH 012 s op3HHa 3BYK3 113HOCI1 340 m s

a) KOTJHiO c~ UC1tlOUIf )1ueHIf 011 lJeCTa fllje je II)BeneH c106oaaH yaashypall

6) AKO flpaHau KOjl1 cnaja npBor nelltlOlla ca ljCCTOM I13Bol)el-ba cl060llHOr yaapua IaKlana ca nptlBUel KOjll cnaja lpyror rlenaoua ea MjecTo~1 II3BOshyI)el-ba cl0601Hor )llt1rua )1lt10 01 90 Ollpe1IfTiI pacTojeHc 113(1)) r le1 laua

~ 1 YlTpa3sYYHII Talac npOiBBelleH Ha 6pollY nocllije 12 s peruCTpyje ce Ha 6poshy

llY nOCJ1l1je oll6l1jaf-ba 01 llHa Mopa KOJIIIKa Je Jly6l1Ha Mopa aKO 6p311Ha 3BYK

y BOllll 113HOCII 1460 ms

42 Ca jellOr 6pona cy IICTOBpeMemiddot 1-10 ynyheHII 3B)-IHII TalaCII KpOi BOay II Ba1JlYX H a npyshy

rOM 6pOllY cy OBII HJ1aCIl npll IJbeHIf ) pa1~taKY 5 s Dp311Ha

30YKa y Ba1JlY-XY je 340 ms iI )

1l0t1l 1460 mis KOl II KO JC pashy

cTojal-be IUMelJy 6ponoBa

43 KaMeH je IICIT)lllTel-l y 6YHap KOJIIIKO BpeMeHa npOTeKHe 011 TpeHYTKa lIenyshy

WTaf-ba KaMella 110 TpeH)TK3 Kalla ce Ha BPXY 6YHapa 4yje 3BYK nana Ka~eHa )

BOllY lly611Ha 6YHapa je 15 Ill

J

I KaKo cc ryMil411 Bella TCl4HOCT gtfIgteKapCKor TepIOMeTpa 011 c06Hor TepMOMemiddot

rpa

2 Jla J111 ce 1I0lOhy Tep~ OMeTpa ea )KHBOM l OIY Mjeplm1 3111CKe TeMneparype Y ClI6l-1py

3 06jacHifTe npmtjeHY TJIlHeapHOr TOTlJlOTHOr Wllpef-bil KOll 611)leTaJ1HHX npeKT1 ta4a Kojllla ce a)TOMaTCKII )lUbyt-lyjy II IICKJhYlyjy eneKTpI14HH ypel)ajl1

4 -Ia KOjl 06J111K el-lepfllje ee CROlll YH)TpaWl-bil eHeprllja racoBa

- 01 ltJera 3aBllClI KOll11I1Ha TonlOTe KOJ) Tllje_lo nplllCl npll 3arpl1jaBaf-bY HJU1

omyulTa npll xla~)e~bY

6 KaldlU je pa31l1Ka Intejy H)TpaWl-be eHepnlje J1 KOlItlJIIHe TOnJlOTe

a 111 ce YHyrpaWf-ba eHepmja Te4HOCTlI II lJBPCTIIX TIIje1a MO)l(e CBeCnt Ha

dHeTIlIKY eHepn1JY leCTlsua Koje IIX CalJlIl-baBaJY

8 Ita 111 a~OpcentHa TIIje13 Illajy TaJHO ollpe1]eHY Te ~mepaTypy Tonhel-ba

9 KaKo Temeparypa KlYlalba 1i1BlfClI Oll npltT1ICKa

10 KJKO ce Ha1ltBa centa3HIt npe1a)ak 113 lJBpnOr arpenlTHor CTal-ba 1lI1peKTHO Y rashy

conllTO arperaTHO CTal-be

II KaKo ce lIljel-ba TemepaTypa gt1ella npll TO nbeI-by

12 TetnepaTYpa Ra3lIyxa je 27middot C KOJlIIK3 je ancoTf)THa Te~tneparypa Ba3ryxa

13 TetnepaTypa Iena je _3 C KOJ1IIKH je anCOlTH3 Telneparypa Jlella

14 Ancol ) THa TetnepaTypa Ha noopWlIlI1I CYllua II3HOCll 6300 K J13pa311Te o sy

l lIlepar) P ) Ue13I1j) WBUJ rerIepaT) PllUJ CI--LlII

15 AnCOJTyrHa TelnepaTypa Ha KOjOj Ba3ll) npela3f1 y IBpCTO CTaf-be je 73 K il13pa31lTe ony TclnepaTYPY Y UeJ1HljYCOBOj Te~lnepaTYpHoj CKaJ1H

16 KOmlK)1 KOJlIIlJJ1Hy TOilllOTe npllMI1 05 kg BOlle npll )lt1

rplljaBal-bY 011 10 C no J00 C

npH nOBlIwel-bY Ter-lneparype 3a 5 C 200 g )a npll shyl1 KO111lt1l1HY TOilllOTe 4100 1 KOJTIIKI I je cneullcjgtIIYHI

TOrtJlOTH I KanaUIITeT Y_ba

33

r - - -- -~ ~ bull bull J O O O O O O O O~~ lleJJ JloHrwrylll1HanHOr Tanaca BCD E F KO]JIKO TanaCHIiX ll)I(IIHa 113shy

Hoce paCTojaHgta AB Ac AE

16 LIa JIB ce 3BYIHH TaJlaCII Mory npelfOCllTIl Kp03 B3KYY~I

17 Mory ~ 11 KOCIOHaYTH Ollp)l(aBaTII Be]y -Ieoy cneSIIpshy

CKHf 6pOllOBmia ]nYYHIIIoI Talacmf3l

18 On Iera ]aRI1CII 6p311H3 3nYKa Y 1l0llH

19 YTspl)eHo je na 3BY IHI1 TalaCIl 1I1je cy q)peKBeHullje Mal-be on 20 Hz KOIl Jbyshy

Ill I Il3a]lIllan ocjeTlaj HelarOllHOCTII KaKo ce Ha3111lajy OBI1 ]BYYHII TaJIaC11

20 360r yera ce TOKO o~1yje npao RlllllI ~IYHgta

a 3aTB1 1yje rpL1gtaBIIHa

Z1 (1)pekBellul-lja OCUIlIOnal-bltt ILleTa eek

TpYHO1 anapaT) ]a 6plljal-be je 120 Hz a) KO1JlKII je neplIOll OCWIJ10llai ba 6) KO1IlKO OCUlLlaUllja lIaYI1Hl1 )KILleT 3ll

5 s

22 KT11Iua o6jeweHa 0 onpyry HaIIIHII 5 OCUlllaul1ja ]a I s KO1J1KII je neplIOll a

fOlI1Ka cPpeKIlCHUflja OCUl1lOBal-ba

23 Kyr1J1ua lace 5 g nplILJBpwheHa je 3a eJlashy

CTIIIH) leTalHY onpyry DplI npo1acKY

P03 paBHOTe)(HII nolo)(aj 6p3JtHa KyrJ1l1shy

ue je 5 ms KOJlHKa je faKCrLI3J1Ha nOTeHshy

ulljalHa eHepnlja ltjLlllue TaKOM KpeTashy

Ina

24 najall ce HaJa]H ) Tlljll nplI1BpwheH 3a

e]JacTI1YH) onpyry KoecentuUlljeHTa eJJacnlYshy

HOCTl 500 Nm Kalla je )Tllja 3aTaopeHa

onpyra ie 5 em Kpaha y () 1110C) H3 HeICshy

centop~nlcaHo CTal-be KomlKo he 61fT11 y6p3ashy

I-be najaLla IIcnocpellHO no oTBapal-bY K)TII shy

j e Maca najaua je 100 g

25 Kalla je onpyra )eI11jcKe OJ10llKe laKCIIlaJ1 shy

HO ca6l1jcHa nOTellllllja1Ha eHepnlja litHe

je 2 J KOJIII-a he 611TII 6p3HHa MIlHe npi l

pOJlaeKY KPO] paBHOTe)f(HlI nOJlOiKai aKO je l-beHa Maca 5 g

-aw26 KOJlIIKI1 je nepHOll OCUlVlOraquoUHgta MUTeManIYshy

Kor KJlaTHa ll))I(IIHe 1 111

30

27 MaTeMaTHYKO KJlaTHO HalHHI1 24 OClUiJlallHje s LJeMY je jellHaK nepl10D 11

cI1peKBeHUHja l-berOBor OClIIUlOBal-ba

28 AKO MaTelltanllKO KJlaTH O HayHHH 72 OCUllJ13ultje 3a J80 S KOJlI1Ka je l-berOBa lIY)l(IHa]

29 najf)bIiRI1~1 Ijepefhe 1 crylleHT cI1H311Ke yTUpJlIlO je llU jc neplIOll OCUIIJ10BaHgta lalelaTIlIKor KJlaTHa 24 75 s llYAltIlHa ~~aTHa II3HOCIl 1518 em K OJJl1KO j e

6p3aHgte 3elJbllle Te)l(e y ~a6opaToplljl1 rnje je Mepel-be BpweHo

30 0JaTHo llY)KI1He L oCUllJ1yje Ha Ha411H np~I Ka3aH Ha CJ1II shy

Ull Ca A je 061IJbe)KeH eKcep II OH je 3aKyuaH Ha panojashy

I-b) 12 01l TaLIKe Iljewafha Kao Ha Cm1U11 OIlpellHTl1 nepll shy

on IalllX OCUlLlaUllja 33 onaj CIICTell

31 lIlJeTe ce urpa H3 b)lbaWUI1 ]aHeMapblllle lacelllljeTe Ct

3a byba TaKO 11a ce by1baWK3 Hana311 Ha BHCIIHII I m y Ollshy

HOC) Ha paBHOTe)KHH II0JlO)f(aj KOTJIfKa he

611TII 6p311Hltl lIjeTeTa npI1 npo1aeKY KpOJ paBshy

HOTeJKHII nO_1O)I(aj

32 OpJIIHa npocmpaHgtU TltLlaCa je 240 ms Ao je TltLHlCHa ilYiIJIHa 32 m KOJllIKII ey

a) cppeKBellulIja

6) neplloil Talaca

33 PI16ap je npllll1jenloIa (iplljer TaJ1aCa npOJa311 nopM Kple theroBe Jlal)e CBashy

KII 6 0 OH je ~TBPllI10 la paCTojafhe I31el)) ana cycjenHa 6pujera Taflaca 113shy

OCII 20 m KOH1Ka je 5p31lHa T3TJaca

34 JbY_bal-bel yalua )]je4aK npaB~1 nOBpwlIHcKe BOlleHe Tanace Ha je3epy 1lieQaK

YOlaBa 11a lalau HaQIlHII 12 oCUILlaUl1ja 3a 20 s CllaKa OCUHJJauHja CTBapa no

jeJIaH 6plljer BoneHor Tanaca lll1ja BIlCIIHa y onHOCY Ha HIIBO Ilolle Y MHPHOM

je3epy 113HOCII 15 cm opljer T31aCa CTIf)Ke no o6ale YlIaJbeHe 12 m 3a 6 s ODshy

penliTe

a) neplIOll Talaca

6) 6p311HY Taflaca

B) TaJ1aCHY 1l))f1I HY

r) aln_l IlTYllY Ta1aca

35 3aTerH)Ta )I(11ua Ha nlTapu nyra je 065 m Kalla 1)31shy

lap OKIIHe lillY 10331t no ltpopMllpal-ba cTojeher Tashy

]laca Lmja cPpeKBeHUl1ja je 440 Hz AKo je TaJlaCHa nyshy

)I(IlHa cTojeher Tanaca 3a 13 MaHgta Oll 11)0KIIHe )K11Jle

OIlpellllTe 6PjIIHY npOCTJlparba Tanaca

36 OIlpellllre TalacHy JlY)f(11HY LJOBjeKoBor L1aca Koje~1 onshy

rOBapa ltppeKBeHullja

a) 80 Hz

6) 1400 Hz

31

aJ Y bVJUJ

6 ) Y Ba3llYxy

EP311H3 3HYKa y BU3LlYXY jc 340 ms a YAOllU 1460 ms

38 HajMalla TalaCHa )])iKIIHU TL1Lca KOjl1 cnlfjenlf 1-IIW IOillte Ila e~lIlTyje IUHOCII 33 mm KOjlllKLl 113HOCII tPPCI--neHullju

ODor TaTJaca Jla 111 lonjeK lOgtKe Ila r a penICTp)je

39 npernocTuHIIMO Ila ce ala31lTe Ha liel1IKO1 KOHllepTY Ha pacTojal-bY 300 01

OIl 1B)nlHIIKa KOHuepT ce TaKol)e npeHOCU II npeKO CaTeJ1I1T3 IlO cIJ)IUJaoua Koshy

jlf je 5000 km YIl3fIgteH OJ ~ljecTa rnje ce KOHuepT OllpAltalla Ko npBJI Iyje MY

31IK) BJI IIHII YIl3TbeHIf cIYWaJ1au

~Omiddot LLBa ne1aOua HLla3e ce 11lt1 $)lI6aICKO1 CT(LllI1OH~ Kana je 13BelleH c-T06ushylall Ylapau npBl rlanalaulyje Jlt1 JC Ionnl YllapeH3 023 s nOIJ)TO je BlIlllIO 1a je Yllapau 113Be)1CII a npYl1I Hlt1lOH 012 s op3HHa 3BYK3 113HOCI1 340 m s

a) KOTJHiO c~ UC1tlOUIf )1ueHIf 011 lJeCTa fllje je II)BeneH c106oaaH yaashypall

6) AKO flpaHau KOjl1 cnaja npBor nelltlOlla ca ljCCTOM I13Bol)el-ba cl060llHOr yaapua IaKlana ca nptlBUel KOjll cnaja lpyror rlenaoua ea MjecTo~1 II3BOshyI)el-ba cl0601Hor )llt1rua )1lt10 01 90 Ollpe1IfTiI pacTojeHc 113(1)) r le1 laua

~ 1 YlTpa3sYYHII Talac npOiBBelleH Ha 6pollY nocllije 12 s peruCTpyje ce Ha 6poshy

llY nOCJ1l1je oll6l1jaf-ba 01 llHa Mopa KOJIIIKa Je Jly6l1Ha Mopa aKO 6p311Ha 3BYK

y BOllll 113HOCII 1460 ms

42 Ca jellOr 6pona cy IICTOBpeMemiddot 1-10 ynyheHII 3B)-IHII TalaCII KpOi BOay II Ba1JlYX H a npyshy

rOM 6pOllY cy OBII HJ1aCIl npll IJbeHIf ) pa1~taKY 5 s Dp311Ha

30YKa y Ba1JlY-XY je 340 ms iI )

1l0t1l 1460 mis KOl II KO JC pashy

cTojal-be IUMelJy 6ponoBa

43 KaMeH je IICIT)lllTel-l y 6YHap KOJIIIKO BpeMeHa npOTeKHe 011 TpeHYTKa lIenyshy

WTaf-ba KaMella 110 TpeH)TK3 Kalla ce Ha BPXY 6YHapa 4yje 3BYK nana Ka~eHa )

BOllY lly611Ha 6YHapa je 15 Ill

J

I KaKo cc ryMil411 Bella TCl4HOCT gtfIgteKapCKor TepIOMeTpa 011 c06Hor TepMOMemiddot

rpa

2 Jla J111 ce 1I0lOhy Tep~ OMeTpa ea )KHBOM l OIY Mjeplm1 3111CKe TeMneparype Y ClI6l-1py

3 06jacHifTe npmtjeHY TJIlHeapHOr TOTlJlOTHOr Wllpef-bil KOll 611)leTaJ1HHX npeKT1 ta4a Kojllla ce a)TOMaTCKII )lUbyt-lyjy II IICKJhYlyjy eneKTpI14HH ypel)ajl1

4 -Ia KOjl 06J111K el-lepfllje ee CROlll YH)TpaWl-bil eHeprllja racoBa

- 01 ltJera 3aBllClI KOll11I1Ha TonlOTe KOJ) Tllje_lo nplllCl npll 3arpl1jaBaf-bY HJU1

omyulTa npll xla~)e~bY

6 KaldlU je pa31l1Ka Intejy H)TpaWl-be eHepnlje J1 KOlItlJIIHe TOnJlOTe

a 111 ce YHyrpaWf-ba eHepmja Te4HOCTlI II lJBPCTIIX TIIje1a MO)l(e CBeCnt Ha

dHeTIlIKY eHepn1JY leCTlsua Koje IIX CalJlIl-baBaJY

8 Ita 111 a~OpcentHa TIIje13 Illajy TaJHO ollpe1]eHY Te ~mepaTypy Tonhel-ba

9 KaKo Temeparypa KlYlalba 1i1BlfClI Oll npltT1ICKa

10 KJKO ce Ha1ltBa centa3HIt npe1a)ak 113 lJBpnOr arpenlTHor CTal-ba 1lI1peKTHO Y rashy

conllTO arperaTHO CTal-be

II KaKo ce lIljel-ba TemepaTypa gt1ella npll TO nbeI-by

12 TetnepaTYpa Ra3lIyxa je 27middot C KOJlIIK3 je ancoTf)THa Te~tneparypa Ba3ryxa

13 TetnepaTypa Iena je _3 C KOJ1IIKH je anCOlTH3 Telneparypa Jlella

14 Ancol ) THa TetnepaTypa Ha noopWlIlI1I CYllua II3HOCll 6300 K J13pa311Te o sy

l lIlepar) P ) Ue13I1j) WBUJ rerIepaT) PllUJ CI--LlII

15 AnCOJTyrHa TelnepaTypa Ha KOjOj Ba3ll) npela3f1 y IBpCTO CTaf-be je 73 K il13pa31lTe ony TclnepaTYPY Y UeJ1HljYCOBOj Te~lnepaTYpHoj CKaJ1H

16 KOmlK)1 KOJlIIlJJ1Hy TOilllOTe npllMI1 05 kg BOlle npll )lt1

rplljaBal-bY 011 10 C no J00 C

npH nOBlIwel-bY Ter-lneparype 3a 5 C 200 g )a npll shyl1 KO111lt1l1HY TOilllOTe 4100 1 KOJTIIKI I je cneullcjgtIIYHI

TOrtJlOTH I KanaUIITeT Y_ba

33

aJ Y bVJUJ

6 ) Y Ba3llYxy

EP311H3 3HYKa y BU3LlYXY jc 340 ms a YAOllU 1460 ms

38 HajMalla TalaCHa )])iKIIHU TL1Lca KOjl1 cnlfjenlf 1-IIW IOillte Ila e~lIlTyje IUHOCII 33 mm KOjlllKLl 113HOCII tPPCI--neHullju

ODor TaTJaca Jla 111 lonjeK lOgtKe Ila r a penICTp)je

39 npernocTuHIIMO Ila ce ala31lTe Ha liel1IKO1 KOHllepTY Ha pacTojal-bY 300 01

OIl 1B)nlHIIKa KOHuepT ce TaKol)e npeHOCU II npeKO CaTeJ1I1T3 IlO cIJ)IUJaoua Koshy

jlf je 5000 km YIl3fIgteH OJ ~ljecTa rnje ce KOHuepT OllpAltalla Ko npBJI Iyje MY

31IK) BJI IIHII YIl3TbeHIf cIYWaJ1au

~Omiddot LLBa ne1aOua HLla3e ce 11lt1 $)lI6aICKO1 CT(LllI1OH~ Kana je 13BelleH c-T06ushylall Ylapau npBl rlanalaulyje Jlt1 JC Ionnl YllapeH3 023 s nOIJ)TO je BlIlllIO 1a je Yllapau 113Be)1CII a npYl1I Hlt1lOH 012 s op3HHa 3BYK3 113HOCI1 340 m s

a) KOTJHiO c~ UC1tlOUIf )1ueHIf 011 lJeCTa fllje je II)BeneH c106oaaH yaashypall

6) AKO flpaHau KOjl1 cnaja npBor nelltlOlla ca ljCCTOM I13Bol)el-ba cl060llHOr yaapua IaKlana ca nptlBUel KOjll cnaja lpyror rlenaoua ea MjecTo~1 II3BOshyI)el-ba cl0601Hor )llt1rua )1lt10 01 90 Ollpe1IfTiI pacTojeHc 113(1)) r le1 laua

~ 1 YlTpa3sYYHII Talac npOiBBelleH Ha 6pollY nocllije 12 s peruCTpyje ce Ha 6poshy

llY nOCJ1l1je oll6l1jaf-ba 01 llHa Mopa KOJIIIKa Je Jly6l1Ha Mopa aKO 6p311Ha 3BYK

y BOllll 113HOCII 1460 ms

42 Ca jellOr 6pona cy IICTOBpeMemiddot 1-10 ynyheHII 3B)-IHII TalaCII KpOi BOay II Ba1JlYX H a npyshy

rOM 6pOllY cy OBII HJ1aCIl npll IJbeHIf ) pa1~taKY 5 s Dp311Ha

30YKa y Ba1JlY-XY je 340 ms iI )

1l0t1l 1460 mis KOl II KO JC pashy

cTojal-be IUMelJy 6ponoBa

43 KaMeH je IICIT)lllTel-l y 6YHap KOJIIIKO BpeMeHa npOTeKHe 011 TpeHYTKa lIenyshy

WTaf-ba KaMella 110 TpeH)TK3 Kalla ce Ha BPXY 6YHapa 4yje 3BYK nana Ka~eHa )

BOllY lly611Ha 6YHapa je 15 Ill

J

I KaKo cc ryMil411 Bella TCl4HOCT gtfIgteKapCKor TepIOMeTpa 011 c06Hor TepMOMemiddot

rpa

2 Jla J111 ce 1I0lOhy Tep~ OMeTpa ea )KHBOM l OIY Mjeplm1 3111CKe TeMneparype Y ClI6l-1py

3 06jacHifTe npmtjeHY TJIlHeapHOr TOTlJlOTHOr Wllpef-bil KOll 611)leTaJ1HHX npeKT1 ta4a Kojllla ce a)TOMaTCKII )lUbyt-lyjy II IICKJhYlyjy eneKTpI14HH ypel)ajl1

4 -Ia KOjl 06J111K el-lepfllje ee CROlll YH)TpaWl-bil eHeprllja racoBa

- 01 ltJera 3aBllClI KOll11I1Ha TonlOTe KOJ) Tllje_lo nplllCl npll 3arpl1jaBaf-bY HJU1

omyulTa npll xla~)e~bY

6 KaldlU je pa31l1Ka Intejy H)TpaWl-be eHepnlje J1 KOlItlJIIHe TOnJlOTe

a 111 ce YHyrpaWf-ba eHepmja Te4HOCTlI II lJBPCTIIX TIIje1a MO)l(e CBeCnt Ha

dHeTIlIKY eHepn1JY leCTlsua Koje IIX CalJlIl-baBaJY

8 Ita 111 a~OpcentHa TIIje13 Illajy TaJHO ollpe1]eHY Te ~mepaTypy Tonhel-ba

9 KaKo Temeparypa KlYlalba 1i1BlfClI Oll npltT1ICKa

10 KJKO ce Ha1ltBa centa3HIt npe1a)ak 113 lJBpnOr arpenlTHor CTal-ba 1lI1peKTHO Y rashy

conllTO arperaTHO CTal-be

II KaKo ce lIljel-ba TemepaTypa gt1ella npll TO nbeI-by

12 TetnepaTYpa Ra3lIyxa je 27middot C KOJlIIK3 je ancoTf)THa Te~tneparypa Ba3ryxa

13 TetnepaTypa Iena je _3 C KOJ1IIKH je anCOlTH3 Telneparypa Jlella

14 Ancol ) THa TetnepaTypa Ha noopWlIlI1I CYllua II3HOCll 6300 K J13pa311Te o sy

l lIlepar) P ) Ue13I1j) WBUJ rerIepaT) PllUJ CI--LlII

15 AnCOJTyrHa TelnepaTypa Ha KOjOj Ba3ll) npela3f1 y IBpCTO CTaf-be je 73 K il13pa31lTe ony TclnepaTYPY Y UeJ1HljYCOBOj Te~lnepaTYpHoj CKaJ1H

16 KOmlK)1 KOJlIIlJJ1Hy TOilllOTe npllMI1 05 kg BOlle npll )lt1

rplljaBal-bY 011 10 C no J00 C

npH nOBlIwel-bY Ter-lneparype 3a 5 C 200 g )a npll shyl1 KO111lt1l1HY TOilllOTe 4100 1 KOJTIIKI I je cneullcjgtIIYHI

TOrtJlOTH I KanaUIITeT Y_ba

33

18 Bona Mace 05 kg 3arpHjasa cc 3 min eJleKTPH4HHM rpl1jaQeM CHare 700 W AKo je Ha nOfeTKY Te1mepaTYpa B01le 611JIa 20 C KOJnlKa he 6HTH J-beHa TeMshynepaTypa nOCJlHje 3arplljaBaHxi

19 K OMan MeTaJla Mace 2 kg II cneuI1qH1mor TOnJlOTHOr KanaUHTeTCl 440 J (kgK) OXJlaLUI ce ca Te~meparype 150 C H3 TeMllepaTYPY 50 C J13pa4YHajTe KOJlHshyYHImiddotIYTOIlIIOTe KOjy (eTaJI OTIlYCTI1 npl1 XJlal)eJ-by

20middot JbeKap caBjeTyje naUHjcHTI1Ma HallHjeTl1 118 OMpwaBe IlI-Ijynl1 X1I3llHY BOllY OH TBPlll1 1Ia ce y OpraHI131) ~Iopa caropjeTI1 ollpel)eHa KOJlHnLHa MaCHOne lla 611 ce TeMrrepal)pa Jle)lCHe BOlle ca 0 C lojellHa411JJa ca TjeJJeCHOM Termcpa shyTYPOM Koja I1JHOCI1 37 C KOJI11 KO JJI1Tapa nenelle BOlle oc06a Koja je Ha 1II1jem Mopa lla nonl1je lla 61-1 ~nry6ILTU 400 g MacHone aKO ce npH caropujeBal-by ORe KOJlI1YHHC MaCHohe OCJ10601111 KOJlHlHHa ronJlOTe 011 147 M J

21 Y K)tlU Koja I1Ma conapHo rpHjal-be CYHyeBa eHepnlja ce TPOllHl Ha 3arplfjaBashy

I-be BOlle y pe3epBOapl1Ma 113 KOjl1X BO)la ul1peKTHO llocnl1jeBa Y paul1jaTope

TOKOM neT Be3aHliX 05Jl aYHHX uaHa je nOTpe5Ho 4 000 kJ eHepmje ua 5H TeMshynepal)pa y Kylil1 5l1na CTarrHO 22deg C AKo je TeMnepaTypa SOlle Y pe3epBoapHshy

~a 50deg C KOJlHKa Mopa 6lfTl1 I-bHXOBa 3anpe~fIIHa lla 611 Kyliu MOrJla lla ce

rpl1je

1 2 EleKTpI1-lHl1 yajHBK lmiddotmnYI-bCH je ca 2 I Bone 113 80shy

llOBona YI1ja Te~llleparypa j e 20 C BO)la Y -lajHHshy

KY je nOlleJa lla KJbyya noc~lIje 7 min

a) vl3pa4)tf3jTe KOJlllYIIHY TOrLIOTe Kojy j e Bona

npmuuJa npfl 3arplljaBal-bY

6) KOJJIK3 je CHara CJJeTPHYHOr rplljaYa yrpal)cshyHor y YajHHK aKO cy TOf1JlOTHII ry6111111 3aHeshy

MaplbI1BI

23 K alla ce 360 g BOlle Koja KJby-la CIIna YCTaKJIeHY -law) ~lace 120 g YHja Ter shy

nepaTypa 113HOCH 15deg C no ycnOCTaBJbal-b) TOTVIOTHC paBHOTe)e Tellnepal)pa

BOlle 13HOCH 96deg C KOJHfKlI je cneUHltpJ1YHII TOruIOTH I KanamITeT CTaKJIa

24 Y cyny ce Haija311 J kg BO)le Ha TeMneparypH 25deg C 3aTIIM nOllaMO jow 2 kg

BOlle Ha TeMnepal)pl 35 C KOJl IIKa he 6HTl1 Te~meparypa cMjecel

25 fie6e 06wIll0 fDaIY Kaila ce KYllamiddot

JY Y BOI1B Ifja Te~meparypa je MHoro HIDKa OIl I-bl1X0Be TjenecHe

Tel-meparype (37 C) POlll1TeJbH

oJle CBojy 6e6y 11 npmpeMajy B0shy

llY YCYIJY 3a Kynal-be TaKO WTO 11111 shyjewajy 10 I BO)le H3 60jJlepa TeMshy

neparype 87 C ca RO)lO~1 113 B0shy

uOBOlla reMneparype 12deg C KoshyllH KO rpe6a Y3eTH BOlle 113 BouOBoua lla 611 TeMneparypa Mj ewaBI-lHe 6wla jellshyHaKa TjenecHoj TermeparyplI 6e6e

34

26 J1HTaP BOlle Koja KlhYla el10a ce y 6aKapshyHH mjHI1K llJlja TeMl1eparypa je 10deg C AKO je no ycnOCTaBJhaJ-by paBHOTelKe TeMshyneparypa noue 11 YajHHKa 75deg C H3pal JYshylIajTe lacy lJajH11 Ka C nellJlltpHYHII TOshy

fL10THII Kanall~1TeT 6aKpa je 390 J(kgK)

27 KOtall 1tTltLTa Yllja TCMncpnrypa je 100 C CTUBJbtH je YCYll Y KOMe ce HaJTashy111 3(JO I Tel Hocm lll fja TCM ncpilTypa jt 16 C no ycnOCT3BJbal-bY paBHOTe)f(e JcllIcpaTypa TelHOCTH je 20 C OLlPC1IIITli Macy CT3Jla aKO jc cneumpWIHH IOILlOTlIII KallltlllllTel TC4110CTI1 neT lyra senJl OLl cnelUHpll4Hor TOf1JloTHor KarWUlITcra eT3IH

28 HltljsJlwlI IlO)lOnan I-la cBlljeTY 1-lltL1am ce y BeHeuyeJlII II BlICOK je 979 m lobshy palYl-lajTe 3a KOlIIKO CTeneHH ce nOBeha Te~lIlepaTypa Hone npH nauy cMaTpashy

jyl1Jl 1a ce eaa KllHenl l lKa eIIeprllja Boue nOTpOWJl Ha IbeHO 3arpHjaBal-be

29 Moryhc je lW ce Ien IInonl rplgtal-beI jellHe KOUKllue 0 lp~ ry KO1HKJI je Hajshyl3l-b1 raJ nOTpe6aH 1a 611 ce Ha Taj HaIIIH IICTonllO I g leIla

30 JClellll 6peroBII KOjll rLllmajy y cj c-

BepH() JjeIY AT_1UHTCKor OKeaHa ~

IIpeJCTaBbao onaCHOCT 1a 6pOllOBe bull 360r Tora ce nYT KOJII 6P010811 npcshy

l-13e TOOl ce30HC nOJ311bIlBaI--ha 1eshy

1CH ilX 6perona noaehalla II 33 30 deg0 npCTnOCT3IHI1O la j c nOKYWltlHO

~ l-IWTaBa~lgte _~elleHOr 6plljcra Mace

20 000 I nOlohy Tonl OTHor IBBopa KO1I1KO cHeprlljc je nOTpe6Ho Y_lO)l(iTI-1 Tl fill ce 0111[1 ~O 10 1e)leHOr 6plljera

31 npll OllllpUlhaBUI-bY (lIpeTllapal-bY y 1 e) I kg 1I0lC 1I1111aja CC KO111111113 TOnJlOshyIC 01 ~40 000 J 3a KOlJ1IKO CC MO)f(e nOBIlCIITII e ~lIlepaTypa BOlle lace I kg Ha

pallYII TC KO_1 111 II IIC Tonlon- CnCUI(LHl1 Htl TonIOTa HOlleie 4200 J (kg K)

J KO_111 lIfHIIICllH) cHern lJj Ie nOTpeoHo )middotIOgtIltITI ita 51 1ce 2 kg BOlle Ha Terlshy

nepaTyplf 100middot C IIpeSe)IO) BOlieHY napy CneUIICplllHa TOfllOTll IIcnUpaBal-ha nO1e je 226 MJ kg

33 YajHIIK CHare 2 kW oCTaO je YIObYleH jow 2 min nOWTO je BOlla nOllena lla KTbYlla y13pa 1 lYHajTe Mac) nOlle KOJa je IlcnaplI18

34 Y anapUTY Ja ecnpeco Kacenty BOlleHa n apa l1ja je TCMIlepaTypa 100 C MHjewa cc ca x~a)lHI1M rullIjeKoM Y3HMajyl1ll uaje cncUIIltpIILIHII TOfUJOTHl1 KanaUHTeT

~UJlIJeKa 4200 J (kgK) 113pal lYHajTe S8CY BOJleHe nape nOTpe6HY 118 ce 150 g ~m1jeKa 3arpl1je ca 20deg C Ha 80middot C

35

35 llBwje KOUKl1ue Jlella TeMneparype Omiddot C CTaBJbeHe cy y wwy C3 IGIceJlOM BOshy110M Maca jellHe KOUKHue JleIla je 50 g a y l3WH je npl1je CTaBJb3J-ta )lelIa 6 11 shyJlO200 g KMceJle Balle

a) AKo je TemepaTYpa BOlle 6HJla 25 C KOJlI1Ka tie 6H TI1 TeMneparypa BOlle no ycnocTaBlbaJ-bY paBlWTeJKe

6) K OJlWKa 611 6J1J1a TeMoeparypa Balle llaje y laUJY YMjecTo llBHje CraBJbeHa Call0 jellHa KOUKHua JleLI

36 KomlKa je Maca BOlIeHe nape KOjy 611 Tpe6ano nm1l1jewant ca 150 g Jl eaa 411shy

j a TeMnepaTYpa je Omiddot C aa 611 ce ao6l1Jla Boaa TeMoeparype SOmiddot C T eMnepaTYshy

pa IlOlleHe nape je 100 C

37 KOJIHKO nyrepa Mapa aa noj eae 40BjeK Mace 80 kg aa 611 ce ca HHBoa tapa noneo Ha MOHT EsepecT BHCI1Ha MOHT EaepecTa je 9000 rn a CneUHltjHf4Ha

TormOTa caropJ1jesal-ba nyrepa 113HOCJ1 24 kJ kg

PJEIIIEHlA

36

KUHeMaUlUKG u middote a_~_______----qUflGI-ZUKa UlUII

I HI13 K001 )K]IlIjeo KyrJlJlUa ce A

c DKpehe paBHNljepHo yfiP3lt1HO ( ~ ~)~JlOK jc l-beHO KpeTal-be HltI XOPI1shy

JOHTltL1HOj nOIlT10311 6WlO paBH0shyljepHO 113KJJe HajBcha fip3J1H3

K~Tllllle je YTalKala C 11 D c

Y 3 KOCII iKlllje6 KyrlllUa ce Kpeshy ~ ( he paBHOloljcPHo ycnopeHO LlOK je HeHO KpeTal-be no npenacKY Ha

0pluoHTalHY nOJllory paBH0shy

ljepHo 11aloe Hajlal-b3 fip31lHa

K)Tlllue je ~ TaIKala C II

3 He 3aTo WTO ce TIIje13 MOl) H31111 ~ npecjeYHoj TaIKlI Tpaj elTOpHj a y pa3JTH

1l1T1I TpellrUlIla BpeleHa

KpeTltll-be ~ KOMe je cpeJll-b3 fip3J1Ha Y CBaKOM TpeHYTKY jellHaKa rpeHyrHoj j eshy

CTe paliHOljepHo npar3011IHlIjc KO

5 11a TlIjel0 10)e 11a nOBenaBa fiP3lfHY 11 aKo My ce y6p3al-be ClaHgtyj e yKOJUIshy

KO je npOljeHa y6p3al-ba TaKBa Jl3 0110 oCTaje n0311T1IBHO

6 Tlljelo I 1l1a Rehy cpeJll-by 6p311HY jep je l-berOBa TpeHyrHa 6p3IDla TOKOM lH1shy

TaBor KpeTal-ba Beha on TpeWfTHe 6p3HHe TTljela 2 Tj Tl1jeJIO I 3a BpHjeMe to np(1)e Behll mrr Hero TlIieJlo 2

7 J) n ((l()T ce KPeT(lO lY)I( CPIHHlj3H3 npelil cjcBer~llM nO1Y 6P311HOM l ~ljH je

(IHTCIIJIITeTJelHtlK IlHTcH31ITeTY 6p3JHC B03a 6) nIL10T cc KpeTao llVAlt ~ l cpllulljaHa Kltl cjeBepHO1 1l01Y 6p3HHOM lHjH je

lIHTcll1llTCT Betlll 9D II11TcH31ITeT3 6P311HC B033

8 )lan) nOllaLI1 middot

~a = 5 0 s - V=lOOImh

ybpa311~o Hajnpllje 6P31lHY ayrolOfiHJJa y ~

100000 m = 2778J V = 100 ~ = 3600 s

39

KUHeMaUlUKG u middote a_~_______----qUflGI-ZUKa UlUII

I HI13 K001 )K]IlIjeo KyrJlJlUa ce A

c DKpehe paBHNljepHo yfiP3lt1HO ( ~ ~)~JlOK jc l-beHO KpeTal-be HltI XOPI1shy

JOHTltL1HOj nOIlT10311 6WlO paBH0shyljepHO 113KJJe HajBcha fip3J1H3

K~Tllllle je YTalKala C 11 D c

Y 3 KOCII iKlllje6 KyrlllUa ce Kpeshy ~ ( he paBHOloljcPHo ycnopeHO LlOK je HeHO KpeTal-be no npenacKY Ha

0pluoHTalHY nOJllory paBH0shy

ljepHo 11aloe Hajlal-b3 fip31lHa

K)Tlllue je ~ TaIKala C II

3 He 3aTo WTO ce TIIje13 MOl) H31111 ~ npecjeYHoj TaIKlI Tpaj elTOpHj a y pa3JTH

1l1T1I TpellrUlIla BpeleHa

KpeTltll-be ~ KOMe je cpeJll-b3 fip3J1Ha Y CBaKOM TpeHYTKY jellHaKa rpeHyrHoj j eshy

CTe paliHOljepHo npar3011IHlIjc KO

5 11a TlIjel0 10)e 11a nOBenaBa fiP3lfHY 11 aKo My ce y6p3al-be ClaHgtyj e yKOJUIshy

KO je npOljeHa y6p3al-ba TaKBa Jl3 0110 oCTaje n0311T1IBHO

6 Tlljelo I 1l1a Rehy cpeJll-by 6p311HY jep je l-berOBa TpeHyrHa 6p3IDla TOKOM lH1shy

TaBor KpeTal-ba Beha on TpeWfTHe 6p3HHe TTljela 2 Tj Tl1jeJIO I 3a BpHjeMe to np(1)e Behll mrr Hero TlIieJlo 2

7 J) n ((l()T ce KPeT(lO lY)I( CPIHHlj3H3 npelil cjcBer~llM nO1Y 6P311HOM l ~ljH je

(IHTCIIJIITeTJelHtlK IlHTcH31ITeTY 6p3JHC B03a 6) nIL10T cc KpeTao llVAlt ~ l cpllulljaHa Kltl cjeBepHO1 1l01Y 6p3HHOM lHjH je

lIHTcll1llTCT Betlll 9D II11TcH31ITeT3 6P311HC B033

8 )lan) nOllaLI1 middot

~a = 5 0 s - V=lOOImh

ybpa311~o Hajnpllje 6P31lHY ayrolOfiHJJa y ~

100000 m = 2778J V = 100 ~ = 3600 s

39

1 pa)KeHO apl1JeMe Hana3~fMO no qJOPMYJlH

V 2778 0 - 6I = - I = -- I = J S

a 50

9 )JaTi I DonaUIt

a = 3 2 i V =96 l = 25 s

Tpa)KeHY Gp3I1HY oGIIbeAlt-IIIO ca 11 middot

v= v -a middot6I V =96 -(- - (32-S-)middot 25s V = 16 7

6) Tpa)KeliY GP3I1HY 0611begtKIIMO ca 12

V =l+ a~ l =96 -m

+ (32 -m

)middot25 s lie = 17 6 ms s s

10 )Janl nonallll

I = 2s I = 5~ I = IO s

TpagtKeH) 6p311H) o611betkI1MO ca 7

) lpel I liO npHo ) 6p331-be MOTOUl lKl lltTC

I 5 ~ a=- u = - = 25 r

I I S

)JUbe Ha1a31110 6p311HY v~

= a = (1 ) ) middot IOsmiddot V =I 5l - - ~ bull ~ _ s

II )JaTII nOllaUII

O GILbegtilII IO v6p3Rl-be ay-rmloGIUla ca a ~1 y6p3al-be 6I1UIIKIJIICTC ca al middot

V = ))- lm = S5 ~ [=30so - h l - 11

= 30 1 = 30 s

LlalC JC

1-V 833 a= 0 a= - a = O)8 J middot lO s

l 8 1J_ ) ( = J ( O2S 0= 30~

)JaKJIe y6p3al-bU aYToMo61Ula 11 611UlIKJI l1CTe cy jeJlHaKa n o I1HTe1l311TeTY

11 )Jam nOJlaUI1

a = 98 ~ c = 300 000 ~

40

a) U OHJbe)KHMO OP3HHY CBet-mpCKor op oJla Y Tpa)l(eHOM TpeHyrKY apeMeHCI ca v )JaJbe j e

v =~middot v= 30 000k~ v=30000000~ ]0

Tpa)l(CHO flpHjeMe je

V1= - 13 061224s 850 h

(J

6) nyr KOjll cRe~lIlpcKIi 6pOll npe T) e 3a TO BpujCle je

(98 m )(306 1 0 6 s) ~ al = - 5 = --------- )~46middotIOlJm2 2

11 )JaTII nOJaulI

v =360 ~ I = lOs

a I Y6pJ8l-be tHI IOHa Hala3I1O no CPOPM)lIII

l (100 m) a = a = a = I OJ

t lOs lt

6) H ajlal-b3 JYIKIIH3 flIlCTe ca Koje aBIi0H -fO)e na yueTl I jellH3Kaje n)T) 1(0shy

I II aRllOH npebe JO yln lljcTal-ba

a ~ J =- ~ = 500m2

14 )JaTII nOllltlUII

= 360 ~ s = 18 m

a) KaKo 3pHO nOIIII-bC KpeTal-be 113 CTal-ba llposal-ba II l-berOBO KpeTal-be je

pallHoMjepHo y6p3allO l-beroB8 cpenl-ba llpl1jenHOCT 6p311He Ie

11l = I = 180 m

lt tt 1

1 ) Bpllje~le Koje npoTeKH~ on nOlleTKa KpeTal-ba JpHU 110 l-berOBOr H3J1aCK3

IJ ulljeHll HWlaJ~I~ I O Ha OCHOBY pe1amlje KOjU CJJI1jellll IB llecplIH llU1lje cpeJl-be Hpllje)lHOCDI 6P3I1HC

s 18 111 = - = --- = OOls

v 180~

B) l[aJhe JlaKO Hana3HMO y6p3al-be 3p Ha TOKOM KpeTal-ba Kp 03 UHj eB

V0= - =36 000 4

( smiddot

41

15 11anl nonaUH

(1=2s I =8 ~ 2=4s V2=5~

YfHTeH1lfTeT y6p3al-ba 611 UI IK1IICTe jc

v -v~ 8 m - 5 ~ a = -- (J= (J =15 -

( - ( 4s - 2 s

16 11am noaaulI

a = 6 -n- Vu =12 ~

OllpellllMO Iajnpllje llplIjeMe Koje npOTeKlie 011 no~eTKa KOJelha ao JayCTashyn_bal-ba

f t = 1=2 s

a

Tpar KOleHa lIalUIIO no ltpOplylll

1I1 = = 12 m

2 17 11uTII nOlallll

1= 2 min==120s vo=30~

a) YcJlopel-be HlBa je

I~ 0 = - a = OJ5 lI ~

5) n)T KOjl1 B01 npeTw TOKO KOIel-ba je

~ -- ~ s=1800m )

18 llanl nOlIaUI

11I = 40 ~ s=1200m )[= 15s

a) KaKo je KpeT3l-be aHltOHa paSHOJepHO ycnopeHO TO je V v = ~ 7 1 = 20

jl 2 J I fi

5) BplljeMe Koje je nOTpe6Ho UBIIOHY ua ce 3aycTaBil lIala3mlO 113 ltPopMYlle Koja nl1peKTHO cJJllj cnl1 If] JleltpIIHl1ullje cpelIlhe BpI1jenHOeTlI 6p311He

S =60s

l~

H) 11a 6l1co 01lpelUUTII nYT KOjlf aBI10H npei)e TOKm KOLlel-ba l13palJ)Haj O Hajnpnje ycnopeHe aS110Ha

[ a = - a = 06 7~

[

4]

11aJbe HaJla311MO npel)eHIl nyr no CPOPMYJllf Koja Ba)fltfl 3a paoHoMjepHo yenDshypeHO KpeTa~be ca nOllCTHOM 6P311HOII

1 1 =v tI-a(tI) s =S2Sm

19 I bnll nona Uli

V u = 75 llf lI = 45 ~ s = 88 m

a) 11a fHC~IO HUWJlI opl1jeMe KOjC je npOTeKJlO TOKOlt Koel-ba OJlpelII LlO lIajnpl1je CpellHgt) oplljenHocT 6p311He 8yTmo611f1a

(vu +(1

) ~ J - 60 l middot V =1667 n I -- 2 bull - h JY

3plljeMe Koje npOTeKHe TOKO KO~el-ba je

1=-v 1=5-)8 c0gt bull

or

0) ~IHTelmrreT y6p3aHa a)TO06Ilfla je

(I - 7) _ IS8 -1 = -- 0 -

lO 11a [I nOlaulI

= 1000 m a = 1~

06ILbe)KIIO nplljelle TOKO Iojerce 003 KpeTao paoHoMjepHo y6p3aHo ea II

Bplljele TOKO Koje r ce BO) KpeTao paSHojepllo ycnopeHO ca I HeKa j e [ laKCIIMalHa 6pmHa Imj) 1303 nOCTII)Ke YTOK) KpeTal-ba Tana je c jenHe cTpashy

lie I = al l a TUKof)e Ba)KJ I l = 0l2 IlaKle Ba)l(l I I ~ f2

a) Y)llHO Bpllje~le KpeTal-b3 06ILbe)K11 10 ca t KaKo ce 1303 HU npBoj nOlQshy

Bill III n)Ta KpCTao paoHoMjepHo y6p3aHo TO je

J _ lIl l- ri ) ) shy

I S I m l ] = 1- = 1000 - =3 L62s

V G ~ III

naJbe jc

1= 1 1= 632s

6) MaKCI1MaJlHa 6p311Ha RO)a TOKO KpeTaI-ba je

7= all V= 3162 ~

B) CpenHgtY BpHjeJlHOCT 6p31111e 8ma HarJa311O no aecPIIHllulljll s

11 = - [ - 1 58 $ 1 l fT - bull S

-13

--

a=2 7 v= IOfmiddot

a) AyroM06uJ1 he nperefll1 KaMI10H Y TpeHyrKY Kalla npel)eHH nyreBH B03lffia

6yny jellHaKIl 2

2V I =lO s al 1= - 1 s~ 2 c=V a

6) nyr KOjl1 B0311J1a npeJy 3a TO BplIjeMe 06I1lbe)IUIMO ca s llaKJ1e

=VI ~=IOOm

21 naTl1 nonaUIl

Vo= 30 ~ s = 200 m t = lOs

vfJpallHajMo HajnplIje II HTCI I3I1TeT y6p3alba BarOHa H I3pl1jeMe Koje npOTeKshyHe on OTK34Hflal-b3 BaroH3 no l-berOBor 3aycraBlbal-ba CpeJll-ba BplijeJlHOCT 6p shy

JIIHe BaroHaje

v =~ 7 =ISIm V =417l ~ 2 v h Sf I S

BplIJele Koje npOTeKHe 01 OTKa4aBatba 110 3aYCTaBJbaHgta BarOHa je 5

1= 48 s V

11 flreH 311TeT y6p33Hgta BarOH3 je

10 a c= 01 7 Jla=(

Y 3allaTK) ce Tpli)l(H 11a H3pa4YHa~lo pacTojaHgte 113Mel)y B03a 1-1 sarOHa lOs HaKOH UIIO ce BarOH OTKaHlO To pacTojaibe je)lHaKO je pamIlUH rryreBa Koshy

jll opeJy SO) II BarOH

d = o5 l - s ==luI - (Vol- ~ at 1

) 85 m

23 11aTI OOllaUII

lh=90 0=75- d=50m

lla 611CMO yTsP11IiJlI1 na nl1 he B03a4 ycnjeTII lla I136jerHe cynap 1i3pat lYHaheMo OYI KojB aYTo06~1JI npeJe Il0 3aycTaBJbal-ba BpHj eMe Koje npoTeKHe on noshy eTKa KOiel-ba no 3aycTaRJbaiba aYTm106lJIa je

I =UQ 1=333 s a

I S=lV - 2 01 = 4166m

naKJIe J lt d cy11ap je 1i36jerHYT

44

_ bullbull __ _4 --~

v IO~ Q= j 2 m 1= l s a =O5 T-

a) 113palJYHajMo Hajnpl1j e Bpl1j eMe 3a Koje BarOH npol)e nopen PYJlapa

p 1= 1=432sv

KaKO npBa nonaTa yrJba nana Ha ca nOYeTaK BarOHa a pynap CDaKe ceKYHJle y6auyje jOlll no jeJlH) nonny yrJba TO he OH ycnjem 11a y6aUlf YKYnHO 5 JJonashyTa yrJba y BarOH

6) Bp~tjeMe 3a Koje BaroH npolje nopell pynapa je

r2Jt =Va 1=693s

C1114HJI pe30HOBaibeM K30 y Jll1jeny 3anaTKa non a) nofil1jaMo na he pynap ycnj eTl1 n a y6au1I 7 Jonara yrJba y BarOH

25 11aTll non allH

I I =2min=120s ~ =IOmin=600s t 1 =lmin=120s a l =O5 ~

OapelJlIO HajnpJlje 6p311H) KOjy je B03 IfMao Ha ililOllllUlI nyra Ha KOjOj ce KpeTao paBHoMjepHo npaBOrJJIHlijCKll

v = altl V= 60 ~

C aila IIJpa4YHajMo 1HTeH3IITeT y6p3aHgta BOJa Ha JlJlOHlIlllI nyra Ha KOjOj ce DO] KpeTao paBHoMjepHo ycnopellO

v O J = 05 ~

YKYOIIiI ny-r KOjll B03 npcl)e je

ar a r ~ = SI + 1 + 5) 5 = _I_I + ITt + -21 5=431 km2 ~ 2

26

a V = JO m I o - 5 6 KaKO je KpeTaHgte pallHoMjepHo )cnopeHO TO 11HTeH31ITeT y6p3al-ba HaJIashy

311 MO no ltpOp~f)JII

V 20 7 a = Q middot a=-- a=J5 m

t 8s - - bull

B) ITyr KOj ll je T1j eJIO npeLllJlo ie

I 5= - ar 5 =80m

2

5

lUljarpaMY DaJbe aKO Ha noronaH HallHH ~non IljeMIMO nOBpUJinry rTOa rpaqm shyKOM llo6~ljalo

2s ) 45 s=(l0~) - - + (IO~)4 s + (IO ~+ 20-i- --

2 shy1= 120 m

6) Cpelll-b3 OpJII1I3 KpeTalla TIljcla j e s

V = V =10- T I ~

28 e -lll llHO Kao y npeTXOIlHO~I 3lt1JUlTKY noollj alo

- 45 4s = (S ) - +(8-) middot 8 + (S + 4 1]1) middot shy ~ s 2

s = 104 m

29 OGllbeiKlIO ca l Hajllen) 6pJIIHY Kojy Tflje10 mla TOKO KpeTal-ha Ca rpashy

ltpIIK3 jc

I=20 ~

113pal)lIajlo calla II11TeH311TCT y6p3ltll-ha Koje T1IJeqo ID la TOKO npalL 20 s -peTal ba

a [m ~ 1I

1I = =1--I

Tllje10 ce 3aTI I Kpehe pasHoMjepHo na Je a lIpyroj 1l1lOHlIUII nyTCl y6p3albe jeJHaKo H1111 QaKle (pacentIIK 3aFlllCHOCT1I y6pJal-ha 011 Ilpelemiddot 10 20 30 I~J Ita npltKa3aH Je Ha C1I1UlI

U [ms] JO Qa OIlCMO CKllUllpa111 rpacentItK 3alH1CHOCHI

40 pJJIHC 011 FlpeleHa HajnpllJe IIcnYHllMo cbCIlCny Tafie1Y

o 5 10 15ilsW 30

VI~il 20 25 35 35 -J 20

10 n yr KOjll npel)e ayrmlO61tl IO)f(e lO Haim Kao nOllpUJHHY noll rpacentIIKOI

5 10 15 f [j ] 5s Ss

s = (20 ~+257) middot 2 +(25 1+ 3 5 ~ ) 2 + (35 7) 55

s = 4375m

46

bull - - -~ middot ~ ~ I 4-rJr au-u ILL IU bull - ~)JJ I J I UYliV O CI shy

3YJlTatna jeIlHaKa HYJJJ1

32 T o ce o6j awI-baBa Ha OCHOBY 3aKOHa IIHCPUlljC (I i-byrHoBor 3aKoHa)

33 Be11I1YIIHa Koja KapaKTepllWe I1HepTHOCT TlljcJla je Maca

34 K OJlllua he ce KpeTaTlI YJlHj eBo

35 I - y6p3aHo npaSOJl HlIl1jcKO 2 - paBlioIJCPHO npaBorlllHlljcKO 3 - ycnopellO npanoJII IHl ljcKO

36 He Maci ie cIlojCTIIO Koje 3aBllCII on KOJJl lYIIHe cyncTaHUllje 011 Koje je THjenO CaYl l l-heHO K Ol11 O ce lloBeha CWa TOJlIIKO ce ynehaBa y6p3al-he TaKO na KOmlII IlIK oCTaje eTaJlall

37 A KO JC F = 0 (~i Ha TIIjel0 He lJjenyjy C1Lqe lU ll je I-hllXOB8 pe3YJITaHTa jenHashya HYJIII) Talla je 0 = 0 (Tj 1IIje1o ce HaJIa311 Y CTalbY MJfpOBal-ha ~111 ce Kpehe paBHoMjepHo npallOJlllHl1jCKJI )

38 K aKO cy IIflTCH31lTeTl1 CILla Kojl1Ma TlIjela IIHTeparyjy lel)yc06HO jellHaKH ern J-b)THOIl 3aKOIl) TO Ha OCHOIlY lpyror J-bJTHoRor 3aKOHa c1lljealllla je OJI1I0C Iaca Ollll X Tl1jeqa 06PHyro nponopllllOHaJaH ollHOCy I-hllXOB1IX y6p3al-ha Tj

i = a~ 7 ( shy2

39 Cll1e aKllllje II peaKllllje pal1J11yjy ce no Cljep) II HanallHoj TaYKlI

~(j KO11111a he ce KpeTaTll Y cIjep) cynpOTHOM 01 KpCraJ-ba ROlle

41 Ilpeaenello Ha je]IIIlt centOplyla APHCTOTe1 TBpnll F - I lIOK M il 3HaMO aa 113 II i-b)THOBor JaOHa Cll1jeJlJl F - a Tj IIHTell31ITeT Cllle -oja lJjenyje IJa TIjeshy_10 cpa3l11jepaH jc y6p]aJ-bY TIIjela QaK1C A pIICTOTel Hllje 6JfO y npaBY

42 06ILbe)j~I IO y6pJaJ-be npBor mjcla ca ( 1 y6p3al-he apyror m j e13 ca al TTyr Koshyjll TlljelJa npela3e ca s KaKo je Iaca llpyror TlljeTJa lila nyra lI1al-ha ollll1ace npshyHOI Tlljela II Ha TIIje1a lljel yj ) C~Lle IlcTor IlllTeHmiddot3JITeTa TO j

a = 2 0 1

AKO npernoCTaRIlMO 118 THjela nOYII I-bY na CC Kpehy In CTal-ba fIIpOBal-ha Tana Ie

S = -2 0 1 = 1I

a

~ -

KaKO a2 = 2 01 TO je

~ 1 2 = _T

- Mf - I ~ 2

Tj TBpIll-ha Koj) je lICKa3ao JleoHapJIona BlIIiYlI HlIje TallHa

47

lUljarpaMY DaJbe aKO Ha noronaH HallHH ~non IljeMIMO nOBpUJinry rTOa rpaqm shyKOM llo6~ljalo

2s ) 45 s=(l0~) - - + (IO~)4 s + (IO ~+ 20-i- --

2 shy1= 120 m

6) Cpelll-b3 OpJII1I3 KpeTalla TIljcla j e s

V = V =10- T I ~

28 e -lll llHO Kao y npeTXOIlHO~I 3lt1JUlTKY noollj alo

- 45 4s = (S ) - +(8-) middot 8 + (S + 4 1]1) middot shy ~ s 2

s = 104 m

29 OGllbeiKlIO ca l Hajllen) 6pJIIHY Kojy Tflje10 mla TOKO KpeTal-ha Ca rpashy

ltpIIK3 jc

I=20 ~

113pal)lIajlo calla II11TeH311TCT y6p3ltll-ha Koje T1IJeqo ID la TOKO npalL 20 s -peTal ba

a [m ~ 1I

1I = =1--I

Tllje10 ce 3aTI I Kpehe pasHoMjepHo na Je a lIpyroj 1l1lOHlIUII nyTCl y6p3albe jeJHaKo H1111 QaKle (pacentIIK 3aFlllCHOCT1I y6pJal-ha 011 Ilpelemiddot 10 20 30 I~J Ita npltKa3aH Je Ha C1I1UlI

U [ms] JO Qa OIlCMO CKllUllpa111 rpacentItK 3alH1CHOCHI

40 pJJIHC 011 FlpeleHa HajnpllJe IIcnYHllMo cbCIlCny Tafie1Y

o 5 10 15ilsW 30

VI~il 20 25 35 35 -J 20

10 n yr KOjll npel)e ayrmlO61tl IO)f(e lO Haim Kao nOllpUJHHY noll rpacentIIKOI

5 10 15 f [j ] 5s Ss

s = (20 ~+257) middot 2 +(25 1+ 3 5 ~ ) 2 + (35 7) 55

s = 4375m

46

bull - - -~ middot ~ ~ I 4-rJr au-u ILL IU bull - ~)JJ I J I UYliV O CI shy

3YJlTatna jeIlHaKa HYJJJ1

32 T o ce o6j awI-baBa Ha OCHOBY 3aKOHa IIHCPUlljC (I i-byrHoBor 3aKoHa)

33 Be11I1YIIHa Koja KapaKTepllWe I1HepTHOCT TlljcJla je Maca

34 K OJlllua he ce KpeTaTlI YJlHj eBo

35 I - y6p3aHo npaSOJl HlIl1jcKO 2 - paBlioIJCPHO npaBorlllHlljcKO 3 - ycnopellO npanoJII IHl ljcKO

36 He Maci ie cIlojCTIIO Koje 3aBllCII on KOJJl lYIIHe cyncTaHUllje 011 Koje je THjenO CaYl l l-heHO K Ol11 O ce lloBeha CWa TOJlIIKO ce ynehaBa y6p3al-he TaKO na KOmlII IlIK oCTaje eTaJlall

37 A KO JC F = 0 (~i Ha TIIjel0 He lJjenyjy C1Lqe lU ll je I-hllXOB8 pe3YJITaHTa jenHashya HYJIII) Talla je 0 = 0 (Tj 1IIje1o ce HaJIa311 Y CTalbY MJfpOBal-ha ~111 ce Kpehe paBHoMjepHo npallOJlllHl1jCKJI )

38 K aKO cy IIflTCH31lTeTl1 CILla Kojl1Ma TlIjela IIHTeparyjy lel)yc06HO jellHaKH ern J-b)THOIl 3aKOIl) TO Ha OCHOIlY lpyror J-bJTHoRor 3aKOHa c1lljealllla je OJI1I0C Iaca Ollll X Tl1jeqa 06PHyro nponopllllOHaJaH ollHOCy I-hllXOB1IX y6p3al-ha Tj

i = a~ 7 ( shy2

39 Cll1e aKllllje II peaKllllje pal1J11yjy ce no Cljep) II HanallHoj TaYKlI

~(j KO11111a he ce KpeTaTll Y cIjep) cynpOTHOM 01 KpCraJ-ba ROlle

41 Ilpeaenello Ha je]IIIlt centOplyla APHCTOTe1 TBpnll F - I lIOK M il 3HaMO aa 113 II i-b)THOBor JaOHa Cll1jeJlJl F - a Tj IIHTell31ITeT Cllle -oja lJjenyje IJa TIjeshy_10 cpa3l11jepaH jc y6p]aJ-bY TIIjela QaK1C A pIICTOTel Hllje 6JfO y npaBY

42 06ILbe)j~I IO y6pJaJ-be npBor mjcla ca ( 1 y6p3al-he apyror m j e13 ca al TTyr Koshyjll TlljelJa npela3e ca s KaKo je Iaca llpyror TlljeTJa lila nyra lI1al-ha ollll1ace npshyHOI Tlljela II Ha TIIje1a lljel yj ) C~Lle IlcTor IlllTeHmiddot3JITeTa TO j

a = 2 0 1

AKO npernoCTaRIlMO 118 THjela nOYII I-bY na CC Kpehy In CTal-ba fIIpOBal-ha Tana Ie

S = -2 0 1 = 1I

a

~ -

KaKO a2 = 2 01 TO je

~ 1 2 = _T

- Mf - I ~ 2

Tj TBpIll-ha Koj) je lICKa3ao JleoHapJIona BlIIiYlI HlIje TallHa

47

3 11aT11 nonaUI1

F = 40 k N III = lOt

113 n HJy-rHOBOr 3aKOHa Clll-1jenH

F 40 kN 40000 N a =4a = - a = -- a= 1

In 10 l I 0 000 kg

4 11aTII nonaUIl

= 5 N ( = 50f

vl3 II l-by-rHoBor laKOl-a cJHljenl1

F 5 N 11= - 11= --- m = OJ kg

a ( 50 )

15 LIaTIl nonauu

In =20t TTl = ) l a =1--

YKynHa Iaca Bma je

m = II + 11~ m = 25 t TTl =25 000 L

CILla sy-le je

F =ma F = 25 000 N F = 25 kN

~6 )laTII nonauu

11 = L5 l = 1 500 kg f = 8 5 V =20 ~

ybpaI)llajMo Hajnpllje y6p3athe 3)rrOM 06lIna

V (20 ) a = 25 a= - a = -g- - f

BYlHa CllHa MOTopa je

F=ma a=1500kg middot 2s ~ F = 3750N

47 llan1 nonauu

In = 2 160 kg (= 30 s s = 500 m

l--i3pa-lYHajMo HajnpHje y6p3al-he ay-ro106 ~Jla

2s a =-- a= 111 ~

f gt gt

i1lrreH3HTeT cHIle Koja njeHyje Ha KaMUOH je

F=ma F = 2 400N

48

48 llaTli nonauH

m = 100 kg F = 100 N I = lOs

Y6p3al-he rpatleBIIHcldlX KOlll1ua

F 1I = -

bull a=J

1m

KaKO KOJll1ua nOYllJ-bY KpeTaJ-be 113 CTal-ha Mllpollalha II peily ce pasHoMjepHo y6pJaHO TO je

V=ar v=10 -yen-

1 2 5 = - af s = 50 m

2

49 LIaTll nonaUII

m = I t = 1000 kg V = 1 5 T 1 =05 s

Y 6pJal-be Hocopora

1 a = - a=30 JI

CILl a KOjO~1 je Hocopor ajeloBao Ha n pBO jellHaKa j e 110 11HTeHJllTeTY CILll1 Koshy

j O1 je npBO uje)IOBaJlO H3 Hocopora )laue

F = ilia F =30000 N F = 30 kN

50 llan nonault

m =350 kg 1 0 =120 V =62 ~ 1= 17 s

HirreH3l1TeT y6p3aJ-ba Ka~HOHa

V -1 a=~ a = 09 5 ~ middot

f

Kao caHllYK He K111311 no KaMIIOH) TO je -beroBO y6p ~a-be jelHaKO yGp3aHgtY ltt lIlnH CI HHTeHmTeT Cll~e Koj a lie_~)~ie Ha caWl) j e

F =Ina F =332 N

51 flaTU nonaUII

F = 20N m = 900kg 1= 24h = 86400s

a) Y6p3al-be CBe~lIIpCKor fipolla je

F ([ = - a = OO))

111 bull --

6) Oy-r KOjH cBe~IHpCIGI GpOll npel]e 3a jellaH llaH je

I s=-ar s = 82114560m s=82 11456km

49

naTH nOLlaUI1 nil =40 kg 1I12 =50 kg F = lo N

OCHOSY 3aKOHa aKUllje 11 peaKul1je je

FJ=lON

)he je

F 0 1 = 02 54- S bulldeg1 = In

Fl 0 = 011 s - m

I nanl nO)la1ll1

1 == 40 kg 111 =84 kg d = 15 m F2 =52 N 1

HHTeH3UTeT CI~e KojOM caHKe I1jerlyjy Ha njeBoj4HUY je no 3aKOHY aKwlje 11

pea KllIlje

F = 51 N

a Y6p3albe caHKlt je F

o=~ a =062- - nl bull bull J

6) Y6p3albe ljeBoj4llUe je

F a = 1 0 1 = 0 1~1

l 1 - 51

B) O)lpe)lIlMO Hajnpllje KOlI1KO he BpeMeH a npOTenl1 O)l n04eTKa KpeTal-ba LlO TpeHyrKa Ka)la ce njeBojlllua 11 ca~e cycpeTH) n 04eTHo paCTojal-be njeBojltIHUe II eaHKJi jellHaKo je 36Hpy nyreBa Koje OHe npe)y no eyepeTa

a al = 51 + s~ d == ~ +2 2d = (0 +a1)

-- shy1d

= ~al+a2 1= 633 s

nyr KOj l1 njenoj4Hua npelje je 1

5 =- deg11 sl = 26 m 2

54 )laTtl noaaUI1

v = 10P-1 == 05 s m=50g

Onpe)lI1MO HajrrpHje y6p3a~be Jlonntue K aKo je 6p311Ha KOjoM ce nonnrua 0 611ja oa 3HLla I1CTor npasua Ii IIHTeH3IHeTa a cynpOTHor cMjepa OLl 6p311He Koshy

JOM je JIOnHlUa Yllapwa Y 311Ll TO je

50

a= 2l a =40 l I shy

lJaKJle

= I a F = 2

55 npallau ClUTe I npaauu 6p311He 3aK1anajy yrao 011 90

56 TfljeJlo he ce KpeTaTlt no TaHreHTI1 y Ta4KH npeKIILla

57 naTIt noaaml

U=91~ a=38 ~

el) nOJl)llpeltIHltK alleTcKe CTa3e ie

7 2 R=(i =213m

KoplICTefllf OH-laTI Inpa] 3a o6ml Kpyra llo6llja1O 113 je UY)KltHCl aBeTshyeKe CTa3e

t = 2Rr = 140 m

(i) I3plljele J oje j e nOTpc6HO cnpil HTep) 13 npclw UIfJCl) ltTa3) je

t1= - =15 l - J

SR LaTtl IloaUII

Ilt = 11400 km 1= 24 h

Tl1j elo Koje ce HClla31f 11lt1 3eLblHOI elU3aTopy o6111)e Kpyr lllljlt je nOl) npeIHltK jelHa nlllynpelHIIK) 3e~ -be Ja jeaall JaH llaKTJe 6p31tHa HgtCmiddot one pOTallltje Je

1R = ~ = 16 7551l~ = 46542 -i-

I

UeHTpltneTalHO y6p3aHgtC je

l a =R = 0034 no bull

i Y cl)lajy lla ce TlfjeIO IHi1Cl311 ) ra4H 1l1Ja Je reorpatPCka WltpltHa 45 middot OHO 3a jC1lall Llall o611be Kpyr nO1ynpe IIlIIKa

rv2

r = R 2 = 4 52548 km WTO ce ~IO)Ke Bl lJlJeTlt ea clI IKe

~ Taua j e 6p3ltHa TujeTJa

V == 27 = J 18477 ~ = 32910

5

U eHTpHneTallHO y6p3al-be je 2

a=~= O024 - r bull

59 llaTH nOllaul1 t

a =200middot V = 30000 Im mu sl i

MI1HHMaJUH1 nOJlynpe4HI1K Kpyra )1) Koj er COHQa MO)f(e lla ce Kpehe 113shy

HOCH ~ 9 108

R n = IL = m = 45 middot 106 m = 4500 km m a 200

60 nam nOQaUH

n=5 T= 1 min R= 10 m Bp~tjeMe 3a Koje ce BawapCKa BpTewKa 06pHe OKO cBoje oce je

I = ~ = 11 s

~HTeH3HTeT 6p311He njeTeTa je

2Iar71= -- = S24

t

UeHTpJ-meTaJIHO y6pJa-be H3HOCI1

- vmiddot = 274~ a- R

6L nanl nOllaUI1

R == 27 m

Y HajBHwoj TalKlt -berone nyr3-be Ha apTHc-ry njeJlyjy ClUla 3eMJbHHe Te)e 11

ClfJla peaKUl1je nOllJlore Kao WTO je npHl(a3aHO Ha CJlI1UH

N - G

KaKO ce apTHcr3 Kpehe KP)I(HO TO Bpoundl)(H l

N +mg= mV R

WHTeH3lHeT CHJle peaKUl1je nOllJlOr e j e

2 N== mvR -mg

52

MHHHMamry 6P3KHy apTl1cTe npH KojOj 01-1 11 llaJbe ocraje Y KOtmucry C DOMoshyrOM HaJJa3l1MO 113 YCJlOBa lla je HHTeH3l1TeT Cl1Jle peaKllHje nOllJlore jeQHaK H)shynH Tj

N =0 ~V2 = mg v =gR V= fiR = 514~

62 naT nOllaUI1

m = I 600 kg R = 190 m v = 20 ~

UellTp~meTaJIHa CJ1Jla Koja njeJlyje Ha ayroMo611JJ j e CHna Tpel-ba

F = mv-1

R

Lla ayroM06lUl He 611 CJleTItO c nyra Mopa lla B3)I(I1

Fr lt mgJ1 Tpa)f(eHa MHHHMaJJHa BpHjeJ(HocT KoeqmUI1jeHT8 Tpelha je

mg = v Ii = = 02L

63 11a111 nOQaUI1

R = 25011

- HajBlIwoj 184KI[ -ber OBe nyrafhe Ha ayrm106~Ul njerryje CHrla 3 eMJbHHe Te)f(e II Cilla peaKlll1je nOJVTOre Kao WTO je npl1Ka3aHO Ha CJIlHlH

bull

Pe3YJITaHTa OBIIA nB~ ljy CI1Jla npellCTaBJba ueHTPl1fTeTaJJHY CI1JJ) naKlle

mvmiddot Ii y=mg -I

jl1J npen01He jeIHaIIfHc c1I1ieQI I

nnZN=mg - shy

R

MaKC~n1aJTHY 6p3HHY npu KOjOj he ayTOM06l-U1 OCTaTH Y KOHTaKTY C nOllJlOrOM HltLla31IMQ 113 YCJlOBa

N =O naKJIe

Jg_mv-1

mg = -_ v = gR =495) lR - s

-

TpaBUWauUOHO LlOfbe

l He I paSllTUUlIOIIU CILla 1I~la TaKBY npJlp0ny 11a ce nljeJla He IOry H30110nanl on l-beHOr nejcna nOK iC TO lOryhe 3a lIeKe upyre CIlJle Ha npl-IMjep eJleKshy

Tp l lillIe ILq 1 ~tarHCrHe

2 AKO npeTnocTaBlIMo na je HljeJJo 3anOLH~JlO KpeTal-be 113 CTaJ-ba MltpOSalba OHO 611 ce KpeTaao y6p3allo CBe nOK lie crllme no ueHTpa 3e~l)be rnje 511 6p3~IHa TJljC13 Gll13 IUKCll1a1Ha no npoJaCKY KP03 uellTap 3eMbe TlljeJlo 611 ce Kpeshy

ralO ycnopeHo II 3aycTanlLIO 611 ce Ha IUlac) In ryHela

~ rIpauulI no Kojmta Ka 3eLbll narajy TlIjela Koja Hiley nOilynpTa Will 06jeweshy

lIa elljelty cc y ueHTpy 3eLle

4 OOILbeJKIIIO rpaBIIHlUlloHY CIL1Y ea r Iacy Tlljel a Koje ce Kpehe non ncjshyClBml rpuBlITaulloHc CILle ca 11 II y6p3al-be TlljCJJa ca a Ta11a Ha OCHOS) II I-bnHoMor 3aKOHa saiKlI

= JIllbull

l-byrHOU 3aKOH rpaBIITaUllje LIaCII

JIlF= r

1--1 j OMIIX lI1l1ljy pelaullja no6I1jaI-lO

- ylt(1--

r

flalCII y6pJaibe rpaBllTaUi lOHe tlLle He JaBllCl1 on ~Iace Tllje1a

5 T epaJllje 61t OILle ) paBHOrCJKl1 II Hltl Mjeceuy jep je Maca nljeJla IICTa 6e3 05middot mpa Ule LI vllu HLItJII

6 K) L1IIua he OCTaTII ) n01o)Kajy Y KOjll ClO je nOCTaSllmt jep Y 6eCTe)KlIHCkOM CTal-bY IIU I-b) He njell)je Cltla Koja 6 11 loma na j e spaTH YpUSHOTe)KH11 nOIOshy

haj

7 Ha Behlt~1 HllCIIHUMa jc Iathe y6p3al-be 3e~LbIlHe Te)(e II Ba3n)X je pje1)H

8 ViHTeH31fTeT rpauliTaUllOHor nOba YToj TaYKH ce Hehe npOIljeHI1nJ

9 fla Te)f11Ha TIIjeml j e CHJla KOjOM Tlljello YC1lgteLl 3eM1lgtHHe Te)le njenyje Ha HeshynOKpCTHl1 OCJJOHau IL~H 33Te)(e KOHau 0 KOjlt je o6jewell0 110K je 3CMJMlHa Te)Ka clUJa KOjOM 1e~Jlba npl1RJ1alIl TJljeJla KOj3 ce HaJJaJe y l-beHoj 6JTH311HH Y cJTyltrajy lla ce THjeJlO HaJJa3H y CTalbY MIlpOB3l-ba IUllt ceo Y OllHOCY Ha 3eM1lgtY Kpehe paBHoMjepHo npaBoJllllmjcKlt OBe nSllje CIUle mrajy 11CTH npaBau oljep

5

H HHTeH311TeT aJJH P33JJI1Ywry HananHY TltlLJKY HanaLlHa TaLJKa 3eMJbHHe Te)f(e je Y TaLJ](f rnje ce HMa311 Te)f(1f1UTe Tl1jeJla a Te)(mta ujeJlyje y TaLJ1ltl1 BjeWatha 111111 OCJlOHua Te)l()1Ha rujeJla Mo)(e 611TI1 jenHaKa HYlIH 31111 Ii Y 6eCTe)lUfHshyCKOM CTaHy Ha TI1jeJlo H LlaJbe ujeJlyje 3eMJhltHU Te)l(a

10 He Te)f(HHa Hfjena ce He MlljeHgta aKO ce T1tjeJlo Kpehe y6p3aHo y XOPI130HTaJJshyHO~f npaBUY

lJ ViHTeH311TeT CllJle 3e~I1lgtIIHe Te)Ke je sehl1 Ha nOJTY Hero Ha eKBaTOpy jep je 3eshyJJba CnJbOWTeHa Ha nOJlOSliMa Tj Ha nOJlY je lal-be pacTojal-be 0Ll TarKe y KOjOj ce TlljeJlO HaJla3U no ueHrpu 3eMJbe

12 He 3e~JJbIlHa Te)(a If ilaJbe ujelIYje Ha TI1jeJIO Koje ce HMa311 y 6eCTe)l(l1l-ICKOM CTaI-bYmiddot

13 )la To je lOryhe yKOJIIIKO ce Tl1j eJlo Hal)e y JHfQgtry KOjH ce Kpehe y6p3aHo J1

4ltje je y6p3al-be YCMjepeHo BepTl1KaJJHO HaHJDllte Tall-a je IIHTeH311TeT Te)f(HHe

0= m (g - a)

3a nOBOJbHO BeTJIIKO a oncer Bar c he 6unt nOBOhaH na ce I-ljep~1 Maca nrjeJla Heka ) TO~I CJTYlajy Bara nOKa)(e ~Iacy 11 KaKO je nOKa31IBal-be Bare nponopshyLlIIOHa1HO re)fIIHII Tnjerla TO je

m Q m g nllKJIe

m m = (g - a)Q

11 111 = ---shy

(g - a )la 6HnO Onpell-iL11I Iacy TIIjeJla MopaMO 3HaTII y6pJal-be JlIIQgtra H BpHjenshy1I0CT ~Iace Tlljel]a y 1] 1IQgtry KojU ce Kpehe paBHOljepHo y6pJaHO y6p3al-beM c ~ljepeHII~1 nepTlIKa1HO HaHlDKe

~

14 061IJbe)Kl I~10 ca Q Te)KllliY JOBjeKa Kana mtQgtT ~IIpyje IUlH ce Kpehe paBHoshyljepHo npaBO]ltHlljcKl1 Tana je

~ ~

a) Q = mg ~ ~ ~

6) Q = m (g - a)

~ ~ ~

) Q = m (g + a) ~ ~ ~

I Q = III (g - oj = 0 ~ ~ ~

il) Q=m(g - O)=mg

nOKa3HllaHgte 1Iare nponOpUl10HaJJHO je Te)lllHl1 tlonjeKa

15 He ApHcroTeJl Hllje 6110 y npaBY jep CBa THjeJIa Koja CJI0fiOnHO nanajy non ynlshyuajeM 3eM1lgtUl-le Te)l(e IfMajy neTO y6p3albe

16 06a THjeJJa he HCToBpeMeHO nocnjeTli Ha XOPI130HTaJlHY nOl ulOry

55

TpaBUWauUOHO LlOfbe

l He I paSllTUUlIOIIU CILla 1I~la TaKBY npJlp0ny 11a ce nljeJla He IOry H30110nanl on l-beHOr nejcna nOK iC TO lOryhe 3a lIeKe upyre CIlJle Ha npl-IMjep eJleKshy

Tp l lillIe ILq 1 ~tarHCrHe

2 AKO npeTnocTaBlIMo na je HljeJJo 3anOLH~JlO KpeTal-be 113 CTaJ-ba MltpOSalba OHO 611 ce KpeTaao y6p3allo CBe nOK lie crllme no ueHTpa 3e~l)be rnje 511 6p3~IHa TJljC13 Gll13 IUKCll1a1Ha no npoJaCKY KP03 uellTap 3eMbe TlljeJlo 611 ce Kpeshy

ralO ycnopeHo II 3aycTanlLIO 611 ce Ha IUlac) In ryHela

~ rIpauulI no Kojmta Ka 3eLbll narajy TlIjela Koja Hiley nOilynpTa Will 06jeweshy

lIa elljelty cc y ueHTpy 3eLle

4 OOILbeJKIIIO rpaBIIHlUlloHY CIL1Y ea r Iacy Tlljel a Koje ce Kpehe non ncjshyClBml rpuBlITaulloHc CILle ca 11 II y6p3al-be TlljCJJa ca a Ta11a Ha OCHOS) II I-bnHoMor 3aKOHa saiKlI

= JIllbull

l-byrHOU 3aKOH rpaBIITaUllje LIaCII

JIlF= r

1--1 j OMIIX lI1l1ljy pelaullja no6I1jaI-lO

- ylt(1--

r

flalCII y6pJaibe rpaBllTaUi lOHe tlLle He JaBllCl1 on ~Iace Tllje1a

5 T epaJllje 61t OILle ) paBHOrCJKl1 II Hltl Mjeceuy jep je Maca nljeJla IICTa 6e3 05middot mpa Ule LI vllu HLItJII

6 K) L1IIua he OCTaTII ) n01o)Kajy Y KOjll ClO je nOCTaSllmt jep Y 6eCTe)KlIHCkOM CTal-bY IIU I-b) He njell)je Cltla Koja 6 11 loma na j e spaTH YpUSHOTe)KH11 nOIOshy

haj

7 Ha Behlt~1 HllCIIHUMa jc Iathe y6p3al-be 3e~LbIlHe Te)(e II Ba3n)X je pje1)H

8 ViHTeH31fTeT rpauliTaUllOHor nOba YToj TaYKH ce Hehe npOIljeHI1nJ

9 fla Te)f11Ha TIIjeml j e CHJla KOjOM Tlljello YC1lgteLl 3eM1lgtHHe Te)le njenyje Ha HeshynOKpCTHl1 OCJJOHau IL~H 33Te)(e KOHau 0 KOjlt je o6jewell0 110K je 3CMJMlHa Te)Ka clUJa KOjOM 1e~Jlba npl1RJ1alIl TJljeJla KOj3 ce HaJJaJe y l-beHoj 6JTH311HH Y cJTyltrajy lla ce THjeJlO HaJJa3H y CTalbY MIlpOB3l-ba IUllt ceo Y OllHOCY Ha 3eM1lgtY Kpehe paBHoMjepHo npaBoJllllmjcKlt OBe nSllje CIUle mrajy 11CTH npaBau oljep

5

H HHTeH311TeT aJJH P33JJI1Ywry HananHY TltlLJKY HanaLlHa TaLJKa 3eMJbHHe Te)f(e je Y TaLJ](f rnje ce HMa311 Te)f(1f1UTe Tl1jeJla a Te)(mta ujeJlyje y TaLJ1ltl1 BjeWatha 111111 OCJlOHua Te)l()1Ha rujeJla Mo)(e 611TI1 jenHaKa HYlIH 31111 Ii Y 6eCTe)lUfHshyCKOM CTaHy Ha TI1jeJlo H LlaJbe ujeJlyje 3eMJhltHU Te)l(a

10 He Te)f(HHa Hfjena ce He MlljeHgta aKO ce T1tjeJlo Kpehe y6p3aHo y XOPI130HTaJJshyHO~f npaBUY

lJ ViHTeH311TeT CllJle 3e~I1lgtIIHe Te)Ke je sehl1 Ha nOJTY Hero Ha eKBaTOpy jep je 3eshyJJba CnJbOWTeHa Ha nOJlOSliMa Tj Ha nOJlY je lal-be pacTojal-be 0Ll TarKe y KOjOj ce TlljeJlO HaJla3U no ueHrpu 3eMJbe

12 He 3e~JJbIlHa Te)(a If ilaJbe ujelIYje Ha TI1jeJIO Koje ce HMa311 y 6eCTe)l(l1l-ICKOM CTaI-bYmiddot

13 )la To je lOryhe yKOJIIIKO ce Tl1j eJlo Hal)e y JHfQgtry KOjH ce Kpehe y6p3aHo J1

4ltje je y6p3al-be YCMjepeHo BepTl1KaJJHO HaHJDllte Tall-a je IIHTeH311TeT Te)f(HHe

0= m (g - a)

3a nOBOJbHO BeTJIIKO a oncer Bar c he 6unt nOBOhaH na ce I-ljep~1 Maca nrjeJla Heka ) TO~I CJTYlajy Bara nOKa)(e ~Iacy 11 KaKO je nOKa31IBal-be Bare nponopshyLlIIOHa1HO re)fIIHII Tnjerla TO je

m Q m g nllKJIe

m m = (g - a)Q

11 111 = ---shy

(g - a )la 6HnO Onpell-iL11I Iacy TIIjeJla MopaMO 3HaTII y6pJal-be JlIIQgtra H BpHjenshy1I0CT ~Iace Tlljel]a y 1] 1IQgtry KojU ce Kpehe paBHOljepHo y6pJaHO y6p3al-beM c ~ljepeHII~1 nepTlIKa1HO HaHlDKe

~

14 061IJbe)Kl I~10 ca Q Te)KllliY JOBjeKa Kana mtQgtT ~IIpyje IUlH ce Kpehe paBHoshyljepHo npaBO]ltHlljcKl1 Tana je

~ ~

a) Q = mg ~ ~ ~

6) Q = m (g - a)

~ ~ ~

) Q = m (g + a) ~ ~ ~

I Q = III (g - oj = 0 ~ ~ ~

il) Q=m(g - O)=mg

nOKa3HllaHgte 1Iare nponOpUl10HaJJHO je Te)lllHl1 tlonjeKa

15 He ApHcroTeJl Hllje 6110 y npaBY jep CBa THjeJIa Koja CJI0fiOnHO nanajy non ynlshyuajeM 3eM1lgtUl-le Te)l(e IfMajy neTO y6p3albe

16 06a THjeJJa he HCToBpeMeHO nocnjeTli Ha XOPI130HTaJlHY nOl ulOry

55

I I XOPl130HTaJlHa KOMnOHeHTa 6p3Htle KOll Kocor XHU8 Kao H KOn XOpI130HTaJIshyHor XI1U8 He MOry 118 6yny jellH8Ke HYJTH K 8ll8 je XOPH30HTaJlH8 KOMflOHeHTa jenH8Ka HYJ1 H OHll8 ce KOCH XJITau CD011H H8 SepTHKaJlHH xwrau 8 XOpH30I-lT8shyJlHl l Ha CJlOfi011HH na11 THJeJl8

18 THjeJlO K011 Kocor gtIlua l1OCTlUe faKCI1ManHY Dl1CHH Y oH11a Kalla je BepTJ1KaJIshyHa Ko~moHeHT8 fip3l1He (KOMnOHeHTa 11))1lt y-oce) jeilHaKa HyJll1

19 Cse Tpl1 ltPYil6aJ1cKe JlOfTTe llOCTIDKY HCry D~ICI1Hy TOKOM KpeT8l-ba na cy BpeMeshyHa Koja OHe npODell) y Sa3il)XY jl el)ycofiHo jellHaKa Tj

I I = 12 = r~ KaKO cy BpeMeHa Koja cy JlOnTe npOBene y Oa3JlYxy I1CTa XOpl130HTaJlHe KOM nOHeHshy

Te nOleTlie 6p31IHe ce Mel)yco6Ho OllHoce Kao H 1-b~IXOBH 110MeTl KaKo je

dl lt d2 lt dJ TO je

V Igt lt v~ lt VJ

10 npna KOCIIfIKa 6p3IlHa Ia pa3)lII l llfTe spBje11HocHI 3a pa3Ha He6ecKa Hjena

Ha nplljep 3a 3eMJbY je 79 kms Mjeceu 17 kInso BeHepy 74 kms a 3a CYHue 437 kms

21 11am n011aUII

1=24~

a) BpHjee TpaJal-ba clo6onHor nalla je

(24 ~j ) J = ~ 1=- shy = 245 s g (981 )

6) BHcHa ca Kojeje LleKlfh nao ie

J bull II = 2 g r II =294 o1

22 11am nOllauu

r = 33 s

a I 6P311H ltI lome np Yllap~ 0 no je

l = g IV = 981 ~ 33 s V = 324 11- bull gt

6) BHClfHJ KplIBor TOpl-ba y nl1m je

g r 1 =2 II = 534 o1

B QaTl1 nonaulI

V u = 12 ~ r = Is

THjeJlo ce Kpehe paBHoMjepl-lo y6p3aHo y6p3al-beM g na je TpagtKeHa 6p311Ha

v=vo +gt V= 12 ~ +9 8 1 ~ middot Is v =2181~

56

24 Jlan nOll8UI1

I = 5 m I == 25 s

061UbegtKl l llfO y6p3al-be cjT060111l0r nalla Ha Mjeceuy CJ gm Tana je

2 _ gI - 27 - 16 1--- g~1 - 2 gM - bull 7

2

JaLlIl Ha rpaBI1T8U1OHOr nQJba Ha Mjeceuy je

GM = 16 fg

25 naTII nonaUII

1 = 300 m

KaKO ltjgtoToanapal lt106011HO Ilalla TO je

I I1 = 2g r l]

(2h = g

1= 781 s

26 Janl 1l0113UIf

II =4501 = 12m

11 3paIYHajMo t-l3JnpHJe Bpllje~le 3a Koje WTan CTlfrHe 110 nOBpWI1He BOlle

2h (=~g

(= 303 s 3a nplfje~e I ya13U npet)e nrr s na je l-beroBa 6p31fHa

sV= - v=4 1l1 1 bull

27 jlaTI nOJaUlt

6s I s

BIIClIHa ea Koje je mjelo naJIo

II = -gr _- h = 17658 m

nrT KOjH THjeno npel)e TOKOI npRllx 5 S KpeT3l-ba je

g( - tlt s = 122625 m$= 2

57

Oyr KOjH HljenO npe~w Y nOCJbeLlIbOj ceKyHJIH KpeTaJ-ba j e

amp = II - s ru ~ 54 m

28 )laTil nOJIaUII

l~= 14 ~ 1=8s

BIICIIH Cl lIa KOjOj ce HaTJa3110 XeJHlKOnTep YTpeH)TK) KaJIa je naKeT IfcnYWTeH 13 Xe1ll lKOmepa jCJlHaKa je n)TY KOj l1 naKeT Ilpel)e OIl TpeH)TKa I1cnyllJTal-b3

110 naJIa lIa TJlO

II =lV +21 g r II ~ 426 m

29 QaTII nOJIaUlt

n = 1225 m 1 =4 s

a) Bpllje~le lloTpe6Ho CTpllj eml JIa JIODe JIO HajBlIllle Ta4Ke cfloje IlYTalbe je

2huu 1 = -g--shy

1 = 5s

6) ViHTeH3lneT 6pJIIHe CTplIJele npl l-beHOM yaap) Y nOJ101) je11HaK je IIHshy

TeH11ITeTY 6p311He CTplljele y -rpeH)TK) Kalla je OHa OllaneTa Tj

1 = V =g I =49 ~

B) 6p311Ha CTpllje~e H3 Kpaj) eTBpTe ceKYHlle KpeTal-ba je

I =[ - g t V I = 981 --

311 )lanl nOJIalUI

SI = 50m a =2 -j v=3~

YynHo BpllJe~le KOJC Je na 106paHaU npOBCO y B3311YXY jerlHaKo je 3611PV Bpeshylelia Tpajal-ba CJl0601ll-1Or nalla If paBHo~ljepHo ycnopeHor KpeTal-bCl vi3palYshy

HajIO Hajnp llje splljele Tpajarba CJI060JIHOr IlClJIa

07 t=~g

1 = 319 s

OJIpe1ll1MO caJIa 6P311HY nClIlo6paHua Y TpeHyTJ OTBapal-ba naIl06paHa

Vo = g tl vQ=3L32-T

BpnjeMc paBHOMjepHo ycnopeHor KpeTaJ-ba je

(vo - v) o = n = 1416 s12

5

IlaKJle YKynHo Bpl1jeMe Koje je nano6paHau npOBeo y Ba3nyXy je

I = I + l~ 1 = 1735 s

31 IlaTII nonaUH

II = 134 m v)= 25 ~

YKYllI-lQ Bplfjele Koje je 10ma npOBCTJa y Ba3JI) xy je 361p npeMeHa Koje nposhyTeKJ-Ie TOKO YCni l l-barb8 _1orTTe 11 Bpele Ha Koje npOTeKHe TOKOM ClI06onHor nalla Vi3pa-l)HajlO Hajnpllje BpujeMe Koje npOTeKlle TOKO~ ycnl1J-barba nomeI

J = ~ = 255 s g

MaKclIMaJlHa BllCI1Ha (y Olll-lOCY Ha lIIBO Jfpane) Ha Kojy loma nocnl1je je

I m-gt = 1gl( 11m = 3186 Ill

HaKOII IIITO -Ioma tOCTllfHe HajBIIW) Tal 1lt) cBoje n)Tarbe OHa CJJ060UHO naJa

H = II + Ii H = 4526 Ill

BrllJel e Tp3Jalla C10UUllHOr nala jc

2H = g

(~ =304 s

Y) III 10 Bpllje~le Koje je _loma IlPOBe13 y Ba3JYXy je

r= II+11 1=56s

32 DaTil noaaJlI

lima = 76 cm =076 m II = 60 em =06 ll1

a) YKyn Ho BplIJe Me KOje KowapKaw npoaelle y B31DYXY Je

217 I=V-gshy

1 == 039 s

6) KowapKaw CJlo6onl-lo r1aJ1a HaKOI-) WTO JIOCTIlfHe HajBllwy Ta-lKY cBoje nyrarbe vl3parYHajMO Hajnpl1je Bpl1jeMe -rpajalM CJl06011HOf nana ea B11 shyCHHe 76 CIll Ha RHCIIHY 60 cm

l = 2(hnux - II)

g

I =O18s

59

YKynHo BpHjeMe Koje KOUJapKalli npOBene Ha BI1CI1HH Behoj on 60 COl je

2 = 21 2= 036 S

33 )lam 110naUH

a = m = 60 kg V = 10 7 ~ i~

a) T egtKIIHa 1IjeqaKa je

Q= IIIg = 5886 N

6) K aKo je clUla IIHepUlije YCljepeHa cynpoTHo on CI1M TegtKe TO je Te)(fHa

njelaKa

Q= meg -- a) Q= 4686 N

34 Ilam nonaUll

m = 100 g = 01 kg Tmu = 15 N

a) Te)IIHa ~) rlilue YlIHtny KOjll c106oQHO nana je

Q = 0 na ce npela TO le H~1T Hehe npeKI1Hyrii

6) KaKo cWla 11HeplHIje II CIUla Te)Ke mlajy UCTH c~ljep TO je TegtKIHta K)DJl1 shy

ue

Q=m (g +a) Q= 1681 N

KaKO je Q gt 7 HilT he ce npeKIIH)lI1

35 l llTII 11011aUII

Uo = I 0 ~ = 019 5

a) PacTojal-he PQ je pacTojal-he Koje crpeJllma npet)e nY)I( BepTI1Kane

PQ = g_ r

= 018 In

6) PacTojat--be IIrpala 011 ~leTe y TpeHYTKY Kanaie 6al1l10 crpeTJ11 uy je

d = ll = 19 m

36 nanl 11011aUlf

= I m d = 12 In

al BpHjele Kojeie ROnTa npOBeJla y 1la3nyxy

[2h 1= Vg = 045 s

60

6) lla 6~ICMO onpenwm HHTeH3HTeT 6p3HHe nonTe HenOCpeQHo npl1je Hero UlTO je OHa nonl1pHYJJa nOMory OnPCnHMO Hajl1p~lje Hl-ITeH3I1TeT XOpHshy30HTanHe 11 BepTHKaJlHe KOMnOHellTe 6pJHHe

V = cJ = 266~ I t ~

V = gf = 443 ~

J1aK1e

v = lv 2 +v 1 =517 v ~ 1 I S

37 llaTII 11011aI1l1

ci = 18m Vo = 150 Lm II = 2 In a) nOlJOllllHY pacrojal-ha no XBaTilLJa Jloma he npehll 33

d

T = = 0216 s c

6) lloma he no XBaTalta cTillm 3a

I = d =0432 s Ib

Da 611 YXllaTIIO 10(11) XRaTalJ Tpe6a ita nOCTltlBI1 PYKaBIIUY Hltl RIICIIHY g~

H = h - 2 = L08 m

38 J1aTII l1onauu

d = 30 m Ii = 2 cm a) Bpl1je~le Koje ie leTaK npOBeo Y B331lYXY je

r]h - = 0064sg

(j ) nOleTHiI 6p311 Ha )lleTKa je

v = q = 46981 o I

39 DaTll nonaUII

R = 15 m 1 = 2 In d = 10m

11a 6uclIIo OJlpemVlIJ ueHTpimeTaTJHO y6p3albe Koje je KaMeH ulao npllje npeshyKI1ilal-ha IHlTII 1I3pa4YHajMo HajnpHje nOLJeTHY 6p311HY KaMeHa

BpHjeMe Koje je KaMeH npOBeo y Ba3nyxy je

2h f = Vg = 0645

6

bull LV lI Ll J -

d V = I = 1566 bull

UeHTpHneTaJlHO y6p3al-be KaMClla npl1je npeKHJlal-ba HI ITIi je

v~ U = ~ = I 6350JJlR 1

40 )lam nOJlaWI

1 = 520 km l = 76 km R = 6400 km m = 79 kg

rIOJTynpe lIlIlK nyral~be 110 KOjOj ce Kpehe ClleMflpCKa CTaHIlua je

= R + II = () l)]O km

UeHrplwe-ranHO yup131he KocMollaynl je

III (I = - =835shyr bull

HHTelHllTeT rpalllITallllOHe ClLle Koja njeJlyje Ha KOCIOHaTa Je

F = 11 = 65940 N r

]

el U uonV fttJfCftU rUIrrFFgtl7Irrrrrerrll

1 He Tlljel0 lie 1O)f(C 611TII y paIlHOTe)f(H aKO Ha I-bera ojeJlyje caMO jeLIHa CIVIa

2 YC101l 1Ia ce TIIje10 HaJla3Jl y paBHOTe)l(H je lla pe3YJrraHTa OBIIX UBl1jy CMa 6yshy

Jle jCllHaKa Ii)ll To je Moryhe aKO CIUle IIMajy 11CTI1 npallau H I1HTeH3HTeT a cynpoTaH cljep

3 )la 611 pe3Ymiddot1TaIlTa mlal3 M3KCH)IltLl3H IIHTeH3I1TeT ClUTe ~Iopajy IlMaTJI HCTM npaB3U II c~ljep Tj I-bIiXORli npasull Mopajy 3a101anaTI1 yrao 011 0deg

4 AKO lIa T1fjeTJo Jljerryje Benl 6poj CILla 11 rb) THOll 3aKOil rJlaclI ~ ~ ~

R = UIII rllje je R pe3YJITaHTa CIl11X cl~a Koje lljelyjy Ha Tllje10 m Maca TIIjeshy~

Ia ltl ( l-beroBo y6pJal-be

5 K oecj)JfUlfjeHT Tpel-ba 3USI1CII 0Jl IOJleKYICKe CTP) KTYpe Tl1jela II nOJlJlore 11 HeshypaBlllllia lIa nOBpWIIHI1 Tllje_la

6 JlaHUIi ce CTaBJbajy Ha TOIKOBe a)TO106IUla KaKO 611 ce nOflenao KoeqmuujeHT Tpel-ba l13feIJ) TOlJKOBa 11 3anei)ellor n)Ta

7 )lccPop laulIje TeTl ll~e Ha ~lYKY ItJa3~lsa Cllla e13CTIIIHOCTII

8 Y TO) Tpe 611U11K1JlCTa nOBuja TIIje~lO II Cn) WTa naB) KaKO 61 CMalMIO CHshyIY oTnopa na3nyxa Koja Ha I-bera ojeJlyje

9 Kll ulHe Kantl II Cl-be)f(He naXYbllUe KP03 aTJlOccentepy Kpehy ce pasHoMjepHo

11panO)1 11Hl1jCKII jaTO WTO ie pe3YJTTaHTa CBltx CILla Koje Ha I-bIIX neJIyjy jeJlHashy

Ka lIy111 Tj CllIla rpallllTaullje je no II11TeH3J1TCTY jeuHaKa 3611PY (Me OTIIopa R83ilyxa II CIIle nOTIICKa ) B83JlYXY

10 Ha nOlllOpHIIUY I1ieJl ~j) cJbenel)e CIIJ1C CIU111 nOTllCKa CI L18 OTnopa BOlle CHshyItl rpaRlnalllje Cllla IlYIe ()Tnpa

11 npi l oTllapal-bY naJl06paHa 6p3HHa naJl06paHUa ce olal-byje a IIHTeH3HTeT cushytIe oTnopa BaJUyxa ce nonehaBa

12 Ha K111Kep njeJlyjy CJbellehe C1Lle C1UI3 nOTIICKa CIUla rpaBilTaul1je CHJ1a peaKshyul1je nHa nOCYlle

3 4elln ce He JlP)f(1I Ha cpellllHI1 llpWKe jep 611 Y TO cTlYlJajy ~IOMeHT CIVIe Koshyj ll njeJlyje Ha PYKY 0110 JHaTHO Betlll

14 lla 611CMO nOllllrJHI Henl TepeT n01lOhy nOJlyre Ha CJl06011aH Kpaj nOJlyre He IOpa-lO ojeJlOBaTH CILfJOM Belll1KOr HHTeH311TeTa YKOJlliKO je KpaK CHJle 1l0BOJbshyHO BCJIHKJ1 OBa TBpJll-ba 61u1a je n03HaTa ApXl1Meny A rlll aKO 6u HeKO nOKyshywao Jla nOW-Irne 3eMJbY nOMohy Ul1HORCKe nOJlyre 6110 611 My HeOfTXonaH

63

ocnOHall KOjH 611 ce Mopao HWTa3HTH naneKO y KOCMH4KOM npoCTopy UITO Hlttshy

paBHO Hl1je Moryhe OCTBapHHI

6paBa Ha BpaTHMa HHje Y4BpwheHa Ha cpellllHI1 Bpan I1JlH 6nIDKe wapKaMa 3ashyTO WTO 611CMO Y TOM cJly~Jajy lOpaJ1l1 njelloBaTI1 CHJlOM 3HaTHO Belier HHTeH311shy

TeTa Ha 6paBY na 611cI0 OTBOp~UlIl BpaTa

I TIljeJlO ce Kpehe TpaHCJlaTOpHO Kana Ha -hera He )ljenyje HHKaKan MmleHT C~Ule UJlI je pe3YJlT3HTa CBIL~ MOMeHaTa CIIJle KOjll Ha TIIjeJlO lJjenyjy jeuHaKa HYJUI

7 HHTeH3HTeT Cl1lle TpeJ-ba je HajBelil1 y CJl)lajy 2 jep je Taua HajBehll 11HTeH3Hshy

TeT CIme KojOM Tl1jeflo ne1yje Hop~lanHo Ha noDJlory

~ Anani (opy1)a) 1Ilja ce ynorpe6a 1aCHlfBa Ha npl1HllImy nOJlyre cy KJll1jewTa

MaKa3e KpUKafll1ua 3a opaxe rpaOeBI111CKa KOJllllla Inn

9 r pacentlllIKJI1 nYTe~1 KOpl1cTetm npaBwlO napaneJlOrpa~3 n06 I1ja~1O na je I1Hshy

TeH11HeT pe1YJlT3HTe

R = 5 N

no IICTor pe3yrrraTCl MOr~11 CMO lloflll I I palfYH-CKII ny-reM nplI ljeJ-bYJyhl1 rTllTarOpIIH) TeOpe ~ry

2 = F 12+ F2 OJlaKle llo6J1ja~1O R = 5 N

~O DaTIl I1Ola UII

FI = 12 N Fl == 8 N

K ana Ha Tllje_lo llel)jy lBllje CILle 3a IIHTeH3ltTeT

pe3Y1TaHTe B3gtK1t

If - F ~ R ~ (~ + F~)

Y KOHKpeTHml cl)4aj) 1l0611jalo

4 N lt R ltlON

Cana je 1a1lt0 plljewllTll 33laTaK

a) rta f)) na R) He r) na

21 naTl1 nonaUII

-1 = F ~ = 1800 N

1 I

II

v 1 ~

PlljewmlO npBO 3anaTaK rpacentlIll shy

KII npIIMjeJ-b)jyhll npaBltJlO napashy_lejJorpaMa (KopHcTehll MIUlIIMeshy

TapCK~1 nanl1p)

i1HTeH3IneT pe3YJlTaHTe je

R = 17 3 FI R = 3 I I 4 N

~

64

LJV u JcsYJJIlttrltt Monll1 (MU uUIII~ IJQ1yn

D 7

(

A B

KaKO je JI3 YCIOBa 3amlTKa (j = 60deg TO je Tpoyrao ABD jeJlHaKOCTpaHlI4Clil na

JC llYgtK AC = ~ h rne je Ii BIlCllHa jeilHllKOCTPClHIIII10r TpOYL1a ABD Tj IlIHel shy311TeT pe3YllTaHTC je

R = v3 f

R=3114N

11 Jl aTII nonaUII ~

1 = F = 500]1 (( = 120

Ha C1I1I3H Ha411H Kao y nperxonHO1 JallaTKYJ0shy6l1ja~1O Ja je HHTeH311TeT pe3YTraHTe

R = 500 N

23 PjeweJ-bc je np1IKa3ltlHO Hll Cl IlUII

-~

J~~ ~

~ FIT

24 UaTl nOllaWI

~ = 80 N F = 40 N (1 = 60deg

rpaCI)MIKO pjeweJ-be je npIIKa3aHO Ha CllI1UI1

Fh = 693 N

3allaraK CIO ~lorT)1 plljellillTii pa4YIiCKII

KaKO je a = 60 II F =20 TO je I1HTeH311TeT XOPl130HTaJlHC KOMnOHCHTe

65

IF

~

~

- 3 F - 2

~ = 693 N

25 flaTH nOJlaUI1

Q = I N i == 00 5

HHTel-l3lITeT CllJIe Tpet-ba j e

Fir = Q p Fir = 005 N

26 IiaTIi nOJlau

F = 150kN Fu= 130 kN

IHreH31HeT pe3YJJraHTe je

R = F - Fr R == 20 kN

KO1n03I1Ullja ce Kpehe paBHoMjepHo y6p3aHo

27 laTH nOnltlUH

Q == 5 kN = 5 000 N Il = 002

It HTeH311TeT BytlHe cme BYl e KOjOM 511 rpe6aJ1o Jla njenyjeMo Ha caHKe Jla 5u ce OHe Kper31e paBHOljepHo npaBo11IHHjcKI1 jeJlHaK je HHTeH3l1Tery Clue rpet-b8

F = Ftr F == u Q F == 100 N

28 ]an1 nonaUI1

III == 20 kg F =80 N

KaKo ce JoYfllja Kpehe paBHoMjepHo npaBoJlHH~ljcKH TO j e I HTeH3~ITeT BY4He

CI1JIe KOjOM njetJaK njeJJyje Ha K)TUjy jenHaK I1HTeH3HTel) calle rpet-ba

F= Fir FIr == 80 N

C npyre crpaHe CIUa Tpet-ba j e

Fir == 1 gm rj

Fu == _ 11_ 1 == 04 mg

29 Jam nonaUI1

I = 100 N rJ == 80 N p == 04

OnpentlMO Haj npllj e Macy opM3Ha KOjH je nyH newa Vl HreH3JITeT cl1J1e KOjOM

njelJyjeMo Ha opMaH nyH Bewa jenHaK j e HHTeH3Hr ery CHle rpel-ba

FF = (M +m)gp M + m == _ I M + m == 2548 kg

gp H a CJJW1aH HalmH MO)KeMO o)]pe)]IITH H mcy n pa3110r 0pMaH3

FM == - M == 203 9 kg

gp

66

~~~ U~LUa UJI1 ce HaJla3HU y vpany )

m = 2548 kg - 2039 kg m = 51 kg

30 flam nOJlauw

F I = 5 N Q~ == 100 N II = 01

Ihpa4YllajMo Hajnplfje TeO IHY caHKH vlI-rreH3l1TeT BytlHe CIUle KojoM M I1JlaH iIjeJlyje H3 npa3He caHe je)]llaK j e I1HTeH3)1TeTY Cl1JJe rpel-ha

Fr = Qp Q =---l Q = 50 N P 1

~fTeH]IITeT BYIlIe CliTJe KOjy 611 MJ1JIaH Mopao lla ynoTpl1je611 aKO Ha caHKe cj eJlHe l-beroBa ~Ilal)a ceeTpa llparaHa jeCTe

Fe = (01+ Q2 )P F2 = 35 N

1 1 Ita-III nOllaUlI

r bull = 72 = 20- M =06

~1JraIYHajIO II HTeH311TeT y5pJut-ba aYTOIOOllJa Ha OCHOB) J-bY-Tl-IOBOr 3a 0 IIa w6I1ja 10

ilia =mgp = fJl a = 5886 no bull(J

BplIjefe oje npOlelVie on nOIeTKa Ollet-ba 110 3aYCTaBbat-bU CI)TO106wJa je

U I = ---- I 34 s a

32 llanl nOJlaUl1

I = 80 kg II = 5 m h = 12 m a) I1HTeH311TeT 3eLbIlHC TeJe Koja 1ljelJ)je Ha 311lapa je

Fg = IIIg Fg = 7848 N 6) il))l(IIHY KpOBa OJlpel]yje1O 113 rr rnaroplIHe TeopeMe

( = II I +b C= 13 m

B) VI HTe1l311TeT aKnIRH C KOtnOHeHTe Cl we Te)l(C je

F = m~h F = 3018 N

r) Vl HTeHJJlTeT HOpt3TlHe KOltnOHeHre CJL~e Te)Je je

f~ = mgb F = 7144N n fl n

33 nanl nonaulI

II == 5 m h = 12 m

KaKO Ma4Ka KJl ll 311 paBHoMjepHo npaBOJHIHHjCKJI HID KPOB IJHTeH31rreT CHJle rpeHa jeJlHaK je HHTeH31HeTY aJoTII BHe KOMnOHeHTe clme re)l(e Koja njellYje Ha

Ma-lKY

67

F = F F = F IJ = mgh = mgLlb oJlaKJIe nOCJlHje cKpali HBal-ha Jl06MjaJO bull umiddot or ~ Q

h = 042=t 34 )]aTI1 nOllaWI

h = 3m Q= 5 m m = I 5 kg

I1HTeH3HTeT CI1ne Tpel-ha Koja JIj enyje Ha JlHjere jeJlHaK je mlTeH311rery aKTUBshy

He KOMnOHeHTe O Ule re)Ke

- F F - I11gh F - 88 29 NFIf - a u--e- tr - I bull

35 )]anl nOllaUI1

Q= 200 N F = 50 N r=== 4 h

VlHTeH3lrfn I3Y4He c~lJIe jeJlH3K je 1611PY HHTCH31HeTa CIIJlC rpetbCl II akTI IBHe

Ko-mOHCHTe clue Te)Ke

Qh F = F + F = Fr+-~ F === 100 N

36 )]anl nonaun

m =40 kg (1 === 30 f1 = 05

II

3(ftmiddotmiddotmiddotmiddotmiddot ~

11 1 t

Cmiddotmiddot~middot

Ha OCHORY cmlKe 3aKJbYl lyjeMO

C b = Qmiddot311=2 2

a) LIaJbe JlaKO Hana31H1O HHTeH3llTeT aKTHBHe KOMnOHeHTe c~UJe Te)Ke

F = mgh F = mg F = 1962 N - J Q 2 ) II t

6) YI HTeH31neT HOpMaTlHe KOMnOHeHTe 3eMJbl1He Te)Ke j e

= ngb F = 339 8 N F e n n -shyB) JtI HTeH3HTeT cl1J1e Tpetba je

Fr === FnLl f r = 1699 N

68

r) KaKO Je F gt Ftr nHje-re ce Kpehe paBHoMjepHo y6p3aHo

37 UaTI1 nonaW1

h = b I = 02

TIpI1Ml1j eHHrIO 11 l-bYrHOB 1aKOH 1-1a KpeT3-be Tl1jeJla HI13 CTPMY pasaH

mgh mell b h Ie ma = F - F ma =-- - - or-middota = g(_ _ ~)

bullbull Ir ~ e Q ~

K aKO je Ii = b TO j e

~ = h-J2

)]CLbe je

2 a= g T(I -u)

a = 5s5~ smiddot

38 LIaTlI nOJlaWI

Q = lOON u=IScm =0)5m

MOeHT CI11e jenHaK je npmnBOny OUle If KpaKa CllJle

H = Q a M = 15 Nm

39 JlaTli nOllltlUII

Q I kN 1000 N M = 1500 Nm 0 0

lIKIlHa ~lexaHII~IKe PYKe j eJlHaKa je KpaK) ClUJe r j

- M a = 15 m a - Q 40 DaTll nonaUII

QI = 300 N Q2 = 800 N aJ =15m

YCJlOB paBHOTe)Ke j e

Qt2 MI = M Q al = Qp~ a l = Q 1=4 m

4 1 )]aTII nOlIaUf

In = 70 kg 1112 = 60 kg 1113 = 20 kg d = d = 2 m

0611Jbe)JI1~10 pacTojalhe rrje4aKa 01 TatlKe OCJIOHua KJIaUKaTlliUe ca dJ 113 YClOBH paRHOTe)l(e MOeHaTa Jl06I1jaMO

n~gd = IJ1gdl + m~dJ

OJlaBlIe je d) = 1m

42 LIanl nOJlaUlI

m = 50 kg ao 1 m b = 06 m

69

- 3 F - 2

~ = 693 N

25 flaTH nOJlaUI1

Q = I N i == 00 5

HHTel-l3lITeT CllJIe Tpet-ba j e

Fir = Q p Fir = 005 N

26 IiaTIi nOJlau

F = 150kN Fu= 130 kN

IHreH31HeT pe3YJJraHTe je

R = F - Fr R == 20 kN

KO1n03I1Ullja ce Kpehe paBHoMjepHo y6p3aHo

27 laTH nOnltlUH

Q == 5 kN = 5 000 N Il = 002

It HTeH311TeT BytlHe cme BYl e KOjOM 511 rpe6aJ1o Jla njenyjeMo Ha caHKe Jla 5u ce OHe Kper31e paBHOljepHo npaBo11IHHjcKI1 jeJlHaK je HHTeH3l1Tery Clue rpet-b8

F = Ftr F == u Q F == 100 N

28 ]an1 nonaUI1

III == 20 kg F =80 N

KaKo ce JoYfllja Kpehe paBHoMjepHo npaBoJlHH~ljcKH TO j e I HTeH3~ITeT BY4He

CI1JIe KOjOM njetJaK njeJJyje Ha K)TUjy jenHaK I1HTeH3HTel) calle rpet-ba

F= Fir FIr == 80 N

C npyre crpaHe CIUa Tpet-ba j e

Fir == 1 gm rj

Fu == _ 11_ 1 == 04 mg

29 Jam nonaUI1

I = 100 N rJ == 80 N p == 04

OnpentlMO Haj npllj e Macy opM3Ha KOjH je nyH newa Vl HreH3JITeT cl1J1e KOjOM

njelJyjeMo Ha opMaH nyH Bewa jenHaK j e HHTeH3Hr ery CHle rpel-ba

FF = (M +m)gp M + m == _ I M + m == 2548 kg

gp H a CJJW1aH HalmH MO)KeMO o)]pe)]IITH H mcy n pa3110r 0pMaH3

FM == - M == 203 9 kg

gp

66

~~~ U~LUa UJI1 ce HaJla3HU y vpany )

m = 2548 kg - 2039 kg m = 51 kg

30 flam nOJlauw

F I = 5 N Q~ == 100 N II = 01

Ihpa4YllajMo Hajnplfje TeO IHY caHKH vlI-rreH3l1TeT BytlHe CIUle KojoM M I1JlaH iIjeJlyje H3 npa3He caHe je)]llaK j e I1HTeH3)1TeTY Cl1JJe rpel-ha

Fr = Qp Q =---l Q = 50 N P 1

~fTeH]IITeT BYIlIe CliTJe KOjy 611 MJ1JIaH Mopao lla ynoTpl1je611 aKO Ha caHKe cj eJlHe l-beroBa ~Ilal)a ceeTpa llparaHa jeCTe

Fe = (01+ Q2 )P F2 = 35 N

1 1 Ita-III nOllaUlI

r bull = 72 = 20- M =06

~1JraIYHajIO II HTeH311TeT y5pJut-ba aYTOIOOllJa Ha OCHOB) J-bY-Tl-IOBOr 3a 0 IIa w6I1ja 10

ilia =mgp = fJl a = 5886 no bull(J

BplIjefe oje npOlelVie on nOIeTKa Ollet-ba 110 3aYCTaBbat-bU CI)TO106wJa je

U I = ---- I 34 s a

32 llanl nOJlaUl1

I = 80 kg II = 5 m h = 12 m a) I1HTeH311TeT 3eLbIlHC TeJe Koja 1ljelJ)je Ha 311lapa je

Fg = IIIg Fg = 7848 N 6) il))l(IIHY KpOBa OJlpel]yje1O 113 rr rnaroplIHe TeopeMe

( = II I +b C= 13 m

B) VI HTe1l311TeT aKnIRH C KOtnOHeHTe Cl we Te)l(C je

F = m~h F = 3018 N

r) Vl HTeHJJlTeT HOpt3TlHe KOltnOHeHre CJL~e Te)Je je

f~ = mgb F = 7144N n fl n

33 nanl nonaulI

II == 5 m h = 12 m

KaKO Ma4Ka KJl ll 311 paBHoMjepHo npaBOJHIHHjCKJI HID KPOB IJHTeH31rreT CHJle rpeHa jeJlHaK je HHTeH31HeTY aJoTII BHe KOMnOHeHTe clme re)l(e Koja njellYje Ha

Ma-lKY

67

F = F F = F IJ = mgh = mgLlb oJlaKJIe nOCJlHje cKpali HBal-ha Jl06MjaJO bull umiddot or ~ Q

h = 042=t 34 )]aTI1 nOllaWI

h = 3m Q= 5 m m = I 5 kg

I1HTeH3HTeT CI1ne Tpel-ha Koja JIj enyje Ha JlHjere jeJlHaK je mlTeH311rery aKTUBshy

He KOMnOHeHTe O Ule re)Ke

- F F - I11gh F - 88 29 NFIf - a u--e- tr - I bull

35 )]anl nOllaUI1

Q= 200 N F = 50 N r=== 4 h

VlHTeH3lrfn I3Y4He c~lJIe jeJlH3K je 1611PY HHTCH31HeTa CIIJlC rpetbCl II akTI IBHe

Ko-mOHCHTe clue Te)Ke

Qh F = F + F = Fr+-~ F === 100 N

36 )]anl nonaun

m =40 kg (1 === 30 f1 = 05

II

3(ftmiddotmiddotmiddotmiddotmiddot ~

11 1 t

Cmiddotmiddot~middot

Ha OCHORY cmlKe 3aKJbYl lyjeMO

C b = Qmiddot311=2 2

a) LIaJbe JlaKO Hana31H1O HHTeH3llTeT aKTHBHe KOMnOHeHTe c~UJe Te)Ke

F = mgh F = mg F = 1962 N - J Q 2 ) II t

6) YI HTeH31neT HOpMaTlHe KOMnOHeHTe 3eMJbl1He Te)Ke j e

= ngb F = 339 8 N F e n n -shyB) JtI HTeH3HTeT cl1J1e Tpetba je

Fr === FnLl f r = 1699 N

68

r) KaKO Je F gt Ftr nHje-re ce Kpehe paBHoMjepHo y6p3aHo

37 UaTI1 nonaW1

h = b I = 02

TIpI1Ml1j eHHrIO 11 l-bYrHOB 1aKOH 1-1a KpeT3-be Tl1jeJla HI13 CTPMY pasaH

mgh mell b h Ie ma = F - F ma =-- - - or-middota = g(_ _ ~)

bullbull Ir ~ e Q ~

K aKO je Ii = b TO j e

~ = h-J2

)]CLbe je

2 a= g T(I -u)

a = 5s5~ smiddot

38 LIaTlI nOJlaWI

Q = lOON u=IScm =0)5m

MOeHT CI11e jenHaK je npmnBOny OUle If KpaKa CllJle

H = Q a M = 15 Nm

39 JlaTli nOllltlUII

Q I kN 1000 N M = 1500 Nm 0 0

lIKIlHa ~lexaHII~IKe PYKe j eJlHaKa je KpaK) ClUJe r j

- M a = 15 m a - Q 40 DaTll nonaUII

QI = 300 N Q2 = 800 N aJ =15m

YCJlOB paBHOTe)Ke j e

Qt2 MI = M Q al = Qp~ a l = Q 1=4 m

4 1 )]aTII nOlIaUf

In = 70 kg 1112 = 60 kg 1113 = 20 kg d = d = 2 m

0611Jbe)JI1~10 pacTojalhe rrje4aKa 01 TatlKe OCJIOHua KJIaUKaTlliUe ca dJ 113 YClOBH paRHOTe)l(e MOeHaTa Jl06I1jaMO

n~gd = IJ1gdl + m~dJ

OJlaBlIe je d) = 1m

42 LIanl nOJlaUlI

m = 50 kg ao 1 m b = 06 m

69

F = F F = F IJ = mgh = mgLlb oJlaKJIe nOCJlHje cKpali HBal-ha Jl06MjaJO bull umiddot or ~ Q

h = 042=t 34 )]aTI1 nOllaWI

h = 3m Q= 5 m m = I 5 kg

I1HTeH3HTeT CI1ne Tpel-ha Koja JIj enyje Ha JlHjere jeJlHaK je mlTeH311rery aKTUBshy

He KOMnOHeHTe O Ule re)Ke

- F F - I11gh F - 88 29 NFIf - a u--e- tr - I bull

35 )]anl nOllaUI1

Q= 200 N F = 50 N r=== 4 h

VlHTeH3lrfn I3Y4He c~lJIe jeJlH3K je 1611PY HHTCH31HeTa CIIJlC rpetbCl II akTI IBHe

Ko-mOHCHTe clue Te)Ke

Qh F = F + F = Fr+-~ F === 100 N

36 )]anl nonaun

m =40 kg (1 === 30 f1 = 05

II

3(ftmiddotmiddotmiddotmiddotmiddot ~

11 1 t

Cmiddotmiddot~middot

Ha OCHORY cmlKe 3aKJbYl lyjeMO

C b = Qmiddot311=2 2

a) LIaJbe JlaKO Hana31H1O HHTeH3llTeT aKTHBHe KOMnOHeHTe c~UJe Te)Ke

F = mgh F = mg F = 1962 N - J Q 2 ) II t

6) YI HTeH31neT HOpMaTlHe KOMnOHeHTe 3eMJbl1He Te)Ke j e

= ngb F = 339 8 N F e n n -shyB) JtI HTeH3HTeT cl1J1e Tpetba je

Fr === FnLl f r = 1699 N

68

r) KaKO Je F gt Ftr nHje-re ce Kpehe paBHoMjepHo y6p3aHo

37 UaTI1 nonaW1

h = b I = 02

TIpI1Ml1j eHHrIO 11 l-bYrHOB 1aKOH 1-1a KpeT3-be Tl1jeJla HI13 CTPMY pasaH

mgh mell b h Ie ma = F - F ma =-- - - or-middota = g(_ _ ~)

bullbull Ir ~ e Q ~

K aKO je Ii = b TO j e

~ = h-J2

)]CLbe je

2 a= g T(I -u)

a = 5s5~ smiddot

38 LIaTlI nOJlaWI

Q = lOON u=IScm =0)5m

MOeHT CI11e jenHaK je npmnBOny OUle If KpaKa CllJle

H = Q a M = 15 Nm

39 JlaTli nOllltlUII

Q I kN 1000 N M = 1500 Nm 0 0

lIKIlHa ~lexaHII~IKe PYKe j eJlHaKa je KpaK) ClUJe r j

- M a = 15 m a - Q 40 DaTll nonaUII

QI = 300 N Q2 = 800 N aJ =15m

YCJlOB paBHOTe)Ke j e

Qt2 MI = M Q al = Qp~ a l = Q 1=4 m

4 1 )]aTII nOlIaUf

In = 70 kg 1112 = 60 kg 1113 = 20 kg d = d = 2 m

0611Jbe)JI1~10 pacTojalhe rrje4aKa 01 TatlKe OCJIOHua KJIaUKaTlliUe ca dJ 113 YClOBH paRHOTe)l(e MOeHaTa Jl06I1jaMO

n~gd = IJ1gdl + m~dJ

OJlaBlIe je d) = 1m

42 LIanl nOJlaUlI

m = 50 kg ao 1 m b = 06 m

69

11 HTeH3~ITeT CHIle KOjOM )(eH3 Mopa lla lJjenyje Ha KOJ1Hua je

F = Qb F = mgb F = 2943 N a a

43 LlaTiI nO)laUlI

Q = XO N if == 4 p

Vi J YCJJOBa paBHOre)l(e MOleHHTa ll06I1jalO

Q(IF=p F==4Q F == 320N

44 LlaTl1 nO)laUII

Eu = 40 N a == 26 cm b =12 cm

l-b YCJJOBa pallllOTe)l(e IOleHaTa HaJla3I1MO

F = 0 f F == 867 N

0$5 laTli nO)laUII

r= 101 r = 5 N F = 15 N

MjecTo Ha KOIC 611 Tpe6alo 110CTaBIlTIi OC10HaU Ha1U311O 113 yCl0Ba paBHOshy

TeiKe IOleIIaTa

FI a l = Fc o ~

1aljeHo~1 BplljeJHOCTIl JU IIHTeH31ITeTe CILla no611ja~10

al == 3 a~

Kao je

I +o = t TO Je

0 = l C 1I1 = 07 5 m (1 = i (J = 025 n 1 4 4

AKO I1pBII TepeT Bllell Ha 1l1jeBO1 pajy WTana OHna 611 OCl0Hau Tpe6alo noshy

CT3BIITII ~5 CIll eCHO on uellTpa wrana

46 ilaTl1 nOllaUII

= 100 cm Q = 2 N A = 10 cm Q = 3 N d = 30 cm d1 = 70 cm

W Tan he 6mll y paoHOTe)l(lI ao pe3y1Tyjyrlll 1-IOMeHT CILle y onHoCY Ha ueHshy

Tap Iace WTana 6yte jeJ1Hallt Hyml Onpe)lHIO Cltll1a pacTOjat-ba T3llaKa Bjewamiddot

I-ba TepeTa ol ueHTpa WTana

(J I = 50 COl - J0 em 01 = 40 cm

(J =SO cm - 30 em (l =20 em

0 = 70 cm - 50 cm a = 20 em

LlaJbe 3 ycnoBa paBHOTe)(e MOMCHara n06Hjal-W

Qo + Qpl = Qp3 Q =7 N

70

Paq eHepiuja U cHaia

L nplIMjep 3a BpWel-be paJla Y TOKY Kojer CIUTa Ml1jel-ba 06JJI1K T11jeny je ca6Hjashyt-be IUH1 11CTe3al-be leTa1He onpyre

2 nOK TT1jeno cno6011Ho naJla pan BPWI1 3eMJMIHa Te)(a

3 cDopfyrla A = F I CC MO)(C ynoTpuje61TII 3a Il3pal lYHaBat-be IeXaHJflKOr pa shylUI y C1~ lJajy Kan ce ~I HTeH311TeT CHJle He l11jef-bCl YTOKY l-beHOr njeJlOBal-ba H KaLl

ce npaBau I-bCHOr lje~OBat-ba nOKJlana Cil npaBUCM 11 cMjepOM nOMjepal-baflllela

4 YlJellilK He BPWII pa~

5 Pan CILle je HeraTIIBaH Y c1)4ajy 4

6 a) CIL1a elaCTlllJHOCTI BPWI( n031fTlIBaH pall y npyro cl)rtlajy a Her1lTJ1BaH Pail y npBOM CIYlajy

) 3eM1bllHa Te)(a BplUll n03lfTllBaH pall - npBOJ C1) lJajy a Hera1l1BaH pan y llpyro1 cl)4aJY

7 GYlIyhil lla je BllC~IHCKa pa3J111Ka 113el)y n0lV10re 11 Bpxa KynacTor MpaB~II-baKa ~ICTa 3a 06je nyTat-be pal KOjll I13BPWI1 ~lpaB jeJlHaK je y 06a CJJ-Iaja

8 5YJlyl1ll lIa je npaBau 3eJbIIHe Te)Ke HOpMaJlaH Ha npaBau KpeTal-ba nljena 3e~IJb Il Ha Te)l(a Y OBOl Cll)1ajy He BPW II pan

9 PaJl KOjB 113BPWII 6116fJlIOTeKap npll nOJl1l3at-by KI-bJ1fe ca HII)(e Ha Slimy nOJlHshyuy je

= mgtl rJlje je m Iaca Kt-bllre It BlICIIHca pa31l1Ka 113lel)y nOJll1Ua Cana j e lltil-V uJr OIlOPIlTll lfa nOT3BbeHa nlITaI-ba

el) lIa 6) lla B) lla r) He Jl) He

10 He 3aTo WTO rpaBI1TaUUOHa CJ1JJa KojOM CYHue npltBJIalJI 3eMJbY njelT)je HOPMaJlHO Ha nYTal-bY no KOjoj ce 3e~lJba oKpefie OKO CYHlla

II 3aTo WTO je Ha Y36pllHllJ1 norpe6Ho CaBJIanaTI1 OCBM Cl1JJe TpeI-ba jow H aKshy

TUBHY KOMnOHeHT) 3e~DhlJHe Te)(e na je nOTpe6Ho )la 11HTeH3HTeT B-IHe CHshy

Jl e ayroj10611JJa 6YJle Berm Hero Ha npaBOM nYT)

12 K oecj)HuHjeHT KopllcHor tejcTBa ~ faWHHe je YBl1jeK MaI-b11 on jetaH 3aTO WTO ce jenaH tHO YJJO)(eHOr paaa yrpOWJl Ha ry6HTKe HaCTaJle YCJben Tpel-ba y nOKpeTshyHI1M tlljenoBlfMa ypel)aja Ha TOflJloTHe ryfiHTKe ITJl

7

13 ITPH nOlta3Imal-b) c-laHgtyjy ce ry6HuH YCJbeJl TPeHgta MelJY Jll1JeJJOBI1M3 y ptIJ 4shy

ja na ce KoeqmUl-ljeHT KopHCllor Jlej CTBB nOBehaBa

) 4 K lllieTI14Ka eHepfllja Tl1jen3 ce

a) nOBehaBa

6) c~la thyje

15 KU HeTJI4Ka eHeprllja je E~ 11 V ~2 II 3aB1 IC l1 cal0 on IIHTeH31HeTa 6p3HHe TIIjeJla 3 He 0 11 npaRua IL~I I cMjepa lberOBe fip311He Iia ce npeMa TOM e n p l1 H3shy

MjeHH clfj cpa 6p311He TIIjeJ1 3 l-berORa KIfHeTIIIKa eHeprJ1ja He Ml ljel-b3

16 n pil KptTal-bY H ljeJ1 a H~f3 CTPM) paBaH YKOlIfKO He1v13 TpeJ-ba pan BPWH 3 eshy

(JbI1H l re)fa (Tj J-beHa atCnlBHa Ko~moHeHTa) Pall He 3aBHCiI on ll))KI1He CTPshy

Me paBHII Beh cal-to OJl I-beHe BHCIIHe

17 n pl1 KpeTaJ-bY ntj e~a BepTHKalHO H31ll iwe -herOBa nOTeHUl lj~Ha eHep rl1j a ce

nOBehalla

18 He npll KpeTal-bY Tllje_~a napWl eJ1 HO nOllpwrIHII 3e~L1be l-beroBa nOTeHUllja~Ha elepnlja ce He mjel-ba

19 nOTeHUlfja~ H a eHepr llja em1CTl I l He OIlPYrc 33BIICII Oll KoecentHUlljeHTa eJ1aCTlI-ishy

Hocnl on pyre k II KBallpaTa 113Jl))I(eJ-ba TaKO lla cy nOTeHuHjanHe eHeprHje

ORIIX JBlIj ) onpyra jelHaKe

20 ilaTII nOJ3UII

F = 250 N s = 3 2 m

Pall KOJ II 13IlPWlI pailHllK je

== h A == 25 0 N 32 m A = 800 J

11 ilanl nOllaUII

= I00 N ~ s = 2 m

~h YCloBa 3aaaTKa cJlIljen1 113 je pM CILle HeraTllOaH

A = -FI = - 200 J

12 llam 0011aUII

F = 080 N SI = ~ = I m 5 = ~ = I m a =30

vbpaQYHajMo npl30 pall cl ute HOI IlPBOj nOJlOBI1HII llyn

A = F) I~ A = 08 1

H a 1Pyraj nOlOBllHH ny-ra p an npw l1 XOPH30HTa1 Ha F KOMnOHeHTa CIVle KojOM 1IHjeTe AieJlyj e Ha Hrpa-lKy

vbpJiYHaj IO XOPH30HTaJlHY KOMnOHeHT) CHJ1e F

K OPIlCTChll CJII1KY_ llo6Hja~1O F = J3 F h 2

~ ~ ~-

Fh = 069 N -

7]

)

-~ u u LIUuHJaMO PM UsIIJ-gtwcn Hltl AJJJIUJ IIUIUHlIlIl Ilyli

A ~ = Fh S2 A = 069 J

YKynaH PM j e

A = A + 111 A = 149 1 23 Aanl nonaUI1

= 800 N = 12 m

Pan Kojll ce 113I1PWII ie

II = Q Ii 1 = 9 600 J A = 96 kJ

24 UaTJI nOllaUII

Q == 2 500 N II = 2 m a) Pan KOjll l3BPWII 6yrapcK1 1I113al TeraBa je

A = Q II A = 5 000 J II = 5 kJ 6 ) 3elTblfHil Te)f(a I3PW~1 npll nOilll3aJ-bY Teroaa Her aTII l3aH pan

A = -Q 11 A = -5 kJ n) CnOpTlICTltI He BPLUll pan 1l0K M flPHO lp)l(~1 TerORe II3Han cBoje fJJaBe

25 ilarll 11 0 l taUl l

11 = 15 000 = 15 000 000 kg Ii = 50 Ill

PaJ I-oj ll IURPUIII (I L13 I1 pI1TI1CKa Ha Kl l1n xlIJlpaYl lPIHe 1U13alllue je

A = I[h A = 736 IOQ J

26 llam nOllaUII

111 == 800 kg ( = 2 ~ 5 == 50 m

I1Jpa LIYHajIO npBO IIHTeHJIITeT B)liHe CILle ~tOTopa

= ilia j = I 600 N

PM fojll 1I3BPWH BYlJHCl CI Lla MOTopa je

-I = F~ 1 = RO kJ

27 UaTl nOllaUJ

m = 102 kg V o ==53 7 a=2 ~

a) (IfHTeH311TeT ClLl e Koja je lIjeJlOIlMa H3 Tllje10

F = ma F = 204 N 6) (lf3paljYHaj~ lo npllo Bplljele koje n poTeKHe OIl nOleTKa QjeJ10Batba Cl lJle n o

3aYCTaBJbal-ba

~r= VO

bull = 265 s a

73

nyr KOjl1 THjeJIO npet)e no 3ayCTaBJba-ba je

2 ts = a2 s = 70225 o1

B) K3KO ce TllJeI10 KpeTaJlO paSHO ljepHo ycnopeHO pan KOj H 113BPWH cl1na je

HeraTlIBaH

A - F s A = - 143259 J A - 1433 kJ

28 llanl nOllaUl1

4 = 30 kJ = 30 000 J I = I O1i n = 60 s

CHar3 MOTopa 6poJ]cKe llll3aJJllue je

p= P=500W t

29 llanl nOllaUII

P = 40 W I =I h = 3600 s

Pall CllJe efleKTPOMoTopa Je

I = P I A = 144 000 J = 144 kJ

30 llan nonaulI

J 25 MW = 2 106 W (= 315 36 10 s

Pall KOjll ce lI JBPWll Y XIIJlpoueHTpaJlll Je

A = PI A = 7884 middot lO Ll J

31 llaTll nOllaUII

= 250 W = 025 kW 1 =12 h

vl3palYHaj~lo pajnpllje yrpoweHY eleKTplllJHY eHepnljy

A = P I A = 3 kWh

AKO Ie UlIJeHJ C-lIe lTplIIHe eHepfllje 004 KM no KI1-10Ba [-lacy ) nOTpe6a CIIshy

jaJIllue he HanOWTaTl1 012 KM

32 llaTII nO)1allll

11 = 75 kg II = 150 01 I = 2 min

vt Jpall)Hajlo 13jn plIje pan KOjl1 113BPWII CKI1-JlHqn npl1 nOJunal--bY llBjllue

CK11Jawa

A 2 mgh A = 220 725 J

H3ra Koja je nOTpefiHa CKJI- JlHcjrry je

p=4 P=183938 WP =L8kW

7f

33 LlaTH nOllaUJI

M = 4500 kg 11= 1800 kg = 38 ~

BYlHa CWla nOTpefiH3 1I1ltjny jc

= (Ii + m)g F= 61803 N

Cllar3 nOTpe6H3 mlqny je

P = Pu P= 2349 KW

34 lletTl1 noaaUII

III = 110 kg Ii = 73 m I = 72 s P = 200 W

11 jpal~majMo Hajnpllje pall Kojll aCTpoHayr 113BPWI1 npl1 nel--ba--bY Ha 6PlIO

A = P I A = 1440)

C l pyre cTpallC paJ je 6pojHO jeItllaK

f == IIgh rllje j e K - y6p3a--be rpaBIITaUll0He CILle Ha ljecTY rnje ce HaJla311 aCTpoHa)T

labe JC

ft= -- 11111 g = 179 ~

Kao je y5p33l-be rpaBIITaUl IOHe CIl1e 3eLbe 981 ms~ IlCTPOHllyr Ce He HaJlashy311 Htl JelbJI

35 flaT II nOiletUlf

II = 2000 kg v = 72 IIl =20 ~

OlIpellll1O Hajnpllje IfHTelHllTeT BYlHe clme J OTOpa vt3 YC1l0Ba 3alIaTK3 je

F = 005 mg F = 981 N

CHar nt pa3Rllja WTOP IIIOHI je

= fl P = 19620 W P = 196 2 kW

J6 JlaT11 nOllaUlI

111 = 100 t = 100 000 kg 1 = 20 ~ M = 005

vt HTeH311Ter ByY He clue Kojy pa3Bllja ~IOTOp )lOKOOTlJBe jellHaK je II HTeH3HTeshyl CllJle Tpe--bet

F = Fir = Illig F = 49 050 N

CHara Koja je nOTpefiHa JlOKO MOTIIBU je

P = If p = 981 000 W P = 98 J kW

37 )lam nOllauu

p = 2000 W P = 800 W

CTeneH KopHCHor AejCTBa illTellligtaK3 pallYHaMo no llelt)gtHHI1uHjl1

PorJ = rJ =04 rJ = 40~o

38 LlaTII nOllaUlI

F = I N v = 25 ~ = 0025 ~ p = 2 W

Kopl1CHa CHara je

p~ = Fv Pl = 0025 W

Koeltp11UHjeHT KoplICllor llejCTB3 jc

rJ = p

t = 0015 rJ = 125

39 ~Ielajy Ben) rpaRIITaUl10HY noreHUlljaJIHY eHepmjy 11Ma rB03lleHa K)fJ1a j e

lIa Behy 1aC)

40 KaKO je pound~ = 1111 2 TO ce lJIHeTIIKa eHeprllja nOBeha 16 nyra

41 He nplI c106oJHO1 naaatby TIIjeJla l-befOBa YKYrHla MeXaHI4Ka eHepmja je

KOHCTaHTHa

42 npoMjeHa leXaHIIIe eHeprl1je TIIjcla jellHaKa je pallY KOjH apwe CIUle Koje lleshy

1Yjy Ha TIIJerIO

43 AKO TIIjeJlo Bpillil pall ligterona ~ e)aHI1IKa eHepmja ce o lal-byje

44 LlaTII nOllaUll

11 = 15 kg v = 37 Il = 3g =0003 kg Vz = 400--1113=60 kg uJ = 9~ 1

nu

a)F =~L E = 1125l I

6) E - IIIpoundVl ~ - -~ E = 240 J2

_ miv3middot - B) Eu - 2 E[J - _430 J

-

45 LlaTI1 nonaul1

III = 1 (=OOO kg Ekl = 4500 J 1112 = 45 kg m = 15 kg El1 = 2430 J

a) o p311Ha )J(eJbe3HHlKOr BarOl~a je

76

~2EIV = ---

V =3 ~

6) op311Ha njeBojllIue je

2Eu 1l =1(1112 +mil

VI == 9 ~

46 naTII nOll3UII

m = IOOOkg 1~ = 60 ~ = 1 667 7 A=50kJ

vhpaIYHujMO KllHeTllllKY eHepmjy ayro~106liJJa npl1je K04elha

2

- = mvo E = 88 94 kJE l l - ~ bull

KltHenllKa eHeprllja aYToM06111a HaKOH K04eligta je

E = pound0 - A pound1 = 88 94 kJ

OP311HU a)ToMo6ILJa HaKOH KOIel-ba je

middot2poundl V=Vm = 1 3J4 ~

47 naT nOl laUl1

111 = 200 kg II = 3 m

[paBIITaUlIOJla nOTellUlljanlla eHeprnja 63J1B3Ha y OllHocy Ha UHPKYClGl nOll j e

poundp = mgh pound p = 58861 Ep = 5886 kl

48 )laTII nOllaUII

111 = 05 kg h i = 075 m h~ = 080 Ill

a) [p3BIITaUI-IOHa nOTeHul1jarIHa eHeprHja KI-bHre y OllHOCY Ha HliBO CTOTla je

Epl = mglll Epl = 368 J

6) Bucl1Ha nOJll1ue Ha KOjOj ce HaJla311 KligtlIra y OllHOCY Ha HIIBO nOlla je

fI = 11 + II H = 155 m

rpaBInaUl10Ha nOTeHulljaJIHa eHepmja IObll re y OllHOCy Ha Hl1lJO nOIla je

p~ = mgH pound p1 = 76 J

7

nyr KOjl1 THjeJIO npet)e no 3ayCTaBJba-ba je

2 ts = a2 s = 70225 o1

B) K3KO ce TllJeI10 KpeTaJlO paSHO ljepHo ycnopeHO pan KOj H 113BPWH cl1na je

HeraTlIBaH

A - F s A = - 143259 J A - 1433 kJ

28 llanl nOllaUl1

4 = 30 kJ = 30 000 J I = I O1i n = 60 s

CHar3 MOTopa 6poJ]cKe llll3aJJllue je

p= P=500W t

29 llanl nOllaUII

P = 40 W I =I h = 3600 s

Pall CllJe efleKTPOMoTopa Je

I = P I A = 144 000 J = 144 kJ

30 llan nonaulI

J 25 MW = 2 106 W (= 315 36 10 s

Pall KOjll ce lI JBPWll Y XIIJlpoueHTpaJlll Je

A = PI A = 7884 middot lO Ll J

31 llaTll nOllaUII

= 250 W = 025 kW 1 =12 h

vl3palYHaj~lo pajnpllje yrpoweHY eleKTplllJHY eHepnljy

A = P I A = 3 kWh

AKO Ie UlIJeHJ C-lIe lTplIIHe eHepfllje 004 KM no KI1-10Ba [-lacy ) nOTpe6a CIIshy

jaJIllue he HanOWTaTl1 012 KM

32 llaTII nO)1allll

11 = 75 kg II = 150 01 I = 2 min

vt Jpall)Hajlo 13jn plIje pan KOjl1 113BPWII CKI1-JlHqn npl1 nOJunal--bY llBjllue

CK11Jawa

A 2 mgh A = 220 725 J

H3ra Koja je nOTpefiHa CKJI- JlHcjrry je

p=4 P=183938 WP =L8kW

7f

33 LlaTH nOllaUJI

M = 4500 kg 11= 1800 kg = 38 ~

BYlHa CWla nOTpefiH3 1I1ltjny jc

= (Ii + m)g F= 61803 N

Cllar3 nOTpe6H3 mlqny je

P = Pu P= 2349 KW

34 lletTl1 noaaUII

III = 110 kg Ii = 73 m I = 72 s P = 200 W

11 jpal~majMo Hajnpllje pall Kojll aCTpoHayr 113BPWI1 npl1 nel--ba--bY Ha 6PlIO

A = P I A = 1440)

C l pyre cTpallC paJ je 6pojHO jeItllaK

f == IIgh rllje j e K - y6p3a--be rpaBIITaUll0He CILle Ha ljecTY rnje ce HaJla311 aCTpoHa)T

labe JC

ft= -- 11111 g = 179 ~

Kao je y5p33l-be rpaBIITaUl IOHe CIl1e 3eLbe 981 ms~ IlCTPOHllyr Ce He HaJlashy311 Htl JelbJI

35 flaT II nOiletUlf

II = 2000 kg v = 72 IIl =20 ~

OlIpellll1O Hajnpllje IfHTelHllTeT BYlHe clme J OTOpa vt3 YC1l0Ba 3alIaTK3 je

F = 005 mg F = 981 N

CHar nt pa3Rllja WTOP IIIOHI je

= fl P = 19620 W P = 196 2 kW

J6 JlaT11 nOllaUlI

111 = 100 t = 100 000 kg 1 = 20 ~ M = 005

vt HTeH311Ter ByY He clue Kojy pa3Bllja ~IOTOp )lOKOOTlJBe jellHaK je II HTeH3HTeshyl CllJle Tpe--bet

F = Fir = Illig F = 49 050 N

CHara Koja je nOTpefiHa JlOKO MOTIIBU je

P = If p = 981 000 W P = 98 J kW

37 )lam nOllauu

p = 2000 W P = 800 W

CTeneH KopHCHor AejCTBa illTellligtaK3 pallYHaMo no llelt)gtHHI1uHjl1

PorJ = rJ =04 rJ = 40~o

38 LlaTII nOllaUlI

F = I N v = 25 ~ = 0025 ~ p = 2 W

Kopl1CHa CHara je

p~ = Fv Pl = 0025 W

Koeltp11UHjeHT KoplICllor llejCTB3 jc

rJ = p

t = 0015 rJ = 125

39 ~Ielajy Ben) rpaRIITaUl10HY noreHUlljaJIHY eHepmjy 11Ma rB03lleHa K)fJ1a j e

lIa Behy 1aC)

40 KaKO je pound~ = 1111 2 TO ce lJIHeTIIKa eHeprllja nOBeha 16 nyra

41 He nplI c106oJHO1 naaatby TIIjeJla l-befOBa YKYrHla MeXaHI4Ka eHepmja je

KOHCTaHTHa

42 npoMjeHa leXaHIIIe eHeprl1je TIIjcla jellHaKa je pallY KOjH apwe CIUle Koje lleshy

1Yjy Ha TIIJerIO

43 AKO TIIjeJlo Bpillil pall ligterona ~ e)aHI1IKa eHepmja ce o lal-byje

44 LlaTII nOllaUll

11 = 15 kg v = 37 Il = 3g =0003 kg Vz = 400--1113=60 kg uJ = 9~ 1

nu

a)F =~L E = 1125l I

6) E - IIIpoundVl ~ - -~ E = 240 J2

_ miv3middot - B) Eu - 2 E[J - _430 J

-

45 LlaTI1 nonaul1

III = 1 (=OOO kg Ekl = 4500 J 1112 = 45 kg m = 15 kg El1 = 2430 J

a) o p311Ha )J(eJbe3HHlKOr BarOl~a je

76

~2EIV = ---

V =3 ~

6) op311Ha njeBojllIue je

2Eu 1l =1(1112 +mil

VI == 9 ~

46 naTII nOll3UII

m = IOOOkg 1~ = 60 ~ = 1 667 7 A=50kJ

vhpaIYHujMO KllHeTllllKY eHepmjy ayro~106liJJa npl1je K04elha

2

- = mvo E = 88 94 kJE l l - ~ bull

KltHenllKa eHeprllja aYToM06111a HaKOH K04eligta je

E = pound0 - A pound1 = 88 94 kJ

OP311HU a)ToMo6ILJa HaKOH KOIel-ba je

middot2poundl V=Vm = 1 3J4 ~

47 naT nOl laUl1

111 = 200 kg II = 3 m

[paBIITaUlIOJla nOTellUlljanlla eHeprnja 63J1B3Ha y OllHocy Ha UHPKYClGl nOll j e

poundp = mgh pound p = 58861 Ep = 5886 kl

48 )laTII nOllaUII

111 = 05 kg h i = 075 m h~ = 080 Ill

a) [p3BIITaUI-IOHa nOTeHul1jarIHa eHeprHja KI-bHre y OllHOCY Ha HliBO CTOTla je

Epl = mglll Epl = 368 J

6) Bucl1Ha nOJll1ue Ha KOjOj ce HaJla311 KligtlIra y OllHOCY Ha HIIBO nOlla je

fI = 11 + II H = 155 m

rpaBInaUl10Ha nOTeHulljaJIHa eHepmja IObll re y OllHOCy Ha Hl1lJO nOIla je

p~ = mgH pound p1 = 76 J

7

37 )lam nOllauu

p = 2000 W P = 800 W

CTeneH KopHCHor AejCTBa illTellligtaK3 pallYHaMo no llelt)gtHHI1uHjl1

PorJ = rJ =04 rJ = 40~o

38 LlaTII nOllaUlI

F = I N v = 25 ~ = 0025 ~ p = 2 W

Kopl1CHa CHara je

p~ = Fv Pl = 0025 W

Koeltp11UHjeHT KoplICllor llejCTB3 jc

rJ = p

t = 0015 rJ = 125

39 ~Ielajy Ben) rpaRIITaUl10HY noreHUlljaJIHY eHepmjy 11Ma rB03lleHa K)fJ1a j e

lIa Behy 1aC)

40 KaKO je pound~ = 1111 2 TO ce lJIHeTIIKa eHeprllja nOBeha 16 nyra

41 He nplI c106oJHO1 naaatby TIIjeJla l-befOBa YKYrHla MeXaHI4Ka eHepmja je

KOHCTaHTHa

42 npoMjeHa leXaHIIIe eHeprl1je TIIjcla jellHaKa je pallY KOjH apwe CIUle Koje lleshy

1Yjy Ha TIIJerIO

43 AKO TIIjeJlo Bpillil pall ligterona ~ e)aHI1IKa eHepmja ce o lal-byje

44 LlaTII nOllaUll

11 = 15 kg v = 37 Il = 3g =0003 kg Vz = 400--1113=60 kg uJ = 9~ 1

nu

a)F =~L E = 1125l I

6) E - IIIpoundVl ~ - -~ E = 240 J2

_ miv3middot - B) Eu - 2 E[J - _430 J

-

45 LlaTI1 nonaul1

III = 1 (=OOO kg Ekl = 4500 J 1112 = 45 kg m = 15 kg El1 = 2430 J

a) o p311Ha )J(eJbe3HHlKOr BarOl~a je

76

~2EIV = ---

V =3 ~

6) op311Ha njeBojllIue je

2Eu 1l =1(1112 +mil

VI == 9 ~

46 naTII nOll3UII

m = IOOOkg 1~ = 60 ~ = 1 667 7 A=50kJ

vhpaIYHujMO KllHeTllllKY eHepmjy ayro~106liJJa npl1je K04elha

2

- = mvo E = 88 94 kJE l l - ~ bull

KltHenllKa eHeprllja aYToM06111a HaKOH K04eligta je

E = pound0 - A pound1 = 88 94 kJ

OP311HU a)ToMo6ILJa HaKOH KOIel-ba je

middot2poundl V=Vm = 1 3J4 ~

47 naT nOl laUl1

111 = 200 kg II = 3 m

[paBIITaUlIOJla nOTellUlljanlla eHeprnja 63J1B3Ha y OllHocy Ha UHPKYClGl nOll j e

poundp = mgh pound p = 58861 Ep = 5886 kl

48 )laTII nOllaUII

111 = 05 kg h i = 075 m h~ = 080 Ill

a) [p3BIITaUI-IOHa nOTeHul1jarIHa eHeprHja KI-bHre y OllHOCY Ha HliBO CTOTla je

Epl = mglll Epl = 368 J

6) Bucl1Ha nOJll1ue Ha KOjOj ce HaJla311 KligtlIra y OllHOCY Ha HIIBO nOlla je

fI = 11 + II H = 155 m

rpaBInaUl10Ha nOTeHulljaJIHa eHepmja IObll re y OllHOCy Ha Hl1lJO nOIla je

p~ = mgH pound p1 = 76 J

7

49 nanl nonaul1

11 = 40 kg ~ = 4 m a =30

BllCllHa To50ra lla YOllHOCY H3 nOllJlOry je

V h= 1 h = 2 m

paBlITaUIIOll3 nOTeIlulljaJIHa eHepnlja njeTeTa y OnHOCY H3 nOllJlor y je

Er = mxll Ep = 7848 J

50 11am nOllaUII

II = 5 m

113 611CMO plljewIL111 3aaaTaK npwll1jeHl1he~1O 3aKOH onp)lal-ba ~eXaHJIIKe eHeprJlje 3611p nOTellullja1He II KJIHeTlIlJKe eHeprllje caKcllje TOKOI CJ106011shy1101 nana je KOHCTaIITaH YrpeHyTKY Kalla je caKcl1ja IlcnYWTeHa l-beHa yKynshy

11lt1 leXalllf lJKa eHeprllja Je

~ = EI E = IIIgil

C lpyre CTpaHC HenocpeIlHO npllje ynapa () TpOTOap yKyru-m lexaHIilK3

elleprl1ja caKcllje je

E = Imshyt = E 2

LIabe je

ml( mgh = TJ

I =99 ~

51 11aTII noaaUII

II = li Eu - ~

ila OIICHl plliewlIl l l 33Jl3TaK npllljetbyjeMo 3aKOH onpgtKal-ba MexaHlIlKe eHeprllJe KIIHeTlfIKa eHeprllja KOjy JC 1onTa IMaTJa npll 1136aqan JellHaKa j ncnellullja1Hoj el-teprlljlf nome) HajBllwoj TaIKII -heHe Ilyral-be

rH v~

E = E --o =mgr hm = L27 m ml p 1 = 2g

52 11aTII nonaulI

H = 3 111 II = 05 m ~

npI LljeligtyjeMo 3al(01l onp)l(al-ba eHepruje

I 1 1 fmgH = mgh + - Im - gH = gh + 2 V V= 2g(H - II)

v=7 7 middot

R

53 YKYnHa MeXaHI1IKa eHeprHja B0311ha je KOHCTaHTHa II 113HOCW

1111 shy( ) E = Q + mgh

2

Y T34KII A YKynH3 leXaHlI4Ka eHeprlfja R03)1i1a jC

ll () E == 2 t lll +mgh

vb peJJaul1ja () II () l106uj ar-lO

I I 2 1117( + mgh = I Im~ +mgh v = v

Y TaYKH B YlltynHa MeX3HIIYKa eHeprl1ja 1I0311ha je

( E = ~nl1~ + mgll _ 2

113 pelaUlfja () II () 106I1ja)0

Im~ mgh mT~ _T+2 =T+mgh liS == lU+gh

li R = (vg+ gilL

Y laYKI) C YKynllJ leX31111IKa eHepnlja B0311ha je

I () E=l 117Vc

113 peolaUllja () I ( ) no6I1ja lo

llle_nTll l = )2 - 2 + Ilgh Uc 10+ _gh

V c vg+ 2gh

t Lllll 110dlttUH

111 = 50 g II = J 111 v = 3 ~

a) Y KynHa ~leXaHIlIKa eHepmja K)rJlllUe je

E == ~ IIn l +mgh E =0 72 J

6) HenocpeuHo npllje yuapa 0 nOJl10ry 6p3IIHa Kyfll1ue je

v=

V= 535~

7

B) Y HajBllwoj TaYKIl cBoje nyTal-be tltyrJlllUa 611 I1Mana ea~lO nOTeHuHjanH Y

eHeprlljy TO jeCT

EE = mgH H = 1I1f H = 14 7 m

55 IlaT11 nOllaUII

hi = 50 em = 05 m gJ = 22 ~

MaKCIIMalIHa nOTeHuHj anHa eHepnlja Kojy I a njeyaK npllJl lI KO~ 1 OllPa3a Ha

3 e llJb11 je

() En = IIIgh

O Ba eHeprllja 611 61lJ1a IICTa II Ha ]ymlTepy na je no 3aKOHY onp)Kal-ba eHeprl1shyje OHa jellHaKa nOTeHul1ja1Hoj eHepmjH DjelaKa y Hajnl1woj TaIlltl1 l-beroBe nyshy

Tal-be Ha JYnl lTepy

( ) E~ = mgJ 112

Vi 3 peJaUllja () II () JIo61IjaO

mgll = I11g h gh = gi ii = gil II = 022 mJ - - - g shy

56 naTII nOlla UlI

h = S3m m = 6000f = 6000000 kg 1= Is

Kalla 611C10 eny lOTeHulljaJIHY eHcpflljy BOlle OLl11 Da TpaHccentopMHwe~O Y

KOPIlCTaH pall D061l111 611c l0 CJbeDe~y CHary

p == mgh p =12 10 W I

OClIWlalluje u UUlJzacu

1 BpljeMc 3( KOle ce IIJBPIlJll jellHa OCUl L13UlIja HaJllBa ce neplIOD OCUI1JIOBaJ-ta

2 OCUI aUllje LlIlja ce a~m~HTyDa cMafuyje y TOK) IIpeeHa 30BY ce npl1ryUleHe

3 a) Eip]lIlIa Tlljela nplflBpWneHor Ja leTa1Hy onpyry jellHaKa je H)JlI1 y aMrurnshyT)JIHO~I nmoAltajy

0) Y6p3al-be Tlljela nplIlspwhcHor 3a MeT31HY onpYr) jcnHaKo je HyJHl y paBshyIIClTe+Hml lIo1oiKajy

He 3aTO WTO q rpaHIITaUIOHa y6p3afua Ha 3elbll 11 Mjeceu pa3J1lllJlna

5 nlTpe6HO Ie nOHllJeTiI IaCOIlHIIK ca elaCTlIlJHO~1 Onp)TOl jep je nepl10JI OCUlishy

10Hafua Illjela npl11111pheHor 3a tJlaCTllIHY onpyry IICTII II I-Ia 3elJbJI H Ha Mapc)

i lrLllfl1ua cl06011HIIX OCUILTlaullja ce lie llljel-ba y TOK) Bpe~feHa

7 CILla Tpel-ba KOll OCUll~aTOpHor KpeTal-ba )Jpohyje Claligtefue eHeprl1je ocu~ashylopa 3 Cafm TlSS II alrLll1T)llC OCUILlOBHligta

8 MalelaTIILIKo KlaTHO oCUlllyje nUll YTliuaje 3e UbllJle TelKe

9 He nepl loll OCUIL10llal-ba laTelaTlI4KOr uaTHU ca ~131I1M alnJJlIT)llaMa He 3)II IICII OJI MaCe II a~ln_ll1T)lle -1aTHa Ben ca1O 0] HcrOBe L(y)KIIHe 11 rpaBHTashy11IJOliOr y6p3afua

10 Y pCJOHaHUlljll MOry 611T11 KlaTiia B II D jep mlajy IICTy ItYgtK~IHy a CaMI1M TI1M IICTII neplloIt OCUlLIOB3Ha

II OipeD BOjHIlJo3 YBlljCK npeJlaHI npeKO IOCTa clo60aHIIM (BOJbHO) KopaKoM iaTO WTO 611 Y clYlajy Da BOjHllU11 Mapwllpajy ItOUJJlO no npUHYllHHX OCl11111ashyuuja -IOCTa Koje y eJlYlJajy Ita lloDe IO nojane peJOHaHUllje MOry 1loneCTI1 JIO l-beroBor pyweJ-ba

12 KpeTa-be 3c Je OKO CYHua je neplfODIl HO a111 Hllje oCUlLlaTopHo jep nyrashyH)a no KOjOj ce 3cMJba Kpehe OKO CYHUa Hllje npana 1J1lHllja

13 Kana leCTllue CpeDlHe OCUltJlyjy HOP-laJ1HO Ha npallau npOCTllpal-ba TaJlaCa Jl3CTajy TpaHCBep]aJlHI1 T3lJaCII

14 T aJacl-la LJY)IltllIlU j e pacTojafue DO KOJer ee OCUILIOB3fue npeHOC11 3a Bpl1jeMe 0 jeItHOr neplfOlla

15 AB 1 AC= AE = 2A

B) Y HajBllwoj TaYKIl cBoje nyTal-be tltyrJlllUa 611 I1Mana ea~lO nOTeHuHjanH Y

eHeprlljy TO jeCT

EE = mgH H = 1I1f H = 14 7 m

55 IlaT11 nOllaUII

hi = 50 em = 05 m gJ = 22 ~

MaKCIIMalIHa nOTeHuHj anHa eHepnlja Kojy I a njeyaK npllJl lI KO~ 1 OllPa3a Ha

3 e llJb11 je

() En = IIIgh

O Ba eHeprllja 611 61lJ1a IICTa II Ha ]ymlTepy na je no 3aKOHY onp)Kal-ba eHeprl1shyje OHa jellHaKa nOTeHul1ja1Hoj eHepmjH DjelaKa y Hajnl1woj TaIlltl1 l-beroBe nyshy

Tal-be Ha JYnl lTepy

( ) E~ = mgJ 112

Vi 3 peJaUllja () II () JIo61IjaO

mgll = I11g h gh = gi ii = gil II = 022 mJ - - - g shy

56 naTII nOlla UlI

h = S3m m = 6000f = 6000000 kg 1= Is

Kalla 611C10 eny lOTeHulljaJIHY eHcpflljy BOlle OLl11 Da TpaHccentopMHwe~O Y

KOPIlCTaH pall D061l111 611c l0 CJbeDe~y CHary

p == mgh p =12 10 W I

OClIWlalluje u UUlJzacu

1 BpljeMc 3( KOle ce IIJBPIlJll jellHa OCUl L13UlIja HaJllBa ce neplIOD OCUI1JIOBaJ-ta

2 OCUI aUllje LlIlja ce a~m~HTyDa cMafuyje y TOK) IIpeeHa 30BY ce npl1ryUleHe

3 a) Eip]lIlIa Tlljela nplflBpWneHor Ja leTa1Hy onpyry jellHaKa je H)JlI1 y aMrurnshyT)JIHO~I nmoAltajy

0) Y6p3al-be Tlljela nplIlspwhcHor 3a MeT31HY onpYr) jcnHaKo je HyJHl y paBshyIIClTe+Hml lIo1oiKajy

He 3aTO WTO q rpaHIITaUIOHa y6p3afua Ha 3elbll 11 Mjeceu pa3J1lllJlna

5 nlTpe6HO Ie nOHllJeTiI IaCOIlHIIK ca elaCTlIlJHO~1 Onp)TOl jep je nepl10JI OCUlishy

10Hafua Illjela npl11111pheHor 3a tJlaCTllIHY onpyry IICTII II I-Ia 3elJbJI H Ha Mapc)

i lrLllfl1ua cl06011HIIX OCUILTlaullja ce lie llljel-ba y TOK) Bpe~feHa

7 CILla Tpel-ba KOll OCUll~aTOpHor KpeTal-ba )Jpohyje Claligtefue eHeprl1je ocu~ashylopa 3 Cafm TlSS II alrLll1T)llC OCUILlOBHligta

8 MalelaTIILIKo KlaTHO oCUlllyje nUll YTliuaje 3e UbllJle TelKe

9 He nepl loll OCUIL10llal-ba laTelaTlI4KOr uaTHU ca ~131I1M alnJJlIT)llaMa He 3)II IICII OJI MaCe II a~ln_ll1T)lle -1aTHa Ben ca1O 0] HcrOBe L(y)KIIHe 11 rpaBHTashy11IJOliOr y6p3afua

10 Y pCJOHaHUlljll MOry 611T11 KlaTiia B II D jep mlajy IICTy ItYgtK~IHy a CaMI1M TI1M IICTII neplloIt OCUlLIOB3Ha

II OipeD BOjHIlJo3 YBlljCK npeJlaHI npeKO IOCTa clo60aHIIM (BOJbHO) KopaKoM iaTO WTO 611 Y clYlajy Da BOjHllU11 Mapwllpajy ItOUJJlO no npUHYllHHX OCl11111ashyuuja -IOCTa Koje y eJlYlJajy Ita lloDe IO nojane peJOHaHUllje MOry 1loneCTI1 JIO l-beroBor pyweJ-ba

12 KpeTa-be 3c Je OKO CYHua je neplfODIl HO a111 Hllje oCUlLlaTopHo jep nyrashyH)a no KOjOj ce 3cMJba Kpehe OKO CYHUa Hllje npana 1J1lHllja

13 Kana leCTllue CpeDlHe OCUltJlyjy HOP-laJ1HO Ha npallau npOCTllpal-ba TaJlaCa Jl3CTajy TpaHCBep]aJlHI1 T3lJaCII

14 T aJacl-la LJY)IltllIlU j e pacTojafue DO KOJer ee OCUILIOB3fue npeHOC11 3a Bpl1jeMe 0 jeItHOr neplfOlla

15 AB 1 AC= AE = 2A

IV _ J 1v_ JDJ1n lClJIG n MU IY IIVCMUn1YJ JJ) D4JYJNI

17 n OWTO ce 3BYIHI TaJlaCH lie Mory npeHOCI1TM KP03 BaK)YM KOCMOHaYTl~ Be3Ymiddot

~et1Y CBe~1I1pCKIM 6pOnOBI1Ma onp)I(aBajy nO~lOhy pan~IO-TaJ1aca

18 Op3Mlia 3BYKa y Bonll 3aBHCH on Ter-meparype BOne II KOHUCHTpaw1j e COJJl

19 OBH 3BY llil1 TanaC H Hoce Ha311B HHltppa3BYllt middot

20 TOKOM OJT)jc ce npno BI111~1 MyHgta a nOTOM Iyje rpMJbaBHHa jep je 6p3HHa cBjeshy

TJ10CTI1 MHOro Bena on 6p3HHe 3syKa Y sa3nyxy

21 HaTH nonaUlI

== 120 Hz I = 5 s

a) Oepl1on OCUl1JlOSaHgta je

T == ~ T = 00083 s

6) 6poj OCUILlalllja Koje Ha411HII )l(I1JleT 3a neT ceKYHllI1 j e

A == II N = 600

22 HaTII nonaUI

N == 5 t == 1 ~

nepllon OCUl110llal-ba je

T - T-Os- N - -

ltigtpeKBeHUJlja OCUJUJOBaHgta je

V HI == - v =) Z

23 Ham nouaUl1

m==5g=0005kg v=5 7 middot

OOTeliultja1Ha c llcpmja K)TlIIUC TOKO KpeTaHgta je MaKCHMaJlHa Y a~H1JJJlTynshyHO~ nOJlo)ajy nOK jc y paBHOTe)HOM nono)f(ajy nOTeHUl1jaJIHa eHeprllja Jellshy

HaKa HYJ1l1 KaKO je 6p3J1Ha KYTJlI1Ue Y aMfUlI1T)llHOM nOJ1o)l(ajy jenHaKa IiYJlH

TO je Ha OCIIOSY 3aKOHa onp)ialila eHepmje

Im ll L = E Ep =-2 Ep = O0625Jt

24 HaTH nOllau

k == 500 N 1m == 5 elll = 005 m m 100 g == 01 kg

Y6p3al-be najaua HenocpellHO no oTBapaHgtY KYTHje je

F kx a = 250~a=m lI=m s

2

L llaTJoI nonaul1

Ep == 2 J m = 5 g

KOpl1CTellll 3aKOH onp)(a~ba eHepnrje no61ljaMo

E = E Im 2P l En = ] v = 2E~ iii

7 == 2828 l

26 naTll nOllaul1

1 = 1 m

nepltoll OCUHJlOIl3f-ha laTelanI4Kor KqaTHa je T 27r If T == 2 s

27 flaT II nOllalU1

= 24 I = I s nepl1011 OCUIL10Baf-ha Ie

T== f T == 0042 s

ltPpeKIlCHllIlja oeUILl0Ba~ha je

_ V I == 24 Hz

2R flaTli nonaUII

V == 72 I = J80 s

OnpeJlIl10 Hajnplfje neplIOl OeUJL100Cll-ba laTelanllIKor KJlaTHa

- T - s- II - _oJ

K aKO e r shy

I ~ T= -Vg

TO Ie

r== gT r== 155 m 4n shy

29 1lanl nonaUlI

T = 24 7 5 s C== 1518 em == 15 18 m

Y6p3aIDe 3e~IJbIIHe TC)fe y lJa60paToplljll je

47d 978 mg = y g== -

8

30 nepHOll OClll1JlOBalha MaTeManN)(Or KJIaTHa lJYgtIUIHe L j e

1 =2n~ nepl10ll OCUHJlOBa-ba MaTeMaTll4KOr KJlaTHa AY)IUIHe L2 je

l = 2lt~flepllOA OCUiJJOBalha onllcaHor CJ1CTeMa je

lT~ +-1 T =]( - (1 + )flgT = 2 2 2g gt12

31 lIaTl1 nOllaUM

h = 1m

Ilpl11jeJ-hyjyhJl 3aKOH OllP)l(aJ-ha eHeprnje no6Hja1-1O

mr- =mgh i = gh

V= J 2gh

v = 443-i-

32 lIaTII nOllaUlf u =240 ~ A=32m

a) lttgtpeKBeHUllja TaJlaCa je

I = A v =75 Hz

6) flepllon TaJlaCa je

= ~ T = 0 deg13 S1

33 lIaT nOllaUI1

T =6 s ) =20 m

6p3JiHa TaJlaCa je

u=-r 11=333~

34 flaT nOllaU1

N = t2 1 == 20 s x = 15 cm Q= 12 m IJ =6 s

84

aJ LlepHOll Tanaca j e

T= N T= 167s

6) b p311Ha TaJiaca je

p U=- u = 21

tl bullj

TI) TanacHa llYJKI1Ha je

- I 1 - V J = II T = 334m

r ) AMruJlIl)lla Tarraea je

x = 15 em II = 015 m

35 AaTii nonaUH

~ == 06 5 m == 440 Hz

O dpelllMO Hajnpllje TaJlacHY l)+I1HY Tanaea OHaie 33 13 MaFb3 Oll IfY)I01He )Kltue Ti

A=t~ =O433m

6p311Ha npOeTflp3lha TaJJaca je

II =h II = 19052 7

36 11am nonallH

11 == 80 Hz 12 == J400 Hz

a) K aKo je 6p311Ha ]BKa y Ba31IYXY c = 340 ms TO je

== pound A == 4 5m11 I - bull

6)) == pound A == 024 m - v

J7 11aTII nOllaun

= 2000 Hz ( I = 340 --- c =1460 7 c

a) AI = -f )1 = 017 m

C 6))1 = 7 A2 == 073 m

38 l(aTl1 nOlaW1

= 33 mm lttgtpeKBeHUllja OBor Tanaca je

c = 103 kHz 1 =1

85

OlljeK He MO)fe na penlCTpyje oaaj TaJlaC jcp je lberOBa ltppeKBeHUI1ja BcM 00

20 kHz

ilanl nonaUII

= 3000 m I = 5000 kin

Bpl1jeMc Koje je nm pe6Ho 3RYLIHO1 TaJl3CY 11a CTl1rHC on 611HC no Incnaoua je

r 300m I = (~ I = 340~ I I = 088 s

Bplljele rwje npOTeKHc nOK cnywanau KOjit npanl KOHuepT npeKo CaTem~Ta

wje MY311KY j e

~ 5000 km t = 00 17 s I = c II =

300 000 l~

ilaK~e CJywanau KOjll npaTl KOHuepT npeKO caTelllTa tlyj c IY311Y npllje cnyshy

waolla y KOHuepTHOJ clt1IIf

I ilaTlt nOllallll

=023 s ~ = O1 2s c=340~

a) KaKo je 6P31t HCl cBjeTlocTII o lHoro Beha on 6~1He 1B)Ka BplljeMe 3a KOj cBjenoCT npel)c 011 MjeCTa 113Boljelba c1060nHor YLlapua no rlella1aUa MOgtKe na ce )aHelaplt PaCTojalbe npBor L1enaOLl3 OJl ~ljecTa rnjc ie I13BenCH 0060shy

LiaH Yl1apau jc

I =c l = 782 m

PaCToj alM llpyror LncnaOla OJl ljeCTa rllje jc lImeneH cJl060JlaH Yllapau je

~ = c C = 408m

6) PaCTojal be 1131e11Y tlellallall3 je

( = rl1 + r ~ r= 882 m

ilanl nonault

== 12 s C = 1460 --

Bpl1je~le nOTpeliHo ylTpa3BYIHml Tuacy ua CTl1rHe no nH3 Mopa 11 na ce noshy

cJlltje on611jal-b3 apaTII ao 6poua je

= -2d naKJle Jly6111ia Mopa je C

c d = ~ d= 876 m

2

86

42 n aTl1 nonaQJ1

I1t =5s ci = 340 T c2 = J460 ~

3 BYYHI1 TaJTaC KOj H ce npOCTlfpe Kp03 Ba3JlYX no J(pyrof 6poJla CTl l fHe nocJlltj e BpCMeHa

_I - C-d

3BY l i HU TaJJac KOj~1 ce npocH1pe Kp03 BOJ(Y 110 Qpyror 6pona CTTlrHe nOCJll1j e BpeMcHa

d [ 1 = c middot

1

BpellleHcKH pa3~laK H3e t)y npHCTH3alba OBa Qua TaJJ3ca je

ll = t 1 - t ~

PaCTojaJ-be H3~leby 6pOllOBa je

= ll C1(2 d = 22J 6 m

C~ - (I

middot0 llaTl1 nonaulI

d = 15 m c =340 7

Bplljee nOTpe6Ho KaMeHY na CTlfrHe JlO llH3 6YHapa je

I == L7 5s

B) YHlj Ta1aC CTilfHe all lHa 110 Bpxa 6YHapa 3a Bplljele

2 = - 12= 0044 s

Bplfjee Koje npOTeKlle OJ( TpeHyrKa IfcnYWTaJ-ba KateHa 110 TpCHYTKa Kana ce I)Je lilY naJJ alefld ) BOa je

[= 1+12 =l79s

87

r l oilJlozua

I Beha T34Hocr beKapCKor Tep~lOleTpa 1)13111 ce Llill-beHHUOM u3 JbeKapCKH

Tep IOMerap II Ia BeOMa yny KamIJlapy

2 )KllBa Mpme Ha _39 0 C a 311MCKe Te~meparype Y CImiddot16upy cy 4eCTO 3H3THO HIOIlte na ce -repIOMeTap ca IIBOM He IOgtKe KOPIICTIITI1 3a Mjepe~be TaM0shy

WlbllX lllMCKIIX Te~lnepaTypa

3 LlltHlHII lUlO OJ1MenIJIHOr npeKHnaLla C) llBllje mpCTO cnojeHe MeTaIlHe TpaKe (Ojc ce pa3Jll141ITO IlCTC)() npll ]arpllj aBaI-bY WTO 0080011 110 I-bllXOBOr KPI1shyBhel-ba Ha je11HY CTpaHY II npeKll11al-bU crpyjHor KOla DII lera1HII npeKII11a4M

ce Hajllewtle InpalJ~jy Oil UllHKa I fBO)(f)a

4 YH)paWl-ba eHepnlja raCOBa ce Haj4ewhe CBOlll1 Ha KlllIeTIIIK) eHeprllj) IeshyCTl1l1a raca (~Ionel IIlea1HOr raca) jep Je YJajalHO iljefloBaH)e LJeCTlllla raca

(aTola II MOleKY-lJa) 4eCTO JaHelapbIlBO 1ltLl0

5 KOIJIIIIHa Tomore KOjy Tlljelo npu~la npll ]C1rpltjaBa~bY ILl 11 oTrrywra npH xlalle~bY 33BIICII Oil Iace TIIje1C1 cneUlIltp1I4Hor TOruJOTHOr KanaUlfTera MaTeshyplljaTJa 011 Kora j e TIIje10 Ha411HgteHO II pnl llKe KpajHgte II nOlieTHe Tel-IITeparyshy

pe TIIje1JltI y nOClaTpaHml npouecy (Q = IIIC(r~ -II))

6 KOHIIIHa Tonl or e je KB3HTlnaTlml Ja ~ Ijepa npoMjeHe YH)rrpawl-be eHepmje OaHOCHO pa3HjeHgteHe )H)TpaWl-be eHepnlj e 1I3Metw Tlljena pa3TJlI4ltTIlX Telshy

nepnypa

7 He 3aTo WTO pajClIHO njellOBaHgte l leCTllua 011 KOj lLX ce cacToje Te4HOCTII 11 1BpCTa Tlljeqa Hllje mHCMapJblIBO 1 nO~HIHaHTaH 41aH Y YHypaWl-boj ellepnlshy

jll je nOTcHulljalHa eHeprllja

8 He AIOPltP H3 1 IIjC1la 3a pa31IlK~ Ull KpllcralHllx HeMajy TaliHO onpel)eHY Te~ishy

lIepaT~ py TOnJbeHgta

9 TeMnepa1)pa KTJYlaHa je HIDKa YKO~lIlKO je nplm1caK MaHgt11

) ltPa3HII npeqa] In 1npCTor arperaTHor CTaHgta 11llpelltHO y raCOBlITO arperaTHo

naJ-be (napy) Ha31IBa ce cy6nmlaUllja

I TelnCpaTypa TOnJbel-bltl lena je Dmiddot C II o CTaje KOHCTaHn ta TOKOl ltpa3Hor npeshy

)JaCKa

~ llaTl1 nonaUII

I = 27 C

88

AnCOJIYllIa Termeparypa ua3nyxa je

= (273 + I rC) ~ = (273 + 27 ) K T= 300 K

13 11ani nOllaUl

I = _3deg

A ncollyma TeMnepaTypa qe11a je

f = (273 + tre) K T= (173 - 3) K T= 270 K

l~ )laTII nOlaUll

T = 6300 K

Te~lITepa1)lpa Hel nonpWllHIt CYHUa Y U eJl311jyconoj TeMnepaTYPHoj CKaJlH je

I = (T K - 273 re = 6027 degC

15 11aTII nODHUII

T = 73 K

emepaT)pa Ha KOjoj Ba3J[YX npela31f y 1BPCTO CTal-be y Ue1 3IljYCOBoj TemeshypaTYPHoj C1GL~11 je

I = ITK - 273)middotC I = - lOOT

16 IlaTII nOIallll

11 =05 kg (= 4200 K I = 10( 1_ = 100 C

KU11JLIIIHa TOrL10Te lltojy BO11a nplnlll npll larplljanalb) je

Q = 111( U~ - I) Q = IB9 kJ

17 aaTiI nonallll

Q = -lIOOJ m=200g=02kg t1=5dege

KaKO je

Q = 111 C t1 TO je cneUlHtllllHl1 TOrLl0rHII KanCilliITeT Y_1gta

Q t = A (= 4 IOU ft

mul f

IS DaTil nonaUII

m=O5 kg c=4200 ~ 3min = lBOs P = 700 W 1 = 20 C

vl3pa11)HujIO npBO KOJ1I141111) TOrLlJOTe KOjy Bona npll1I1 OD rpllja4a

Q =PI Q = 126 kJ

K aKO j e

Q = me (l ~ - t I ) TO je TpagtKeHa TeMneparypa

I = BO e

89

llam nOnaUH

m=2 kg c =440 -J-middot 1== 150 C (= 50 C kJK I 2

K OllIILIIIII3 TonllOTe Kojy MeTan omycTI Opll Xll al)eJ-bY je

Q = me (II - 12) Q = 88 kJ

n aTI nOllaUl I

Q == 147MJ II =OC 1) =37 C ( == 4200~K p=IOOO ~gbull

KOllfHllIa TOJlJ1OTe Koja ce oCllo6ollli caropHjeSatbeM MaCHohe TPOWI1 ce Ha

3arpljaSaJ-be sone

Q = mc(12 - ) Tj ~aca llelleHe Bone Kojy oc06a Ha llHjeTII Mopa lla oonHje je

1) = c([ - I 111 = 946 kg

3anpC IIHa )leneHe BOile KOjy oco6a lopa na normje je

V = 111 V =946Q p

)laTII nonaUl J

= 1000 ~Q == 4000 kJ 1 = 22 C I~ = 50 C (== 4200 l~K m

Maca SOlIe y peJepBOapll~la je

111 = Q 11= 34 kg ((I_ - I )

3anpeMlIHa BOlle y pe3epnoapi lMa Je

V = 11 V= 14 CP

2 llaTl1 1l0naUJ1

V = 2 Ci = 20 Cl = 100 Cc =4200 ~h- p = 1000 ~~ = 7 min = 420 s l

a) KOlllllJlIHa Ton1 0Te kOjy je Bona npmnma npl1 3arplljaBaJ-bY j e

Q = 111( ((] - I) Q = p fie (I] - II) Q == 672 kJ

6) CHara eJleKTpll lJHOr rplljalla yrpal)eHor y YajHI1K aKO cy TO[JJJ OTHH ry611UH

3aHeMapJbl1BH j eCTe

p = P =1600 W P =16 kW

90

111 = 360g =036 kg m2 = 120g = O 12 kg t = 100 C 2 = 15 CI = 96 Ce =4200 k~K

KOlllJYlIHa TOnJ10Te KOjy OTflyCTl1 BOlla jenHaKa j e KOllllII IHH TOfU10Te Kojy nplfMI1 LlallJa JellHaLlIIHa TonllOTHor 6J1JJ3HC3 j e

QI = Q~

1lLbc je

I1IICI(t -l) = 111( - l )

J111( (T1 - T) c = - m(l - l)

I = 622 -Jshy1 24 llaTll nOllaUII

fII == I kg 11 = 2 kg lo = 25deg C l = 35degC

JellH3YIIH3 TOfFIOTHor 61LTlaHCa je

Q = Q m (I - Ii ) = 11I ~ ( ~ - ()

llabe je

= ml +mh gt In +m~

= 3L7

25 llam n OllaUII

VI = I 0 I II 8r = 12 I = 3r C

JellHa~lIlHa TOf1IOlHOI 6IlJHIHla j e

Q i = Q~ Nile (I I - l j = IIC (I - i ~ ) VjC (1 1 - 1lt1 = Ji2c (r - I~ nalbe je

V (l -l ) _ _ _I ~ j - I - l 2

v) = 20 e

26 lInlJ n OllaWI

VI 1 r l = JOOCl_ = ]0 Ct = 75 Cc1 = 4200 c~ = 390 d

K OJll1II IHa TOfUlOTe KOjy OTnYCTI I SOll3 jellHaKa j e KoHIIJIHII TOMOTe KOjy npllMH 13jHHK

QI = Q~ 111 1(1 (r - r) = 1l2 (2 (t - ( ~ ) pVl e l (1 1 - I) = 1112 c~(t - --)

9

I

DaJbe je p Vc(t - t)

n~ = f l (t -(2)

m~ = 414 kg

27 llanl nonaUlJ

Ill] = 300 g = 03 kg r ] = 16 0 C I~ = 1000

C I = 20middot C ( I = )

JenHilcll1Ha TonnOTHor 611--1ilHCa je

Q = Q~ III] ( ] (t - II) = 1112 (1(11 - I) 5 1 1 n (r - I I) = 11 2 (2 (1 - I)

5m1(1 - I) 171 =

- I~ - r

71 = 75 g

28 HaTH 1I0llaUll

11= 97901 c = 4200 ~K _ 6

n OTeHUIj alHa eHeprllja BOlle Ha npxy Bononana

E = mgh

~b yc~oBa 3a1aTKa je

Ep = Q

llabC j e

mgl1 = Q mgh = mc15t

Te~mepaTYpa BOAe ce nOBIlCfl 3a

gilDI = c t = 229 C

29 llUTl1 non3WJ

11= Ig J = 340 ft k~

113spweHII pall jeJlHlt1K j e KOlIll1I1HII TOf1JlOTe Koja je nOTpe6Ha na ce IICTOnl1

naTa ~lac3 Jlella

A = Q A = iliA = 340~

30 11aTII nonaUJ1

m = 20000 t A= 340 Aa 611 ce OTonWlO 10 neneHor 6pHjera nOTpe6Ho je YJlO)l(lITl1 eHeprnjy

Q = 0 1 ntA Q = 68 middot 10 J

92

31 DaTH nonalU1

m= Ikg A = HOg middot C =4200 - 1shybull - bull kd~

vb YCJJOBa 3anaTKa CJJ Hjen II

m = mc15t 151 = )1 = 8rc 32 DaTIl nonaUIl

III == 2 kg q = 226 ~~ t = 100 C

M IIHH[a1Ha eHeprHja KOjy 611 Tpe6ano YJJO)(]1TIr na 51 ce naTa Maca nOAe flpeshylleJJa Y BOnel-lY napy je

=mq Q = 452 MJ

33 )laTl1 nOnaUlI

P = 2kW = 2000 W T = 2 min == 120 s q = 226 ~

Maca Ilone Koja j e IIcnaNL~a je

11= ~ m= 106g

34 llaTII nOllaUB

I = 100 Cm = I SO gr = 20 Cr = 80 Cc =4200q = 126 ~

KOlIPHlHa TOfLl0Te Koja ce OCJlo6oJllI npll)lI1KO~ 1 oHlleH33ullje BOneHe nape Ii XJlal]el-ba TaKO llo611JeHe none TpOWII ce Ha 3arpujaRal-be x~anHor ~LnltjeKa

fII]q + lI e (II - r) = f11 2C (r - I)

Maca BOlleHe nape je

mc(r - I) m = - -

I II +C( - 1) bull

III = 16lg

35 UaTII nonaUI1

m = 50 g M = 00 gmiddott = 0 CI =YC 1 = ~40L middot ( = 4200-1- t - u - lJ UK

a) nplLnIlKOM XJJal)el-ba BOlle y LJaWH ca TeMneparype 25deg C Ha Te1-mepaTYPY 0 C oC)lofiomf ce KOJlJ1IHHa TonnOTe

Q = Mdt - to) Q 21 kJ

O Ba KOnWII1I-a TOf1Jl OTe yTpOWI1 ce Ha TOnJbel-be Mace Jlena

Q )m = y = 618 g

93

r l oilJlozua

I Beha T34Hocr beKapCKor Tep~lOleTpa 1)13111 ce Llill-beHHUOM u3 JbeKapCKH

Tep IOMerap II Ia BeOMa yny KamIJlapy

2 )KllBa Mpme Ha _39 0 C a 311MCKe Te~meparype Y CImiddot16upy cy 4eCTO 3H3THO HIOIlte na ce -repIOMeTap ca IIBOM He IOgtKe KOPIICTIITI1 3a Mjepe~be TaM0shy

WlbllX lllMCKIIX Te~lnepaTypa

3 LlltHlHII lUlO OJ1MenIJIHOr npeKHnaLla C) llBllje mpCTO cnojeHe MeTaIlHe TpaKe (Ojc ce pa3Jll141ITO IlCTC)() npll ]arpllj aBaI-bY WTO 0080011 110 I-bllXOBOr KPI1shyBhel-ba Ha je11HY CTpaHY II npeKll11al-bU crpyjHor KOla DII lera1HII npeKII11a4M

ce Hajllewtle InpalJ~jy Oil UllHKa I fBO)(f)a

4 YH)paWl-ba eHepnlja raCOBa ce Haj4ewhe CBOlll1 Ha KlllIeTIIIK) eHeprllj) IeshyCTl1l1a raca (~Ionel IIlea1HOr raca) jep Je YJajalHO iljefloBaH)e LJeCTlllla raca

(aTola II MOleKY-lJa) 4eCTO JaHelapbIlBO 1ltLl0

5 KOIJIIIIHa Tomore KOjy Tlljelo npu~la npll ]C1rpltjaBa~bY ILl 11 oTrrywra npH xlalle~bY 33BIICII Oil Iace TIIje1C1 cneUlIltp1I4Hor TOruJOTHOr KanaUlfTera MaTeshyplljaTJa 011 Kora j e TIIje10 Ha411HgteHO II pnl llKe KpajHgte II nOlieTHe Tel-IITeparyshy

pe TIIje1JltI y nOClaTpaHml npouecy (Q = IIIC(r~ -II))

6 KOHIIIHa Tonl or e je KB3HTlnaTlml Ja ~ Ijepa npoMjeHe YH)rrpawl-be eHepmje OaHOCHO pa3HjeHgteHe )H)TpaWl-be eHepnlj e 1I3Metw Tlljena pa3TJlI4ltTIlX Telshy

nepnypa

7 He 3aTo WTO pajClIHO njellOBaHgte l leCTllua 011 KOj lLX ce cacToje Te4HOCTII 11 1BpCTa Tlljeqa Hllje mHCMapJblIBO 1 nO~HIHaHTaH 41aH Y YHypaWl-boj ellepnlshy

jll je nOTcHulljalHa eHeprllja

8 He AIOPltP H3 1 IIjC1la 3a pa31IlK~ Ull KpllcralHllx HeMajy TaliHO onpel)eHY Te~ishy

lIepaT~ py TOnJbeHgta

9 TeMnepa1)pa KTJYlaHa je HIDKa YKO~lIlKO je nplm1caK MaHgt11

) ltPa3HII npeqa] In 1npCTor arperaTHor CTaHgta 11llpelltHO y raCOBlITO arperaTHo

naJ-be (napy) Ha31IBa ce cy6nmlaUllja

I TelnCpaTypa TOnJbel-bltl lena je Dmiddot C II o CTaje KOHCTaHn ta TOKOl ltpa3Hor npeshy

)JaCKa

~ llaTl1 nonaUII

I = 27 C

88

AnCOJIYllIa Termeparypa ua3nyxa je

= (273 + I rC) ~ = (273 + 27 ) K T= 300 K

13 11ani nOllaUl

I = _3deg

A ncollyma TeMnepaTypa qe11a je

f = (273 + tre) K T= (173 - 3) K T= 270 K

l~ )laTII nOlaUll

T = 6300 K

Te~lITepa1)lpa Hel nonpWllHIt CYHUa Y U eJl311jyconoj TeMnepaTYPHoj CKaJlH je

I = (T K - 273 re = 6027 degC

15 11aTII nODHUII

T = 73 K

emepaT)pa Ha KOjoj Ba3J[YX npela31f y 1BPCTO CTal-be y Ue1 3IljYCOBoj TemeshypaTYPHoj C1GL~11 je

I = ITK - 273)middotC I = - lOOT

16 IlaTII nOIallll

11 =05 kg (= 4200 K I = 10( 1_ = 100 C

KU11JLIIIHa TOrL10Te lltojy BO11a nplnlll npll larplljanalb) je

Q = 111( U~ - I) Q = IB9 kJ

17 aaTiI nonallll

Q = -lIOOJ m=200g=02kg t1=5dege

KaKO je

Q = 111 C t1 TO je cneUlHtllllHl1 TOrLl0rHII KanCilliITeT Y_1gta

Q t = A (= 4 IOU ft

mul f

IS DaTil nonaUII

m=O5 kg c=4200 ~ 3min = lBOs P = 700 W 1 = 20 C

vl3pa11)HujIO npBO KOJ1I141111) TOrLlJOTe KOjy Bona npll1I1 OD rpllja4a

Q =PI Q = 126 kJ

K aKO j e

Q = me (l ~ - t I ) TO je TpagtKeHa TeMneparypa

I = BO e

89

llam nOnaUH

m=2 kg c =440 -J-middot 1== 150 C (= 50 C kJK I 2

K OllIILIIIII3 TonllOTe Kojy MeTan omycTI Opll Xll al)eJ-bY je

Q = me (II - 12) Q = 88 kJ

n aTI nOllaUl I

Q == 147MJ II =OC 1) =37 C ( == 4200~K p=IOOO ~gbull

KOllfHllIa TOJlJ1OTe Koja ce oCllo6ollli caropHjeSatbeM MaCHohe TPOWI1 ce Ha

3arpljaSaJ-be sone

Q = mc(12 - ) Tj ~aca llelleHe Bone Kojy oc06a Ha llHjeTII Mopa lla oonHje je

1) = c([ - I 111 = 946 kg

3anpC IIHa )leneHe BOile KOjy oco6a lopa na normje je

V = 111 V =946Q p

)laTII nonaUl J

= 1000 ~Q == 4000 kJ 1 = 22 C I~ = 50 C (== 4200 l~K m

Maca SOlIe y peJepBOapll~la je

111 = Q 11= 34 kg ((I_ - I )

3anpeMlIHa BOlle y pe3epnoapi lMa Je

V = 11 V= 14 CP

2 llaTl1 1l0naUJ1

V = 2 Ci = 20 Cl = 100 Cc =4200 ~h- p = 1000 ~~ = 7 min = 420 s l

a) KOlllllJlIHa Ton1 0Te kOjy je Bona npmnma npl1 3arplljaBaJ-bY j e

Q = 111( ((] - I) Q = p fie (I] - II) Q == 672 kJ

6) CHara eJleKTpll lJHOr rplljalla yrpal)eHor y YajHI1K aKO cy TO[JJJ OTHH ry611UH

3aHeMapJbl1BH j eCTe

p = P =1600 W P =16 kW

90

111 = 360g =036 kg m2 = 120g = O 12 kg t = 100 C 2 = 15 CI = 96 Ce =4200 k~K

KOlllJYlIHa TOnJ10Te KOjy OTflyCTl1 BOlla jenHaKa j e KOllllII IHH TOfU10Te Kojy nplfMI1 LlallJa JellHaLlIIHa TonllOTHor 6J1JJ3HC3 j e

QI = Q~

1lLbc je

I1IICI(t -l) = 111( - l )

J111( (T1 - T) c = - m(l - l)

I = 622 -Jshy1 24 llaTll nOllaUII

fII == I kg 11 = 2 kg lo = 25deg C l = 35degC

JellH3YIIH3 TOfFIOTHor 61LTlaHCa je

Q = Q m (I - Ii ) = 11I ~ ( ~ - ()

llabe je

= ml +mh gt In +m~

= 3L7

25 llam n OllaUII

VI = I 0 I II 8r = 12 I = 3r C

JellHa~lIlHa TOf1IOlHOI 6IlJHIHla j e

Q i = Q~ Nile (I I - l j = IIC (I - i ~ ) VjC (1 1 - 1lt1 = Ji2c (r - I~ nalbe je

V (l -l ) _ _ _I ~ j - I - l 2

v) = 20 e

26 lInlJ n OllaWI

VI 1 r l = JOOCl_ = ]0 Ct = 75 Cc1 = 4200 c~ = 390 d

K OJll1II IHa TOfUlOTe KOjy OTnYCTI I SOll3 jellHaKa j e KoHIIJIHII TOMOTe KOjy npllMH 13jHHK

QI = Q~ 111 1(1 (r - r) = 1l2 (2 (t - ( ~ ) pVl e l (1 1 - I) = 1112 c~(t - --)

9

I

DaJbe je p Vc(t - t)

n~ = f l (t -(2)

m~ = 414 kg

27 llanl nonaUlJ

Ill] = 300 g = 03 kg r ] = 16 0 C I~ = 1000

C I = 20middot C ( I = )

JenHilcll1Ha TonnOTHor 611--1ilHCa je

Q = Q~ III] ( ] (t - II) = 1112 (1(11 - I) 5 1 1 n (r - I I) = 11 2 (2 (1 - I)

5m1(1 - I) 171 =

- I~ - r

71 = 75 g

28 HaTH 1I0llaUll

11= 97901 c = 4200 ~K _ 6

n OTeHUIj alHa eHeprllja BOlle Ha npxy Bononana

E = mgh

~b yc~oBa 3a1aTKa je

Ep = Q

llabC j e

mgl1 = Q mgh = mc15t

Te~mepaTYpa BOAe ce nOBIlCfl 3a

gilDI = c t = 229 C

29 llUTl1 non3WJ

11= Ig J = 340 ft k~

113spweHII pall jeJlHlt1K j e KOlIll1I1HII TOf1JlOTe Koja je nOTpe6Ha na ce IICTOnl1

naTa ~lac3 Jlella

A = Q A = iliA = 340~

30 11aTII nonaUJ1

m = 20000 t A= 340 Aa 611 ce OTonWlO 10 neneHor 6pHjera nOTpe6Ho je YJlO)l(lITl1 eHeprnjy

Q = 0 1 ntA Q = 68 middot 10 J

92

31 DaTH nonalU1

m= Ikg A = HOg middot C =4200 - 1shybull - bull kd~

vb YCJJOBa 3anaTKa CJJ Hjen II

m = mc15t 151 = )1 = 8rc 32 DaTIl nonaUIl

III == 2 kg q = 226 ~~ t = 100 C

M IIHH[a1Ha eHeprHja KOjy 611 Tpe6ano YJJO)(]1TIr na 51 ce naTa Maca nOAe flpeshylleJJa Y BOnel-lY napy je

=mq Q = 452 MJ

33 )laTl1 nOnaUlI

P = 2kW = 2000 W T = 2 min == 120 s q = 226 ~

Maca Ilone Koja j e IIcnaNL~a je

11= ~ m= 106g

34 llaTII nOllaUB

I = 100 Cm = I SO gr = 20 Cr = 80 Cc =4200q = 126 ~

KOlIPHlHa TOfLl0Te Koja ce OCJlo6oJllI npll)lI1KO~ 1 oHlleH33ullje BOneHe nape Ii XJlal]el-ba TaKO llo611JeHe none TpOWII ce Ha 3arpujaRal-be x~anHor ~LnltjeKa

fII]q + lI e (II - r) = f11 2C (r - I)

Maca BOlleHe nape je

mc(r - I) m = - -

I II +C( - 1) bull

III = 16lg

35 UaTII nonaUI1

m = 50 g M = 00 gmiddott = 0 CI =YC 1 = ~40L middot ( = 4200-1- t - u - lJ UK

a) nplLnIlKOM XJJal)el-ba BOlle y LJaWH ca TeMneparype 25deg C Ha Te1-mepaTYPY 0 C oC)lofiomf ce KOJlJ1IHHa TonnOTe

Q = Mdt - to) Q 21 kJ

O Ba KOnWII1I-a TOf1Jl OTe yTpOWI1 ce Ha TOnJbel-be Mace Jlena

Q )m = y = 618 g

93

llam nOnaUH

m=2 kg c =440 -J-middot 1== 150 C (= 50 C kJK I 2

K OllIILIIIII3 TonllOTe Kojy MeTan omycTI Opll Xll al)eJ-bY je

Q = me (II - 12) Q = 88 kJ

n aTI nOllaUl I

Q == 147MJ II =OC 1) =37 C ( == 4200~K p=IOOO ~gbull

KOllfHllIa TOJlJ1OTe Koja ce oCllo6ollli caropHjeSatbeM MaCHohe TPOWI1 ce Ha

3arpljaSaJ-be sone

Q = mc(12 - ) Tj ~aca llelleHe Bone Kojy oc06a Ha llHjeTII Mopa lla oonHje je

1) = c([ - I 111 = 946 kg

3anpC IIHa )leneHe BOile KOjy oco6a lopa na normje je

V = 111 V =946Q p

)laTII nonaUl J

= 1000 ~Q == 4000 kJ 1 = 22 C I~ = 50 C (== 4200 l~K m

Maca SOlIe y peJepBOapll~la je

111 = Q 11= 34 kg ((I_ - I )

3anpeMlIHa BOlle y pe3epnoapi lMa Je

V = 11 V= 14 CP

2 llaTl1 1l0naUJ1

V = 2 Ci = 20 Cl = 100 Cc =4200 ~h- p = 1000 ~~ = 7 min = 420 s l

a) KOlllllJlIHa Ton1 0Te kOjy je Bona npmnma npl1 3arplljaBaJ-bY j e

Q = 111( ((] - I) Q = p fie (I] - II) Q == 672 kJ

6) CHara eJleKTpll lJHOr rplljalla yrpal)eHor y YajHI1K aKO cy TO[JJJ OTHH ry611UH

3aHeMapJbl1BH j eCTe

p = P =1600 W P =16 kW

90

111 = 360g =036 kg m2 = 120g = O 12 kg t = 100 C 2 = 15 CI = 96 Ce =4200 k~K

KOlllJYlIHa TOnJ10Te KOjy OTflyCTl1 BOlla jenHaKa j e KOllllII IHH TOfU10Te Kojy nplfMI1 LlallJa JellHaLlIIHa TonllOTHor 6J1JJ3HC3 j e

QI = Q~

1lLbc je

I1IICI(t -l) = 111( - l )

J111( (T1 - T) c = - m(l - l)

I = 622 -Jshy1 24 llaTll nOllaUII

fII == I kg 11 = 2 kg lo = 25deg C l = 35degC

JellH3YIIH3 TOfFIOTHor 61LTlaHCa je

Q = Q m (I - Ii ) = 11I ~ ( ~ - ()

llabe je

= ml +mh gt In +m~

= 3L7

25 llam n OllaUII

VI = I 0 I II 8r = 12 I = 3r C

JellHa~lIlHa TOf1IOlHOI 6IlJHIHla j e

Q i = Q~ Nile (I I - l j = IIC (I - i ~ ) VjC (1 1 - 1lt1 = Ji2c (r - I~ nalbe je

V (l -l ) _ _ _I ~ j - I - l 2

v) = 20 e

26 lInlJ n OllaWI

VI 1 r l = JOOCl_ = ]0 Ct = 75 Cc1 = 4200 c~ = 390 d

K OJll1II IHa TOfUlOTe KOjy OTnYCTI I SOll3 jellHaKa j e KoHIIJIHII TOMOTe KOjy npllMH 13jHHK

QI = Q~ 111 1(1 (r - r) = 1l2 (2 (t - ( ~ ) pVl e l (1 1 - I) = 1112 c~(t - --)

9

I

DaJbe je p Vc(t - t)

n~ = f l (t -(2)

m~ = 414 kg

27 llanl nonaUlJ

Ill] = 300 g = 03 kg r ] = 16 0 C I~ = 1000

C I = 20middot C ( I = )

JenHilcll1Ha TonnOTHor 611--1ilHCa je

Q = Q~ III] ( ] (t - II) = 1112 (1(11 - I) 5 1 1 n (r - I I) = 11 2 (2 (1 - I)

5m1(1 - I) 171 =

- I~ - r

71 = 75 g

28 HaTH 1I0llaUll

11= 97901 c = 4200 ~K _ 6

n OTeHUIj alHa eHeprllja BOlle Ha npxy Bononana

E = mgh

~b yc~oBa 3a1aTKa je

Ep = Q

llabC j e

mgl1 = Q mgh = mc15t

Te~mepaTYpa BOAe ce nOBIlCfl 3a

gilDI = c t = 229 C

29 llUTl1 non3WJ

11= Ig J = 340 ft k~

113spweHII pall jeJlHlt1K j e KOlIll1I1HII TOf1JlOTe Koja je nOTpe6Ha na ce IICTOnl1

naTa ~lac3 Jlella

A = Q A = iliA = 340~

30 11aTII nonaUJ1

m = 20000 t A= 340 Aa 611 ce OTonWlO 10 neneHor 6pHjera nOTpe6Ho je YJlO)l(lITl1 eHeprnjy

Q = 0 1 ntA Q = 68 middot 10 J

92

31 DaTH nonalU1

m= Ikg A = HOg middot C =4200 - 1shybull - bull kd~

vb YCJJOBa 3anaTKa CJJ Hjen II

m = mc15t 151 = )1 = 8rc 32 DaTIl nonaUIl

III == 2 kg q = 226 ~~ t = 100 C

M IIHH[a1Ha eHeprHja KOjy 611 Tpe6ano YJJO)(]1TIr na 51 ce naTa Maca nOAe flpeshylleJJa Y BOnel-lY napy je

=mq Q = 452 MJ

33 )laTl1 nOnaUlI

P = 2kW = 2000 W T = 2 min == 120 s q = 226 ~

Maca Ilone Koja j e IIcnaNL~a je

11= ~ m= 106g

34 llaTII nOllaUB

I = 100 Cm = I SO gr = 20 Cr = 80 Cc =4200q = 126 ~

KOlIPHlHa TOfLl0Te Koja ce OCJlo6oJllI npll)lI1KO~ 1 oHlleH33ullje BOneHe nape Ii XJlal]el-ba TaKO llo611JeHe none TpOWII ce Ha 3arpujaRal-be x~anHor ~LnltjeKa

fII]q + lI e (II - r) = f11 2C (r - I)

Maca BOlleHe nape je

mc(r - I) m = - -

I II +C( - 1) bull

III = 16lg

35 UaTII nonaUI1

m = 50 g M = 00 gmiddott = 0 CI =YC 1 = ~40L middot ( = 4200-1- t - u - lJ UK

a) nplLnIlKOM XJJal)el-ba BOlle y LJaWH ca TeMneparype 25deg C Ha Te1-mepaTYPY 0 C oC)lofiomf ce KOJlJ1IHHa TonnOTe

Q = Mdt - to) Q 21 kJ

O Ba KOnWII1I-a TOf1Jl OTe yTpOWI1 ce Ha TOnJbel-be Mace Jlena

Q )m = y = 618 g

93

I

DaJbe je p Vc(t - t)

n~ = f l (t -(2)

m~ = 414 kg

27 llanl nonaUlJ

Ill] = 300 g = 03 kg r ] = 16 0 C I~ = 1000

C I = 20middot C ( I = )

JenHilcll1Ha TonnOTHor 611--1ilHCa je

Q = Q~ III] ( ] (t - II) = 1112 (1(11 - I) 5 1 1 n (r - I I) = 11 2 (2 (1 - I)

5m1(1 - I) 171 =

- I~ - r

71 = 75 g

28 HaTH 1I0llaUll

11= 97901 c = 4200 ~K _ 6

n OTeHUIj alHa eHeprllja BOlle Ha npxy Bononana

E = mgh

~b yc~oBa 3a1aTKa je

Ep = Q

llabC j e

mgl1 = Q mgh = mc15t

Te~mepaTYpa BOAe ce nOBIlCfl 3a

gilDI = c t = 229 C

29 llUTl1 non3WJ

11= Ig J = 340 ft k~

113spweHII pall jeJlHlt1K j e KOlIll1I1HII TOf1JlOTe Koja je nOTpe6Ha na ce IICTOnl1

naTa ~lac3 Jlella

A = Q A = iliA = 340~

30 11aTII nonaUJ1

m = 20000 t A= 340 Aa 611 ce OTonWlO 10 neneHor 6pHjera nOTpe6Ho je YJlO)l(lITl1 eHeprnjy

Q = 0 1 ntA Q = 68 middot 10 J

92

31 DaTH nonalU1

m= Ikg A = HOg middot C =4200 - 1shybull - bull kd~

vb YCJJOBa 3anaTKa CJJ Hjen II

m = mc15t 151 = )1 = 8rc 32 DaTIl nonaUIl

III == 2 kg q = 226 ~~ t = 100 C

M IIHH[a1Ha eHeprHja KOjy 611 Tpe6ano YJJO)(]1TIr na 51 ce naTa Maca nOAe flpeshylleJJa Y BOnel-lY napy je

=mq Q = 452 MJ

33 )laTl1 nOnaUlI

P = 2kW = 2000 W T = 2 min == 120 s q = 226 ~

Maca Ilone Koja j e IIcnaNL~a je

11= ~ m= 106g

34 llaTII nOllaUB

I = 100 Cm = I SO gr = 20 Cr = 80 Cc =4200q = 126 ~

KOlIPHlHa TOfLl0Te Koja ce OCJlo6oJllI npll)lI1KO~ 1 oHlleH33ullje BOneHe nape Ii XJlal]el-ba TaKO llo611JeHe none TpOWII ce Ha 3arpujaRal-be x~anHor ~LnltjeKa

fII]q + lI e (II - r) = f11 2C (r - I)

Maca BOlleHe nape je

mc(r - I) m = - -

I II +C( - 1) bull

III = 16lg

35 UaTII nonaUI1

m = 50 g M = 00 gmiddott = 0 CI =YC 1 = ~40L middot ( = 4200-1- t - u - lJ UK

a) nplLnIlKOM XJJal)el-ba BOlle y LJaWH ca TeMneparype 25deg C Ha Te1-mepaTYPY 0 C oC)lofiomf ce KOJlJ1IHHa TonnOTe

Q = Mdt - to) Q 21 kJ

O Ba KOnWII1I-a TOf1Jl OTe yTpOWI1 ce Ha TOnJbel-be Mace Jlena

Q )m = y = 618 g

93

KaKO je 1aca llBl1je KOllKHue Jlella 100 g TO ce BOlla OXJlaoH llO TeMnepaT)pe Omiddot C II Y laWH npeOCTaHe jow llella Ha HCTOj TeMneparypH

6) I-h lllljena 3UlaTKa nOA a) cnl1jellll na aKO Y 4awy CTaBJMO CaMO jeliHY KOU KIIUY JleJla BOlla y laWII ce Hehe OXllall11T11 )10 0 C Beh fIe ce TOIlJlOTHa paBshyHOTe)(a ycnocTLlBIIT11 Ha HeKoj Bllwoj Te~tnepaTypl l JellHalllHl a TOIlJlOTHOr 611

11aHca je

dm) + 11( (I - II) = M e (I - I)

PjewaBaHeM Je)lIIa4Hf-Ie )lo6Hja~lO

Mel - 6m 1 =

c(M +111)

= 38 C

~6 llaTJI nonall1

MJ == 340 II = 150 g =015 kg 10 = 0 C 1 = lOOT I = 50 C q = 22 Q lg bull

( = 41 00 - Jshy- lltK

KO11I11I1Ha TO[1HOTe Koja ce OC1060)l11 KOHneH3aUlljo BO)leHC nape II Nlal)emiddot

Hgte1 TaKO A0611jeHe Rone TpaWI ce Ha TOnJbeHgte 1el1a H ]arpHjaJIal-he TaKO noshy

611jeHe Bone

lq + le (I - I ) = In) + lilt (I - (0 )

nOTpe6H3 ~Iaca BOllef-le nape j e

AI == m(A +[(1 - Iu))

q +C(I - I)

M = 334g

37 llanl nOilaUlI

=80kg 1-=900001 q=24 yen

[pal1llTaWtOHa nOTcHulljaJ1Ha eHepnlja 40BjeKa KOjl 1 CTOjll Ha MOHT EBepecry je

Er = MgH

Maca nyTepa Koja caroplI nplI neJ-bal-bY lOBjeKa Ha MOHT EBepeCT j e

If H 2943m=-q- m= g

H apaBHO npeTrl0CTaBHJl II CIIO na IoBjeK nopen nyrepa )HOCI1 Y opraHI3aM 11

l1Pyry xpaHY HeorrxOJlHY ]a Ollp)(aBaHgte )I(J1BOTHI1 X centYHKlIl1ja

94

JlA])OPATOPIIJCKE BJElKliE

Jla6opaTopHjcKI1 paJl (BjegtK6e) liMa BeJllIKJI 06pa30BHO-BaCfU1TIfI1 3Ha4aj TIpeshy1anaHgta yU6eHIIK eKCnepl1MeHTII H na60paTopHjcKe BjegtK6e cy OCHOBHH II3BOPl1 cashy

JHalba y cent1f3HLJH JIa6opaToplljcKe Bje)(6e Ha jenHOCTaBHHM npHMjepJ-IMa nOKa3yjy

KaKO cc nocMaTpajy nojeL1I1IIe nojaBe II Hgt11XOBII 3aKOHII KaKO ce Mjepe spHjeQHOshy

CTII noje1I1HIIX cent1I311lKHX Bemt41111a Ii KaKO ce Ha OCHOBY pe3YJlTaTa Mjepel-ba 113Boshy11e 3aKhYIUl I If Ty~ r aJel-ba

Y npOllecy peaHl13aul1je 1a6opaTOpl1jcKIIX sjel611 CTH4Y ce 3Hal-ba 11 BjellITl1Ha KopllWnel-ba ~jepHJIX ypel)aja 11 OJlpel)eHI1X anapaTa WTO 3HaTHO Donpl1HOCH

centOplllpaI-bY HaSI1Ka onrOBopHocm 036ILbHOCTII If Ta4HOCTI1 y pany nOD113aJ-bY TCXHII4KC KYJ1Type Ha BIIWII HIIBO

npIUHlKOJ lnpa)le 1afiopaTopHjcKIlX Bje)lGII rrsPQyje ce npel)eHo rpa)UIBO 11 )lll KaKO ce CTeIeHa 3Hal-ba lory npI1MjeHgt~IBanl y npaKCl1 II csaKonHeSHOM )(HBoshyry

flpl1 113paJlII cBaKe JIa60paToplljcKe Bje)K6e TpeGa

bull nOHOBI1T11 HaCTaBHO rpaaIlBO Koje o6yxnaTa sje)(6y 11 06paTHTJI nltDlCl-by Ha

nojMose BeJIIl41111C IJIIJe ce BpnjenHOCTII jepe 1 I-bltXOBe MjepHe jeJlI1H11Ue

bull yn03HaTll Ii KpaTKO onllcaTII npllfiop KOjll ce KOPllCTl1 npl1 113panJ1 JlafiopashyTopl1jcKe Bje)(fie

bull Y TOKY palla KOPIICTUTH onWTe yny-rCTBO JlaTO Ha nOJeTKY KJ-bl1re

bull MjepHe nOJlaTKe npeDCTaBIITII TafieJlapHO a aKO nocTojl1 MoryhHOCT bull 110611 shyjeHe pe3YJJTaTe If rpacent1f4Kll npl1Ka3aTl1

bull HanpaBlml 3H31J1l3) 1106I1je~[Jv pe3)naTa II JloHlljem oJlroBapajyhu 3aKlbyshyyaK

95

llPBA JIAEOPATOPl1JCKA BJE)I(poundA

O)lPEBJIBAI-hE CTAJIHOr YliP3AIbA ITPH KPETAlhY KYrJlHlIE Hl13 CTPMY PABAH MiJIOr HAnffiHOr YrJ1A

YBOlI

DpY paBHOljepHo npmrjeHJbl1BOl IlpaBOJHIHl1jCKOM KpeTaJ--bY ca CTarJHIIII y6pshy

mf-be1 a TI1jeJIO npel)e nyr s 3a Bpllj eMe I

1 ~ S = lar

Y311Ma ce lla j e TlIJeJlO 3anOlfeJJO KpeT3J--be 113 CT3J--ba 111 II pOBaJ--ba TO jeer na j e

noyeTHa 6pJI1Ha jenHaKa Hy~H (Vu = 0) jib npeTxollHe centop-IYJI e HLlaJII ce y6p3aJ--be nrjeJla

25 a = ---

1

Y6p3aJ--be Tuje13 (KYLlllue) a HIB CTpll) paBaH ollpel)yje ce TaKa UlTO ce Mjepshy

1111 nonaUII 3a nYT (s) It Bpllje~le (I) nOTpe6HO lla TI1jeJIO npel)e Taj ITyr YBpCTe y npeTxanHY ltPOP)IYJ1)

3aqafiiaK f1jcJlCe OllpeorTBalbe y6p3alba paBHoMjepHo npoMjeHJbJ1BOr npaB0shy

111 tllIjcKor KpeTalba THjela Mjepelbel npel)eHor nyra 11 BpeMeHa

nPH60P

JleTBa ca )I(~lje6011 nYgtKIIHe OKO 15 m CTaJlaK MeTpoHoM (UJl I1 WTOnepl1Ua )

ca HajMat--bOM alJA~why 02 s K) r~l1ua MeTapcKa TpaKa IIlH1 net--bl1p n~I1He OKO

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l be KYrJlHue

96

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nOCTaBHru nopeJl lIeTBe Ha ueMOHCTpaUYIOHl1 CTO

o fIonecl11e Harl16 )f(JlHje6a (lIeTBe) TaKO Ila np lf lJeTBpTOM OTlcYIlaj y MeTposhyHOM a (aKO je 6110 HaMjellITeH Ila HMa 120 OTKYuaja y jellHoM MHHyry) KYfnl1ua yJla

pa y UI11THHnap nOCTaBJbeH Ha Il0J--beM (HIDKeM) Kpajy )JJl1je6a OrKYuaj MeTpoHoMa y MOMeHTy t1yIl1Ta~ba K)rlll1ue (HJJH npl1rucKa Ha nyrMe WTOnepl1lJe) cMaTpaTH HYk fI11 Y TOM CJTYlajy KpeTaJ--be KYfJll1Ue no npenpeKe (UHJJHH)]pa) Tpaje nBHje ceKyH ne

o 113MjepHTe npel)eH n)T K)flll1ue (s)

o MjepHe nOllaTKe 33 BpMjeMe H nyr YBpCHrre y ltP0PMYny

2s a= r

II H3 OCHOBY Tora J13palYHajTe Bpl1jellHoCT yGp33J--ba

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nPHEO P

PallHI1 eTO ea XOPI130HTaIlHOII nOSpUliIHOM JleTBa ea MHJnlMeTapeKO~1 noDjeshy

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Bbal-be KOJrHua npeKO llI1RaMOMeTpa ca TaCOM Ha KOj H ce nOCTaBJbajy TerOB~1

TOK PAllA

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8 ilHHaMoMeTap Be)(lITe KOHueM KOjU ce npe6auyje n peKO Korypa 11 0 I-bera OKaIHTe Tac

t) n OMony llHHaMOMeTpa 113MjepHTe CHJl Y Tpel-ba 113Mel)y KOJUma 11 JleTBe H a TaC nOCTaBJbajTe nOCTeneHO TerORe nOK ce KOJll1Ua He nOKpeH) T 3lla ce ypaBHOTeshy

98

JJJ ~~na ICIUBa 11 T3ca ca CI1JlOM Tpel-ba (KOJTl1ua 6H ce KpeTaJla paBHoMj ep Ho KOHCTaHHIOM 6p3I1HOM) CI1JIa TpeJ-ba ce OIHTaBa Ha nl1HaMOMeTpy

ITPl1naJbeM pany Tpe6a Y3eTH y 06311P Aa je CI1JJa ltlgt Koja caonruTasa y6p3al-be KOJHluajeAHaK3 pa3JUrUl1 cl1JIe Koja ce MjcPII nHHaMoMeTpoM 11 CI1JJe Tpel-ba

bull Ha Tac llollajTe Ter 1I1ja TegtKJ1Ha npenCTaBlba ClfJ1y F ~ KOJHIla nOCT3BI1Te Ha pacToj3l-be S 011 rpaHIfIHI1Ka VlCTOBpee~O Cil nYWTaHeM KOnHla YIUbY-ll1Te XpoHo~leTap (wToneplIUY) II 1l3ljcpHTe BpujeMe Kpn3l-ba KOJlHla t 1l0K njenyje CI1shy_~a F OllHOCHQ 1l0K KOJJJfU3 He Yllape y rpaHlIlHI1K Kana ce Mj epel-be BpeMeH CTaSJba

o 113MjepilTe npe~leHII nyr KOJ~Ilua (s ) Ii npoHlTajTe Ha XpoHoMerpy BpHjeMe (I) 3C1 Koje cy KOJlJJua npeUlJl3 raj nyr

o JiIJ I13pa3a 3a npel)eH II nYT paBHoMjeptio y6p3aHor KpeT3l-ba TI1j eJl3 Kao llIT( je II Kperal-be KOJJHua

s = ~atl

liala311 ce y6p3aHgtC KO)lIlua

2s () = --

r

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e llocTaBllTe llBa Tera Ha Tac CUBa nYTa Beha CILla) na nOHOBIlTe npeTXOllHJ1 nocl) naK a 3aTmi IfCTO TO ypanlfTe 11 ca TPll Tera jenHaKlfX Te)KJIHa npl1 TOMe He llIjellajTe llY)(~IHY nYTa (s)

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I

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99

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TaneJlQ 3

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jn ce npl1Ka3yje ltP0PMYJlOM

a= F -n

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F = m~

Qua je jellHllKa UPOH3BOlY Mace H y6p3alha rnjeJI3

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npl160P

Y OBOj Bje)l(611 KOpl1CHlne ce onpeMa Koja OMoryhyje BPlJO npeUl13H3 Mjepefh3 BpeMeHa (Mjepllhe1o neceTOJ(J1JbaJllITe nl1jenoBe ceKYHJle) OBaKBy npeLUf3HOCT

oMorylil1JJa j e ynorpe6a KOMnjyrepa OCHOBHH nl1jeJIOBH anaparype llaHf cy Ha CJllishyUl l ( I)

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fJPUHIUfi paqa THjeJJ O (3) npl1 npOJIacKY H3Metw 113BOpa cBjeTJlOCTI1 (2) H npshyBor ceH30pa ( I) npeKJIQa CHon cBjeTJloCTIf (4)_ To pefHCTpyje ceH30p 11 W3Jbe eneKshy

TP1-f1-lHI1 CI1THaTI K36JJOM (5) 110 noce6Hor eJleKrpoHCKor ypel)aja (JiliTepcentejca) Kojl1 eneKrpHYHl1 CHTHaTI n06l1jeH ca ceH30pa npMJIarol)aBa KOMnjyrepy TaKaB CI1rHaTI je 3HaK KOMnjyrepy 3a n04eT3K Mjepel--ba BpeMeHa T OKO] lIaJher KpeTaJ--ba THjeJ10 npeshycHjeua CHon cBjeTJlOCTI1 113Mel)y If380pa cBjeTlIoCTIl If upyror ceH30pa Taj Cl1fHaTI 03Ha-laBa lltpaj Mjepel-ba npBor BpeMeHCKor HHTepBaTl3 11 nOQeT3K Mjepel--ba npyror BpeMeHCKor Hl-ITepBaJla Ha cnWlaH HalJ1H HaCTaBJba ce Mjepel--be H OCTaIlI1X Bpeshy

101

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