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MODÜL Alt bölümlerin HJCJ'LVWWFUJJMF¿FLJMJZPS L©HUHQNDUPDWHVWOHU EDĜOñNODUñQñL©HULU TZMB F1, F2 ve F3 LVWWFUMFSJJMF¿FLJMJZPS \\HUDOñU NEWTON’UN HAREKET YASALARI BİR BOYUTTA SABİT İVMELİ HAREKET F3 m T1 2m T2 F İKİ BOYUTTA HAREKET 3m a F2 m ôFLJMm*** m m F1 ôFLJMm** NWFNLÑUMFMFSJBSBTOEBLJJQHFSJMNFTJ5 N ôFLJMm* 1 WFNBSBTOEBLJJQHFSJMNF52PMEVôVOBHÌSF JQHFSJMNFMFSJPSBO5152LBÀUS $JTJNMFSLVWWFUMFSJMFBZOZÌOEFWFFöJUöJEEFU- 6 B) 5 $ 3 3 E) 1 A) 3 2 D) 3 MJJWNFMFSJMFI[MBOEôOBHÌSF '1 '2WF'3 LVW- WFUMFSJOCÑZÑLMÑLMFSJBSBTOEBLJJMJöLJOFEJS 5 5 (g = 10 m/s2) \" '1 ='2 ='3 # '1 >'2 >'3 $ '1 ='2 >'3 % '2 >'3 >'1 & ' >' >' 321 NEWTON’UN HAREKET YASALARI ³ Dengelenmiş ve Dengelenmemiş Kuvvetler t 1 ³ Newton’un Hareket Yasaları t 4 6ñQñIð©LðĜOH\\LĜ YAZILI SORULARI <D]ñOñ6RUXODUñ /&850/6/)\"3&,&5:\"4\"-\"3* 2NXO\\D]ñOñVñQDYODUñQGD ©ñNDELOHFHNVRUXODUñL©HULU ³ Sürtünme Kuvveti t 13 LHMLCJSDJTJNBõBóEPóSVTBCSJüUrItü[nMBmeIsBiSzFLyFaUtay düzlem de%kVi SmNBvLeUBm PMBkOütCleJSliBcSiB- DO UBWBOOB N LÐUMFMJ DJTJN 11. SINIF .0%·- /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 www.aydinyayinlari.com.tr FUNFLUFEJS TJN JQ ZBSENZMB CJSCJSJOF CõBFóLMJBMEO1FQLJõHFJCL2JJMEBFTLMNJ HõJCUJS ³ Serbest Cisim Diyagramları t 23 /FXUPOVO)BSFLFU:BTBMBS EÐõFZ TFSCFTUCSBLMZPS ø øi Sürtünmesiz yatay düzlemde m ve m kütleli ci- m m 12 m1 ÷MJöLJMJ,B[BONMBS TJNMFSFTOFNFZFOCJSJQJMFCBóMBOBSBLõFLJMEFLJHJ- ³ Karma Testler t 37 /FULVWWFUJOZËOÐOÐCFMJSMFZFSFLCÐZÐLMÐóÐOÐIFTBQMBS %XE¸O¾PGHNL¸UQHN CJ ' LVWWFUJ JMF ¿FLJMEJóJOEF JQUF PMVõBOFHSFSJMNFm 5= 10 kg VRUXODUñQ©¸]¾POHULQH ôFLJMm* ôFLJMm** DNñOOñWDKWDX\\JXODPDVñQGDQ LBEBSPMVZPS $JTJNMFSF&ULJZFO/FU,VWWFU ÖRNEK 18 XODĜDELOLUVLQL] 0,8 F ³ Yazılı Soruları t 46 2500 gram ZBUBZ \"SBÀBJWNFTJJMFIBSFLFUFHFÀUJôJOEFDJTJNöF- 7$1,0%m/*m 37° LJM**EFmL2JLPOVNVBMZPSTBiBÀTN ù BWFHOJ- DFMJLMFSJOEFOIBOHJMFSJOFCBôMES ³ Yeni Nesil Sorular t 48#JSDJTNFFULJFEFOCJSEFOGB[MBLVWWFUJOZBQUó m1 T m2 F FULJZJUFLCBõOBZBQBOLVWWFUFOFULVWWFU de- 100 N 0,6 F OJS/FULVWWFUDJTNFFULJFEFOLVWWFUMFSJOCJMFõ- F=? LFTJEJS/FULVWWFUTGSEBOGBSLMJTFDJTJNMFSJW- NFMJIBSFLFUZBQBSMBS F 5 jsabit 5Y =NH T = 3 PMEVôVOB HÌSF DJTJNMFSJO LÑUMFMFSJOJO Fnet = m.a TY 5X =NB :Ñ[FZJOTÑSUÑONFLBUTBZT PNMEVWôFVNOBHLÑÌUSMFF MFSJÌ[EFöPMiEVôTVOBHÌSF TJTUF- T . sin i = m .a PSBON1N2LBÀUS 12 VZHVMBOBO'LVWWFUJLBÀ/EVS NJOJWNFTJLBÀHEJS ( gm=ZFS¿FLTJNXJJWNFTJ T . cos i = m .g (sin37° =7 DPT9= H= 10 m/1s2) %ÐOZB (F[FHFO 1 B) 3 5 B) 3 % 5 a 1MÐUPO A) 2 2 tan i = $ D) E) A) $ mg E) 3 2 g $J2TJNTBCJUI[2MBHJUUJôJJÀ2JOIBSFLFUEPôSVMUVTVO2EBLJOFULVW-2 HSBN LÑUMFMJ CJS DJTJN ÀFLJN JWNFTJ EÑOZBOO %VSHVO CJS DJTNF FULJ FEFO OFU LVWWFU IBOHJ WFUJOTGSPMNBTHFSFLJS 0IBMEFiBÀTBWFHZFCBôMES ZËOEFJTFDJTJNPZËOEFIBSFLFUFHF¿FS ZFSÀFLJNJJWNFTJHOJOZBSTPMBOCJSHF[FHFOEFLBÀ 100 ='S+ ' OFXUPOMVLBôSMôBTBIJQUJS D B 100 = ' L+ ' 37 E A 1. ? 2. ? 1 1. ? (2g. ?= 10 N/kg) 100 = '+ ' ÖRNEK 17 g '=/PMVS = 5N/kg 4ÑSUÑONFTJ[ ZBUBZ CJS EÑ[MFNEF EVSNBLUB PMBO CJS H=/LH %ÐõFZLFTJUJWFSJMFOõFLJMEFLJTJTUFNEFCJSCJSJOFJQ- DJTNJOIBSFLFUFCBöMBZBCJMNFTJJÀJO G =NH 2 MFCBóM LÐUMFMFSJTSBTZMBLHWFLHPMBO9WF: N=H g DJTJNMFSJOF'LVWWFUJFULJFUNFLUFEJS * /FULVWWFUTGSEBOGBSLMPMNBMES ** %FOHFMFONJõLVWWFUMFSFULJFUNFMJEJS = LH G' = m. 2 <HQL1HVLO6RUXODU = 2, 5.5 = 12, 5 N 0RG¾O¾QJHQHOLQGH\\RUXP $FWBQ / \\DSPDDQDOL]HWPHYE EHFHULOHUL¸O©HQNXUJXOX *** \"óSMóOEBOCÐZÐLCJSLVWWFUFULJFUNFMJEJS F=? 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N = –5G3° 37° G -5=NyB '#neVt O=BNHBÌSF BöBôEBWFSJMFOHÑOMÑLIBZBUN[EB * m'gLcVoWsaWFUJBSNUHSTMJSOTaB 5JQHFSJMNFTJBSUBS F S 5m Y -LB'S=öMBö UôN[ ÌSOFLMFSEFO IBOHJTJOEF ZVLBS- a= F Fs Fs = m.a 10-5 =B E'BL=J2C0JMNHJJMFCFO[FSCJSIFEFGZPLUVS 5m F= A) 4FSCFTUUSNBOõZBQBOEBóDMBSOFMMFSJOJQVE- ** m1LÐUMFTJaBSUSMSTB 5JQHFSJMNFTJBSUBS S5 a =NT2 SBMBNBT G = mg *** m2LÐUMFTJBSUSMSTB 5JQHFSJMNFTJBSUBS F 1 N1F=2 LH N2 =LHPMEVôVOBHÌSF 5JQJOEFLJ B) #JTJLMFU [JODJSMFSJOJO QFSJZPEJL CBLNMBSEB ZBó- HFSJMNFLVWWFUJLBÀ/PMVS G = mg G = mg (sin53° =Ay TJO= H= 10 m/s2) ôFLJM* MBONBT $ .FSNFSLBZHBONFSEJWFOCBTBNBLMBSOOV¿L- \"óSMLZFS¿FLJNJJWNFTJOFCBóZMBESHSM:BSFSO¿EFBLOJNIJBJWONHFJM-FSJEPôSVEVS BWFH 2T0NNMBSOO[NQBSBMBONBT D)5FLOJL ¿J[JN LBMFNMFSJOJO UVUBDBL LTNMBSOO TJ DJTNJO IBOHJ HF[FHFOEF PME\"V ó:VBOMOB[WF* HF[FHFO#JO *WF** $ *WF%***ÐOZB 5BIUBZÐ[FZEF & * **WF*** ¿FLJMFODJTJN 46 QÐSÐ[MÐQMBTUJLPMNBT OFSFTJOEFCVMVOEVóVOBHËSFEFóJõJS:BOJEFóJõLFO F1 = –\"F 2 # $ % & 100 N F E) ,BSZBóEóOEBBSB¿MBSOUFLFSMFSJOF[JODJSUBLM- F = CJSLVWWFUUJS % **WF*** NBT S5 :BMO[* 18 / Sürtünmesiz yatay düzlemde m ve 2m kütleli cisim- ôFLJM** 0MJNQJLIBWV[NVTBCBLBMBSOEBTFSCFTUTJUJMEFZB- MFSCJSJQMFCBóMBOBSBLõFLJMEFLJ'LVWWFUJZBSENZ- *TMBLDBNNBTB SõBOTQPSDVMBSIBWV[VOTPOVOBHFMEJLMFSJOEF IB- MB¿FLJMJZPSMBS Ð[FSJOEF¿FLJMFO WV[EVWBSOBZBLMBõSLFOTPOTFSCFTULPMVBUULUBO DJTJN TPOSBTVJ¿JOEFUBLMBBUBSBLBZBLMBSZMBEVWBSõF- T LJMEFLJHJCJJUNFLUFEJS 2m ôFLJMEFEÐõFZLFTJUJWFSJMFOTJTUFNEF9WF:DJTJN- MFSJ'LVWWFUJZBSENZMBZVLBSZËOEF¿FLJMJZPS F X ôFLJM*** #VOBHÌSF m #VOBHÌSF ²ôSFODJ ZBQUôCVEFOFZEFBöBô- TF EBLJTPSVMBSEBOIBOHJTJOFDFWBQBSBEôTÌZMF- OFCJMJS #VOBHÌSF * 4QPSDVTVEBZÐ[FSLFOTQPSDVZBTVZVOWFIB- * 'LVWWFUJBSUSMSTB5JQHFSJMNFTJBSUBS A) 4ÐSUÐONFLVWWFUJDJTJNMFSJOBóSMóOBCBóMN- WBOOTÐSUÐONFLVWWFUJFULJFEFS ** NLÐUMFMJDJTJNZFSJOFNLÐUMFMJDJTJNCBóMB- ES Y OSTB5JQHFSJMNFTJBSUBS ** 4QPSDVOVOEVWBSBVZHVMBEóLVWWFUJMFEVWB- B) 4ÐSUÐONFLVWWFUJDJTJNMFSJOUFNBTZÐ[FZBMBO- SOTQPSDVZBVZHVMBEóLVWWFUFULJ-tepki kuv- 5ÑNTÑSUÑONFMFSJOJINBMFEJMEJôJTJTUFNEF *** NLÐUMFMJDJTNJOZFSJOFNLÐUMFMJDJTJNCBóMB- OBCBóMNES WFU¿JGUJEJS * :OJOLÐUMFTJBSUSMSTB 5JQHFSJMNFTJBSUBS OSTB5JQHFSJMNFTJBSUBS ** 'LVWWFUJBSUSMSTB 5JQHFSJMNFTJBSUBS $ Sürtünme kuvveti temas edilen yüzeylerin cinsi- *** 4QPSDVOVOBóSMóJMFTVZVOTQPSDVZBVZHVMB- OFCBóMNES EóLBMESNBLVWWFUJFULJ-UFQLJLVWWFU¿JGUJEJS *** :OJOLÐUMFTJBSUSMSTB 5JQHFSJMNFTJB[BMS D) Sürtünme kuvveti cisme etki eden net kuvvete ZBSHMBSOEBOIBOHJMFSJEPôSVEVS CBóMNES \" :BMO[* # :BMO[** $ *WF** E) 4ÐSUÐONFLVWWFUJZFS¿FLJNJJWNFTJOFCBóMN- ZBSHMBSOEBOIBOHJMFSJEPôSVEVS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS ES % *WF*** & * **WF*** \" :BMO[* # *WF** $ *WF*** \" :BMO[* # *WF** $ *WF*** C 48 B C % **WF*** & * **WF*** % **WF*** & * **WF*** B D 20 B A
www.aydinyayinlari.com.tr 11. SINIF 2. MODÜL NEWTON’UN HAREKET YASALARI BİR BOYUTTA SABİT İVMELİ HAREKET İKİ BOYUTTA HAREKET NEWTON’UN HAREKET YASALARI ³ Dengelenmiş ve Dengelenmemiş Kuvvetler t 1 ³ Newton’un Hareket Yasaları t 4 ³ Sürtünme Kuvveti t 13 ³ Serbest Cisim Diyagramları t 23 ³ Karma Testler t 37 ³ Yazılı Soruları t 46 ³ Yeni Nesil Sorular t 48 1. ? 2. ? 1 1. ? 2. ?
KONUYA HAZIRLIK #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS /FXUPOVO)BSFLFU:BTBMBS ÷MJöLJMJ,B[BONMBS %FOHFMFONJõLVWWFUMFSJOFULJTJOEFLJDJTJNMFSJOIBSFLFUEVSVNMBSOËSOFLMFSMFB¿LMBS ,VWWFU JWNFWFLÐUMFLBWSBNMBSBSBTOEBLJJMJõLJZJB¿LMBS &ULJm5FQLJLVWWFUMFSJOJËSOFLMFSMFB¿LMBS 4ÐSUÐONFLVWWFUJOJOCBóMPMEVóVEFóJõLFOMFSJBOBMJ[FEFS %FOHFMFONJöWF%FOHFMFONFNJöLVWWFUMFS 7$1,0%m/*m 7$1,0%m/*m %FOHFMFONFNJöLVWWFU Bir cisim ya da sistem üzerine uygulanan tüm %FOHFMFONJöLVWWFU LVWWFUMFSJO CJMFõLFTJ TGSEBO GBSLM JTF LVWWFUMFS Bir cisim ya da sistem üzerine uygulanan tüm EFOHFMFONFNJõUJS LVWWFUMFSJOCJMFõLFTJTGSPMVZPSTBLVWWFUMFSEFO- HFMFONJõUJS #BõLBCJSJGBEFZMF #BõLBCJSJGBEFZMF F2 F1 F2 F1 Yatay Yatay Fnet = F1 + F2 ! 0 JTFDJTJNEFOHFEFEFóJMEJS Fnet = F1 + F2 = 0 JTFDJTJNEFOHFEFEJS ÖRNEK 1 ÖRNEK 2 Yatay sürtünmesiz düzlemde F1, F2 ve F3 kuvvetleri et- #JS DJTJN õFLJMEFLJ HJCJ ZBUBZ TÐSUÐONFTJ[ EÐ[MFNEF LJTJBMUOEBPMBODJTJNõFLJMEFLJHJCJEFOHFEFEJS F1, F2 ve F3 LVWWFUMFSJFULJTJBMUOEBES F2 = 6 N F1 = 10 N F2 = 12 N F1 = 20 N F3 = 4 N Yatay F3 = 8 N Yatay ,VWWFUMFSEFO' WF' öFLJMEFHÌTUFSJMEJôJHJCJPMEV- $JTJN CV ÑÀ LVWWFUJO FULJTJ BMUOEB EFOHFEF EFôJM 12 JTF'3LVWWFUJOJOCÑZÑLMÑôÑLBÀOFXUPOPMBNB[/F- EFOJOJöFLJMÑ[FSJOEFHÌTUFSFSFLBÀLMBZO[ ôVOBHÌSF '3LVWWFUJOJOZÌOÑWFöJEEFUJJÀJOOFTÌZ- MFOFCJMJS $JTJNEFOHFEFJTFFULJFEFOLVWWFUMFSUPQMBNTGSES $JTJNEFOHFEFPMNBEôJÀJOFULJFEFOLVWWFUMFSUPQMBN 4N TGSEBOGBSLMPMNBMES 8N 4N 2 8N
TEST - 1 #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS Bilgi: Bir cismin üzerine uygulanan kuvvetlerin bi- #JSTJTUFNEFOHFEFJTFFULJFEFOLVWWFUMFSUPQMBN MFõLFTJTGSJTFDJTJNEFOHFMFONJõLVWWFUMFSJOFULJ- TGSES TJOEFEJS I. I. \"óB¿UBOEÐõFO 6¿VõQJTUJOEFO FMNB LBMLõBHF¿FO V¿BóOIBSFLFUJ II. II. 'SFOZBQBO )BMUFSJLBMESNõ BSBCBOO TQPSDV IBSFLFUJ III. III. 4BCJUI[MB )BWBEBI[MBOBO IBSFLFUFEFO V¿BL USFOJOIBSFLFUJ :VLBSEBLJ IBSFLFUMFSEFO IBOHJMFSJ EFOHFMFO- NJöLVWWFUMFSJOFULJTJOEFHFSÀFLMFöJS \" :BMO[* # :BMO[** $ :BMO[*** % *WF** & **WF*** #VOB HÌSF WFSJMFO ÌSOFLMFSEFO IBOHJMFSJ EFO- HFMFONJöLVWWFUFULJTJBMUOEBES 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFÐTUUFOHËSÐOUÐTÐõF- \" :BMO[* # :BMO[** $ *WF** LJMEFLJHJCJPMBODJTJN '1 '2 '3WF'4 kuvvetleri ile % *WF*** & * **WF*** EFOHFMFONJõUJS F2 :BUBZEÐ[MFNEFIBSFLFUFEFO, -WF.DJTJNMFSJ- F1 F3 OFFULJFEFOLVWWFUMFSWFIBSFLFUZËOMFSJõFLJMEFLJ HJCJEJS )BSFLFUZËOÐ F4 )BSFLFUZËOÐ F F LF Ka Yatay Yatay ôFLJMm** #VOBHÌSF ôFLJMm* )BSFLFUZËOÐ * $JTNFFULJFEFOLVWWFUMFSJOCJMFõLFTJTGSES F Yatay ** '1 LVWWFUJOJO CÐZÐLMÐóÐ BSUUSMSTB DJTJN EÐ[- M HÐOI[MBOS ôFLJMm*** *** $JTJNTBCJUI[MIBSFLFUZBQBS #VOB HÌSF , - WF . DJTJNMFSJOEFO IBOHJMFSJ ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS EFOHFMFONJöLVWWFUMFSFULJTJOEFPMBCJMJS \" :BMO[* # :BMO[** $ :BMO[*** \" :BMO[* # :BMO[** $ *WF*** % *WF** & **WF*** % **WF*** & * **WF*** C A 3 B E
KONUYA HAZIRLIK #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS /FXUPOVOIBSFLFUZBTBMBS .qk(7$k, (ÐOMÐL IBZBUN[EB DJTJNMFSJO FZMFNTJ[MJóJ JMF 7$1,0%m/*m JMHJMJCJSLB¿ËSOFóJJODFMFZFMJN /FXUPOVO * )BSFLFU :BTBT &ZMFNTJ[MJL )BSFLFUMJ )BSFLFUMJ 1SFOTJCJ &ZMFNTJ[MJLCJSDJTNJOõFLMJOJWFLPOVNVOVLPSV- )BSFLFUMJ %VSVODB NBJTUFóJEJS \"SB¿ Ð[FSJOEFLJ DJTJN IBSFLFU IBMJOEF JLFO &óFSCJSJTNFFULJFEFOOFULVWWFUTGSJTFDJTJN BSB¿ EVSEVóVOEB ÐTUÐOEFLJ DJTJN IBSFLFU FU- J¿JOJLJEVSVNTË[LPOVTVEVS NFZFEFWBNFEFS %FOHFMFONJõ,VWWFUMFS )BSFLFUTJ[$JTJN )BSFLFUMJ$JTJN &óJL EÐ[MFN Ð[FSJOEF LBZBO QMBUGPSN FOHF- (j0 NT (jáNT MF ¿BSQQ EVSEVóVOEB ÐTUÐOEFLJ LÐSFMFS BõBó j=0 j 4BCJU LBZNBZBEFWBNFEFS FF FF $JTJNIBSFLFUTJ[LBMS $JTJNIBSFLFUFUNFZF EFWBNFEFS \"ZOI[JMF ÖRNEK 3 %PóSVTBMCJSZPMEBEVSNBLUBPMBOBSBDOUBWBOOBJQZBS- #BSEBóO ÐTUÐOEFLJ LBóU I[MDB ¿FLJMEJóJO- ENZMB BTM PMBO N LÐUMFMJ DJTNJO EFOHF EVSVNV õFLJM- EFCP[VLQBSBLPOVNVOVLPSVNBZB¿BMõBSBL EFLJHJCJEJS CBSEBóOJ¿JOFEÐõFS (FSJZËO öMFSJZËO \"SBDO GBSLM IBSFLFU EVSVNMBS JÀJO WFSJMNJö ÑÀ öF- ÖRNEK 4 LJMEFDJTNJOEFOHFLPOVNVOVÀJ[FSFLOFEFOJOJUBS- UöO[ %FOHFMFONJöLVWWFUMFSFULJTJOEFLJCJSDJTJN * %Ð[HÐOZBWBõMBZBO I II III \"SBÀTBCJUI[MBJMFSMFSLFO ** %Ð[HÐOI[MBOBO cisim *** 4BCJUI[M **EVSVNEBES$JTJN IBSFLFUMFSJOEFOIBOHJMFSJOJZBQBCJMJS EFOHFMFONJöLVWWFU FULJTJOEFEJS 'net =PMEVôVOEBDJTJNEFOHFMFONJöLVWWFUFULJTJOEF- EJS%FOHFEFLJDJTJNZBEVSVZPSEVSZBEBTBCJUI[MIB- I II III \"SBÀJMFSJZÌOEF SFLFUZBQBS I[MBOSLFODJTJN $FWBQ:BMO[*** *EVSVNEBES$JTJN FTLJLPOVNVOVLPSVNBL JÀJOHFSJZÌOEFTBWSVMVS I II III \"SBÀJMFSJZÌOEF ZBWBöMBSLFODJTJN ***EVSVNEBES$JTJN JMFSMFNFFZMFNJOJEFWBN FUUJSNFLJÀJOJMFSJZÌOEF TBWSVMVS ** * *** 4 :BMO[***
TEST - 2 #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS i&ZMFNTJ[MJLCJSDJTNJOIBSFLFULPOVNVOVLPSVNB LHLÐUMFMJCJSDJTJNõFLJMEFLJHJCJZVLBSZËOEF' FóJMJNJEJSWFDJTNJOLÐUMFTJOJOCJSËM¿ÐTÐEÐSu LVWWFUJ VZHVMBOEóOEB PL ZËOÐOEF IBSFLFU FU- NFLUFEJS #VOBHÌSF F I. .BTBÐ[FSJOEF PL EVSBOCJSLJUBQ II. #VOBHÌSF 'LVWWFUJOJOöJEEFUJ * 30 N 4BCJUI[MBIBSFLFU ** 50 N FEFOCJSWBQVS *** 60 N III. 20 N ;UZËOEF/WF EFôFSMFSJOEFOIBOHJMFSJOFFöJUPMVSTBDJTJNTB- 5N /LVWWFU CJUI[MIBSFLFUZBQBCJMJS (g = 10 m/s2) VZHVMBOBOCJSDJTJN \" :BMO[* # :BMO[** $ :BMO[*** WFSJMFOMFSEFOIBOHJMFSJOEFDJTJNMFSJOFZMFNTJ[- % *WF** & **WF*** MJôJWBSES \" :BMO[* # :BMO[** $ *WF** % **WF*** & * **WF*** :BUBZ WF TÐSUÐONFTJ[ EÐ[MFN Ð[FSJOEF IBSFLFU FEFOCJSBSB¿J¿JOEFCVMVOBONLÐUMFMJDJTJN'1 '2 ' WF' gerilme kuvvetleri bulunan esnemeyen ip 34 ZBSENJMFõFLJMEFLJHJCJCBóMBONõUS 4ÐSUÐONFTJ[EÐ[MFNEFõFLJMEFLJHJCJEVSBODJTNF F2 N 'LVWWFUJLTBCJSTÐSFVZHVMBOQLBMESMZPS F1 F3 F4 F Yatay $JTJNLVWWFUJOFULJTJOEFOLVSUVMEVLUBOTPOSB \"SBCB PL ZÌOÑOEF TBCJU I[MB IBSFLFU FUUJôJOF * %Ð[HÐOZBWBõMBNB HÌSF ** %Ð[HÐOI[MBONB * $JTJNIBSFLFUEVSVNVOVLPSVNBLJTUFS ** $JTJNEFOHFMFONJõLVWWFUMFSJOFULJTJOEFEJS *** 4BCJUI[MBJMFSMFNF *** $JTNFFULJFEFOOFULVWWFUTGSEBOGBSLMES IBSFLFUMFSJOEFOIBOHJMFSJOJZBQBCJMJS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ :BMO[*** \" :BMO[* # :BMO[** $ :BMO[*** % *WFZB** & **WFZB*** % *WF** & **WF*** E C 5 B D
KONUYA HAZIRLIK #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS 7$1,0%m/*m .qk(7$k, Bir cisme uygulanan net kuvvet artarsa cismin /FXUPOVO**)BSFLFU:BTBT5FNFM:BTB JWNFTJEFBSUBS %FOHFMFONFNJõ LVWWFUMFS FULJTJOEFLJ DJTJNMFS OFU LVWWFU JMF BZO ZËOEF JWNFMJ IBSFLFU ZBQBS- /FU,VWWFU 'OFU MBS 2F #BõLBCJSJGBEFZMF F FOFUáJTF a 0a 2a öWNF B /FULVWWFUDJTNJO /FULVWWFUDJTNJO (SBGJóJO FóJNJ UBOa TBCJU PMVQ CV FóJN IFS IBSFLFUZËOÐJMFBZO IBSFLFUZËOÐJMF[U [BNBODJTNJOLÐUMFTJOFFõJUUJS ZËOEFJTFDJTJNI[MBOS ZËOMÐJTFDJTJNZBWBõMBS #BõLBCJSJGBEFZMF j j FOFU FOFU FOFU NB öWNF NT2 Yatay Yatay $JTNFFULJ ,ÐUMF LH FEFOOFULVWWFU /FXUPO #VJGBEFEFDJTNJOLB[BOBDBóJWNFEBJNBOFU LVWWFUJMFBZOZËOMÐEÐS ÖRNEK 5 4ÐSUÐONFTJ[ ZBUBZ EÐ[MFNMFSEFLJ DJTJNMFS õFLJMMFSEFLJ ÖRNEK 6 LVWWFUMFSJOFULJTJOEFEJS I. II. 4F 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFIBSFLFUFUNFLUFPMBO9WF F 2F F Y cisimlerine ait net kuvvet-JWNFHSBGJóJõFLJMEFLJHJCJ- EJS Yatay Yatay F Net Kuvvet III. 3F X F 2F Y Yatay F #VOBHÌSF DJTJNMFSEFOIBOHJMFSJJWNFMJIBSFLFUZBQ- 0 a 2a 3a İvme NBLUBES m $JTJNMFSJO LÑUMFMFSJ N WF N PMEVôVOB HÌSF X XY m *' âDJTJNJWNFMJIBSFLFUZBQBS PSBOLBÀUS Y net X $ 3F = m .2a $ m = 9 **'netâDJTJNJWNFMJIBSFLFUZBQBS X X ***'net =DJTJNEFOHFEFEJS Y $ 2F = m .3a m 4 Y Y $FWBQ*WF** *WF** 6 9 4
TEST - 3 #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS 4ÐSUÐONFTJ[ ZBUBZ EÐ[MFNEF EVSNBLUB PMBO DJT- :BUBZEÐ[MFNEFIBSFLFUFEFO, -WF.DJTJNMFSJ- NF'LVWWFUJõFLJMEFLJHJCJVZHVMBOBSBLPLZËOÐO- OFBJULVWWFUJMFJWNFJMJõLJTJOJJ¿FSFOHSBGJLMFSõFLJM- EFIBSFLFUFUUJSJMJZPS EFLJHJCJEJS öWNF ,VWWFU L K F Yatay a ,VWWFU b öWNF 0 0 #VOBHÌSF ôFLJMm* ôFLJMm** * $JTNFVZHVMBOBOLVWWFUBSUUSMEóOEBDJTNJO CJSJN[BNBOEBLJI[EFóJõJNJBSUBS ,VWWFU M ** ,VWWFU TBCJU UVUVMVQ DJTNJO LÐUMFTJ BSUUSMSTB DJTJNZBWBõMBS i öWNF 0 *** $JTNFVZHVMBOBOLVWWFUF[UZËOEFCJSLVWWFU EBIBVZHVMBOEóOEBDJTJNTBCJUI[MBIBSFLFU ôFLJMm*** FEFCJMJS (SBGJLUFLJBÀMBSBSBTOEBLJJMJöLJa > b > i oldu- ôVOBHÌSF ZBSHMBSOEBOIBOHJMFSJEPôSVEVS * ,OJOLÐUMFTJ -OJOLÐUMFTJOEFOCÐZÐLUÐS ** ,OJOLÐUMFTJ .OJOLÐUMFTJOEFOCÐZÐLUÐS \" :BMO[* # :BMO[** $ *WF*** *** -OJOLÐUMFTJ .OJOLÐUMFTJOEFOCÐZÐLUÐS % **WF*** & * **WF*** ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS \" :BMO[*** # :BMO[** $ :BMO[* % *WF** & **WF*** 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFCJSCJSJOFJQJMFCBóM, 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFEVSNBLUBPMBOLH WF-DJTJNMFSJ 'LVWWFUJJMFõFLJMEFLJHJCJ¿FLJMNFL- LÐUMFMJDJTNF'1 =/WF'2 = 10 N luk kuvvetler UFEJS õFLJMEFLJHJCJVZHVMBOEóOEBDJTNJOJWNFTJB1 '1 LVWWFUJ UFST ¿FWSJMJQ [U ZËOEF VZHVMBOEóOEB DJT- JQ F KL min ivmesi a PMVZPS Yatay 2 $JTJNMFSIBSFLFUIBMJOEFJLFO,WF-BSBTOEBLJJQ F2 = 10 N LFTJMJZPS 53° #VOBHÌSF F1 = 3 N LH Yatay * , EFOHFMFONJõLVWWFUMFSJOFULJTJOEFLBMS ** -OJOJWNFTJBSUBS :BUBZ EPôSVMUVEB IBSFLFU FEFO DJTNJO JML WF TPOEVSVNEBLJJWNFMFSJPSBOB1 / a2LBÀUS *** , CJSTÐSFTPOSBZBWBõMBSWFEVSVS (sin53° = 0,8; cos53° = 0,6) ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ *WF** A) 2 B) 1 $ 1 D) 7 7 3 2 2 E) 3 % *WF*** & * **WF*** C C 7 A B
TEST - 4 #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS :BUBZ TÐSUÐONFTJ[ EÐ[MFNEF EVSNBLUB PMBO CJS 4ÐSUÐONFTJ[ EÐõFZ EÐ[MFNEF DJTJN ' LVWWFUJ JMF DJTNFõFLJMEFLJHJCJ'LVWWFUJaB¿TZBQBDBLõF- õFLJMEFLJHJCJIBSFLFUTJ[UVUVMNBLUBES LJMEFVZHVMBOZPS F N PL yatay a F yatay #VOBHÌSF #VOBHÌSF * 'LVWWFUJ * 'LVWWFUJOJOõJEEFUJBSUUSMSTBDJTJNPLZËOÐO- ** aB¿T EFI[MBOS ** $JTNJO LÐUMFTJ BSUUSMSTB DJTJN BõBó ZËOEF *** $JTNJOLÐUMFTJ I[MBONBZBCBõMBS OJDFMJLMFSJOEFO IBOHJMFSJ BSUUSMSTB DJTNJO JW- *** $JTJNEFOHFMFONJõLVWWFUMFSFULJTJOEFEJS NFTJBSUBS \" :BMO[* # :BMO[** $ :BMO[*** ZBSHMBSOEBOIBOHJMFSJEPôSVEVS % *WF** & **WF*** \" :BMO[* # :BMO[** $ *WF** % * **WF*** & *WF*** Sürtünmesiz yatay düzlemde bulunan m = 2 kg ve Yatay sürtünmesiz düzlemdeki 6 kg kütleli cisim K m-= LH LÐUMFMJ DJTJNMFSF VZHVMBOBO '1= 8 N ve 'LVWWFUJJMFPLZËOÐOEFIBSFLFUFUUJSJMJZPS ' =/LVWWFUMFSõFLJMEFLJHJCJEJS 2 NK LH NL LH F2 = 15 N yatay F = 50 N L Yatay 53° F1 = 8 N K 6 kg yatay $JTJNMFSJOJWNFMFSJOJOCÑZÑLMÑLMFSJB1 WFB2 ol- #VOBHÌSF DJTNJOJWNFTJLBÀNT2EJS EVôVOBHÌSF B / a PSBOLBÀUS (sin37° = TJO= H=10 m/s2) 12 3 B) 3 $ 2 D) 4 5 \" # $ % & A) 2 3 5 E) 4 6 A D 8 D C
KONUYA HAZIRLIK ##VVTBTZBGZBGEBBELBJJLÀJFJSÀJLFiS/JLFXi0UPMOBTVOM)LuBSLFLPFOUV:TBVTBZMMBBSJuMHLJPMJOVTVZTMBOJMGHUJBMJHÌTSEOÑGUôBÑHOÌÑSE[ÑLôPÑOOÑV[MBLSPOOVUMFBSLOSBUSFLBSBNSBBDNZBMDBZIMBBI[BS[MBSMOBONNööUUSS :FSÀFLJNJ÷WNFTJWF\"ôSML .qk(7$k, 7$1,0%m/*m Bir gezegenin üzerinde bulunan cismin kütlesi- OFVZHVMBEóLÐUMF¿FLJNLVWWFUJOFBóSMLEF- :FSÀFLJNJJWNFTJ OJS#BõLBCJSJGBEFZMF (F[FHFOJO LÐUMF ¿FLJN LVWWFUJ OFEFOJZMF CJSJN LÐUMFZF VZHVMBEó LVWWFUF ¿FLJN JWNFTJ EFOJS ZFS¿FLJNJJWNFTJ g PMBOCJSHF[HFOEFNLÐUMFMJ %ÐOZBOOVZHVMBEó¿FLJNJWNFTJZFS¿FLJNJJW- CJSDJTNJOBóSMó NFTJPMBSBLBEMBOESMS Çekim ivmesi ^ g h \"óSML / G = m.g (F[FHFOJOZBS¿BQOBWFLÐUMFTJOFCBóMES Yerçekimi ivmesi (F[FHFOJO ZÐ[FZJOEFO V[BLMBõUL¿B ¿FLJN JW- NT2 NFTJB[BMS ,ÐUMF LH %ÐOZBOOõFLMJOFCBóMPMBSBLLVUVQMBSEBO&LWB- UPSBEPóSVHJEJMEJL¿F¿FLJNJWNFTJB[BMS Dünya’da Ay’da %ÐOZBEBLJ ¿FLJN JWNFTJ \"ZEBLJOEFO CÐZÐL PMEVóV J¿JO BZO DJTJN EJOBNPNFUSFEF GBSLM BóSMLEFóFSMFSJOFTBIJQPMVS ÖRNEK 7 ÖRNEK 8 ôFLJMEF%ÐOZBÐ[FSJOEFCVMVOBO9 :WF;DJTJNMFSJOJO i%VSHVOCJSDJTJNÐ[FSJOEFLJLVWWFUMFSEFOHFMFONJõUJSu LPOVNMBSWFSJMNJõUJS T1 T2 T3 Kuzey kutup m m X mg Y mg m Ekvator Z mg Güney kutup NLÑUMFMJDJTJNMFSõFLJM-*WFõFLJM-**EFLJHJCJEFO- #VOBHÌSF %ÑOZBOO9 :WF;DJTJNMFSJOFVZHVMB- HFEFJTFJQMFSEFPMVöBOHFSJMNFLVWWFUMFSJ51 52WF Eô ÀFLJN JWNFMFSJOJO CÑZÑLMÑôÑ HX HY WF HZ ara- 53BSBTOEBLJJMJöLJOFEJS TOEBLJJMJöLJOFEJS $JTJNMFSEFOHFEFPMEVôVJÀJOIFSCJSJOJOÑ[FSJOEFLJOFU :FSÀFLJNJJWNFTJLVUVQMBSEBO FLWBUPSBEPôSVB[BMS LVWWFUTGSPMNBMES $FWBQHX >HY >HZ #VOBHÌSF 51 =52 =53 =NH HX HY HZ 51 52 53
TEST - 5 #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS %ÐOZBOODJTNFVZHVMBEóLÐUMF¿FLJNLVWWFUJOF %ÐOZBLVUVQMBSEBOCBTLWF&LWBUPSEBOõJõLJOHF- ZFS¿FLJNLVWWFUJZBEBBóSMLEFOJS PJECJSõFLMFTBIJQUJS #VOBHÌSFBôSMLJMFJMHJMWFSJMFO #VOBHÌSF LVUVQMBSBHJEJMEJLÀFCJSDJTNJO * \"óSML ZFS¿FLJNJJWNFTJOFCBóMEFóJMEJS * Kütlesi ** \"óSMLEJOBNPNFUSFJMFËM¿ÐMÐS ** \"óSMó *** #JS DJTNJO BóSMó %ÐOZB Ð[FSJOEFLJ UÐN LP- *** ¶[FSJOFFULJFEFOZFS¿FLJNJLVWWFUJ OVNMBSEBBZOEFóFSEFEJS OJDFMJLMFSJOEFOIBOHJMFSJBSUBS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ :BMO[*** \" :BMO[* # :BMO[** $ **WF*** % **WF*** & * **WF*** % *WF*** & * **WF*** i%ÐOZBOOVZEVTVPMBO\"ZEB¿FLJNJWNFTJZBLMB- LH LHWFLHML9 :WF;DJTJNMFSJJQMFSZBSE- õLPMBSBL%ÐOZBOO¿FLJNJWNFTJOJOBMUEBCJSJEJSu NZMBôFLJM-*WFôFLJM-**EFLJHJCJBTMBSBLEFOHF- %ÐOZBEBBõBóEBOZVLBSBUMBOCJSDJTJNõFLJMEF- MFONJõUJS LJHJCJFOGB[MBILBEBSZÐLTFLMJóF¿LBCJMNFLUFEJS h XX yer T1 YY \"ZODJTJN\"ZEBBZOI[JMFBUMSTB T2 * $JTNFFULJFEFOLÐUMF¿FLJNLVWWFUJB[BMS ZZ ** $JTNJO ¿LBCJMFDFóJ NBLTJNVN ZÐLTFLMJL BS- UBS ôFLJMm* ôFLJMm** *** $JTNJOBóSMóEFóJõNF[ õFLJM-*EF9WF:DJTJNMFSJBSBTOEBLJJQHFSJM- NFTJ 51 õFLJM-** EFLJ : WF ; DJTJNMFSJ BSBTO- ZBSHMBSOEBOIBOHJMFSJEPôSVEVS T1 T2 daLJ JQ HFSJMNFTJ 52 PMEVôVOB HÌSF PSBO kaçUS ( g = 10 m/s2) (Hava direnci önemsizdir.) \" :BMO[* # :BMO[** $ *WF** 5 B) 7 % 7 E) 7 A) 4 3 6 % **WF*** & * **WF*** $ 4 B C 10 D B
KONUYA HAZIRLIK ##VVTBTZBGZBGEBBELBJJLÀJFJSÀJLFiS/JLFXi0UPMOBTVOM)LuBSLFLPFOUV:TBVTBZMMBBSJuMHLJPMJOVTVZTMBOJMGHUJBMJHÌTSEOÑGUôBÑHOÌÑSE[ÑLôPÑOOÑV[MBLSPOOVUMFBSLOSBUSFLBSBNSBBDNZBMDBZIMBBI[BS[MBSMOBONNööUUSS 7$1,0%m/*m 7 /FXUPOVO *** )BSFLFU :BTBT &ULJ-5FQLJ m ............N....=....F............... 1SFOTJCJ NF &ULJMFõJNEF CVMVOBO JLJ DJTJNEFO CJSJ EJóFSJOF LVWWFU VZHVMBEóOEB JLJODJ DJTJN EF EJóFSJOF mg FõJUõJEEFUUFGBLBU[UZËOEFCJSLVWWFUVZHVMBS Simülasyonu var! #VFõJUõJEEFUMJWF[UZËOMÐFULJMFõJNLVWWFUMFSJOF etki-UFQLJLVWWFUMFSJEFOJS #VLPOVJMFJMHJMJEFOFZWJEFP- MBS WFZB TJNÐMBTZPOMBSB ZBO- &ULJ WF UFQLJ LVWWFUMFSJOF HÐOMÐL IBZBUN[EBO daki 2SLPEJMFVMBõBCJMJSTJOJ[ CJSËSOFLJMFUFLSBSCBLBSTBL F ¥JWJOJO¿FLJ¿FVZHVMBEóUFQLJLVWWFUJ F ¥FLJDJO¿JWJZFVZHVMBEóFULJLVWWFUJ ÖRNEK 10 Etki-UFQLJ LVWWFUMFSJ BZO DJTNF FULJ FUNFEJóJ 4ÐSUÐONFTJ[ ZBUBZ EÐ[MFNMFS Ð[FSJOEF õFLJMEFLJ HJCJ J¿JOUPQMBOBNB[ EVSNBLUB PMBO DJTJNMFSF GBSLM õJEEFUMFSEFLJ ' LVWWFUMF- SJFULJFUNFLUFEJS ÖRNEK 9 N LÐUMFMJ DJTJN WF ZÐ[FZJOF EJL VZHVMBOBO ' LVWWFUJ- F=3N F = 10 N nin NFZEBOBHFUJSEJóJZÐ[FZJODJTNFVZHVMBEóLVWWFU N ='+NHEJS FN m = 3 kg N1 m = 2 kg N2 m 30 N yatay 20 N yatay mg .......N..1...=....2...7...N............. .......N...2...=....1..0...N............. :VLBSEBLJËSOFóJJODFMFZFSFLWFSJMFOGBSLMEVSVNMBSJ¿JO m = 2 kg N3 m = 2 kg ZÐ[FZJODJTNFVZHVMBEóLVWWFUMFSJCVMVOV[ 20 N yatay F = 20 N N4 * F ** .......N...3...=....2..0...N............. yatay m N F F.sina 20 N a N .......N...4..=.....2..0...N............. F.cosa m ' NH mg mg .........N....=...m....g...–....F........ ....N....=...F.....s..i.n...a...+....m...g.... #VOB HÌSF ZBUBZ ZÑ[FZMFSEFO DJTJNMFSF VZHVMBOBO *** *7 F.cosa F LVWWFUMFS/1 /2 /3WF/4ÑOCÑZÑLMÑLMFSJLBÀOFX- m mg F > mg a UPOEVS (g = 10 m/s2) N F Nm N1 = 27 N .........N....=...F....–...m....g........ ' NH N = 30 N mg ....N....=...m....g...–...F.....c..o...s..a... 2 N = 20 N 3 N = 20 N 4 * / NHm'**/ 'TJOa NH***/ 'mNH 11 N1 / /2 / /3 / /4 = 20 N *7/ NHm'DPTa7/ '
TEST - 6 #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS %ÐõFZ EPóSVMUVEB ' LVWWFUJ VZHVMBOBO N LÐUMF- /FXUPOVO***ZBTBTOBHËSFIFSLVWWFUFLFOEJTJ- MJ DJTJN TÐSUÐONFTJ[ ZBUBZ EÐ[MFNEF õFLJMEFLJ HJ- OF[UZËOEFFõJUCÐZÐLMÐLUFUFQLJLVWWFUJVZHVMB- CJEVSNBLUBES OS%JóFSCJSJGBEFZMFFULJUFQLJFZMFNMFSJLVWWFUMFS B¿TOEBOEFóFSMFOEJSJMJS F #VOBHÌSF m yatay * F1 F2 N S N S ;FNJODJTNFLVWWFUVZHVMBEôOBHÌSF * 'LVWWFUJBSUSMSTB[FNJOJOUFQLJLVWWFUJB[B- ** MS ** NLÐUMFTJBSUUSMSTB[FNJOJOUFQLJLVWWFUJBSUBS Fm N *** $JTJNEFOHFEFJTF'LVWWFUJDJTNJOBóSMóOB %ÐõFZ FõJUUJS *** N ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS \" :BMO[* # *WF** $ *WF*** & * **WF*** % **WF*** G öFLJMMFSEFLJ LVWWFUMFSEFO IBOHJMFSJ /FXUPOVO ***ZBTBTOBHÌSFJGBEFFEJMFOFULJ-UFQLJLVWWFU ÀJGUJEJS \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** 5ÐN ZÐ[FZMFSJO TÐSUÐONFTJ[ PMEVóV CJS PSUBNEB õFLJMEFLJNLÐUMFMJ¿PDVLLFOEJOEFO¿PLCÐZÐLLÐU- MFMJCJSDJTNJJUNFZF¿BMõZPS ** * Etki-UFQLJLVWWFUMFSJJMFJMHJMJ #VOBHÌSF * öLJ DJTJN BSBTOEBLJ FULJMFõJNEF FULJ LVWWF- * ¥PDVL DJTNJJUNFZF¿BMõUóOEBLFOEJTJ**ZË- UJPMVõNVõJTFLFTJOMJLMFUFQLJLVWWFUJEFPMVõ- OÐOEFIBSFLFUFEFS NVõUVS ** $JTJNWF¿PDVLIBSFLFUTJ[LBMS ** Etki-UFQLJ LVWWFUMFSJOJO PMVõBCJMNFTJ J¿JO DJ- TJNMFSJOCJSCJSJOFUFNBTFUNFTJHFSFLJS *** Etki-UFQLJ LVWWFUMFSJOJO PMVõUVóV EVSVNMBSEB LÐUMFTJ CÐZÐL PMBO DJTJN IFS [BNBO EBIB CÐ- ZÐLLVWWFUVZHVMBS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS *** $JTJN*ZËOÐOEFIBSFLFUFEFS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ :BMO[*** \" :BMO[* # *WF** $ *WF*** % *WF*** & * **WF*** % **WF*** & * **WF*** B A 12 A C
KONUYA HAZIRLIK ##VVTBTZBGZBGEBBELBJJLÀJFJSÀJLFiS/JLFXi0UPMOBTVOM)LuBSLFLPFOUV:TBVTBZMMBBSJuMHLJPMJOVTVZTMBOJMGHUJBMJHÌTSEOÑGUôBÑHOÌÑSE[ÑLôPÑOOÑV[MBLSPOOVUMFBSLOSBUSFLBSBNSBBDNZBMDBZIMBBI[BS[MBSMOBONNööUUSS 7$1,0%m/*m .qk(7$k, 4ÑSUÑONF,VWWFUJ 4ÐSUÐONF LVWWFUJ TÐSUÐONF LBUTBZT EFóJõ- NFEJóJ TÐSFDF DJTNJO TÐSUÐOFO ZÐ[FZ BMBOOB )BSFLFUFUNFLUFPMBOZBEBIBSFLFUFUUJSJMNFZF CBóMEFóJMEJS ¿BMõMBO CJS DJTJN JMF ZÐ[FZ BSBTOEB PMVõBO EJ- SFODFTÐSUÐONFLVWWFUJEFOJS j j S 4ÐSUÐONFLVWWFUJOJOCÐZÐLMÐóÐ TÐSUÐOFOZÐ[F- 2S ZJODJOTJOFWF[FNJOFFULJFEFOEJLLVWWFUFCBó- 2S S MES FS1 FS2 #BõLBCJSJGBEFZMF FS1 = FS2 Sürtünme Fs = k . N Yüzeyin cisme VZHVMBOEó kuvveti Yüzeyin cinsine dik kuvvet /FXUPO CBóMTÐSUÐONF /FXUPO LBUTBZT #JSJNTJ[ ÖRNEK 12 ,FOBS V[VOMVLMBS WF DN PMBO EJLEËSUHFOMFS QSJ[- NBTCJ¿JNJOEFLJDJTJNTÐSUÐONFMJZBUBZEÐ[MFNEFõFLJM- EFLJHJCJ'LVWWFUJZMFIBSFLFUFUUJSJMJZPS ÖRNEK 11 Z 4ÐSUÐONFMJZBUBZEÐ[MFNEF'LVWWFUJZMF¿FLJMFOLHML FY DJTJNPLZËOÐOEFIBSFLFUFUNFLUFEJS X 4 cm N = 20 N 6 cm 2 cm m = 2 kg F yatay $JTJN9 :WF;ZÐ[FZMFSJZBUBZEÐ[MFNFEFOLHFMFDFL Fs = 10 N õFLJMEFIBSFLFUFUUJSJMEJóJOEFZÐ[FZJMFBSBTOEBLJTÐSUÐO- 20 N NFLVWWFUMFSJ'9 'YWF';PMVZPS :BUBZ EÑ[MFN CPZVODB TÑSUÑONF LBUTBZT TBCJU WF #VOBHÌSF ' ' WF' BSBTOEBLJCÑZÑLMÑLJMJöLJ- XY Z k = JTF DJTNF FULJ FEFO TÑSUÑONF LVWWFUJ LBÀ OFXUPOEVS (g = 10 m/s2) TJOBTMES F = k.N 4ÑSUÑONFLVWWFUJDJTNJOUFNBTZÑ[FZBMBOOBCBôMEF- ôJMEJS S ' =' =' PMVS = 0, 5.20 = 10 N XYZ 10 N 13 'X 'Y 'Z
KONUYA HAZIRLIK #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS .qk(7$k, ,BZBSBLJMFSMFZFO 7$1,0%m/*m DJTJNMFSEFTÐSUÐONF Hareket yönü kuvveti hareket %VSNBLUB PMBO CJS DJTNJ IBSFLFUF HF¿JSJODFZF LBEBSPMVõBOTÐSUÐONFLVWWFUJOFTUBUJLTÑSUÑO- FS yönüne terstir. NF LVWWFUJ DJTJN LBZBSBL JMFSMJZPSTB FULJ FEFO ,BZBSBLJMFSMFZFODJTJN sürtünme kuvvetine de LJOFUJL TÑSUÑONF LVW- WFUJEFOJS Sürtünme Kuvveti Hareket yönü %ËOFSFLJMFSMFNFZF Cisim kuvvet Cisim kayarak FS CBõMBZBODJTJNMFSEF etkisinde durgun ise JMFSMJZPSJTF sürtünme kuvveti IBSFLFUZËOÐJMF BZOES %ËOFSFLJMFSMFNFZFCBõMBZBODJTJN Statik Kinetik sürtünme kuvveti sürtünme kuvveti Hareket yönü 4BCJUI[MBEËOFSFL @ Statik sürtünme @ Kinetik sürtünme JMFSMFZFODJTJNMFS LVWWFUJOJOEFóFSJ JMFZFSBSBTOEB kuvveti cismi harekete sabittir. sürtünme kuvveti [PSMBZBOLVWWFUJO õJEEFUJOFFõJUõJEEFUUF N PMVõNB[ WF[UZËOMÐEÐS 4BCJUI[MBEËOFSFLJMFSMFZFODJTJN N F yatay F ÖRNEK 13 yatay FS mg FS mg FS = kk.N 4ÐSUÐONFMJ ZÐ[FZMFSEF PLMBS ZËOÐOEF IBSFLFUF CBõMBU- â' 'SâLS.N MBO, -WF.DJTJNMFSJõFLJMEFLJHJCJEJS K L ÖRNEK 14 ôFLJMm* ôFLJMm** )BSFLFUF [PSMBOBO TJTUFN EVSHVO JTF TUBUJL TÐSUÐONF M LVWWFUJ LBZBSBLJMFSMJZPSJTFLJOFUJLTÐSUÐONFLVWWFUJFU- F LJOEJSu #VOB HÌSF BöBôEBLJ GPUPôSBGMBSO ZBOOEB WFSJMFO ôFLJMm*** CPöMVLMBSBIBOHJTÑSUÑONFLVWWFUJOJOFULJOPMEVôV- OVZB[O[ -DJTNJLBZNBEBOZVWBSMBOBSBLIBSFLFUFCBöMBEô- OB HÌSF , - WF . DJTJNMFSJOF FULJ FEFO TÑSUÑONF B #JTJLMFUTÐSFO LVWWFUMFSJOJOZÌOÑOFEJS TQPSDVMBS ............................... K - . ..S..t.a..t.i.k...s..ü..r..t.ü..n...m...e.... ..k..u..v..v..e..t.i.................. C %JLCJSZPLVõUB QBSLIBMJOEF EVSBOBSB¿MBS ..S..t.a..t.i.k...s..ü..r..t.ü..n...m...e.... ..k..u..v..v..e..t.i.................. D :B[ZB[BOËóSFODJ ............................... ..K..i.n..e..t..i.k..s..ü...r.t.ü...n..m...e.. ..k..u..v..v..e..t.i.................. K - . 14 B 4UBUJLTÑSUÑONF,VWWFUJC 4UBUJLTÑSUÑONF,VWWFUJ D ,JOFUJLTÑSUÑONF,VWWFUJ
KONUYA HAZIRLIK ##VVTBTZBGZBGEBBELBJJLÀJFJSÀJLFiS/JLFXi0UPMOBTVOM)LuBSLFLPFOUV:TBVTBZMMBBSJuMHLJPMJOVTVZTMBOJMGHUJBMJHÌTSEOÑGUôBÑHOÌÑSE[ÑLôPÑOOÑV[MBLSPOOVUMFBSLOSBUSFLBSBNSBBDNZBMDBZIMBBI[BS[MBSMOBONNööUUSS .qk(7$k, ÖRNEK 15 Fs / 'PUPóSBGUBLJ LBZLBZDOO IBSFLFUJ TSBTOEB CJS BZBó Fstatik LBZLBZÐ[FSJOEFTBCJUEVSVSLFO EJóFSJZFSFUFNBTFEF- SFLLBZLBZJUNFLUFEJS Fkinetik 0 ' / #VOBHÌSF Cisim Cisim * ,BZLBZJMFBZBóBSBTOEBstatik durgun IBSFLFUMJ ** \"ZBóJMFZFSBSBTOEBstatik F 5FNBTBMBO *** ,BZLBZOUFLFSMFSJJMFZFSBSBTOEBstatik kutu PMVöBO TÑSUÑONF LVWWFUMFSJ TUBUJL WF LJOFUJL ZÐ[FZMFS PMBSBL BZSMEôOEB CPöMVLMV ZFSMFSF IBOHJMFSJ HFMNFMJEJS Sürtünme ÖRNEK 16 Yerçekimi %VSHVOLFO DJTJNMFS BSBTOEBLJ FULJMFõJN LVW- i4ÐSUÐONF LVWWFUJOJO õJEEFUJOJ BSUSNBL HÐOMÐL IBZBU- N[EBCJS¿PLFZMFNJEBIBHÐWFOMJZBQNBN[TBóMBSu WFUJ FO CÐZÐL EFóFSJOJ BMSLFO IBSFLFU CBõMB- #VOBHÌSF EóOEBJTFõJEEFUJB[BMS#VZÐ[EFOTUBUJLTÐS- UÐONF LBUTBZTOO FO CÐZÐL EFóFSJ LJOFUJL * 4FSCFTU USNBOõ ZBQBO EBóDOO FMMFSJOJ QVESBMB- TÐSUÐONF LBUTBZTOEBO IFS [BNBO EBIB CÐ- NBT ZÐLUÐS ** 5FLOJL¿J[JNLBMFNMFSJOJOUVUBDBLLTNMBSOOQÐ- 4ÑSUÑONF LVWWFUJOJO HÑOMÑL IBZBUN[EBLJ SÐ[MÐPMNBT GBZEBMBS *** .FSNFSNFSEJWFOMFSJOV¿LTNMBSOOQÐSÐ[MÐõFSJU r :ÐSÐZFCJMNFNJ[JTBóMBS ZBQõUSMNBT r :B[ZB[BCJMNFNJ[JTBóMBS PMBZMBSOEBO IBOHJMFSJOEF TÑSUÑONF LVWWFUJOJO BSU- NBTHÑWFOMJôJBSUSNöUS r &óJNMJZÐ[FZMFSEFLBZNBN[FOHFMMFS %BôD FMJOF QVESB TÑSEÑôÑOEF FMJZMF LBZBMLMBS BSBTOEBLJ r $JTJNMFSJUVUBCJMNFNJ[JTBóMBS TÑSUÑONF LBUTBZT BSUNö PMVS #V EVSVN EBôDOO EBIB LPMBZUSNBONBTOTBôMBS *EPôSV r )BSFLFU IBMJOEFZLFO ZBWBõMBZBSBL EVSBCJM- ,BMFNJ UVUUVôVNV[ OPLUBOO QÑSÑ[MÑ PMNBT ÀJ[JN ZBQBS- NFNJ[JTBóMBS LFOLBMFNJOFMJNJ[EFOLBZNBTOÌOMFS **EPôSV .FSEJWFOEFO ÀLBSLFO WFZB JOFSLFO NFSEJWFOJO LÌöFTJOJO r :BóNVSWFEPMVUBOFMFSJOJOZBWBõEÐõNFTJOJ LBZNBNBTNFSEJWFOJOLÌöFTJOFCBTUôN[EBBZBLLBCN- TBóMBS [OUVUVONBTOLPMBZMBöUSS ***EPôSV r %BóDMLHJCJTQPSMBSEBUSNBONBZLPMBZMBõ- USS 4ÑSUÑONF LVWWFUJOJO HÑOMÑL IBZBUN[EBLJ [BSBSMBS r &OFSKJLBZCOBTFCFQPMVS r 4JTUFNMFSJOJ¿JOEFTDBLMóOGB[MBBSUNBTOB TFCFQPMVS r :Ð[FZMFSJOBõONBTOBTFCFQPMVS 15 *TUBUJL **TUBUJL ***TUBUJL* **WF***
TEST - 7 #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS ôFLJMEFLJ ZBUBZ EÐ[MFN JMF DJTJN BSBTOEBLJ TUBUJL 4ÑSUÑONFLVWWFUJJMFJMHJMJWFSJMFO TÐSUÐONFLBUTZTL = LJOFUJLTÐSUÐONFLBU- * :Ð[FZJODJOTJOFCBóMES ** )FS[BNBOIBSFLFUZËOÐOFUFSTZËOMÐEÐS S *** $JTNJOI[OBCBóMES TBZTLK = ES m = 4 kg F = 36 N ZBSHMBSOEBOIBOHJMFSJEPôSVEVS $JTNFZBUBZ/FXUPOMVL'LVWWFUJVZHVMBO- \" :BMO[* # :BMO[** $ *WF** EôOEBDJTNJOJWNFTJLBÀNT2PMVS % **WF*** & * **WF*** (g = 10 m/s2) \" # $ % & Yatay düzlemde 5 kg kütleli bir cisme uygulanan kuvvet-TÐSUÐONFLVWWFUJHSBGJóJõFLJMEFLJHJCJEJS 4ÐSUÐONFLVWWFUJ / 15 0 6ZHVMBOBO Yatay sürtünmeli düzlemde jI[JMFIBSFLFUFEFO 20 25 ,VWWFU / DJTJNõFLJMEFLJHJCJEJS j #VOBHÌSF $JTJNJMFZÑ[FZBSBTOEBLJTÑSUÑONFLVWWFUJ * Uygulanan kuvvet 30 N ise sürtünme kuvveti- * $JTJNJMFZÐ[FZBSBTOEBLJUFNBTBMBO OJOCÐZÐLMÐóÐ/EVS ** $JTNJOI[ ** Uygulanan kuvvet 12 N ise sürtünme kuvveti- OJOCÐZÐLMÐóÐ/EVS *** 4ÐSUÐONFLBUTBZT OJDFMJLMFSJOEFOIBOHJMFSJOJOBSUNBTZMBBSUBS *** $JTJNMFZÐ[FZBSBTOEBLJTUBUJLTÐSUÐONFLBU- TBZT UÐS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ *WF** \" :BMO[* # :BMO[** $ :BMO[*** % **WF*** & * **WF*** % *WF** & * **WF*** B E 16 A C
TEST - 8 #VTBZGBEBLJJÀFSJLi/FXUPOVO)BSFLFU:BTBMBSuLPOVTVZMBJMHJMJTOGUBHÌSEÑôÑOÑ[LPOVMBSOUFLSBSBNBDZMBIB[SMBONöUS ôFLJMEFNLÐUMFMJDJTNF'1 '2WF'3LVWWFUMFSJBZS :BUBZ EÐ[MFNEF EVSNBLUB PMBO DJTNF FULJ FEFO BZSVZHVMBOEóOEBNLÐUMFMJDJTJNIBSFLFUTJ[LBM- TÐSUÐONF LVWWFUJOJO VZHVMBOBO LVWWFUF CBóM EF- NBLUBES óJõJNHSBGJóJõFLJMEFLJHJCJEJS F3 4ÐSUÐONFLVWWFUJ / a FSstatik F2 m F1 FSkinetik #VOBHÌSF 0 10 15 20 6ZHVMBOBO ,VWWFU / * $JTNFFULJFEFOTUBUJLTÐSUÐONFLVWWFUJDJTNF FULJFEFOLVWWFUMFSEFOCÐZÐLUÐS #VOBHÌSF * 4UBUJL TÐSUÐONF LVWWFUJOJO NBLTJNVN EFóFSJ ** aB¿TB[BMUMEóOEBDJTJNIBSFLFUFEJZPSJTF /EVS ' LVWWFUJNLÐUMFMJDJTNJOBóSMóOEBOCÐZÐL- ** ,JOFUJLTÐSUÐONFLVWWFUJ/EVS 3 *** Kinetik sürtünme kuvveti cisme etki eden kuv- WFUBSUBSTBBSUBS UÐS *** '1WF'2LVWWFUMFSJCJSMJLUFVZHVMBOSTBLVWWFU- MFSJO CJMFõLFTJ DJTNF FULJ FEFO TÐSUÐONF LVW- WFUJOFFõJUUJS ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS \" :BMO[*** # *WF** $ *WF*** ZBSHMBSOEBOIBOHJMFSJEPôSVEVS % **WF*** & * **WF*** \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** Sürtünmeli yatay zeminlerde cisme etki eden ze- Sürtünmeli yatay düzlemde sabit büyüklükteki ya- NJOF QBSBMFM LVWWFUMFS FULJTJOEF DJTJN IBSFLFUTJ[ UBZ'LVWWFUJJMFõFLJMEFLJHJCJLBZESMBOLBQJ¿JOEF- LBMZPSTB TUBUJL TÐSUÐONF LVWWFUJ DJTNF FULJ FEFO LJLVSVCV[[BNBOMBCVIBSMBõNBLUBES LVWWFUMFSJOCJMFõLFTJOFFõJUCÐZÐLMÐLUFEJS #VOBHÌSF Kuru buz F * 4ÐSUÐONFMJZBUBZEÐ[MFNEFTFSCFTUIBMEFEV- SBODJTNFTÐSUÐONFLVWWFUJFULJFUNF[ #VOBHÌSF ** 4UBUJLTÐSUÐONFLVWWFUJCB[EVSVNMBSEBDJTNJ * ,BCOCJSJN[BNBOEBLJI[EFóJõJNJ IBSFLFUFHF¿JSFCJMJS ** :Ð[FZJMFLBQBSBTOEBLJTÐSUÐONFLVWWFUJ *** 4UBUJLTÐSUÐONFLVWWFUJDJTJNFFULJFEFOZPMB *** :Ð[FZJOLBCBVZHVMBEóUFQLJLVWWFUJ QBSBMFMLVWWFUBSUBSTBBSUBCJMJS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS OJDFMJLMFSJOEFOIBOHJMFSJ[BNBOMBB[BMS \" :BMO[* # *WF** $ *WF*** \" :BMO[* # :BMO[** $ *WF** % **WF*** & * **WF*** % **WF*** & * **WF*** A E 17 A D
11. SINIF .0%·- /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 www.aydinyayinlari.com.tr /FXUPOVO)BSFLFU:BTBMBS ÷MJöLJMJ,B[BONMBS /FULVWWFUJOZËOÐOÐCFMJSMFZFSFLCÐZÐLMÐóÐOÐIFTBQMBS $JTJNMFSF&ULJZFO/FU,VWWFU ÖRNEK 18 7$1,0%m/*m 2500 gram #JSDJTNFFULJFEFOCJSEFOGB[MBLVWWFUJOZBQUó %ÐOZB (F[FHFO FULJZJUFLCBõOBZBQBOLVWWFUFOFULVWWFU de- 1MÐUPO OJS/FULVWWFUDJTNFFULJFEFOLVWWFUMFSJOCJMFõ- LFTJEJS/FULVWWFUTGSEBOGBSLMJTFDJTJNMFSJW- HSBN LÑUMFMJ CJS DJTJN ÀFLJN JWNFTJ EÑOZBOO NFMJIBSFLFUZBQBSMBS ZFSÀFLJNJJWNFTJHOJOZBSTPMBOCJSHF[FHFOEFLBÀ Fnet = m.a OFXUPOMVLBôSMôBTBIJQUJS %VSHVO CJS DJTNF FULJ FEFO OFU LVWWFU IBOHJ ZËOEFJTFDJTJNPZËOEFIBSFLFUFHF¿FS (g = 10 N/kg) ÖRNEK 17 H=/LH g G =NH = 5N/kg 4ÑSUÑONFTJ[ ZBUBZ CJS EÑ[MFNEF EVSNBLUB PMBO CJS N=H DJTNJOIBSFLFUFCBöMBZBCJMNFTJJÀJO 2 = LH g * /FULVWWFUTGSEBOGBSLMPMNBMES ** %FOHFMFONJõLVWWFUMFSFULJFUNFMJEJS G' = m. *** \"óSMóOEBOCÐZÐLCJSLVWWFUFULJFUNFMJEJS 2 ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS = 2, 5.5 = 12, 5 N $FWBQ / $JTNJOIBSFLFUFHFÀFCJMNFTJJÀJOOFULVWWFUJOTGSEBOCÑ- 7$1,0%m/*m ZÑLPMNBTHFSFLJS#VEVSVNEB*ZBSHLFTJOEPôSVPMVS 5FQLJ,VWWFUJ $FWBQ:BMO[* /FXUPOO***ZBTBTOBHËSFCJSZÐ[FZFFULJZFO 7$1,0%m/*m OFULVWWFUFLBSõMLFõJUCÐZÐLMÐLUFWF[UZËOEF bir UFQLJLVWWFUJPMVõVS #JS DJTNF FULJ FEFO HF[FHFOJO ¿FLJN LVWWFUJOF N BôSMLEFOJS\"óSMLIFS[BNBOHF[FHFOJONFS- LF[JOFEPóSVEVS +q –q F1 F2 Yatay %ÐõFZ &óJL G Düzlemde Düzlemde Düzlemde N = –G a F1 = –F2 G = mg mgcosa NHTJOa a G = mg F1 F2 G = mg \"óSMLZFS¿FLJNJJWNFTJOFCBóMES:FS¿FLJNJJWNF- Ay TJ DJTNJO IBOHJ HF[FHFOEF PMEVóVOB WF HF[FHFOJO %ÐOZB OFSFTJOEFCVMVOEVóVOBHËSFEFóJõJS:BOJEFóJõLFO CJSLVWWFUUJS F1 = –F2 :BMO[* 18 /
www.aydinyayinlari.com.tr /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 .0%·- 11. SINIF ÖRNEK 19 ÖRNEK 20 ±[EFõ9 :WF;DJTJNMFSJõFLJMEFLJHJCJEFOHFEFEJS m1 N2 ve m3LÐUMFMFSJõFLJMEFLJHJCJEFOHFEFEJS NX NY X Y mgcos53° NZ Z mgs3i7n°37m° g37m°gcos37° 53m° gmgs5in35°3° T2 T2 mg m2 LH m3 LH T1 20 N 40 N $JTJNMFSF CVMVOEVLMBS ZÑ[FZMFSJO VZHVMBEô LVW- T3 WFUMFS TSBTZMB /X /Y WF /Z JTF CVOMBS BSBTOEBLJ m1 LH CÑZÑLMÑLJMJöLJTJOFEJS (sin37° = DPT= TJO= DPT= 60 N N =NHDPT=NH X N =NHDPT=NH #VOB HÌSF JQMFSEF PMVöBO 5 5 WF 5 JQ HFSJMNF Y 12 3 N =NH LVWWFUMFSJBSBTOEBLJJMJöLJOFEJS (g = 10 m/s2) Z N >N >N 51 =/ 52 =/ 53 = 40 N 5 >5 >5 ZXY 123 ÷QFBTMPMBODJTJNMFSJOBôSMôOÑTUUFLJJQUBöS 7$1,0%m/*m ÖRNEK 21 ÷QMFSEFLJ(FSJMNF,VWWFUJ :Ð[FZEFLJTÐSUÐONFLBUTBZT PMBOõFLJMEFLJTJTUFN &TOFNFZFO JQMFSF CBóM DJTJNMFSF LVWWFU VZHV- LHLÐUMFMJWFLHLÐUMFMJDJTJNMFSFULJTJOEFTFSCFTUC- MBOEóOEB JQMFSEF HFSJMNF LVWWFUJ PMVõVS öQ HFSJMNF LVWWFUJ DJTJNMFSJ TBEFDF ¿FLFCJMJS JUF- NF[ %ÐõFZ SBLMZPS Düzlemde 4ÐSUÐONFTJ[:BUBZ T Düzlemde T T = mg LH TF L LH F=T G = mg 4ÐSUÐONFTJ[&óJL #VOB HÌSF DJTJNMFS BSBTOEBLJ JQ HFSJMNFTJ LBÀ / Düzlemde PMVS (g = 10 m/s2) T LHDJTNFFULJFEFOTÑSUÑONFLVWWFUJ 'S =L/ 'Net =NUPQMBNBEBO 'S = -10 = + B 'S = 10 N 5 NHTJOa a =NT2 a NHTJOa mgcosa a G = mg LHMLDJTJNJÀJO 5-'S =NB 5-10 = 5=/PMVS NZ > N > N 51 52 53 20 N X Y
TEST - 9 /&850/6/)\"3&,&5:\"4\"-\"3* ôFLJMEFLJN ve m LÐUMFMJDJTJNMFSJQMFCBóMBOBSBL ôFLJMEFLJTÐSUÐONFTJ[FóJLEÐ[MFNEFN ve m küt- 12 12 'LVWWFUJZBSENZMB¿FLJMJZPSMBS MFTJIBSFLFUTJ[LBMNBLUBES TF T m2 m1 m2 m1 5ÑNZÑ[FZMFSTÑSUÑONFTJ[PMEVôVOBHÌSF 53° 37° * 'LVWWFUJBSUSMSTB 5JQHFSJMNFTJBSUBS ** m LÐUMFTJBSUSMSTB 5JQHFSJMNFTJBSUBS N1 =LH N2 =LHPMEVôVOBHÌSF 5JQJOEFLJ HFSJMNFLVWWFUJLBÀ/PMVS 1 (sin53° = TJO= H= 10 m/s2) *** m LÐUMFTJBSUSMSTB 5JQHFSJMNFTJBSUBS \" # $ % & 2 ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** ôFLJMEFEÐõFZLFTJUJWFSJMFOTJTUFNEF9WF:DJTJN- Sürtünmesiz yatay düzlemde m ve 2m kütleli cisim- MFSJ'LVWWFUJZBSENZMBZVLBSZËOEF¿FLJMJZPS MFSCJSJQMFCBóMBOBSBLõFLJMEFLJ'LVWWFUJZBSENZ- MB¿FLJMJZPSMBS F T 2m X m TF Y #VOBHÌSF * 'LVWWFUJBSUSMSTB5JQHFSJMNFTJBSUBS 5ÑNTÑSUÑONFMFSJOJINBMFEJMEJôJTJTUFNEF ** NLÐUMFMJDJTJNZFSJOFNLÐUMFMJDJTJNCBóMB- * :OJOLÐUMFTJBSUSMSTB 5JQHFSJMNFTJBSUBS OSTB5JQHFSJMNFTJBSUBS ** 'LVWWFUJBSUSMSTB 5JQHFSJMNFTJBSUBS *** NLÐUMFMJDJTNJOZFSJOFNLÐUMFMJDJTJNCBóMB- *** :OJOLÐUMFTJBSUSMSTB 5JQHFSJMNFTJB[BMS OSTB5JQHFSJMNFTJBSUBS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # *WF** $ *WF*** \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** % **WF*** & * **WF*** B D 20 B A
www.aydinyayinlari.com.tr /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 .0%·- 11. SINIF .qk(7$k, .qk(7$k, :BUBZ EÑ[MFNEF ÑTU ÑTUF EVSBO DJTJNMFSJO &óJLEÐ[MFNÐ[FSJOEFIBSFLFUFEFODJTJNMFSEF IBSFLFUJJÀJO DJTNJO BóSML WFLUËSÐ ¿J[JMFSFL ZÐ[FZF EJL WF ZÐ[FZFQBSBMFMPMBOCJMFõFOMFSJOFBZSMS:Ð[F- N Tüm yüzeyler sürtünme- ZF QBSBMFM PMBO CJMFõFO DJTNJ BõBó ZËOEF ¿F- A sizken ' kuvveti alttaki LFSLFOZÐ[FZFEJLPMBOCJMFõFOJTFDJTJNJMFZÐ- F DJTNF VZHVMBOZPS JTF # [FZ BSBTOEBLJ TÐSUÐONF LVWWFUJOJO PMVõNBT- B DJTNJ LVWWFU ZËOÐOEF OTBóMBS I[MBOSLFO\"DJTNJ#ZF FõMJLFUNF[WFEÐõFS FS N NHDPTa a m N F Tüm yüzeyler sürtünme- A sizken ' kuvveti üstteki NHTJOa DJTNF VZHVMBOZPS JTF \" B DJTNJ LVWWFU JMF BZO G = mg ZËOEFI[MBOSLFO#DJT- NJ \"ZB FõMJL FUNF[ WF a EVSNBZBEFWBNFEFS N Yüzeyler sürtünmeli ise A ' LVWWFUJOJOCÐZÐLMÐóÐ- OFWFIBOHJDJTNFVZHV- B MBOEóOBHËSFCJSMJLUFEF BZSBZSEBIBSFLFUFEF- CJMJS ÖRNEK 22 ÖRNEK 23 :BUBZEÐ[MFNÐ[FSJOEFÐTUÐTUFLPONVõLHWFLHML :BUBZMBMJLB¿ZBQBOFóJLEÐ[MFNÐ[FSJOEFLJLHML LÐUMFMFSõFLJMEFLJHJCJDJTJNMFSJCJSMJLUFIBSFLFUFUUJSFCJMF- DJTJNõFLJMEFLJHJCJTFSCFTUCSBLMZPS cek maksimum ' LVWWFUJJMF¿FLJMNFLUFEJSTüm yüzey- MFSTÐSUÐONFMJWFTÐSUÐONFLBUTBZT UJS FS N N LH N1 mg.sin37° = 30 N LH 37° mg.cos37° = 40 N LH 20 N F N2 G = mg = 50 N yatay 37° 30 N #VOB HÌSF DJTJNMFS BSBTOEBLJ TÑSUÑONF LVWWFUJ &ôJL EÑ[MFN TBCJU TÑSUÑONFMJ WF TÑSUÑONF LBUTBZ- T JTFDJTJNJMFFôJLEÑ[MFNBSBTOEBLJTÑSUÑONF 'S1 DJTJNMFS JMF ZBUBZ EÑ[MFN BSBTOEBLJ TÑSUÑONF LVWWFUJLBÀ/EVS (sin37° = DPT= LVWWFUJ'S2PMNBLÑ[FSF'S1'S2PSBOLBÀUS g = 10 m/s2) (g = 10 m/s2) $JTJNMFSBSBTOEBLJ:Ñ[FZEFLJUFQLJLVWWFUJ NHTJO= =/ 'S =L/ ZÑ[FZFQBSBMFMCJMFöFO = UFQLJLVWWFUJ/1 = 20 N N = 50 N NHDPT= = 40 N ZÑ[FZFEJLCJMFöFO = 20 N 2 $FWBQ/ ' =L/ ' =L/ S1 S2 2 = = = 10 N = 25 N F $FWBQ S1 = 2 F5 S2 F 2 21 20 N S1 = F5 S2
TEST - 10 /&850/6/)\"3&,&5:\"4\"-\"3* LHWFLHLÐUMFMJ9 :DJTJNMFSJTÐSUÐONFTJ[ZBUBZ 4ÐSUÐONFLBUTBZTOOL= PMEVóVCJSEÐ[FOFL- EÐ[MFNEFõFLJMEFLJHJCJÐTUÐTUFEVSNBLUBES9WF te m =LHLÐUMFMJDJTJN'=/MVLLVWWFUJMF : DJTJNMFSJ BSBTOEBLJ TÐSUÐONF LVWWFUJOJO FO CÐ- õFLJMEFLJHJCJ¿FLJMNFLUFEJS ZÐLEFóFSJ/EVS F = 120 N X FY m yatay 37° yatay :DJTNJOFVZHVMBOBO'LVWWFUJ #VOBHÌSF * 20 N * $JTNJO FóJL EÐ[MFNF VZHVMBEó EJL LVWWFU ** 30 N /EVS ** $JTNFFULJFEFOTÐSUÐONFLVWWFUJ/EVS *** 40 N *** $JTJNPLZËOÐOEFTBCJUI[MIBSFLFUZBQNBL- CÑZÑLMÑLMFSJOEFOIBOHJMFSJOFFöJUPMVSTBDJTJN- UBES MFSCJSMJLUFIBSFLFUFEFCJMJS (g = 10 m/s2) \" :BMO[* # :BMO[** $ :BMO[*** ZBSHMBSOEBOIBOHJMFSJEPôSVEVS (g = 10 m/s2 TJO= DPT= % *WFZB**& *WFZB**WFZB*** \" :BMO[* # :BMO[** $ *WF** % *WF*** & * **WF*** 9 WF : DJTJNMFSJ TÐSUÐONFTJ[ ZBUBZ EÐ[MFNEF ÐTU ±[EFõ9 :WF;DJTJNMFSJTÐSUÐONFTJ[FóJLEÐ[MFN- ÐTUFEVSNBLUBESôFLJM-*EF' LVWWFUJ:DJTNJOF MFSÐ[FSJOF9DJTNJJMLI[T[CSBLMZPS:DJTNJZV- 1 LBSEPóSVjI[ZMB ;DJTNJJTFBõBóEPóSVj I- [ZMBCSBLMZPS ôFLJM-**EF'2LVWWFUJ9DJTNJOFVZHVMBONBLUBES ' WF' LVWWFUMFSJDJTJNMFSJCJSMJLUFIBSFLFUFUUJSFCJ- X j 12 Y MFOFOCÐZÐLLVWWFUMFSEJS F2 a a X yatay yatay X F1 j Y yatay Z ôFLJMm* Y yatay a ôFLJMm** yatay 4JTUFNEFZBMO[DBDJTJNMFSBSBTTÑSUÑONFMJWF $JTJNMFSJO JWNFMFSJOJO CÑZÑLMÑLMFSJ TSBTZMB DJTJNMFSJOLÑUMFMFSJPSBO mX = 2 ise F1 ora- aX BYWFBZJTFCVOMBSBSBTOEBLJCÑZÑLMÑLJMJö- LJTJBöBôEBLJMFSEFOIBOHJTJEJS OLBÀUS mY 3 F2 A) a9 > a > a; B) a9 > a = a; Y Y $ 3 E) 1 $ BY = a < a D) a > a > a 2 2 ; 9 ; Y 9 \" # D) 1 E) a9 = a = a; Y D C 22 C E
www.aydinyayinlari.com.tr /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 .0%·- 11. SINIF 7$1,0%m/*m 7$1,0%m/*m Bir cisme etki eden tüm kuvvetlerin ve bu kuv- :BUBZEÐ[MFNEFZBOZBOBEVSBODJTJNMFSJ¿JO WFUMFSJO VZHVMBNB OPLUBMBSOO HËTUFSJMNFTJOF TFSCFTUDJTJNEJZBHSBNBEWFSJMJS 4JTUFNJO4FSCFTU$JTJN%JZBHSBN 4JTUFNJO4FSCFTU$JTJN%JZBHSBN j N12 = – N21 j N2 N1 m1 N2 m2 N1 m1 T m2 F F N12 N21 Fs1 Fs2 Fs1 Fs2 m1g m2g m1g m2g N1 N2 N1 N2 m1 m2 T TF F N21 N12 Fs1 Fs2 m1g m2g Fs1 Fs2 m1g m2g m1LÐUMFTJOJOTFSCFTU m2LÐUMFTJOJOTFSCFTU DJTJNEJZBHSBN DJTJNEJZBHSBN m1LÐUMFTJOJOTFSCFTU m2LÐUMFTJOJOTFSCFTU DJTJNEJZBHSBN DJTJNEJZBHSBN ÖRNEK 24 ÖRNEK 25 Sürtünmeli yatay düzlemde m1 N2 ve m kütleli cisim- Sürtünmeli yatay düzlemde m1 N2 ve m kütleli cisimler 3 3 MFS JQMFS ZBSENZMB CJSCJSJOF CBóMBOBSBL õFLJMEFLJ HJCJ ' õFLJMEFLJHJCJ'LVWWFUJZMFJUJMJZPS LVWWFUJZMF¿FLJMJZPS m3 N3 N1 N2 N3 m2 N2 m1 m2 m3 N1 T1 –T1 T2 –T2 F m1 F1 –F1 F F2 –F2 FS1 FS2 FS3 Fs1 Fs2 Fs3 G1 G2 G3 G1 G2 G3 $JTJNMFSFFULJFEFOLVWWFUMFSJöFLJMMFSÑ[FSJOEFHÌT- $JTJNMFSFFULJFEFOLVWWFUMFSJöFLJMMFSÑ[FSJOEFHÌT- UFSJOJ[ UFSJOJ[ N1 N2 N3 m3 N3 m2 m3 m2 N2 m1 T1 –T1 T2 –T2 F FS1 FS2 FS3 m1 N1 F2 –F2 G1 G2 G3 F F1 –F1 23 Fs1 Fs2 Fs3 G1 G2 G3
11. SINIF .0%·- /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 www.aydinyayinlari.com.tr 7$1,0%m/*m ÖRNEK 27 #JSDJTJNZBEBTJTUFNCJSEFOGB[MBLVWWFUJOFU- 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFCJSJQJMFCJSCJSJOFCBóMN1 LJTJBMUOEBLBMEóOEBOFULVWWFUFULJTJZMFJWNFMJ ve m LÐUMFMJDJTJNMFSõFLJMEFLJHJCJEJS IBSFLFUFEFS4JTUFNFFULJFEFOOFULVWWFUIBSF- LFUZËOÐJMFBZOJTFTJTUFNI[MBOS4JTUFNFFULJ 2 FEFOOFULVWWFUIBSFLFUZËOÐJMFUFSTJTFTJTUFN ZBWBõMBS m1 LH m2 LH T F = 50 N jj FOFU FOFU #VOB HÌSF DJTJNMFSJO JWNFMFSJ WF JQUF PMVöBO HFSJM- m m NFLVWWFUJ5LBÀ/EVS yatay yatay F = m.a F = m.a LHMLDJTJNJÀJO i)[MBOBODJTJNu i:BWBõMBZBODJTJNu net net ôFLJMm* ôFLJMm** 50 = 5.a 5= 2 5= 30 N a = 10 m/s ÖRNEK 26 ÖRNEK 28 4ÐSUÐONFMJZBUBZEÐ[MFNEFCJSJQJMFCJSCJSJOFCBóM9WF Sürtünmeli yatay düzlemde bulunan 3 kg kütleli m ve :DJTJNMFSJõFLJMEFLJ'LVWWFUJOJOFULJTJZMFTBCJUI[MBIB- SFLFUFUNFLUFEJS 1 X YF 2 kg kütleli m DJTJNMFSJOFCJSJQJMFCBóMWFõFLJMEFLJHJCJ #JS TÑSF TPOSB DJTJNMFS BSBTOEBLJ JQ LPQBSTB 9 WF 2 :OJOCVOEBOTPOSBLJIBSFLFUJJÀJOOFTÌZMFOFCJMJS ' LVWWFUJZMF ¿FLJMNFLUFEJS :BUBZ EÐ[MFN WF DJTJNMFS 9 DJTNJ TÑSUÑONF LVWWFUJ FULJTJZMF ZBWBöMBZBSBL EVSVS BSBTOEBLJTÐSUÐONFLBUTBZTTBCJUWFL= UJS : DJTNJ JTF Ñ[FSJOF FULJ FEFO OFU LVWWFU BUUô JÀJO JMFSJ ZÌOEFI[MBOS m1 LH N1 N2 m2 LH .qk(7$k, T F = 50 N 4ÐSUÐONFLVWWFUJ TJTUFNMFSJOJWNFMFSJOJB[BMUS fS1 BODBL DJTJNMFS BSBTOEBLJ JQ HFSJMNF LVWWFUJOJ ve etki-UFQLJLVWWFUMFSJOJFULJMFNF[ 30 N fS2 20 N #VOB HÌSF DJTJNMFSJO JWNFMFSJ WF JQUF PMVöBO HFSJM- NFLVWWFUJ5LBÀ/EJS 'S1 =L/ 'S2 =L/ = = = 15 N = 10 N F = m.a F = m.a net net 50 - 15 - 10 = 5.a T - F = 3.5 a = 5 2 S1 m/s T = 30 N 9ZBWBöMBSEVSVS :EÑ[HÑOI[MBOS 24 a = 10 2 5 / a = 5 2 T = 30 N m/s m/s
/&850/6/)\"3&,&5:\"4\"-\"3* TEST - 11 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFLJ, - .WF/DJTJN- Sürtünmesiz yatay düzlemde yan yana durmakta MFSJOJOLÐUMFMFSJTSBTZMBN N N WFNEJS$J- PMBON1 ve m2LÐUMFMJDJTJNMFSõFLJMEFLJHJCJ ' kuv- TJN'LVWWFUJZMFõFLJMEFLJHJCJ¿FLJMNFLUFEJS WFUJJMFJUJMNFLUFEJS K L T1 M T2 N F F m1 m2 Yatay -WF.DJTJNMFSJBSBTOEBLJJQHFSJMNFTJ51 .WF /DJTJNMFSJBSBTOEBLJJQHFSJMNFTJ52JTFJQHF- SJMNFLVWWFUMFSJPSBO5152LBÀUS A) 1 B) 1 $ % & m kütlesinin m1F VZHVMBEó UFQLJ LVWWFUJOJO CÐ- 3 2 2 ZÐLMÐóÐ/EJS F = 5 PMEVôVOBHÌSF DJTJNMFSJOLÑUMFMFSJPSB- N3 ON1N2LBÀUS A) 2 # $ 3 D) 2 E) 3 3 2 )BWBTÐSUÐONFTJOJOJINBMFEJMEJóJCJSPSUBNEBLH 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFõFLJMEFLJHJCJZBOZB- WFLHMLDJTJNMFSFTOFNFZFOJQJMFCJSCJSJOFCBó- OBEVSNBLUBPMBOTSBTZMBN NWFNLÐUMFMJDJ- MBOQ õFLJMEFLJ HJCJ / CÐZÐLMÐóÐOEFLJ TBCJU ' simler ' LVWWFUJJMFJUJMNFLUFEJS LVWWFUJZMF¿FLJMJZPS 3m F = 120 N Fm 2m LH N LÑUMFMJ DJTNJO N LÑUMFMJ DJTNF VZHVMBEô T UFQLJ LVWWFUJOJO CÑZÑLMÑôÑ / N LÑUMFMJ DJT- LH 1 #VOBHÌSF JQUFPMVöBOHFSJMNFLVWWFUJ5LBÀ/ EVS (g = 10 m/s2) NJO N LÑUMFMJ DJTNF VZHVMBEô UFQLJ LVWWFUJ \" # $ % & OJOCÑZÑLMÑôÑ/ ise N / N PSBOLBÀUS 2 12 A) 3 B) 2 $ 1 D) 5 E) 5 5 5 5 2 3 B C 25 A E
11. SINIF .0%·- /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 www.aydinyayinlari.com.tr .qk(7$k, ÖRNEK 30 &óJLEÐ[MFNEFIBSFLFUFEFODJTJNMFSJOJWNFMFSJ LHLÐUMFMJJLJË[EFõDJTJNõFLJMEFLJHJCJIBSFLFUFUNFL- LÐUMFMFSJOFCBóMEFóJMEJS UFEJS LH LH &óJLEÐ[MFN &óJLEÐ[MFN 37° 20.sin37° 53° 20.sin53° TÐSUÐONFTJ[JTF TÐSUÐONFMJJTF 20.cos37° 20.cos37° mj j 20 37° 20 53° N m ôFLJMm* ZBUBZ ôFLJMm** ZBUBZ Fs mg.sina a mg.sina a &óJLEÐ[MFNMFSZBUBZEÐ[MFNJMFWFEFSFDFMJLB¿ mg.cosa a a ZBQZPS mg.cosa #VOBHÌSF DJTJNMFSJOJWNFMFSJOJOCÑZÑLMÑôÑõFLJM-* G = mg G = mg de a õFLJM-**EFB ise a / a PSBOLBÀUS 1 2 12 (g: 10 m/s2 TJO = DPT= TJO = DPT= Fnet = m.a Fnet = m.a õFLJM-*JÀJO õFLJM-**JÀJO mg. sin a = m.a mg. sin a - FS = m.a mg. sin a - k.mg. cos a = m.a 'net =NB 'net =NB a = g. sin a a = g. sin a - kg cos a TJO=B1 TJO=B2 =B1 =B2 a =NT2 a =NT2 1 2 a = 3 1 a 4 3 $FWBQ 2 4 ÖRNEK 29 ÖRNEK 31 NWFNLÐUMFMJDJTJNMFSTÐSUÐONFTJ[FóJLEÐ[MFNMFSÐ[F- ôFLJMEFLJ TÐSUÐONFTJ[ FóJL EÐ[MFNEF LH WF LH ML SJOEFõFLJMEFLJHJCJIBSFLFUFUNFLUFEJS LÐUMFMJDJTJNMFSCJSJQJMFCJSCJSJOFCBóMBOQTFSCFTUCSBL- MZPS m 2m a mg.sina a 2mg.sina T mg.cosa a 2mg.cosa a m2 LH mg 2mg ôFLJMm* ZBUBZ ôFLJMm** ZBUBZ m1 LH 30° 20.sin30° 20.sin30° = 10 N #VOBHÌSF DJTJNMFSJOJWNFMFSJOJOCÑZÑLMÑôÑõFLJM-* 30 N 20 N 30° a1 õFLJM-**EFB2 a2PSBOLBÀUS de ise a / ZBUBZ 1 HZFS¿FLJNJJWNFTJ #VOBHÌSF DJTJNMFSJOIBSFLFUJTSBTOEBJQUFPMVöBO HFSJMNFLVWWFUJLBÀ/EVS NLÑUMFMJDJTJNJÀJO NLÑUMFMJDJTJNJÀJO (g = 10 m/s2, sin30° = 1 ) ' =NB ' =NB 2 net net NHTJOa =NB NHTJOa =NB 'net =NB 'net =NB 30 - 10 =B 5-10 = 1 2 5= 18 N a =NT2 a =HTJOa a =HTJOa $FWBQ5= 18 N 1 2 a 1 =1 a 2 $FWBQ 1 26 3 5 / 4
/&850/6/)\"3&,&5:\"4\"-\"3* TEST - 12///////////////////////////// 4ÐSUÐONFTJ[FóJLEÐ[MFNEFLHWFLHLÐUMFMJDJ- ôFLJMEFLJFóJLEÐ[MFNJO-.BSBTTÐSUÐONFTJ[ ,- TJNMFS'=/MVLLVWWFUZBSENZMBõFLJMEFLJHJCJ BSBTJTFTBCJUTÐSUÐONFMJEJS ¿FLJMNFLUFEJS K F = 50 N L 53° LH T LH 37° M 37° ZBUBZ ZBUBZ $JTJN,-WF-.BSBTOEBBZOCÑZÑLMÑLUFJWNF #VOB HÌSF DJTJNMFS BSBTOEBLJ JQ HFSJMNFTJ 5 JMFIBSFLFUFUUJôJOFHÌSF ,-BSBTOEBLJTÑSUÑO- LBÀ/EVS NFLBUTBZTLBÀUS (sin37° = DPT= H= 10 m/s2) (g = 10 m/s2 TJO=DPT= \" # $ % & sin53° =DPT= 1 B) 1 $ 1 1 1 A) 5 4 D) E) 6 3 2 LHMLLÐUMFõFLJMEFLJFóJLEÐ[MFNJO,OPLUBTOEBO 9 :WF;DJTJNMFSJTSBTZMBLH LH LHLÐUMF- TFSCFTUCSBLMZPS&óJLEÐ[MFNZÐ[FZJOEF,-BSB- MJEJS $JTJNMFS JQMFS ZBSENZMB CJSCJSJOF CBóMBOBSBL TTÐSUÐONFTJ[ -.BSBTJTFTBCJUTÐSUÐONFMJEJS õFLJMEFLJEÐ[FOFLLVSVMNVõUVS N LH LH K Y =////6////3/N//7////°////////////// L //////////////////////////////////////// FS KL M ZBUBZ X Z LH LH 4ÑSUÑONFLVWWFUJ'S =/JTFDJTNJO-OPLUB- TOEBOTPOSBLJIBSFLFUJJÀJOOFTÌZMFOFCJMJS 53° (sin37° = DPT= H= 10 m/s2) A) %Ð[HÐOEPóSVTBMIBSFLFUZBQBS 4JTUFNEF,-BSBTTÑSUÑONFMJPMVQTJTUFNTFS- B) 4BCJUCJSJWNFZMFZBWBõMBS $ 4BCJUCJSJWNFZMFI[MBOS CFTUCSBLMEôOEBDJTJNMFSEFOHFEFLBMZPSJTF D) \"[BMBOCJSJWNFZMFZBWBõMBS E) \"[BMBOCJSJWNFZMFI[MBOS TÑSUÑONFLBUTBZTFOB[LBÀUS (sin53° = DPT= H= 10 m/s2) A) 2 B) 1 $ 1 D) 1 E) 1 3 6 4 3 2 D A 27 D E
11. SINIF .0%·- /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 www.aydinyayinlari.com.tr .qk(7$k, .qk(7$k, 4BCJU I[MB ZVLBS WFZB BõBó ZËOEF IBSFLFU öWNF B FEFO CJS BTBOTËS UBWBOOB DJTJN CJS JQ ZBSE- a NZMBBTMEóOEB 5JQHFSJMNFTJ a ,VWWFU ' F1 F2 T öWNF-LVWWFUHSBGJóJOEFDJTNFFULJFEFOLVWWFU m '1 EFO LпÐL PMEVóVOEB DJTNJO JWNFTJ TGSES mg 6ZHVMBOBOLVWWFU' EFOCÐZÐLPMEVóVOEBJTF $JTJNEFOHFEFPMEVóVJ¿JO 1 'net =ES DJTJNJWNFMJIBSFLFUZBQNBZBCBõMBS#VSBEB'1 T - mg = 0 TÐSUÐONFLVWWFUJOFFõJUCÐZÐLMÐLUFEJS T = mg EJS (SBGJóJO&óJNJ tan a = a = a = 1 >F2 - F1 m.a m Net kuvvet ÖRNEK 32 ÖRNEK 33 4ÐSUÐONFMJZBUBZEÐ[MFNEFEVSNBLUBPMBONLÐUMFMJDJT- :VLBS ZËOEF NT MJL TBCJU I[MB JMFSMFZFO CJS BTBO- NFEÐ[MFNFQBSBMFM'LVWWFUJVZHVMBONBLUBES TËSEFLHLÐUMFMJCJSDJTJNBTBOTËSUBWBOOBõFLJMEFLJHJ- CJBTMNõUS B NT2 4 0 ' / T j = 10 m/s 20 40 LH $JTNJOJWNFTJOJOVZHVMBOBO ' LVWWFUJOFCBôMHSB- 20 N GJôJöFLJMEFLJHJCJJTFDJTJNJMFZÑ[FZBSBTOEBLJTÑS- UÑONFLBUTBZTLBÀUS ( g = 10 m/s2) ' =NB ' =L/ #VOB HÌSF DJTNJO CBôM PMEVôV JQUFLJ HFSJMNF LVW- WFUJLBÀOFXUPOEVS (g = 10 m/s2) net net $JTJNEFOHFEFPMEVôVJÀJO 40 - 20 =N =LNH 'net =ES =L 5-20 = 0 N=LH 5=/ES k = $FWBQL= $FWBQ/ L 28 20 N
www.aydinyayinlari.com.tr /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 .0%·- 11. SINIF .qk(7$k, .qk(7$k, :VLBS ZËOEF a JWNFTJ JMF I[MBONBLUB PMBO :VLBSZËOEF a JWNFTJJMFZBWBõMBZBOBTBOTË- BTBOTËSÐOUBWBOOBCJSDJTJNJQZBSENZMBõF- SÐO UBWBOOB CJS DJTJN JQ ZBSENZMB õFLJMEFLJ LJMEFLJHJCJBTMEóOEB5JQHFSJMNFTJ HJCJBTMEóOEB5JQHFSJMNFTJ \"TBOTËSÐO \"TBOTËSÐO \"TBOTËSÐO \"TBOTËSÐO I[ JWNF I[ JWNF T WFLUËSÐ WFLUËSÐ T WFLUËSÐ WFLUËSÐ ja ja m m mg mg \"TBOTËS I[MBOEó J¿JO I[ WF JWNF WFLUËSMFSJ \"TBOTËS ZBWBõMBEó J¿JO I[ WFLUËSÐ JMF JWNF BZOZËOMÐEÐS WFLUËSÐ[UZËOMÐEÐS öQFCBóMDJTJNJ¿JO öQFCBóMDJTJNJ¿JO 'net =NB Fnet = m.a $JTNJOJWNFTJBõBóZËOEFPMEVóVOEBO NH> T) $JTNJOJWNFTJZVLBSZËOEFPMEVóVOEBO5> mg) mg - T =NB T-mg =NB T = m^ g - a h PMVS T = m^ g + a h PMVS ÖRNEK 34 ÖRNEK 35 :VLBSZËOEFNT2MJLJWNFJMFI[MBOBOBTBOTËSÐOUB- g WBOOBJQZBSENZMBLHMLCJSDJTJNõFLJMEFLJHJCJBTM- :VLBSZËOEF JWNFTJJMFZBWBõMBNBLUBPMBOBTBOTË- NõUS 2 SÐOUBWBOOBJQZBSENZMBNLÐUMFMJCJSDJTJNõFLJMEFLJHJ- CJBTMNõUS T T LH m 40 N mg #VOB HÌSF DJTNJO CBôM PMEVôV JQUFLJ HFSJMNF LVW- #VOBHÌSF JQUFPMVöBOHFSJMNFLVWWFUJDJTNJOBôSM- WFUJLBÀ/ES (g = 10 m/s2) ôOOLBÀLBUES (g =ZFS¿FLJNJJWNFTJ \"TBOTÌSÑOI[WFLUÌSÑ \"TBOTÌSÑOJWNFWFLUÌSÑ \"TBOTÌSÑOI[WFLUÌSÑ \"TBOTÌSÑOJWNFWFLUÌSÑ j a j g $FWBQ/ 2 'net =NB ' =NB 5-NH=NB 1 5-40 = net $FWBQ 5=/ g 2 5-NH=N 2 5=NH 48 N 1 2
11. SINIF .0%·- /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 www.aydinyayinlari.com.tr .qk(7$k, .qk(7$k, \"õBó ZËOEF a JWNFTJ JMF I[MBONBLUB PMBO \"õBó ZËOEF a JWNFTJ JMF I[MBONBLUB PMBO BTBOTËSÐOUBWBOOBCJSDJTJNJQZBSENZMBõF- BTBOTËSÐOUBWBOOBCJSDJTJNJQZBSENZMBõF- LJMEFLJHJCJBTMEóOEB5JQHFSJMNFTJ LJMEFLJHJCJBTMEóOEB5JQHFSJMNFTJ \"TBOTËSÐO \"TBOTËSÐO \"TBOTËSÐO \"TBOTËSÐO I[ JWNF I[ JWNF T WFLUËSÐ WFLUËSÐ T WFLUËSÐ WFLUËSÐ ja ja m m mg mg \"TBOTËS I[MBOEó J¿JO I[ WF JWNF WFLUËSMFSJ \"TBOTËSZBWBõMBEóJ¿JOI[WFJWNFWFLUËSMFSJ BZOZËOMÐEÐS [UZËOMÐEÐS öQFCBóMDJTJNJ¿JO öQFCBóMDJTJNJ¿JO Fnet = m.a Fnet = m.a $JTNJOJWNFTJZVLBSZËOEFPMEVóVOEBO $JTNJOJWNFTJZVLBSZËOEFPMEVóVOEBONH> T) mg > T) T-mg =NB mg-T=NB T = m^ g + a h PMVS T = m^ g - a h PMVS ÖRNEK 3 ÖRNEK 3 \"õBóZËOEFNT2MJLJWNFJMFI[MBOBOBTBOTËSÐOUB- \"õBó ZËOEF NT2 MJL JWNF JMF ZBWBõMBZBO BTBOTËSÐO WBOOBLHLÐUMFMJCJSDJTJNõFLJMEFLJHJCJBTMNõUS UBWBOOBLHLÐUMFMJCJSDJTJNõFLJMEFLJHJCJBTMNõUS T T LH LH 60 N 100 N #VOBHÌSF JQUFPMVöBOHFSJMNFLVWWFUJLBÀ/ES #VOBHÌSF JQUFPMVöBOHFSJMNFLVWWFUJLBÀ/ES (g = 10 m/s2) (g = 10 m/s2) \"TBOTÌSÑOI[WFLUÌSÑ \"TBOTÌSÑOJWNFWFLUÌSÑ \"TBOTÌSÑOI[WFLUÌSÑ \"TBOTÌSÑOJWNFWFLUÌSÑ ja ja $JTNJOJWNFTJBöBôZÌOEFPMEVôVJÀJONH>5 $JTNJOJWNFTJBöBôZÌOEFPMEVôVJÀJO5>NH 'net =NB 'net =NB 60-5= 5-100 = 5=/ $FWBQ/ 5=/ $FWBQ/ 36 N 30 120 N
/&850/6/)\"3&,&5:\"4\"-\"3* TEST - 13 NLÐUMFMJCJSLJõJõFLJMEFLJBTBOTËSÐOJ¿JOEFUBSUÐT- NLÐUMFMJCJSDJTJNCJSZBZWFFTOFNFZFOJQZBSE- UÐOF¿LZPS NZMB õFLJMEFLJ HJCJ CBóMBONõUS \"TBOTËS TBCJU I[MBBõBóJOFSLFOJQUFLJHFSJMNFLVWWFUJ5 ZBZEB- LJLVWWFUJTF'EJS \"TBOTÌSZVLBSZÌOEFNT2MJLJWNFJMFZBWBö- T MBSTBUBSULBÀ/MVLBôSMLHÌTUFSJS m (g = 10 m/s2) F \" # $ % & \"TBOTÌSBöBôZÌOEFZBWBöMBNBZBCBöMBEôO- EB5WF'OBTMEFôJöJS ' T A) %FóJõNF[ Artar B) Artar %FóJõNF[ $ %FóJõNF[ %FóJõNF[ D) Artar \"[BMS E) Artar Artar ôFLJMEFLJBTBOTËSJ¿JOFNLÐUMFMJCJSTBSLB¿BTMNõ- t =BOOEBj = jJMLI[OBTBIJQPMBOCJSBTBO- 0 US\"TBOTËSEVSHVOLFOJQUFLJHFSJMNFLVWWFUJ' TB- TËSZVLBSEPóSVIBSFLFUFUNFLUFEJSNLÐUMFMJCJSDJ- CJUJWNFZMFI[MBOSLFOJQUFLJHFSJMNFLVWWFUJ'EJS TJNBTBOTËSUBWBOOBCJSJQZBSENZMBBTMNõUS )[ ip j m * ** *** 0 U U U Zaman #VOB HÌSF BTBOTÌSÑO IBSFLFU ZÌOÑ WF JWNF- \"TBOTÌSÑOI[-[BNBOHSBGJôJöFLJMEFLJHJCJJTF TJOJO CÑZÑLMÑôÑ JÀJO BöBôEBLJMFSEFO IBOHJTJ DJTNJO CBôM PMEVôV JQUFLJ HFSJMNF LVWWFUJ * ** EPôSVEVS (g = yerçekimi ivmesi) WF***BSBMLMBSOEB5 5 WF5 JTFCVOMBSBSBTO- 12 3 g \" \"õBóEPóSV # \"õBóEPóSV H EBLJJMJöLJBöBôEBLJMFSEFOIBOHJTJEJS 2 A) T > T > T B) T = T > T g 123 132 $ :VLBSEPóSV % :VLBSEPóSV H $ 52 > T = T D) T > T > T 2 1 2 321 & :VLBSEPóSV H E) T = T = T 1 2 3 D D 31 A D
11. SINIF .0%·- /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 www.aydinyayinlari.com.tr .qk(7$k, .qk(7$k, a JWNFTJZMFTBóBEPóSVI[MBONBLUBPMBOBSB- a JWNFTJZMF TBóB EPóSV ZBWBõMBNBLUB PMBO DOUBWBOOBBTMPMBONLÐUMFMJDJTNFFULJFEFO BSBDO UBWBOOB BTM PMBO N LÐUMFMJ DJTNF FULJ LVWWFUMFSõFLJMMFSEFHËTUFSJMEJóJHJCJEJS FEFOLVWWFUMFSõFLJMMFSEFHËTUFSJMEJóJHJCJEJS j 4PM 4Bó j 4PM 4Bó a a T T.cosa T T.cosa Ta a aT a m m mg a T.sina = m.a mg T.sina a ZBUBZ mg ZBUBZ mg #V EVSVNEB JQ HFSJMNFTJOJO EÐõFZ CJMFõFOJ #V EVSVNEB JQ HFSJMNFTJOJO EÐõFZ CJMFõFOJ BóSMóEFOHFMFSLFO JQHFSJMNFTJOJOZBUBZCJMF- BóSMóEFOHFMFSLFO JQHFSJMNFTJOJOZBUBZCJMF- õFOJDJTNJTBóBEPóSV a JWNFTJJMFI[MBOESS õFOJDJTNJTPMBEPóSV a JWNFTJJMFZBWBõMBUS 5TJOa =NB 5TJOa =NB a =HUBOa a =HUBOa 5DPTa =NH 5DPTa =NH ÖRNEK 38 ÖRNEK 39 NLÐUMFMJDJTJNøV[VOMVóVOEBLJJQZBSENZMBCJSBSBDO NLÐUMFMJDJTJNJQZBSENZMBõFLJMEFLJHJCJBSBDOUBWBO- UBWBOOBBTMNõUSôFLJM-*EFBSB¿EVSHVO ôFLJM-**EF OBBTMNõUS JTFPLZËOÐOEFBJWNFTJZMFI[MBONBLUBES ø a 30° ø øi mm m ZBUBZ ZBUBZ ZBUBZ ôFLJM* ôFLJM** \"SBÀ PL ZÌOÑOEF a JWNFTJZMF ZBWBöMBSLFO DJTJN EÑöFZMFMJLBÀZBQZPSJTFBSBDOJWNFTJ a kaç NT2EJS f sin 30° = 1 cos 30° = 3 , g = 10 m/s2 p 22 #VOBHÌSF iBÀT øJQV[VOMVôV HZFSÀFLJNJJWNF- TJ NLÑUMFEFôJöLFOMFSJOEFOIBOHJMFSJOFCBôMES T.cos30° T 30° T.cosi i T T.sin30° T.sini i mg mg T . sin 30 = m .a T . cos 30 = m .g T . sin i = m .a $FWBQBWFH 1 T . cos i = m .g 2a a= 10 3 2 = 3 m/s 10 3 2 3 10 $FWBQ m/s 3 2 BWFH 32 10 3 2 m/s 3
www.aydinyayinlari.com.tr /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 .0%·- 11. SINIF .qk(7$k, .qk(7$k, \"UXPPEEÐ[FOFóJ öMLI[TGSPMBOJWNFMJIBSFLFUZBQBODJTJNMFSJO BMELMBSZPM T (m1 > m2) x = 1 at2 EJS a m1 Ta 2 #VOBHËSFDJTJNMFSJOFõJUTÐSFMFSEFBMELMBSZPM- MBSJMFJWNFMFSJOJOCÐZÐLMÐóÐEPóSVPSBOUMES 2a G1 = m.g m2 G2 = m.g 4JTUFNTFSCFTUCSBLMEóOEBDJTJNMFSFõJUTÐSF- a EFFõJUNFTBGFMFSBMBSBLJMFSMFEJLMFSJJ¿JOBZOCÐ- ZÐLMÐLUFLJJWNFMFSFTBIJQPMVSMBS#VJWNFJTF aa m1LÐUMFTJJ¿JO N2LÐUMFTJJ¿JO ÖRNEK 41 'net =NB 'net =NB m ve m LÐUMFMFSJJQJMFCJSCJSJOFCBóMBOBSBLIBSFLFUMJCJS G - T = m1.a T - G2 = m2.a 12 %FOLMFNMFSUPQMBOEóOEB m1.g - m2.a = m1.a + m2.a NBLBSBZBSENZMBõFLJMEFLJEÐ[FOFLLVSVMNVõUVS a = g m1 - m2 PMVS m1 = 2 kg T T m1 + m2 a T 2a ÖRNEK 40 m2 = 4 kg 40 4BCJUNBLBSBJMFLVSVMVõFLJMEFLJEÐ[FOFLUFLHWFLH MLLÐUMFMFSCJSJQZBSENZMBCJSCJSJOFCBóMBONõUS T 4ÑSUÑONFTJ[TJTUFNTFSCFTUCSBLMEôOEBJQUFPMV- a 3 kg öBOHFSJMNFLVWWFUJLBÀ/PMVS (g = 10 m/s2) Ta LH 'net =NB 5=B 30 2 kg LH 'net =NB 20 40 -5=B 4ÑSUÑONFTJ[EÑ[FOFLTFSCFTUCSBLMEôOEBLHML T = 4a & 40 = 3T DJTNJOJWNFTJLBÀNT2PMVS (g = 10 m/s2) 40 - 2T = 4 a 40 LHMLDJTJNJÀJO LHMLDJTJNJÀJO T= N 3 'net =NB 'net =NB 5- 20 =B 40 30 -5=B $FWBQ T = N 3 10 = 5a $FWBQNT2 a =NT2 NT2 33 40 T = N 3
TEST - 14 /&850/6/)\"3&,&5:\"4\"-\"3* ôFLJMEFLJ QBSL IBMJOEF EVSBO CJS TW ZBLU UBõNB N NWFNLÐUMFMJDJTJNMFSJQMFSZBSENZMBCJSCJ- UBOLFSJZBSIBDNJOFLBEBSEPMVEVS SJOF CBóMBOBSBL TBCJU NBLBSB ZBSENZMB õFLJMEFLJ TJTUFN LVSVMNVõUVS ' LVWWFUJZMF TJTUFN EFOHFEF UVUVMNBLUBES 5BOLFS PL ZÌOÑOEF I[MBONBZB CBöMBEôOEB T1 2m EFQPEBLJ TWOO HÌSÑOÑNÑ BöBôEBLJMFSEFO m F IBOHJTJHJCJPMVS T2 3m A) B) ' LVWWFUJ LBMESMSTB 51 WF 52 JQ HFSJMNFTJ JÀJO 4W 4W OFTÌZMFOFCJMJS $JTJNMFSBSBTOEBLJJQMFSZFUFSJODFV[VOEVS C) D) T T 4W 4W 1 2 E) 4W A) Artar Artar B) \"[BMS \"[BMS $ Artar \"[BMS D) %FóJõNF[ %FóJõNF[ E) \"[BMS \"[BMS N LÐUMFMJ DJTJN JQ ZBSENZMB CJS BSBDO UBWBOOB &õJULÐUMFMJ9 :WF;DJTJNMFSJJQMFSZBSENZMBCJSCJ- BTMNõUS SJOF CBóMBOBSBL TBCJU NBLBSB ZBSENZMB õFLJMEFLJ 12 TÐSUÐONFTJ[TJTUFNLVSVMNVõUVS4JTUFNTFSCFTUC- SBLMELUBOCJSTÐSFTPOSB9WF:DJTJNMFSJBSBTOEB- m LJJQLPQVZPS yatay Y $JTNJO BSBÀ JÀFSJTJOEF öFLJMEFLJ LPOVNEB LBM- Z NBT * \"SB¿ZËOÐOEFI[MBOSLFO X ** \"SB¿ZËOÐOEFI[MBOSLFO *** \"SB¿ZËOÐOEFZBWBõMBSLFO ;DJTNJOJOCVOEBOTPOSBLJIBSFLFUJJÀJOOFTÌZ- MFOFCJMJS EVSVNMBSOEBO IBOHJMFSJ TSBTOEB HFSÀFLMFöF- A) %Ð[HÐOEPóSVTBMIBSFLFUZBQBS CJMJS B) \"õBóZËOEFEÐ[HÐOI[MBOBOIBSFLFUZBQBS $ :VLBSZËOEFEÐ[HÐOI[MBOBOIBSFLFUZBQBS \" :BMO[* # :BMO[** $ *WFZB** D) \"õBóZËOEFEÐ[HÐOZBWBõMBZBOIBSFLFUZBQBS E) :VLBS ZËOEF EÐ[HÐO ZBWBõMBZBO IBSFLFU ZB- % **WFZB***& *WFZB**WFZB*** QBS A D 34 A A
www.aydinyayinlari.com.tr /&850/6/:\"4\"-\"3*#÷3#0:655\"WF÷,÷#0:655\")\"3&,&5 .0%·- 11. SINIF )BZBUN[EBLJ'J[JLWF'J[JL%ÑOZBTO\"ZEOMBUBOMBS ÷CO-J4JOBWF,BTS-J.FZM ¶OMÐ5ÐSLCJMJNJOTBO GJMP[PGWFEPLUPSPMBOöCO-J4JOB #VIBSBZBLOMBSOEBLJ&GõFOFLË- ZÐOEF ±[CFLJTUBO ZMOEBEÐOZBZBHFMNJõUJS0SUB¿BóNPEFSOCJMJNJOJOLVSVDVTVPMB- SBLCJMJOJSöCO-J4JOBZBHËSFCJMJNMFSNBEEFWFCJ¿JNJMJõLJTJCBLNOEBOпFBZSMS öCOJ-J4JOB ËODFDJTJNMFSJOIBSFLFUMFSJOJOEFWBNJ¿JO\"SJTUPOVOTBWVOEVóVIBWBWFZBPS- UBNFULJTJOJOZBOMõPMEVóVOVPSUBZB¿LBSUNõUS%BIBTPOSBÐ[FSJOEFOLVWWFUFULJTJLBM- ESMNõ DJTJNMFSJO IBSFLFUF EFWBN FUNFMFSJOJO TFCFCJOJO iLBTSJ NFZJMu ZBOJ DJTJNMFSJO LB- [BOEóIBSFLFUFUNFJTUFóJuPMEVóVOVËOFTÐSNÐõUÐS%BIBTPOSBLJ¿BMõNBMBSZMBCVEV- SVNVO DJTJNMFSJO BóSMLMBS JMF EPóSV PSBOUM PMEVóVOV ËOF TÐSFSFL FZMFNTJ[MJL GJLSJOJO UF- NFMMFSJOJPSUBZBLPZNVõUVS \"UXPPE%Ñ[FOFôJ \"UXPPEEÐ[FOFóJZBEB\"UXPPENBLJOFTJ(FPSHF\"UXPPEUBSBGOEBOTBCJUJWNFMJIBSFLFUEFOFZMFSJT- SBTOEBJDBEFEJMNJõUJS%Ð[FOFL/FXUPOO)BSFLFU:BTBMBSOHËTUFSNFLJ¿JOLVMMBOMNBLUBES4BCJU NBLBSBMCJSCBTJUNBLBSBEÐ[FOFóJPMBOTJTUFNLVWWFUZËOÐOÐEFóJõUJSNFLJ¿JOLVMMBOMS %ÑOZBOO&O)[M\"TBOTÌSÑ öMLZPMDVBTBOTËSMFSJEFZBQMEóOEBNFUSFMJLNFTBGFZJEBLJLBEB¿LBCJMJZPSEV4POZMMBSEBÐSFUJMFOFOI[M BTBOTËSMFSEFO¥JOEFLJNFUSFV[VOMVóVOEBLJ4JOBOHIBJ,VMFTJOEFLVSVMBOCJSBTBOTËSTBOJZFEFNFUSF¿LBCJMJ- ZPS\"TBOTËSCJOBOOFOBMULTNJMFFOÐTUOPLUBTOB ZBLMBõLN CJSEBLJLBEBOEBIBB[TÐSFEF¿LBCJMJZPS\"TBO- TËSÐONPUPSNFLBOJ[NBTOEBNBLBSBM¿FLNFTJTUFNJLVMMBOMZPS ,VMMBOMBONPUPSLJMPXBUUMLCJSHÐDFTBIJQ\"TBOTËSÐOBFSPEJOBNJLZBQT BMUOEBWFÐTUÐOEFCVMVOBOBMÐNJOZVN LBQMBNBMBSTBZFTJOEFZÐLTFLI[MBSBVMBõMEóOEBIBWBEJSFODJOJWFHÐSÐMUÐTÐOÐB[BMUZPS/PSNBMEFGSFOMFNFCJSEJTLJO BTBOTËSNFLBOJ[NBTOEVSEVSNBTZMBZBQMZPS\"ODBLTJTUFNBTBOTËSNPUPSVOVO¿PLI[MIBSFLFUFUUJóJOJQBSLFEFS- TFNFLBOJ[NBSBZMBSTLõUSBSBLNFUSFJ¿JOEFEVSNBTOTBóMZPS#VIBSFLFUTPOVDVOEBB¿óB¿LBDBLZÐLTFLT- DBLMóBLBSõEBGSFOEJTLMFSJFNJDJTFSBNJLJMFLBQMBONõ 35
'(1(<(5(.qi5(1(/m0 /&850/6/: \"4\"-/\"3&*8# ÷35#00/:65/5\")W\"F÷,3÷#&0,:&6555:\"\")4\"\"3-&,\"&35* Malzeme listesi *(5(./m0$/=(0(/(5 r ,BóUQF¿FUFSVMPTV Yumurta r ,BWBOP[ r :VNVSUB ,BóU r .FUBM5BCBL peçete rulosu r 4V Metal tabak ,BWBOP[ '(1(<m1$0$&, 'm..$7 &ZMFNTJ[MJL QSFOTJCJ PMBSBLUB CJMJOFO /FXUPOO * :VNVSUBOO EFOFZ EFOFNFMFSJ TSBTOEB LSMNB ZBTBTJMFJMHJMJHË[MFNZBQBCJMNFL SJTLJPMEVóVJ¿JOIBõMBONõZVNVSUBLVMMBOMBCJMJS '(1(<(+$=,5/,. r /FXUPOO*ZBTBT IBSFLFUJMFJMHJMJIBOHJLPOVZBBÀLMLHFUJSNJöUJS (ÑOMÑLIBZBUN[EBOÌSOFLMFSWF- SFSFLBÀLMBZO[ $FWBQ &ZMFNTJ[MJL QSFOTJCJ PMBSBL EB CJMJOFO /FXUPOO * ZBTBTOB HËSF DJTJNMFS Ð[FSMFSJOF VZHVMBOBO OFU LVWWFUTGSJTFIBSFLFUEVSVNMBSOLPSVSMBS\"OJGSFOZBQBOBSB¿UBLJZPMDVMBSOBSBDOËOUBSBGOBEPó- SV LBZNBMBS V¿BLUBLJ ZPMDVMBSO LBMLõ BOOEB LPMUVóB EPóSV JUJMJZPSNVõ HJCJ IJTTFUNFMFSJ ËSOFL PMB- SBLWFSJMFCJMJS IlLEYIlVEPROSEDpR r %Ð[CJSZÐ[FZÐ[FSJOEFLBWBOP[BTVEPMEVSVO r .FUBMUBCBóUBNPSUBTOBHFMFDFLõFLJMEFLBWBOP[VOÐTUÐOFZFSMFõUJSJO r 1F¿FUFLBóESVMPTVOVUBCBóOPSUBTOB SVMPÐTUÐOFEFZVNVSUBZõFLJMEFLJHJCJZFSMFõUJSJO r 4POPMBSBLNFUBMUBCBóBI[MDBWVSVO '(i(5/(1'm50(9(6218s r 5BCBôBI[MDBWVSEVôVOV[EBZVNVSUBOOIBSFLFUJJÀJOOBTMCJSHÌ[MFNZBQUO[ $FWBQ 5BCBóBI[MDBWVSVMEVóVOEBZVNVSUBLBWBOP[J¿FSJTJOEFLJTVZBEÐõFS r :VNVSUBOOLBWBOP[JÀJOFEÑöNFTJOJO/FXUPOO*IBSFLFUZBTBTJMFJMJöLJTJOFEJS \"ÀLMBZO[ $FWBQ :VNVSUB/FXUPOVO*)BSFLFU:BTBTFZMFNTJ[MJLQSFOTJCJHFSFóJCVMVOEVóVLPOVNVLPSVNBLJTUFNJõUJS #VZÐ[EFOUBCBLJMFCJSMJLUFIBSFLFUFUNFZJQ ZFS¿FLJNJLVWWFUJFULJTJZMFLBWBOP[BEÐõNÐõUÐS 36
/&850/6/)\"3&,&5:\"4\"-\"3* KARMA TEST - 1 4ÐSUÐONFTJ[ZBUBZWFFóJLEÐ[MFNMFSEFLJNLÐUMFMJ 4ÐSUÐONFTJ[ ZBUBZ EÐ[MFNEF N N WF N LÐUMF- DJTJNMFSôFLJM-* ôFLJM-**WFôFLJM-***EFLJHJCJTSB- MJDJTJNMFSFTOFNFZFOJQMFSJMFCBóMBOBSBLõFLJMEFLJ HJCJ'LVWWFUJJMF¿FLJMJZPS TZMB F1, F2 ve F3 LVWWFUMFSJJMF¿FLJMJZPS F3 m T1 2m T2 F 3m a F2 m ôFLJMm*** m m F1 ôFLJMm** NWFNLÑUMFMFSJBSBTOEBLJJQHFSJMNFTJ51 N ôFLJMm* WFNBSBTOEBLJJQHFSJMNF5 PMEVôVOBHÌSF 2 JQHFSJMNFMFSJPSBO5152LBÀUS $JTJNMFSLVWWFUMFSJMFBZOZÌOEFWFFöJUöJEEFU- 6 B) 5 $ 3 3 E) 1 A) 3 2 D) 3 MJJWNFMFSJMFI[MBOEôOBHÌSF ' ' WF' LVW- 12 3 5 5 WFUMFSJOCÑZÑLMÑLMFSJBSBTOEBLJJMJöLJOFEJS (g = 10 m/s2) \" '1 ='2 ='3 # '1 >'2 >'3 $ ' =' >' % ' >' >' 123 231 & '3 >'2 >'1 Sürtünmesiz yatay düzlemde m ve m kütleli ci- Sürtünmesiz yatay düzlemdeki m ve m kütleli ci- 12 12 TJNMFSFTOFNFZFOCJSJQJMFCBóMBOBSBLõFLJMEFLJHJ- TJN JQ ZBSENZMB CJSCJSJOF CBóMBOQ õFLJMEFLJ HJCJ CJ ' LVWWFUJ JMF ¿FLJMEJóJOEF JQUF PMVõBO HFSJMNF 5 TFSCFTUCSBLMZPS LBEBSPMVZPS m1 m1 T m2 F m2 F = 5 PMEVôVOB HÌSF DJTJNMFSJO LÑUMFMFSJOJO N1WFN2LÑUMFMFSJÌ[EFöPMEVôVOBHÌSF TJTUF- T3 NJOJWNFTJLBÀHEJS ( g =ZFS¿FLJNJJWNFTJ PSBON N LBÀUS 12 1 B) 3 $ 5 7 9 A) 1 B) 3 $ % 5 E) 3 A) 2 2 D) E) 2 2 2 2 2 2 D B 37 E A
KARMA TEST - 2 /&850/6/)\"3&,&5:\"4\"-\"3* ±[EFõN ve m LÐUMFMJTÐSUÐONFTJ[FóJLEÐ[MFN- N LÐUMFMJ CJS DJTJN õFLJM-*EFLJ FóJL EÐ[MFNEF \"# 12 MFSEFõFLJMEFLJHJCJTFSCFTUCSBLMZPS #$WF$%ZPMMBSOJ[MFZFSFL\"OPLUBTOEBO%OPL- UBTOBHFMJZPS m2 m1 Am h* 2a 37° 53° B ** h N1 WF N2 LÑUMFMJ DJTJNMFSJO JWNFMFSJ TSBTZMB a *** a WFB PMEVôVOBHÌSF B / a PSBOLBÀUS ôFLJMm* C D 12 12 (g = 10 m/s2 TJO=DPT= )[ CD DPT= sin53° = A) 5 $ 3 3 2 BC 2 4 D) E) # AB 2 5 * ** *** ôFLJMm** Zaman $JTNFBJUI[-[BNBOHSBGJôJõFLJM-**EFLJHJCJ PMEVôVOBHÌSF \"# #$WF$%BSBMLMBSOEBDJT- NF FULJ FEFO TÑSUÑONF LVWWFUMFSJ ' ' WF ' 12 3 BSBTOEBLJJMJöLJOFEJS \" ' >' >' # ' >' >' 123 132 &óJL EÐ[MFNJO , OPLUBTOEBO TFSCFTU CSBLMBO $ '1 ='2 ='3 % '3 >'2 >'1 m =LHMLLÐUMF-OPLUBTOBHFMJODF's =/PMBO & '3 >'2 ='1 TBCJUCJSTÐSUÐONFLVWWFUJFULJTJOEFLBMZPS 4ÐSUÐONFTJ[FóJLCJSEÐ[MFNEFNLÐUMFMJDJTJNõF- N LH LJMEFLJ'LVWWFUJZBSENZMBPLZËOÐOEFIBSFLFUFU- K NFLUFEJS /////////5///3///°////////f/s////=//// L N 8 M F = 15 N m yatay $JTNJO-.OPLUBMBSBSBTOEBLJIBSFLFUJJÀJOOF 37° TÌZMFOFCJMJS (g = 10 m/s2 TJO= DPT= $JTJNTBCJUI[MIBSFLFUFUUJôJOFHÌSF NLÑUMFTJ LBÀLHES A) .OPLUBTOEBEVSVS B) %Ð[HÐOI[MBOS (g = 10 N/kg , sin37° = 0,6; cos37° = 0,8) $ %Ð[HÐOZBWBõMBS D) 4BCJUI[MIBSFLFUFEFS \" # $ % & E) %Ð[HÐOZBWBõMBZQ.EFEVSVS C D 38 A B
/&850/6/)\"3&,&5:\"4\"-\"3* KARMA TEST - 3 ôFLJMEFLJTJTUFNNLÐUMFMJDJTJNWFLHMLDJTJNMFS- ôFLJMEFLJ TJTUFN TFSCFTU CSBLMEóOEB 5 JQ HFSJM- MFIBSFLFUTJ[LBMNBLUBES NFTJ/PMNBLUBES m //////////////////////////////////L///H////////////////////////////5///3///°/////// T 5ÑN ZÑ[FZMFSJO TÑSUÑONF LBUTBZT PMEV- m1 m2 ôVOB HÌSF N LÑUMFTJ NBLTJNVN LBÀ LJMPHSBN PMVS (g = 10 m/s2; sin53° = 0,8; sin37° = 0,6) N LÑUMFTJ LH PMEVôVOB HÌSF N LÑUMFTJ LBÀ 1 2 (g = 10 m/s2) LHPMVS \" C $ % & \" # $ % & 4 kg kütleli cisme etki eden statik sürtünme katsa- ZT LJOFUJLTÐSUÐONFLBUTBZT EJS F = 50 N ôFLJMEFLJTJTUFN'LVWWFUJFULJTJOEFZBUBZEPóSVMUV- 53° LH EBTBCJUI[MIBSFLFUFUNFLUFEJS F $JTJNöFLJMEFLJHJCJ'LVWWFUJJMFÀFLJMJZPSJTF * $JTNJOJWNFTJa = 7, 5 m/s2 EJS a yatay T ** 'LVWWFUJOJOZBUBZMBZBQUóB¿PMTBZEDJT- m1 m2 NJOJWNFTJBSUBS ZFS *** 'LVWWFUJZBSZBJOFSTFDJTJNIBSFLFUTJ[LBMS #VOBHÌSF ZBSHMBSOEBOIBOHJMFSJEPôSVEVS (g = 10 m/s2 TJO = DPT = TJO = * m1LÐUMFTJBSUSMSTB 5JQHFSJMNFTJBSUBS DPT= ** m2LÐUMFTJBSUSMSTB 5JQHFSJMNFTJEFóJõNF[ *** aB¿TB[BMUMSTB 5JQHFSJMNFTJBSUBS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # *WF** $ :BMO[** \" :BMO[* # *WF** $ *WF*** % *WF*** & :BMO[*** % :BMO[** & * **WF*** A D C B
KARMA TEST - 4 /&850/6/)\"3&,&5:\"4\"-\"3* Sürtünmesiz yatay düzlemde bulunan m ve m 4ÐSUÐONFTJ[ZBUBZEÐ[MFNEFLJË[EFõ, -WF.DJ- 12 LÐUMFMJ DJTJNMFS CJS JQMF õFLJMEFLJ HJCJ CJSCJSJOF CBó- TJNMFSJOFZBUBZ'LVWWFUJVZHVMBOEóOEBTJTUFNB JWNFTJJMFI[MBOZPS,WF-DJTJNMFSJBSBTOEBLJJQ MBONõUS HFSJMNFTJ5PMVZPS m1 LH m2 LH T F = 12 N T MF KL 4JTUFN'=/MVLLVWWFUJMFÀFLJMEJôJOEFDJ- :BUBZ EÑ[MFN TÑSUÑONFMJ PMTBZE TJTUFNJO JW- TJNMFS BSBTOEBLJ JQUF PMVöBO HFSJMNF LVWWFUJ NFTJBWFJQHFSJMNFLVWWFUJ5OBTMEFôJöJSEJ LBÀ/PMVS a T \" # $ % & A) Artar %FóJõNF[ B) Artar $ \"[BMS \"[BMS D) %FóJõNF[ %FóJõNF[ E) \"[BMS %FóJõNF[ Artar Sürtünmeli yatay düzlemde bulunan m ve m küt- 12 ôFLJMEFLJZBUBZEÐ[MFNEF'LVWWFUJZMF¿FLJMFOTJT- MFMJ DJTJNMFS CJS JQMF õFLJMEFLJ HJCJ CJSCJSJOF CBóMBO- tem 4 m/s2MJLJWNFZFTBIJQUJS NõUS m1 LH m2 LH m1 LH T F = 12 N F m2 LH $JTJNMFSJMFZBUBZEÑ[MFNBSBTOEBLJTÑSUÑONF 4JTUFNEFTÑSUÑONFMFSÌOFNTJ[PMEVôVOBHÌSF 'LVWWFUJLBÀ/EVS LBUTBZTL= JTFTJTUFN'=/MVLLVWWFU \" # $ % & JMFÀFLJMEJôJOEFDJTJNMFSBSBTOEBLJJQUFPMVöBO HFSJMNFLVWWFUJLBÀ/EVS (g = 10 m/s2) \" # $ % & D D 40 C B
/&850/6/)\"3&,&5:\"4\"-\"3* KARMA TEST - 5 LHLÐUMFMJË[EFõDJTJNMFSBóSMóËOFNTFONFZFO NLÐUMFMJË[EFõJLJDJTJNFTOFNFZFOCJSJQZBSENZ- NBLBSBMBS WF FTOFNFZFO JQ ZBSENZMB õFLJMEFLJ MBCJSCJSJOFCBóMBONõUS EÐ[FOFLLVSVMNVõUVS T LH m T m LH 4ÑSUÑONFTJ[TJTUFNTFSCFTUCSBLMEôOEBJQUF- :BUBZ EÑ[MFN WF NBLBSBMBS TÑSUÑONFTJ[ PMEV- LJHFSJMNFLVWWFUJ5LBÀ/EVS (g = 10 m/s2) ôVOB HÌSF TJTUFN TFSCFTU CSBLMEôOEB 5 JQ HFSJMNFTJLBÀNHPMVS (g = yerçekimi ivmesi) A) 1 B) 1 $ % 3 E) 2 4 2 2 \" # $ % & NLÐUMFMJË[EFõ,WF-DJTJNMFSJFTOFNFZFOCJSJQ ZBSENZMBCJSCJSJOFCBóMBONõUS m K T Lm m ve m2LÐUMFMJDJTJNMFSõFLJMEFLJHJCJ'LVWWFUJZBS- 1 ENZMB ¿FLJMEJóJOEF DJTJNMFS BSBTOEBLJ JQJO HFSJM- 4JTUFNTFSCFTUCSBLMEóOEBTJTUFNJOI[MBONBJW- NFTJB JQUFLJHFSJMNFLVWWFUJ5WFZBUBZEÐ[MFNEF- NFLVWWFUJ/PMVZPS LJTÐSUÐONFLVWWFUJG EJS m1 LH S T=4N :BMO[DB , DJTNJOJO LÑUMFTJ BSUSMBSBL BZO EF- OFZUFLSBSMBOSTB 5WFG OBTMEFôJöJS m2 LH F S a T GS 5ÑNZÑ[FZMFSTÑSUÑONFMJWFTÑSUÑONFLBUTBZT A) Artar \"[BMS Artar k = PMEVôVOBHÌSF 'LVWWFUJLBÀ/EVS B) Artar Artar Artar (g = 10 m/s2) C) Artar Artar %FóJõNF[ D) \"[BMS Artar %FóJõNF[ \" # $ % & E) \"[BMS Artar Artar B E 41 C E
KARMA TEST - 6 /&850/6/)\"3&,&5:\"4\"-\"3* ôFLJMEFLJTJTUFNEFZBMO[DBN ve m kütleleri ara- ôFLJMEFNLÐUMFMJDJTJNTBCJU'LVWWFUJFULJTJOEFDJ- 12 TTÐSUÐONFMJPMVQ TÐSUÐONFLBUTBZT EJS TJNTBCJUI[MIBSFLFUFEJZPS jTBCJU m1 LH F m2 LH F = 46 N ZFS 4JTUFNJO /MVL LVWWFU FULJTJOEF LBMEôOEB #VOBHÌSF LB[BOBDBôJWNFLBÀNT2PMVS (g = 10 N / kg) * $JTNJOUFNBTFUUJóJZÐ[FZJOBMBO LÐUMFTJTBCJU LBMNBLõBSUZMBBSUMSTBDJTJNZBWBõMBS \" # $ % & ** $JTNFFULJFEFOOFULVWWFUTGSES *** 'LVWWFUJJLJLBUOB¿LBSMSTBJWNFWFLUËSÐJMF DJTNJOIBSFLFUZËOÐBZOPMVS ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** ôFLJMEFLJDJTNF'LVWWFUJFULJFUUJóJOEFDJTJNIBSF- ôFLJMEFLJ N LÐUMFMJ DJTJN CÐZÐLMÐLMFSJ CJSCJSJOEFO LFUTJ[LBMZPS GBSLM '1 '2 WF '3 LVWWFUMFSJ FULJTJOEF IBSFLFUTJ[ LBMZPS F F3 F2 F1 #VOBHÌSF #VOBHÌSF * $JTNFFULJFEFOOFULVWWFUTGSES ** $JTNF FULJ FEFO TÐSUÐONF LVWWFUJ ' EFO CÐ- * 4ÐSUÐONFLVWWFUJ'1WF'2LVWWFUMFSJOJOCJMFõ- ZÐLUÐS LFTJOJOCÐZÐLMÐóÐLBEBSES *** $JTNJOLÐUMFTJB[BMUMSTBDJTJNIBSFLFUFEFS ** '3 LVWWFUJ B[BMUMSTB N LÐUMFMJ DJTJN IBSFLFU FEFS *** $JTNJOLÐUMFTJZBSZBJOFSTFDJTJNIBSFLFUFEFS ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS ZBSHMBSOEBOIBOHJMFSJkesinlikleEPôSVEVS \" :BMO[* # *WF** $ *WF*** \" :BMO[* # *WF** $ *WF*** % **WF*** & * **WF*** % **WF*** & * **WF*** C E 42 D A
/&850/6/)\"3&,&5:\"4\"-\"3* KARMA TEST - 7 4ÐSUÐONFTJ[ ZBUBZ CJS ZÐ[FZEF ÐTU ÐTUF ZFSMFõUJSJ- Sürtünmesiz yatay düzlemde 10 kg kütleli cisim len m =LH N2 =LHLÐUMFMJDJTJNMFSõFLJMEFHË- NTMJLI[MBJMFSMFNFLUFEJS F = 50 N 1 53° j = 8 m/s SÐMEÐóÐHJCJ'LVWWFUJJMFIBSFLFUFUUJSJMJZPS $JTNFöFLJMEFHÌTUFSJMFOLVWWFUTBOJZFCP- m1 LH ZVODBVZHVMBOEôOEBDJTNJOI[LBÀNTPMVS (sin53° = 0,8; cos 53° = 0,6, g = 10 m/s2) L \" # $ % & F m2 LH L $JTJNMFSJO BSBTOEBLJ TÑSUÑONF LBUTBZT k = PMEVôVOBHÌSF DJTJNMFSJOCJSMJLUFIBSF- LFUFUNFMFSJOJTBôMBZBOFOCÑZÑL'LVWWFUJLBÀ /EVS (g = 10 m/s2) \" # $ % & ,JOFUJLTÐSUÐONFLBUTBZT PMBO FóJLEÐ[MFNEF öMLI[TGSPMBOCJSDJTNFFULJZFOOFULVWWFUJO[B- m =LHLÐUMFMJDJTJN'LVWWFUJJMFõFLJMEFLJHJCJTB- NBOBCBóMEFóJõJNHSBGJóJõFLJMEFLJHJCJEJS CJUI[MB¿FLJMNFLUFEJS F(N) N LH F 2F 37° 0 2t 3t 5t t(s) m' \"ZO LVWWFU DJTJN ZVLBS ZÌOEF IBSFLFU FEFS- $JTNJO -U [BNBO BSBMôOEBLJ I[ EFôJöJNJ 4jPMEVôVOBHÌSF -U [BNBOBSBMôOEBLJI[ LFO UFST ZÌOEF VZHVMBOEôOEB DJTNJO JWNFTJ EFôJöJNJLBÀjPMVS LBÀNT2PMVS (g = 10 m/s2 TJO= DPT= \" # $ % & \" # $ % & D A 43 D C
KARMA TEST - 8 /&850/6/)\"3&,&5:\"4\"-\"3* ôFLJMEFLJ FóJL EÐ[MFN EÐ[FOFóJOEF * CËMÐN TÐS- ôFLJMEFLJ TJTUFNEF UÐN ZÐ[ZFZMFSEFLJ TÐSUÐONF UÐONFTJ[ ** CËMÐN JTF TÐSUÐONFMJEJS N LÐUMFMJ DJ- LBUTBZTTBCJUWF EJS TJN,OPLUBTOEBOTFSCFTUCSBLMEóOEB,-WF-. OPLUBMBSBSBTOEBBZOJWNFJMFIBSFLFUFEJZPS m1 LH T1 * m L 37° K //////////////////////////////// m2 LH T2 m3 LH ** M 53° #VOB HÌSF ** CÌMÑNEFLJ TÑSUÑONF LBUTBZT 4JTUFN TFSCFTU CSBLMEôOEB N2 WF N3 LÑUMF- LBÀUS TJOJO LB[BOBDBô JWNFOJO CÑZÑLMÑôÑ JMF 5 WF (sin53° = 0,8; sin37° = 0,6; g = 10 m/s2) 1 52 JQ HFSJMNFTJOJO CÑZÑLMÑôÑ BöBôEBLJMFSEFO IBOHJTJEJS (g = 10 N/kg) A) 1 B) 2 $ 3 5 3 aT T 3 3 4 D) E) 12 4 5 A) 2 4 16 B) 2 2 16 C) 2 2 14 D) 5 0 14 E) 1 5 12 ôFLJMEFLJBTBOTËSJ¿JOFNLÐUMFMJCJSTBSLB¿BTMNõ- ôFLJMEFLJ BSB¿ B JWNFTJ JMF I[MBOSLFO TÐSUÐONF- US \"TBOTËS EVSHVO JLFO JQUFLJ HFSJMNF LVWWFUJ 5 TJ[FóJLEÐ[MFNÐ[FSJOEFLJNLÐUMFTJIBSFLFUTJ[LBM- TBCJUJWNFJMFZVLBSI[MBOSLFO5EJS NBLUBES T j m m 37° #VOBHÌSF BTBOTÌSÑOJWNFTJ ZFSÀFLJNJJWNF- #VOBHÌSF BJWNFTJOJOHZFSÀFLJNJJWNFTJDJO- TJOJOLBÀLBUES TJOEFOEFôFSJOFEJS (sin37° = DPT= A) 1 # $ 3 D) 2 E) 5 3g 3g 4g D) g E) 2g 2 2 2 A) B) $ 4 55 A D 44 B E
/&850/6/)\"3&,&5:\"4\"-\"3* KARMA TEST - 9 ôFLJMEFLJEÐ[FOFLUFTÐSUÐONFMFSWFNBLBSBBóSM- ôFLJMEFLJ FóJL EÐ[MFNJO BMU VDVOEBLJ , OPLUBTO- óËOFNTFONFNFLUFEJS dan j0I[ZMBBUMBODJTJN-OPLUBTOBLBEBS¿LQ HFSJEËOÐZPS j0 ///4///Ð//S//U/Ð//O///N///F//M/J////// //////L m1 LH T K //////////////////// m2 LH m3 $JTNJOUFLSBS,OPLUBTOBHFMJODFZFLBEBSIB- SFLFUJCPZVODBI[-[BNBOHSBGJôJBöBôEBLJMFS- EFOIBOHJTJPMBCJMJS 4JTUFN TFSCFTU CSBLMEôOEB N LÑUMFMJ DJTJN A) j B) j 1 0 t0 t JMFN2LÑUMFMJDJTJNBSBTOEBLJ5JQHFSJMNFLVW- WFUJ / PMEVôVOB HÌSF TJTUFNJO JWNFTJ LBÀ NT2EJS (g = 10 N/kg) \" # $ % & C) j D) j 0 t0 t E) j t 0 NLÐUMFMJDJTJN TBóBEPóSVBJWNFTJZMFIBSFLFUFU- NFLUFPMBOBSB¿Ð[FSJOEFLBZNBEBOEVSBCJMNFLUF- EJS a=? m 37° \"SBCBZÑ[FZJJMFDJTJNBSBTOEBLJTÑSUÑONFLBU- %VSNBLUB PMBO CJS BTBOTËSEF EJOBNPNFUSFZMF ËM- TBZT L = JTF B JWNFTJOJO NJOJNVN EFôFSJ ¿ÐMFODJTNJOBóSMó/EVS LBÀNT2EJS \"TBOTÌSZVLBSÀLBSLFONT2MJLJWNFZMFZB- (sin37° = 0,6; cos37° = 0,8; g = 10 m/s2) WBöMBSTB EJOBNPNFUSFZMFÌMÀÑMFODJTNJOBôSM- ôLBÀ/PMVS (g = 10 N/kg) A) 20 B) 21 $ 23 D) 32 E) 35 11 11 11 11 11 \" # $ % & C A 45 D C
YAZILI SORULARI /&850/6/)\"3&,&5:\"4\"-\"3* LHMLCJSDJTJNBõBóEPóSVTBCJUI[MBIBSFLFU %VSNBLUB PMBO CJS BSBDO UBWBOOB N LÐUMFMJ DJTJN FUNFLUFEJS õFLJMEFLJHJCJBTMNõUS EÐõFZ ø øi mm FS m = 10 kg ôFLJMm* ôFLJMm** 0,8 F ZBUBZ \"SBÀBJWNFTJJMFIBSFLFUFHFÀUJôJOEFDJTJNöF- 37° LJM**EFLJLPOVNVBMZPSTBiBÀTN ù BWFHOJ- DFMJLMFSJOEFOIBOHJMFSJOFCBôMES 100 N 0,6 F F = ? jsabit TY 5Y =NH iT 5X =NB :Ñ[FZJOTÑSUÑONFLBUTBZT PMEVôVOBHÌSF VZHVMBOBO'LVWWFUJLBÀ/EVS m TX T . sin i = m .a (sin37° = DPT= H= 10 m/s2) T . cos i = m .g mg a $JTJNTBCJUI[MBHJUUJôJJÀJOIBSFLFUEPôSVMUVTVOEBLJOFULVW- tan i = g WFUJOTGSPMNBTHFSFLJS 0IBMEFiBÀTBWFHZFCBôMES 100 ='S+ ' 100 = ' L+ ' 100 = '+ ' '=/PMVS %ÐõFZLFTJUJWFSJMFOõFLJMEFLJTJTUFNEFCJSCJSJOFJQ- MFCBóM LÐUMFMFSJTSBTZMBLHWFLHPMBO9WF: DJTJNMFSJOF'LVWWFUJFULJFUNFLUFEJS F=? Sürtünmesiz yatay düzlemde m ve m kütleli ci- X mX = 3 kg 12 TJNMFSõFLJMEFLJHJCJÐTUÐTUFLPONVõUVS T 30 m1 = m F m2 = 4m $JTJNMFSJO CJSMJLUF IBSFLFU FEFCJMNFTJ JÀJO JLJ Y mY = 1 kg LÑUMF BSBTOEBLJ TÑSUÑONF LVWWFUJ FO B[ LBÀ ' 10 PMNBMES 5JQHFSJMNFTJ/JTF'LVWWFUJLBÀOFXUPOEVS (g = 10 m/s2) 4JTUFNJOJWNFTJ m F :DJTNJJÀJO 5ÑNTJTUFNJÀJO '=NB F = m. ' =NB G -5=N B F Fs Fs = m.a S 5m net a= F Yy -'= 5m F= 10-5 =B '= 20 N S5 a =NT2 100 N F 46 BWFH 20 N F = S5
/&850/6/)\"3&,&5:\"4\"-\"3* YAZILI SORULARI 4ÐSUÐONFMJCJSZBUBZZPMBNTMJLI[MBHJSFOLH NLÐUMFMJDJTJNIBSFLFUIBMJOEFLJCJSTJTUFNJ¿FSJTJO- MLDJTNFBJUI[-[BNBOHSBGJóJõFLJMEFLJHJCJEJS EFUBSUMNBLJTUFOJZPS j (m/s) m 8 t(s) j = 8 m/s m a 02 #VOBHÌSF DJTJNJMFZÑ[FZBSBTOEBLJTÑSUÑONF LBUTBZTLBÀUS (g = 10 m/s2) $JTNJOZBWBöMBNBJWNFTJ 4JTUFNZVLBSZÌOEFHMJLJWNFJMFZBWBöMBS- Tj 0 - 8 2 TBDJTJNCBTLÑMEFLJBôSMôLBÀNHPMVS a= = = - 4 m/s (g =ZFS¿FLJNJJWNFTJ Tt 2 ' =NB ' =L/ j a ' =NB net S N net 'S = =L NH- N =NB 'S = 8N 2 g k = PMVS NH- N =N 5 5 4 N = mg 5 mg NWFNLÐUMFMJ\" #DJTJNMFSJ'LVWWFUJZMFõFLJMEFLJ :BUBZ WF TÐSUÐONFTJ[ EÐ[MFNEF JML I[ TGS PMBO HJCJ¿FLJMNFLUFEJS CJSDJTNFFULJFEFOOFULVWWFUJO[BNBOBCBóMEF- óJõJNHSBGJóJõFLJMEFLJHJCJEJS 2m T1 m F 2m T2 m F F(N) 2F ôFLJMm* ôFLJMm** 0 5t t(s) 2t 3t õFLJM-* WF õFLJM-** EFLJ TJTUFNMFSJO JWNFMFSJ B1 WFB DJTJNMFSBSBTOEBLJJQHFSJMNFMFSJ5 WF5 m' 2 12 $JTJN -U [BNBOBSBMôOEBLJI[EFôJöJNJj JTF -U [BNBOBSBMôOEBLJI[EFôJöJNJLBÀj JTFJWNFMFSWFJQHFSJMNFMFSJBSBTOEBLJJMJöLJOF- EJS EJS õFLJM-*JÀJO õFLJM-**JÀJO ,VWWFU-[BNBOHSBGJôJ JWNF-[BNBOHSBGJôJOFCFO[FS÷WNF '=NB1 '=NB2 F F [BNBOHSBGJôJOJOBMUOEBLJBMBOI[EBLJEFôJöJNJWFSJS a= a= 4at j 4j a(m/s2) 1 3m 2 3m 4at - 2at j 2j a = a 5 =NB 2a 12 1 1 52 =NB2 4at 51 =52PMVS 0 3t 5t t(s) 2t –2at –a 2 a = a 51 52 47 4 2j k = mg 1 2 5 5
<(1m1(6m/6258/$5 /&850/6/)\"3&,&5:\"4\"-\"3* #JSËóSFODJEÐ[HÐOZÐ[FZMJCJSDJTNJEJOBNPNFUSF- .BHOF[ZVNGPTGBUUV[VPMBSBLCJMFOFOi.H3 104)2u ZFCBóMBZBSBLôFLJM-*EFLJHJCJIBMÐ[FSJOEF ôF- CJS¿PLTQPSEBMOEB TQPSDVMBSOTÐSUÐONFZJBSUSB- kil-**EFLJHJCJUBIUBZÐ[FZEF ôFLJM-***UFLJHJCJT- SBLUVUVONBZHпMFOEJSNFLJ¿JOLVMMBOMBOCJSLJN- MBUMNõ DBN NBTB Ð[FSJOEF ZBUBZ ¿FLFSFL DJTNJ ZBTBMES IBSFLFUFUUJSFDFLNJOJNVNLVWWFUMFSJEJOBNPNFU- SFZBSENZMBËM¿ÐZPS )BMÐ[FSJOEF ¿FLJMFODJTJN ôFLJM* #VOBHÌSF BöBôEBWFSJMFOHÑOMÑLIBZBUN[EB 5BIUBZÐ[FZEF LBSöMBöUôN[ ÌSOFLMFSEFO IBOHJTJOEF ZVLBS- ¿FLJMFODJTJN EBLJCJMHJJMFCFO[FSCJSIFEFGZPLUVS A) 4FSCFTUUSNBOõZBQBOEBóDMBSOFMMFSJOJQVE- ôFLJM** SBMBNBT *TMBLDBNNBTB B) #JTJLMFU [JODJSMFSJOJO QFSJZPEJL CBLNMBSEB ZBó- Ð[FSJOEF¿FLJMFO MBONBT DJTJN $ .FSNFSLBZHBONFSEJWFOCBTBNBLMBSOOV¿L- TNMBSOO[NQBSBMBONBT D)5FLOJL ¿J[JN LBMFNMFSJOJO UVUBDBL LTNMBSOO QÐSÐ[MÐQMBTUJLPMNBT E) ,BSZBóEóOEBBSB¿MBSOUFLFSMFSJOF[JODJSUBLM- NBT 0MJNQJLIBWV[NVTBCBLBMBSOEBTFSCFTUTJUJMEFZB- SõBO TQPSDVMBS IBWV[VO TPOVOB HFMEJLMFSJOEF IB- WV[EVWBSOBZBLMBõSLFOTPOTFSCFTULPMVBUULUBO TPOSBTVJ¿JOEFUBLMBBUBSBLBZBLMBSZMBEVWBSõF- LJMEFLJHJCJJUNFLUFEJS ôFLJM*** #VOBHÌSF #VOBHÌSF ²ôSFODJ ZBQUôCVEFOFZEFBöBô- * 4QPSDVTVEBZÐ[FSLFOTQPSDVZBTVZVOWFIB- EBLJTPSVMBSEBOIBOHJTJOFDFWBQBSBEôTÌZMF- WBOOTÐSUÐONFLVWWFUJFULJFEFS OFCJMJS ** 4QPSDVOVOEVWBSBVZHVMBEóLVWWFUJMFEVWB- A) 4ÐSUÐONFLVWWFUJDJTJNMFSJOBóSMóOBCBóMN- SOTQPSDVZBVZHVMBEóLVWWFUFULJ-tepki kuv- ES WFU¿JGUJEJS B) 4ÐSUÐONFLVWWFUJDJTJNMFSJOUFNBTZÐ[FZBMBO- *** 4QPSDVOVOBóSMóJMFTVZVOTQPSDVZBVZHVMB- OBCBóMNES EóLBMESNBLVWWFUJFULJ-UFQLJLVWWFU¿JGUJEJS $ Sürtünme kuvveti temas edilen yüzeylerin cinsi- ZBSHMBSOEBOIBOHJMFSJEPôSVEVS OFCBóMNES \" :BMO[* # :BMO[** $ *WF** D) Sürtünme kuvveti cisme etki eden net kuvvete CBóMNES % *WF*** & * **WF*** E) 4ÐSUÐONFLVWWFUJZFS¿FLJNJJWNFTJOFCBóMN- ES C 48 B C
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