BUKU FISIKA KELAS XI

42 Mudah dan Aktif Belajar Fisika untuk Kelas XI Tugas Anda 2.4 Diskusikan bersama teman sekelas Anda. Jika Anda menimbang berat badan, sebenarnya angka yang ditunjukkan oleh timbangan adalah massa badan atau gaya berat badan? Tantangan untuk Anda Anda telah belajar tentang hubungan gaya gravitasi dan massa sebuah planet. Sekarang, hitunglah berapa nilai percepatan gravitasi (g) pada setiap planet di dalam tata surya ini. Kemudian, apakah Anda dapat menduga hubungan antara nilai percepatan gravitasi dan jarijari planet-planet tersebut? :P¥OL]L¥VLY YTWLT 2 , [LOL ;BMN>I>>J ")T).#& [P¥]LXLLY "$# OL[L^ OT^_WT]VLY XPYULOT )] 7 " , , .? =C "$$# HP[P¥^T ^PWLS OTVP^LS_T [LOL [PXMLSL]LY ]PMPW_XYcL& RLcL ]PY^¥T[P^LW ]P^L¥L OPYRLY RLcL R¥L`T^L]T ]PSTYRRL )R¥L`T^L]T 7 )]PY^¥T[P^LW * , ,? C 7 " , , .? =C = 7 , . *, " ",f,3# BP^P¥LYRLY4 = 7 VZY]^LY^L [LOL ?_V_X @@@ BP[WP¥ * 7 VZY]^LY^L R¥L`T^L]T _YT`P¥]LW "DX, )VR, # , 7 XL]]L CL^LSL¥T "VR# HPVL¥LYR& 9YOL ^PY^_ ]_OLS OL[L^ XPYRST^_YR YTWLT VZY]^LY^L ^P¥]PM_^( IP¥YcL^L& ^TOLV ]_WT^ _Y^_V XPY_¥_YVLY [P¥]LXLLY ^P¥]PM_^( 4. Kelajuan Orbit Satelit 9OL O_L XLNLX ]L^PWT^ cLYR OTVPYLW& cLT^_ ]L^PWT^ LWLXT OLY ]L^PWT^ M_L^LY( HL^PWT^ LWLXT& XT]LWYcL :_WLY& ]POLYRVLY ]L^PWT^ M_L^LY& XT]LWYcL ]L^PWT^ (IB>AC7C! -;?4FD! OLY ,;63D( HL^PWT^ M_L^LY cLYR [P¥^LXL MP¥SL]TW XPYRZ¥MT^ :_XT LOLWLS ]L^PWT^ 1BFE@;= +& OTW_YN_¥VLY ZWPS JYT HZ`cP^ [LOL . EV^ZMP¥ +3/1( HL^PWT^ TYT XPYRPWTWTYRT :_XT OLWLX aLV^_ +&/ ULX OPYRLY VPWLU_LY ,(22* VX)ULX( @YOZYP]TL XPXTWTVT ]L^PWT^ VZX_YTVL]T [P¥^LXL MP¥YLXL /3>3B3( HL^PWT^ ^P¥]PM_^ OTR_YLVLY _Y^_V XPXMP¥T [PWLcLYLY VZX_YTVL]T& ¥LOTZ& OLY ^PWP`T]T VP[LOL ]PMLRTLY MP]L¥ [PYO_O_V @YOZYP]TL( :LSVLY& MPMP¥L[L YPRL¥L ^P^LYRRL XPYcPaLYcL _Y^_V VP[P¥W_LY cLYR ]LXL( H_XMP¥ PYP¥RT _Y^_V XPYRZ[P¥L]TVLY ]L^PWT^ LOLWLS ML^P¥LT ]PW CL^LSL¥T& cLT^_ ]PW ]TWTVZY cLYR XPYR_MLS ]TYL¥ CL^LSL¥T XPYULOT PYP¥RT WT]^¥TV( H_XMP¥ PYP¥RT WLTY cLYR OTR_YLVLY LOLWLS RPYP¥L^Z¥ cLYR WLYR]_YR XPYRSL]TWVLY PYP¥RT WT]^¥TV OL¥T ^PYLRL L^ZX ]PSTYRRL ]L^PWT^ OL[L^ MP¥RP¥LV [LOL Z¥MT^YcL XPYRPWTWTYRT :_XT OPYRLY VPWLU_LY ^P^L[( >LcL R¥L`T^L]T :_XT MP¥Q_YR]T ]PMLRLT RLcL ]PY^¥T[P^LW ]PSTYRRL ]L^PWT^ ^P^L[ MP¥LOL [LOL Z¥MT^YcL _Y^_V XPYRPWTWTYRT :_XT( ATVL XL]]L ]L^PWT^ ? MP¥RP¥LV OPYRLY VPWLU_LY G OLWLX Z¥MT^ WTYRVL¥LY MP¥UL¥T'UL¥T C XLVL LVLY OT[P¥ZWPS [P¥]LXLLY MP¥TV_^ TYT( , , G ,? ? * C C # ]PSTYRRL VPWLU_LY ]L^PWT^ LRL¥ ^P^L[ MP¥LOL [LOL Z¥MT^YcL LOLWLS *, G C # ",f-*# BP^P¥LYRLY4 , 7 XL]]L :_XT "VR# C 7 UL¥T'UL¥T Z¥MT^ ]L^PWT^ "X# * 7 VZY]^LY^L R¥L`T^L]T _YT`P¥]LW "DX, )VR, #

Gaya 43 FLOL VPWLU_LY MP¥L[LVLS ]L^PWT^ M_L^LY SL¥_] XPYRZ¥MT^ :_XT [LOL VP^TYRRTLY + , 0 OL¥T [P¥X_VLLY :_XT& UTVL OTVP^LS_T XL]]L :_XT /&31 g +*,. VR OLY UL¥T'UL¥TYcL 0&-1 g +*0 X8 8>R>?0 <TVP^LS_T4 AL¥LV ]L^PWT^ OL¥T [P¥X_VLLY :_XT 7 + , 0( <PYRLY OPXTVTLY& UL¥LV ]L^PWT^ VP [_]L^ :_XT LOLWLS C 7 + + , 0( * 7 0&01 g +*f++ DX, )VR, , 7 /&31 g +*,. VR 0 $ 0&-1 g +*0 X OPYRLY XPXL]_VVLY YTWLT *& ,& OLY 0 XLVL G 7 - , *, *, C 0 # 7 ,. ++,, 0 /&31g+* VR "0&01 +* DX ) VR # - "0&-1g+* X# , $ 0 2 & 4 6 4 6 1 3 7 0(.//&/1 X)]& OTM_WL^VLY XPYULOT 0(./0 X)] ALOT& ]L^PWT^ SL¥_] XPYRZ¥MT^ OPYRLY VPNP[L^LY 0(./0 X)]( Contoh 2.11 Tantangan untuk Anda Geosynchronous satellite adalah istilah untuk satelit Bumi yang mengorbit pada daerah yang sama di ekuator Bumi. Dengan menggunakan pemahaman Anda, dapatkah Anda menduga bagaimana caranya satelit tersebut selalu mengorbit di tempat yang sama? Mengapa orbitnya harus berada di ekuator? 5. Periode Satelit pada Orbitnya (Materi Pengayaan) 9[LVLS 9YOL XL]TS TYRL^ ?_V_X @@@ BP[WP¥8 BP[WP¥ XPYcL^LVLY MLSaL V_LO¥L^ [P¥TZOP ¥P`ZW_]T [WLYP^ ^P¥SLOL[ CL^LSL¥T ]PMLYOTYR OPYRLY [LYRVL^ ^TRL UL¥LV [WLYP^ ^P¥]PM_^ OL¥T CL^LSL¥T( BZY]P[ ^P¥]PM_^ OL[L^ OT^P¥L[VLY U_RL _Y^_V ]L^PWT^( ALOT& 9YOL OL[L^ XPYPY^_VLY [P¥TZOP ]PM_LS ]L^PWT^ OPYRLY [P¥]LXLLY MP¥TV_^( , - 2 C 7 = 2, 7 =C- ",f-+# EWPS VL¥PYL = 7 - . *, " XLVL 2, 7 - . *, " C - ",f-,# BP^P¥LYRLY4 2 7 [P¥TZOP Z¥MT^ ]L^PWT^ "]# * 7 VZY]^LY^L R¥L`T^L]T "DX, )VR, # , 7 XL]]L :_XT "VR# C 7 UL¥LV ]L^PWT^ VP [_]L^ :_XT "X# FP¥TZOP CP¥V_¥T_] XPYRPWTWTYRT CL^LSL¥T LOLWLS 22 SL¥T& ]POLYRVLY [P¥TZOP :_XT XPYRPWTWTYRT CL^LSL¥T LOLWLS -0/ SL¥T( ATVL UL¥LV :_XT VP CL^LSL¥T LOLWLS +&/ g +*++ X& ^PY^_VLYWLS UL¥LV CP¥V_¥T_] VP CL^LSL¥T( 8>R>?0 <TVP^LS_T4 2: 7 -0/ SL¥T5 2C 7 22 SL¥T5 C :C 7 +&/ g +*++ X Contoh 2.12

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Gaya 45 GQXMUZ YQYUXUWU ^URM_ QXM^_U^$ NQZPM ¥MPM_ V`SM YQYUXUWU ^URM_ ¥XM^_U^$ cMU_` WQ_UWM SMcM cMZS NQWQ]VM ¥MPM NQZPM PU_UMPMWMZ YMWM NQZPM _UPMW PM¥M_ WQYNMXU WQ NQZ_`W ^QY`XM& GURM_ ¥XM^_U^ _UYN`X VUWM SMcM cMZS PUNQ]UWMZ YQXQNUTU NM_M^ QXM^_U^U_M^ NQZPM& 8QNQ]M¥M O[Z_[T NQZPM cMZS YQYUXUWU ^URM_ ¥XM^_U^ cMZS O`W`¥ NQ^M]$ MZ_M]M XMUZ _MZMT XQY¥`ZS PMZ ¥XM^_U^UZ& AQP`M ^URM_ QXM^_U^ PMZ ¥XM^_U^ _Q]^QN`_ PUYUXUWU [XQT ^Q_UM¥ NQZPM ¥MPM_& 7WMZ _Q_M¥U$ WMPM] WQP`M ^URM_ _Q]^QN`_ `Z_`W ^Q_UM¥ NQZPM NQ]NQPM%NQPM& AM]Q_ YQYUXUWU ^URM_ ¥XM^_U^ cMZS ^MZSM_ ]QZPMT PMZ ^URM_ QXM^_U^ cMZS ^MZSM_ _UZSSU& DXQT WM]QZM U_`$ WM]Q_ ^MZSM_ O[O[W PUS`ZMWMZ ^QNMSMU NMTMZ ¥QYN`M_ NMZ WQZPM]MMZ& 1. Tegangan dan Regangan IZ_`W XQNUT YQYMTMYU QXM^_U^U_M^ ^`M_` NQZPM$ ¥Q]TM_UWMZ 3>H?>K &#%+ !>"& EMPM SMYNM] _Q]^QN`_ _Q]XUTM_ ^Q`_M^ WM]Q_ cMZS YQYUXUWU ¥MZVMZS Y`XM%Y`XM ( & AM]Q_ _Q]^QN`_ PU_M]UW PQZSMZ SMcM ^QNQ^M] ,) ^QTUZSSM WM]Q_ YQZSMXMYU ¥Q]_MYNMTMZ ¥MZVMZS ^QNQ^M] " 1 $ AQ_UWM _M]UWMZZcM PUXQ¥M^$ WM]Q_ WQYNMXU WQ ¥MZVMZS ^QY`XM& ?ZU NQ]M]_U$ WM]Q_ YM^UT NQ]MPM PMXMY PMQ]MT QXM^_U^U_M^ZcM& AQY`PUMZ$ NQ^M] SMcM _M]UWMZ ¥MPM WM]Q_ PU¥Q]NQ^M] YQZVMPU ,* PMZ WM]Q_ YQZSMXMYU ¥Q]_MYNMTMZ ¥MZVMZS ^QNQ^M] " 2 & AQ_UWM SMcM _M]UWMZ PUXQ¥M^$ _Q]ZcM_M WM]Q_ WQYNMXU WQ ¥MZVMZS ^QY`XM& ?ZU NQ]M]_U$ WM]Q_ _Q]^QN`_ NQ]MPM PMXMY PMQ]MT QXM^_U^& GQ_UM¥ NQZPM YQYUXUWU NM_M^ QXM^_U^U_M^ _Q]_QZ_`$ VUWM SMcM cMZS PUNQ]UWMZ ¥MPM NQZPM YQXQbM_U NM_M^ QXM^_U^U_M^ZcM$ NQZPM _Q]^QN`_ MWMZ YQZSMXMYU ¥Q]`NMTMZ NQZ_`W !PQR[]YM^U"& @UWM NQ^M] SMcM _M]UWMZ ¥MPM WM]Q_ UZU PU¥Q]NQ^M] XMSU YQZVMPU ,+ YMWM WM]Q_ MWMZ ¥`_`^& ?ZU NQ]M]_U$ SMcM _M]UWMZ ¥MPM WM]Q_ _QXMT YQZOM¥MU _U_UW ¥`_`^ZcM& IZ_`W XQNUT VQXM^ZcM$ ^UXMTWMZ 7ZPM `XMZSU XMSU YQYNMOM UX`^_]M^U UZU ^MYNUX YQXUTM_ 3>H?>K &#%+!?"& :MXMY ¥QYNMTM^MZ YQZSQZMU QXM^_U^U_M^$ 7ZPM MWMZ YQZQY`WMZ ¥QZSQ]_UMZ GHF;GG !_QSMZSMZ" PMZ GHF7?C !]QSMZSMZ"& =McM cMZS NQWQ]VM ¥Q] ^M_`MZ X`M^ ¥QZMY¥MZS PU^QN`_ _QSMZSMZ& GQOM]M YM_QYM_U^$ _QSMZSMZ PM¥M_ PU_`XU^ ^QNMSMU NQ]UW`_& ) & # F !*g++" AQ_Q]MZSMZ2 & 4 _QSMZSMZ M_M` ^_]Q^^ !C'Y* " , 4 NQ^M] SMcM _M]UW !C" ) 4 X`M^ ¥QZMY¥MZS !Y* " EQ]NMZPUZSMZ MZ_M]M ¥Q]_MYNMTMZ ¥MZVMZS PMZ ¥MZVMZS Y`XM%Y`XM PU^QN`_ GHF7?C M_M` ]QSMZSMZ& GQOM]M YM_QYM_U^$ PM¥M_ PU_`XU^ ^QNMSMU NQ]UW`_& * " # ( !*g+," AQ_Q]MZSMZ2 * 4 ]QSMZSMZ'GHF7?C " ( ¥Q]_MYNMTMZ ¥MZVMZS !Y" ( 4 ¥MZVMZS MbMX !Y" F (N) " (m) batas elastisitas titik putus pertambahan panjang gaya tarik F1 F2 F3 !N" daerah elastis !M" Gambar 2.17 (a) Besar gaya tarik F menyebabkan karet bertambah panjang. (b) Grafik F – seutas karet yang ditarik dengan besar gaya F. 0 F " karet ditarik karet karet

46 Mudah dan Aktif Belajar Fisika untuk Kelas XI 2. Modulus Elastisitas =MZ_`ZSXMT ^QN`MT WM]Q_ NMZ ^Q¥MZVMZS .( OY PMZ ^Q¥[_[ZS WMbM_ PQZSMZ ¥MZVMZS cMZS ^MYM& AQY`PUMZ$ NQ]UXMT NQNMZ NQ]YM^^M *(( S ¥MPM ^Q_UM¥ NQZPM _Q]^QN`_& 7¥M cMZS PM¥M_ 7ZPM MYM_U PM]U MW_UaU_M^ _Q]^QN`_6 EQ]_MYNMTMZ ¥MZVMZS cMZS PUMXMYU WM]Q_ NMZ PMZ WMbM_ _Q]ZcM_M NQ]NQPM& EQ]NQPMMZ _Q]^QN`_ PU^QNMNWMZ [XQT ¥Q]NQPMMZ Y[P`X`^ QXM^_U^U_M^ M_M` B[P`X`^ J[`ZS cMZS PUYUXUWU WQP`M NQZPM _Q]^QN`_& GQOM]M YM_QYM_U^$ Y[P`X`^ QXM^_U^U_M^ MPMXMT ¥Q]NMZPUZSMZ MZ_M]M _QSMZSMZ PMZ ]QSMZSMZ cMZS PUYUXUWU NQZPM& 6 & * # !*g+-" :QZSMZ YQXMW`WMZ ^`N^_U_`^U 9AKL>H>>I !&Q''" PMZ 9AKL>H>>I !&Q'(" WQ 9AKL>H>>I !&Q')" YMWM PUPM¥M_WMZ ¥Q]^MYMMZ2 # " , D 6 ) !*g+." AQ_Q]MZSMZ2 6 4 Y[P`X`^ QXM^_U^U_M^ M_M` Y[P`X`^ J[`ZS !C'Y* "& 3. Hukum Hooke @UWM ^QN`MT ¥QSM^ PUNQ]U SMZSS`MZ ^QTUZSSM ¥QSM^ YQ]QZSSMZS !NQ]M]_U ¥QSM^ PU_M]UW" M_M` YQ]M¥M_ !NQ]M]_U ¥QSM^ PU_QWMZ"$ ¥MPM ¥QSM^ MWMZ NQWQ]VM SMcM ¥QY`XUT cMZS M]MTZcM ^QXMX` YQZ`V` _U_UW M^MX& :QZSMZ WM_M XMUZ$ NQ^M] SMcM ¥QY`XUT ¥MPM ¥QSM^ UZU ^QNMZPUZS PQZSMZ SMZSS`MZ M_M` ^UY¥MZSMZ cMZS PUNQ]UWMZ ¥MPM ¥QSM^& EQ]ZcM_MMZ _Q]^QN`_ PUWQZMX PQZSMZ >`W`Y >[[WQ& GQOM]M YM_QYM_U^$ >`W`Y >[[WQ PU_`XU^ ^QNMSMU NQ]UW`_& , 4 @ " M_M` , 4 @ "x !*g+/" AQ_Q]MZSMZ2 , 4 8Q^M] SMcM ¥QY`XUT ¥QSM^ !C" @ 4 A[Z^_MZ_M ¥QSM^ !C'Y" " 4 "x 4 ^UY¥MZSMZ ¥MPM ¥QSM^ !Y" IZ_`W XQNUT YQYMTMYU NQ^M] W[Z^_MZ_M QXM^_U^U_M^ ¥QSM^ @$ XMW`WMZ% XMT WQSUM_MZ NQ]UW`_ UZU& Aktivitas Fisika 2.2 Hukum Hooke Tujuan Percobaan Menentukan konstanta elastisitas pegas Alat-Alat Percobaan 1. Pegas 2. Statif 3. Penggaris 4. Ember kecil 5. Koin kecil bermassa 50 g sebanyak 10 buah 6. Neraca Ohaus Langkah-Langkah Percobaan 1. Susunlah batang statif dan pegas seperti terlihat pada gambar. 2. Ukurlah panjang mula-mula pegas tersebut. 3. Timbanglah berat ember dengan neraca Ohaus. 4. Gantunglah ember kecil dan sebuah koin bermassa 50 g. 5. Catatlah panjang pegas tersebut pada tabel data pengamatan. 6. Ulangi langkah pada poin ke-3 dengan 2 keping koin, 3 keping koin, dan seterusnya sampai 10 keping koin.

Gaya 47 GQ`_M^ WMbM_ ¥MZVMZSZcM -( OY PMZ X`M^ ¥QZMY¥MZSZcM * OY* & GQN`MT SMcM -( C NQWQ]VM ¥MPM WMbM_ _Q]^QN`_ ^QTUZSSM WMbM_ NQ]_MYNMT ¥MZVMZS YQZVMPU -($0 OY& >U_`ZSXMT2 M& ]QSMZSMZ !GHF7?C" WMbM_3 N& _QSMZSMZ !GHF;GG" WMbM_3 PMZ O& Y[P`X`^ QXM^_U^U_M^ WMbM_& 5>O>?. :UWQ_MT`U2 ( -( OY 4 ($- Y " 4 ($0 OY 4 0 h )(g+ Y , 4 -( C 7 4 * OY* 4 * h )(g, Y* M& FQSMZSMZ2 * # # # " ## # + * ) ( 0h)( Y )$.h)( -h)( Y N& HQSMZSMZ2 & # # # % , * -( C * )( Y , ) 4 *$- h )(- C'Y* O& B[P`X`^ QXM^_U^U_M^2 & * # # # * * * *$-h)( C'Y )$.h)( 6 4 )$. h)(/ C'Y* @MPU$ NQ^M] ]QSMZSMZ$ _QSMZSMZ$ PMZ Y[P`X`^ QXM^_U^U_M^ NM_MZS _Q]^QN`_ NQ]_`]`_%_`]`_ MPMXMT )$. h )(g* 3 *$ - h )(- C'Y* 3 PMZ )$. h)(/ C'Y* & Contoh 2.13 7. Ulangi langkah pada poin ke-4 untuk setiap penambahan koin. 8. Dari data tersebut, buatlah grafik plot dan grafik garis lurus F –"x. 9. Hitunglah nilai konstanta pegas k dari grafik tersebut. 4. Susunan Beberapa Pegas HMT`WMT 7ZPM NQNQ]M¥M ¥QZSS`ZMMZ ¥QSM^ PMXMY WQTUP`¥MZ ^QTM]U% TM]U6 7XM_%MXM_ cMZS 7ZPM S`ZMWMZ$ Y`XMU PM]U MXM_ ^QPQ]TMZM ^MY¥MU MXM_ cMZS YQZSS`ZMWMZ _QWZ[X[SU Y[PQ]Z NMZcMW YQZSS`ZMWMZ ¥QSM^& @UWM 7ZPM YQZSS`ZMWMZ N[X¥[UZ YQWMZUW$ 7ZPM MWMZ YQZQY`WMZ ¥QSM^ PU PMXMYZcM& EQSM^ PMXMY N[X¥[UZ YQWMZUW NQ]R`ZS^U `Z_`W YQZSM_`] WQX`M] YM^`WZcM YM_M N[X¥[UZ& :MXMY NUPMZS [_[Y[_UR$ ¥QSM^ ¥`Z NMZcMW PUS`ZMWMZ& 7ZPM MWMZ YQZQY`WMZ ¥QSM^ ¥MPM ^Q¥QPM Y[_[] M_M`¥`Z Y[NUX& EQSM^ ¥MPM ^Q¥QPM Y[_[] PMZ Y[NUX PUWQZMX PQZSMZ ZMYM G>D9@8F;7@;F& HMT`WMT 7ZPM R`ZS^U G>D9@8F;7@;F ¥MPM ^Q¥QPM Y[_[] M_M` Y[NUX6 EQ]TM_UWMZXMT 3>H?>K &#%,# !M" !N" Sumber:Dokumentasi Penerbit Gambar 2.18 (a) Sepeda motor yang menggunakan monoshockbreaker (b) Sepeda motor yang menggunakan double shockbreaker

48 Mudah dan Aktif Belajar Fisika untuk Kelas XI F k1 k2 k1 k2 4>D9@8F;7@;F ¥MPM ^Q¥QPM Y[_[] MPM cMZS YQZSS`ZMWMZ ^U^_QY BDCDG>D9@8F;7@;F PMZ :DI8A; G>D9@8F;7@;F& BQZ`]`_ 7ZPM$ ^U^_QY YMZMWMT cMZS PM¥M_ YQYNQ]UWMZ WQZcMYMZMZ NMSU ¥QZSQZPM]M ^Q¥QPM Y[_[]$ ^U^_QY BDCDG>D9@8F;7@;F M_M` :DI8A; G>D9@8F;7@;F6 7PMWMT T`N`ZSMZZcM PQZSMZ SMcM cMZS NQWQ]VM ¥MPM ^Q_UM¥ G>D9@8F;7@;F _Q]^QN`_6 GQ¥QPM Y[_[] cMZS YQZSS`ZMWMZ ^U^_QY BDCDG>D9@8F;7@;F PM¥M_ PUMZMX[SUWMZ PQZSMZ ^U^_QY ^M_` ¥QSM^ PMZ ^M_` NQNMZ$ ^QPMZSWMZ ^U^_QY :DI8A; G>D9@8F;7@;F PM¥M_ PUMZMX[SUWMZ PQZSMZ ^U^_QY P`M ¥QSM^ cMZS PU^`^`Z ^QOM]M ¥M]MXQX PQZSMZ ^M_` NQNMZ& 8MSMUYMZMWMT ¥Q]TU_`ZSMZ SMcM PMZ W[Z^_MZ_M ¥QSM^ ¥MPM WQP`M ^U^_QY ¥QSM^ _Q]^QN`_6 8Q]UW`_ UZU MWMZ PUNMTM^ _QZ_MZS ^U^_QY ¥QSM^ cMZS PU^`^`Z ^QOM]M ^Q]U$ ¥M]MXQX$ PMZ ^Q]U%¥M]MXQX& a. Pegas Disusun secara Seri EQ]TM_UWMZ 3>H?>K &#%-& :`M N`MT ¥QSM^ PU^`^`Z ^QOM]M ^Q]U PMZ ^Q_UM¥ ¥QSM^ YQYUXUWU W[Z^_MZ_M ¥QSM^ @) PMZ @* & @UWM ¥MPM `V`ZS ¥QSM^ cMZS PU^`^`Z ^Q]U _Q]^QN`_ PUNQ]U SMcM !$ WQP`M ¥QSM^ _Q]^QN`_ MWMZ YQZQ]UYM SMcM cMZS ^MYM$ cMU_` 2& :M]U ¥QSM^ ) PMZ ¥QSM^ *$ MWMZ PU¥Q][XQT ¥Q]^MYMMZ , @L @L # )) ** " # " EQ]_MYNMTMZ ¥MZVMZS ¥QSM^ _[_MX "x ^MYM PQZSMZ 1 "x # 2 "x ^QTUZSSM ¥MPM ¥QSM^ cMZS PU^`^`Z ^Q]U NQ]XMW`2 # " ) * " " ^ , L L @ # " ^)* ,,, @@@ ^)* ))) @@@ # " ) * ^ ) * @ @ @ @ @ # " !*g+0" AQ_Q]MZSMZ2 @^ MPMXMT W[Z^_MZ_M ¥QSM^ `Z_`W ¥QSM^ cMZS PU^`^`Z ^Q]U& b. Pegas Disusun secara Paralel :`M N`MT ¥QSM^ PU^`^`Z ^QOM]M ¥M]MXQX ^Q¥Q]_U ¥MPM 3>H?>K &#&$$ ^Q_UM¥ ¥QSM^ YQYUXUWU W[Z^_MZ_M @ % PMZ @ & & @UWM ¥MPM `V`ZS ¥QSM^ cMZS _Q]^`^`Z ^QOM]M ¥M]MXQX _Q]^QN`_ PUNQ]UWMZ SMcM ,$ NQ^M] SMcM , PUNMSU YQZVMPU P`M ¥MPM WQP`M ¥QSM^ _Q]^QN`_$ YU^MXZcM ,% PMZ ,& & ) )) ) F # @L @ L " # " * ** * F # @L @ L " # " EMPM ¥QSM^ cMZS PU^`^`Z ¥M]MXQX NQ]XMW`2 , 4 ,) # ,* E E ) ** @L @L@L " # " " " EQ]_MYNMTMZ ¥MZVMZS ¥QSM^ _[_MX ^MYM PQZSMZ ¥Q]_MYNMTMZ ¥MZVMZS ^Q_UM¥ ¥QSM^$ M_M` 1 "x 4 2 "x 4 p "x ^QTUZSSM ¥Q]^MYMMZ W[Z^_MZ_M ¥QSM^ ¥M]MXQX YQZVMPU @E 4 @) # @* !*g+1" Gambar 2.19 Pegas disusun seri. Gambar 2.20 Pegas disusun paralel. k2 k1 F2 F1 F

Gaya 49 :QZSMZ PQYUWUMZ$ ¥MPM ^Q¥QPM Y[_[] cMZS YQZSS`ZMWMZ ^U^_QY :DI8A; G>D9@8F;7@;F _Q]VMPU ¥QYNMSUMZ SMcM [XQT WQP`M G>D9@8F;7@;F$ ^QPMZSWMZ ¥MPM ^U^_QY BDCDG>D9@8F;7@;F SMcM TMZcM NQWQ]VM ¥MPM ^M_` G>D9@8F;7@;F& HUSM N`MT ¥QSM^ PU^`^`Z ^Q]U$ ^Q_UM¥ ¥QSM^ YQYUXUWU W[Z^_MZ_M ¥QSM^ ^QNQ^M] )&*(( C'Y$ .(( C'Y$ PMZ ,(( C'Y& AQ_USM ¥QSM^ _Q]^QN`_ PUNQ]U SMcM ^QNQ^M] ,( C& 8Q]M¥MWMT @ _[_MX ¥QSM^%¥QSM^ _Q]^QN`_6 5>O>?. :UWQ_MT`U2 @ ) ( )&*(( C'Y3 @ * ( .(( C'Y3 @ + ( ,(( C'Y& )*+ ) ))) HDH7A @ @@@ #"" ) )) # # )&*(( .(( ,(( # )#*#+ )&*(( # @ _[_MX 4 *(( C'Y& @MPU$ NQ^M] @ _[_MX ¥QSM^ _Q]^QN`_ MPMXMT *(( C'Y& Contoh 2.14 Tantangan untuk Anda Sepeda motor keluaran terbaru banyak yang menggunakan sistem monoshockbreaker. Menurut Anda, apakah hal tersebut ada hubungannya dengan tingkat kenyamanan sepeda motor tersebut? Selain itu, apakah permukaan jalan yang dilalui oleh sepeda motor akan memengaruhi gaya yang bekerja pada pegas (shockbreaker) sepeda motor? :`M N`MT ¥QSM^ PU^`^`Z ^QOM]M ¥M]MXQX$ ^Q_UM¥ ¥QSM^ YQYUXUWU W[Z^_MZ_M ¥QSM^ *(( C'Y& @UWM ¥MPM ^`^`ZMZ ¥M]MXQX ¥QSM^ _Q]^QN`_ PUNQ]U SMcM NQ]M_ *( C$ TU_`ZSXMT ¥Q]_MYNMTMZ ¥MZVMZS ¥QSM^& 5>O>?. :UWQ_MT`U2 , 4 *( C @ ) 4 *(( C'Y @ * 4 +(( C'Y @ + 4 *( C'Y @ _[_MX 4 @ ) ! @*4 *(( C'Y # +(( C'Y 4 -(( C'Y , 4 @ _[_MX "x *( C4 -(( C'Y! "x " "x 4 ($(, Y 4 , OY @MPU$ ¥Q]_MYNMTMZ ¥MZVMZS ¥QSM^ _Q]^QN`_ ^QNQ^M] , OY& Contoh 2.15 c. Pegas Disusun secara Paralel-Seri HUSM N`MT ¥QSM^ PU^`^`Z ^QOM]M ¥M]MXQX%^Q]U ^Q¥Q]_U ¥MPM 3>H?>K &#&%$ ^Q_UM¥ ¥QSM^ YQYUXUWU W[Z^_MZ_M ¥QSM^ @) $ @* $ PMZ @+ & EMPM `V`ZS ¥QSM^ cMZS _Q]^`^`Z ^QOM]M ¥M]MXQX%^Q]U _Q]^QN`_ PUNQ]UWMZ SMcM ^QNQ^M] ,& :QZSMZ YQZSS`ZMWMZ ]`Y`^MZ W[Z^_MZ_M ¥QSM^ ¥MPM ^`^`ZMZ ^Q]U PMZ ^`^`ZMZ ¥M]MXQX$ W[Z^_MZ_M ¥QSM^ _[_MX PM¥M_ PU_QZ_`WMZ& 9M]MZcM PQZSMZ YQZcQPQ]TMZMWMZ ^`^`ZMZ ¥QSM^ ¥MPM 3>H?>K &#&%& EQ]_MYM$ W[Z^_MZ_M ¥QSM^ @) PMZ @* PUMZSSM¥ YQZVMPU ¥QSM^ ^`^`ZMZ ¥M]MXQX _MZ¥M SMZSS`MZ PM]U ¥QSM^ WQ%+& DXQT WM]QZM U_`$ ¥Q]^MYMMZ W[Z^_MZ_M ¥QSM^ @) PMZ @* YQZVMPU @E 4 @) # @* AQY`PUMZ$ ZUXMU W[Z^_MZ_M ¥QSM^ _Q]^QN`_ PUSMN`ZSWMZ ^QOM]M ^Q]U PQZSMZ ¥QSM^ WQ%+ ^QTUZSSM ^Q]U + ) )) E @ @@ # " M_M` @ ^Q]U 4 + + E E @ @ @ @ " !*g,(" Gambar 2.21 Susunan pegas secara paralel-seri. k2 k1 k3 F Gambar 2.22 Sistem pegas yang digunakan pada shockbreaker mobil. Dapatkah Anda memperhitungkan gaya yang bekerja pada setiap shockbreaker? shockbreaker Sumber: Kamus Visual, 2004

50 Mudah dan Aktif Belajar Fisika untuk Kelas XI HQZ_`WMZ ZUXMU ¥Q]NMZPUZSMZ ¥Q]U[PQ ^`^`ZMZ ¥QSM^ ¥MPM 3>H?>K !>" PMZ 3>H?>K !?" VUWM YM^^M NQNMZZcM ^MYM$ cMU_` B& !M" y1 m !N" m kkk kk 6 k Tes Kompetensi Subbab C 6AKE>F>IG>C @>G>H ?NFN G>MDC>I# )& GQN`MT NMX[W NQ^U NQ]YM^^M )( WS PUSMZ_`ZSWMZ ¥MPM ^QN`MT WMbM_ X[SMY NQ]PUMYQ_Q] ($* OY PMZ ¥MZVMZS -( OY& 7WUNM_ZcM$ WMbM_ X[SMY _Q]^QN`_ YQYMZVMZS ^QVM`T ($(* OY& >U_`ZSXMT _QSMZSMZ$ ]QSMZSMZ$ PMZ Y[P`X`^ QXM^_U^U_M^ WMbM_ _Q]^QN`_& *& :UWQ_MT`U Y[P`X`^ J[`ZS _UYMT )$.h)()( C'Y* & >U_`ZSXMT NQ]M_ NQNMZ YMW^UY`Y cMZS N[XQT PUSMZ_`ZSWMZ ¥MPM ^Q`_M^ WMbM_ _UYMT cMZS NQ]% PUMYQ_Q] )( YY$ VUWM ]QSMZSMZ cMZS _Q]VMPU _UPMW N[XQT XQNUT PM]U ($(()& +& EQ]TM_UWMZXMT S]MRUW TM^UX QW^¥Q]UYQZ NQ]UW`_& =]MRUW _Q]^QN`_ YQZ`ZV`WWMZ SMcM cMZS PUNQ]UWMZ ¥MPM ^QN`MT ¥QSM^ PMXMY ^M_`MZ C !¥MPM ^`YN`%M" ^QNMZPUZS PQZSMZ ¥Q]_MYNMTMZ ¥MZVMZSZcM PMXMY ^M_`MZ YY !¥MPM ^`YN`%L" ^QTUZSSM YQZSTM^UXWMZ ^QN`MT ¥Q]^MYMMZ SM]U^ X`]`^& @UWM ¥MPM SM]U^ _Q]^QN`_ _Q]PM¥M_ _U_UW 7 !*($ +" PMZ _U_UW 8 !,($ ."$ _QZ_`WMZ NQ^M] W[Z^_MZ_M SMcM ¥QSM^ _Q]^QN`_& ,& GQN`MT NQZPM NQ]YM^^M ($- WS PUSMZ_`ZS ¥MPM ^QN`MT ¥QSM^ ^QTUZSSM ¥QSM^ _Q]^QN`_ NQ]_MYNMT ¥MZVMZS - OY& >U_`ZSXMT W[Z^_MZ_M ¥QSM^ _Q]^QN`_& != 4 )( Y'^* " -& :UWQ_MT`U Y[P`X`^ QXM^_U^U_M^ NQ^U MPMXMT *$) h )(- C'Y* & @UWM ^QN`MT NMX[W NQ^U PQZSMZ X`M^ ¥QZMY¥MZS , OY* PMZ ¥MZVMZS )(( OY PU_M]UW PQZSMZ SMcM ^QNQ^M] )( C$ _QZ_`WMZ ¥Q]_MYNMTMZ ¥MZVMZS WMbM_ PMZ _Q_M¥MZ SMcM WMbM_ _Q]^QN`_& .& HUSM N`MT ¥QSM^ UPQZ_UW PU^`^`Z ^QOM]M ¥M]MXQX& @UWM W[Z^_MZ_M ^Q_UM¥ ¥QSM^ @ 4 )(( C'Y$ TU_`ZSXMT ¥Q]_MY% NMTMZ ¥MZVMZS _[_MX ^U^_QY ¥QSM^ ^Q_QXMT PUNQ]U NQNMZ cMZS NQ]M_ZcM +( C& Contoh 2.16 2 k 5>O>?. G`^`ZMZ ¥QSM^ ¥MPM 3>H?>K !>" _Q]PU]U M_M^ _USM N`MT ¥QSM^ cMZS PU^`^`Z ¥M]MXQX$ @ E 4 @ # @ # @ 4 +@$ @MPU$ @ E 4 +@$ G`^`ZMZ ^Q]U PQZSMZ ¥QSM^ . @ YMWM @^ ( !. " . E E @ @ @ @ " ( !+ "!. " + . @ @ @ @ " (*@ M_M` @G 4 *@$ G`^`ZMZ ¥QSM^ ¥MPM 3>H?>K !?"$ YQ]`¥MWMZ ¥QSM^ cMZS PU^`^`Z ^QOM]M ¥M]MXQX M_M` @ ¥ 4 @ # @ 4 *@& @MPU$ @ E 4 *@$ G`^`ZMZ ^Q]U PQZSMZ ¥QSM^ * @ MPMXMT @ ^ 4 ! "!* " * E E @ @ @ @ " 4 !* "!* " * * @ @ @ @ " 4 ) @ M_M` @ G 4 @$ EQ]NMZPUZSMZ ¥Q]U[PQ ^`^`ZMZ ¥QSM^ ¥MPM 3>H?>K !>" PMZ ^`^`ZMZ ¥QSM^ ¥MPM 3>H?>K !?" MPMXMT 57 2 58 ( * 2 * 7 8 B B @ @ ! ! 57 2 58 ( ) ) 2 7 8 @ @ 4 ) ) 2 *@ @ @MPU$ 57 2 58 41: 2 Tugas Anda 2.6 Jika shockbreaker motor mulai terasa tidak nyaman, shockbreaker tersebut dapat direparasi di bengkel. Diskusikanlah bersama teman Anda menurut tinjauan Fisika, apa yang dilakukan teknisi bengkel untuk mereparasi shockbreaker tersebut? Kata Kunci • gaya pulih • konstanta pegas • regangan • susunan pararel • susunan seri • tegangan F (N) x (mm) B (40,6) A (20,3) 20 40 3 6 0

Gaya 51 /& @UWM ^QN`MT NQZPM NQ]YM^^M )$*- WS PU_UYNMZS PQZSMZ ZQ]MOM ¥QSM^$ ¥QSM^ MWMZ YQZcUY¥MZS - OY& HQZ_`WMZ NQ^M] W[Z^_MZ_M ¥QSM^ PM]U ZQ]MOM ¥QSM^ _Q]^QN`_& !PUWQ_MT`U = 4 )( Y'^* " 0& GQN`MT ¥QSM^ YQYUXUWU W[Z^_MZ_M ¥QSM^ ^QNQ^M] @ 4 ,(( C'Y& GMM_ NQNMZ NQ]YM^^M )( WS PUSMZ_`ZSWMZ ¥MPM `V`ZS ¥QSM^$ _Q]ZcM_M ¥MZVMZS ¥QSM^ YQZVMPU 0- OY& @UWM = 4 )( Y'^* $ NQ]M¥MWMT ¥MZVMZS ¥QSM^ Y`XM%Y`XM6 1& GQN`MT ¥QSM^ ¥MZVMZSZcM ,* OY VUWM PUNQNMZU NQZPM ^QNQ]M_ ,( C$ PMZ ¥MZVMZSZcM ,, OY VUWM PUNQNMZU NQZPM ^QNQ]M_ 0( C& >U_`ZSXMT W[Z^_MZ_M ¥QSM^ _Q]^QN`_& )(& HQ]PM¥M_ - N`MT ¥QSM^ UPQZ_UW PQZSMZ W[Z^_MZ_M ^Q_UM¥ ¥QSM^ MPMXMT @ 4 -( C'Y& HQZ_`WMZ ¥Q]_MYNMTMZ ¥MZVMZS _[_MX ^U^_QY ¥QSM^ ^Q_QXMT PUNQ]U NQNMZ ($*- WS$ VUWM ^Q_UM¥ ¥QSM^ PU^`^`Z ^QOM]M2 M& ^Q]U PMZ N& ¥M]MXQX PQZSMZ = 4 )( Y'^* & Gambar 2.23 Sebuah titik bergerak dari posisi Po ke posisi P. y % x Py R Px Po P D. Gerak Harmonik Sederhana GQN`MT NQZPM PUWM_MWMZ NQ]SQ]MW TM]Y[ZUW VUWM NQZPM _Q]^QN`_ YQXMW`WMZ SQ]MW ^QOM]M N[XMW%NMXUW PU ^QWU_M] _U_UW WQ^Q_UYNMZSMZ$ YU^MXZcM Mc`ZMZ ^QPQ]TMZM cMZS NMZcMW PUV`Y¥MU PU M]QZM NQ]YMUZ HMYMZ AMZMW%AMZMW& =Q]MW N[XMW%NMXUW ^QN`MT Mc`ZMZ _Q]`^ NQ]XMZS^`ZS VUWM PUNQ]U SMcM P[][ZS ^QOM]M NQ]WQXMZV`_MZ `Z_`W YQXMbMZ SMcM SQ^QW& =Q]MW N[XMW%NMXUW ¥MPM Mc`ZMZ PU^QN`_ V`SM SQ]MW TM]Y[ZUW ^QPQ]TMZM& 7c`ZMZ MWMZ NQ]TQZ_U PU _U_UW WQ^Q_UYNMZSMZ& @UWM SQ]MWMZ N[XMW%NMXUW _Q]^QN`_ NQ]XMZS^`ZS PMXMY ^QXMZS bMW_` cMZS ^MYM$ SQ]MW _Q]^QN`_ PUZMYMWMZ SQ]MW ¥Q]U[PUW& :MXMY NMN UZU$ 7ZPM MWMZ YQYNMTM^ SQ]MW TM]Y[ZUW ^QPQ]TMZM PQZSMZ YQZSMNMUWMZ MPMZcM SQ^QWMZ cMZS _Q]VMPU& 9[Z_[T SQ]MW TM]Y[ZUW ^QPQ]TMZM PM¥M_ 7ZPM XUTM_ ¥MPM Mc`ZMZ NMZP`X ^QPQ]TMZM M_M` SQ_M]MZ ¥MPM ¥QSM^& 8MUW SQ_M]MZ ¥QSM^ M_M` SQ]MWMZ N[XMW% NMXUW ¥MPM NMZP`X ^QPQ]TMZM$ M]MTZcM ^QXMX` YQZ`V` _U_UW WQ^Q_UYNMZSMZ& 1. Simpangan Gerak Harmonik Sederhana EQ]TM_UWMZ 3>H?>K &#&'& GQN`MT _U_UW NQ]SQ]MW YQXUZSWM] NQ]M_`]MZ& @UWM bMW_` cMZS PU¥Q]X`WMZ `Z_`W NQ]¥UZPMT PM]U ¥[^U^U 1( WQ ¥[^U^U 1 MPMXMT H$ NQ^M] ^`P`_ cMZS PU_QY¥`T _U_UW U_` MPMXMT % 4'H 4 *! < H ( ! * 5 ! H& E][cQW^U _U_UW 1 _Q]TMPM¥ ^`YN`-M MPMXMT 1c PMZ ¥][cQW^U _U_UW 1 _Q]TMPM¥ ^`YN`-L MPMXMT 1L $ ^QPMZSWMZ 01 MPMXMT VM]U%VM]U XUZSWM]MZ 3$ @UWM 7ZPM ¥Q]TM_UWMZ ¥][cQW^U _U_UW 1 ¥MPM ^`YN`-M$ ¥][cQW^U _Q]^QN`_ YQYUXUWU ^UY¥MZSMZ YMW^UY`Y ) cMZS PU^QN`_ MY¥XU_`P[& 8Q^M] ¥][cQW^U PU _U_UW 1 ¥MPM ^`YN`-M PM¥M_ PU_`XU^ 6 ( ) ^UZ'H 4 ) ^UZ *! <H !*g,)" @UWM _U_UW MbMX NQ]SQ]MW Y`XMU PM]U % ( $ 9AKL>H>>I !&Q(%" PM¥M_ PU_`XU^ 6 ( ) ^UZ !'H !% ( " 4 ) ^UZ !*! < H !% ( " !*g,*" AQ_Q]MZSMZ2 6 4 ^UY¥MZSMZ !Y" < 4 R]QW`QZ^U !>d" ) 4 MY¥XU_`P[ !Y" % 0 4 ^`P`_ MbMX !]MP" H 4 bMW_` !^QW[Z" ' 4 R]QW`QZ^U ^`P`_ !]MP'^" 8Q^M] ^`P`_ cMZS PU_QY¥`T ^QN`MT _U_UW PMXMY R`ZS^U ^UZ`^ PU^QN`_ GI:IH <7G;& 8Q^M] ^`P`_ RM^Q MPMXMT % 4'H #% ( 4 2! t T #% ( & @UWM % 4 *! ( * * H 5 % !) ! + - / 0 " # , . PU YMZM ) MPMXMT RM^Q SQ_M]MZ$ ¥Q]^MYMMZ RM^Q SQ_M]MZZcM

52 Mudah dan Aktif Belajar Fisika untuk Kelas XI Tokoh Willems Gravesande (1688–1742) Ilmuwan Belanda, Willems Gravesande (1688–1742) membuat beberapa perkakas untuk melakukan percobaan merangkai gerak. Ia juga membuat peralatan untuk mengamati mengapa pegas yang ditekan dapat menggerakkan bendabenda lain, begitu tekanannya dilepaskan. Terungkap bahwa energi potensial tersimpan di dalam benda, seperti pegas yang menjadi energi gerak, kemudian menyebabkan benda bergerak. Sumber:research.leidenuniv.nl ( * H 5 % ) ! # " !*g,+" GQN`MT _U_UW cMZS NQ]SQ]MW TM]Y[ZUW ^QPQ]TMZM NQ]¥UZPMT PM]U H ) YQYUXUWU RM^Q ) ( ) * H 5 % ) ! # " PMZ ¥MPM ^MM_ H * YQYUXUWU RM^Q * ( * * H 5 % ) ! # " $ YMWM NQPM RM^Q H * PMZ H % `Z_`W H * 5 H ) MPMXMT ")) ) # * ) # # * ) H H g 5 !*g,," EMPM SQ]MW TM]Y[ZUW ^QPQ]TMZM$ NQPM RM^Q PUZcM_MWMZ [XQT MZSWM PM]U Z[X ^MY¥MU PQZSMZ ^M_`& 8QPM RM^Q `Z_`W NUXMZSMZ N`XM_ _UPMW ¥Q]X` PU^Q]_MWMZ$ YU^MXZcM ) ) * $ * ) * $ + ) * 3 PMZ ^Q_Q]`^ZcM$ O`W`¥ PU_`XU^ NQPM RM^QZcM MPMXMT ) * ^MVM& E[^U^U NQZPM !_U_UW" PUWM_MWMZ ^QRM^Q VUWM NQPM RM^QZcM Z[X !("$ PMZ NQ]XMbMZMZ RM^Q VUWM NQPM RM^QZcM ^Q_QZSMT ! ) * & GQOM]M YM_QYM_U^$ PM¥M_ PU_`XU^ ^QNMSMU NQ]UW`_& GQRM^Q2 ") 4 ($ )$ *$ +$ &&& M_M` ") 4 C !*g,-" 8Q]XMbMZMZ RM^Q2 ") 4 ) * $ ) ) * $ * ) * $ &&& M_M` ") 4 C # ) * !*g,." AQ_Q]MZSMZ2 C MPMXMT NUXMZSMZ OMOMT ($ )$ *$ +$ PMZ ^Q_Q]`^ZcM& 2. Kecepatan Gerak Harmonik AQOQ¥M_MZ SQ]MW TM]Y[ZUW ^QPQ]TMZM YQ]`¥MWMZ _`]`ZMZ ¥Q]_MYM PM]U ¥Q]^MYMMZ ¥[^U^U _Q]TMPM¥ bMW_`& 8QZPM ¥MPM MbMXZcM NQ]SQ]MW % ( 4 ( YMWM ZUXMU WQOQ¥M_MZZcM MPMXMT M :M : J :H :H # # !) ^UZ 'H"& J M 4 ') O[^ 'H !*g,/" CUXMU J M MWMZ YQZOM¥MU YMW^UY`Y VUWM ZUXMU O[^ 'H 4 ) ^QTUZSSM ZUXMU YMW^UY`Y PM]U J M 4 ' )& @MPU$ WQOQ¥M_MZ YMW^UY`Y YQYQZ`TU ¥Q]^MYMMZ NQ]UW`_& JY 4 ') !*g,0" :M]U 9AKL>H>>I !&Q(+" PMZ !&Q(," MWMZ PU¥Q][XQT2 J c 4 JY O[^ 'H !*g,1" AQOQ¥M_MZ PU ^QYNM]MZS ¥[^U^U ^QN`MT _U_UW cMZS NQ]SQ]MW TM]Y[ZUW MPMXMT 6 ( ) ^UZ 'H3 6& ( )* ^UZ* 'H3 6& ( )* !) O O[^* 'H"& :QZSMZ YQXMW`WMZ ^`N^_U_`^U PM]U 9AKL>H>>I !&Q(," PMZ !&Q(-" WQ PMXMY ¥Q]^MYMMZ 6 * 4 )* !) O O[^* 'H"$ PU¥Q][XQT J c4 ' * * ) 6 # !*g-(" AQ_Q]MZSMZ2 J c 4 WQOQ¥M_MZ _Q]TMPM¥ ^`YN`-M !Y'^" ) 4 MY¥XU_`P[ !Y" ' 4 R]QW`QZ^U ^`P`_ !]MP'^" 6 4 ^UY¥MZSMZ !Y" Suatu ketika ayunan sebuah lampu yang tergantung tali panjang pada sebuah bangunan di Pisa diamati oleh Galileo. Hal tersebut memberikan inspirasi kepadanya bahwa periode sebuah bandul tidak bergantung pada amplitudonya. One time Galileo saw a lamp swinged over time. It was hang by a long rope and tight to an old building in Pisa. That phenomenon became something that has inspired him for a thought that pendulum’s period was not depend on its amplitud. Informasi untuk Anda Information for You

Gaya 53 3. Percepatan Gerak Harmonik Sederhana GQ¥Q]_U ¥QZVQXM^MZ ¥Q]OQ¥M_MZ ¥MPM SQ]MW X`]`^ ^QNQX`YZcM$ PUWQ_MT`U NMTbM ¥Q]OQ¥M_MZ ^Q^MM_ SQ]MW TM]Y[ZUW ^QPQ]TMZM ^`M_` SQ_M]MZ V`SM YQ]`¥MWMZ _`]`ZMZ ¥Q]_MYM PM]U ¥Q]^MYMMZ WQOQ¥M_MZ SQ_M]MZ$ PMZ PU_`XU^ ^QNMSMU 7M 4 M :J :H 4 : :H !') O[^ ' H"& 7M 4 g '*) ^UZ 'H 4 g'*6 !*g-)" :M]U 9AKL>H>>I !&Q)%"$ ^UY¥MZSMZ 6 NQ]_MZPM ZQSM_UR !g"$ M]_UZcM WQOQ¥M_MZ M]MT 7M YQZ`V` ^`YN` 6 ¥[^U_UR& GQNMXUWZcM$ ¥MPM ^MM_ ^UY¥MZSMZ 6 WQ ^`YN` ¥[^U_UR$ M]MT ¥Q]OQ¥M_MZ 7M YQZ`V` WQ ^`YN` 6 ZQSM_UR& IZ_`W XQNUT VQXM^ZcM$ ¥Q]TM_UWMZ 3>H?>K &#&(& BQZ`]`_ >`W`Y ?? CQb_[Z$ M]MT ¥Q]OQ¥M_MZ 7M ^MYM PQZSMZ M]MT SMcM ¥QY`XUT !SMcM cMZS ^QXMX` YQZ`V` _U_UW WQ^QUYNMZSMZ"& GMYM TMXZcM PQZSMZ WQOQ¥M_MZ YMW^UY`Y$ ZUXMU ¥Q]OQ¥M_MZ 7M MWMZ YMW^UY`Y VUWM ^UZ 'H 4 ) M_M` 'H 4 * ! ]MP& @MPU$ ¥Q]^MYMMZ ¥Q]OQ¥M_MZ YMW^UY`Y SQ]MW TM]Y[ZUW MPMXMT 7B 4 '* ) !*g-*" AQ_Q]MZSMZ2 7B 4 ¥Q]OQ¥M_MZ YMW^UY`Y !Y'^* " ' 4 R]QW`QZ^U ^`P`_ !]MP'^" ) 4 MY¥XU_`P[ !Y" EMPM 3>H?>K &#&) _Q]XUTM_ _USM N`MT S]MRUW$ cMU_` S]MRUW ^UY¥MZSMZ M _Q]TMPM¥ bMW_` H$ S]MRUW WQOQ¥M_MZ J c _Q]TMPM¥ bMW_` H$ PMZ S]MRUW ¥Q]OQ¥M_MZ 7M _Q]TMPM¥ bMW_` H& EMPM ^MM_ H 4 ($ S]MRUW ^UY¥MZSMZ M YQZ`ZV`WWMZ TM]SM YUZUY`Y !M 4 ( PU _U_UW ^Q_UYNMZS"& =]MRUW WQOQ¥M_MZ J c YQZ`ZV`WWMZ TM]SM YMW^UY`Y !J Y 4 ' )"$ PMZ S]MRUW ¥Q]OQ¥M_MZ 7 YQZ`ZV`WWMZ TM]SM YUZUY`Y& GQNMXUWZcM$ ¥MPM ^MM_ ZUXMU ^UY¥MZSMZ YQZOM¥MU YMW^UY`Y !6 ( )"$ ZUXMU WQOQ¥M_MZ YUZUY`Y !J c 4 ("$ PMZ ZUXMU ¥Q]OQ¥M_MZ MWMZ YMW^UY`Y !7YMW^4 '* )"& Gambar 2.24 Arah simpangan Y dan percepatan ay pada gerak harmonik sederhana selalu berlawanan. Gambar 2.25 Grafik gerak harmonik sederhana: (a) simpangan terhadap waktu, (b) kecepatan terhadap waktu, dan (c) percepatan terhadap waktu. Y + aY – Y – aY + x y y t ymak –' A 0 ay v y +' A 0 t t A ay !M" !N" !O" GQN`MT NQZPM YQXMW`WMZ SQ]MW TM]Y[ZUW ^QPQ]TMZM ^Q¥MZVMZS ^`YN`%M& EQ]^MYMMZ ^UY¥MZSMZZcM PUZcM_MWMZ ^QNMSMU 6 4 * ^UZ ! ) . ! ! H " PQZSMZ 6 PMXMY YQ_Q] PMZ H PMXMY ^QW[Z& HQZ_`WMZ2 M& MY¥XU_`P[$ R]QW`QZ^U$ PMZ ¥Q]U[PQ SQ]MWZcM N& ¥Q]^MYMMZ ¥Q]OQ¥M_MZ PMZ WQOQ¥M_MZ O& ^UY¥MZSMZ$ WQOQ¥M_MZ$ PMZ ¥Q]OQ¥M_MZ ¥MPM ^MM_ H 4 * ^QW[Z P& WQOQ¥M_MZ YMW^UY`Y PMZ ¥Q]OQ¥M_MZ YMW^UY`Y 5>O>?. M& EQ]^MYMMZ ^UY¥MZSMZ SQ]MW TM]Y[ZUW ^QPQ]TMZM$ cMU_` 6 ( ) ^UZ !' H ! % 0 "& 8MZPUZSWMZ PQZSMZ ¥Q]^MYMMZ ^UY¥MZSMZ 6 4 * ^UZ ! ) . ! ! H " $ PU¥Q][XQT ) 4 * Y PMZ ' 4 ! ]MP'^$ YMWM *! < 4 ! M_M` < 4 ) * >d 4 ($- >d PMZ 5 4 ) < 4 ) ($- 4 * ^QW[Z N& EQ]^MYMMZ WQOQ¥M_MZ J c PMZ ¥Q]^MYMMZ ¥Q]OQ¥M_MZ 7c MWMZ PU¥Q][XQT J c 4 :6 :H 4 : :H K* ^UZ ! . H ! ! " L 4 *! O[^ ! . H ! ! " Y'^ 7c 4 M :J :H 4 : :H K*! O[^ ! . H ! ! " L 4 g *! * ^UZ ! . H ! ! " Y'^* Contoh 2.17

54 Mudah dan Aktif Belajar Fisika untuk Kelas XI 4. Periode dan Frekuensi pada Gerak Harmonik 8Q^M] ^UY¥MZSMZ SQ]MW TM]Y[ZUW ^QPQ]TMZM ¥MPM ¥QSM^ PMZ NMZP`X$ PM¥M_ PU_QZ_`WMZ PQZSMZ YQZSMYM_U SQ]MW N[XMW%NMXUW ¥MPM SQ_M]MZ ¥QSM^ PMZ Mc`ZMZ ^QPQ]TMZM& 7ZPM MWMZ YQY¥Q][XQT ¥Q]U[PQ SQ_M]MZ !5" PMZ R]QW`QZ^U !<"$ EQ]U[PQ SQ_M]MZ MPMXMT bMW_` cMZS PU¥Q]X`WMZ NQNMZ `Z_`W YQXMW`WMZ ^M_` WMXU SQ]MW N[XMW%NMXUW !SQ_M]MZ"& <]QW`QZ^U SQ_M]MZ MPMXMT NMZcMWZcM SQ]MW N[XMW%NMXUW cMZS PM¥M_ PUXMW`WMZ PMXMY bMW_` ^M_` ^QW[Z& EQ]U[PQ cMZS PUXMW`WMZ [XQT ^QN`MT NQZPM ¥MPM 3>H?>K &#&+ MPMXMT bMW_` cMZS PUN`_`TWMZ NQZPM `Z_`W NQ]SQ]MW PM]U )#0#*#0#)& EMPM 3>H?>K &#&+ !>"$ NQNMZ PU_M]UW ^QTUZSSM ¥QSM^ YQYMZVMZS ^MY¥MU WQ _U_UW )& EMPM Mc`ZMZ NQNMZ !3>H?>K &#&+ !?""$ SQ]MW NQZPM YQZcUY% ¥MZS TUZSSM _U_UW )& AQ_UWM PUXQ¥M^$ NQNMZ NQ]SQ]MW YQZ`V` _U_UW WQ^Q_UYNMZSMZ PMZ YQXQbM_UZcM ^MY¥MU PU _U_UW *& AQY`PUMZ$ NQNMZ NQ]SQ]MW WQYNMXU WQ _U_UW ^QY`XM$ cMU_` _U_UW ) ^Q_QXMT YQXQbM_U _U_UW WQ^Q_UYNMZSMZ `Z_`W WQP`M WMXUZcM PU _U_UW 0& @MPU$ NQ]PM^M]WMZ ¥QZSMYM_MZ$ bMW_` cMZS PUN`_`TWMZ NQNMZ `Z_`W YQXMW`WMZ ^M_` WMXU SQ_M]MZ ¥MPM ¥QSM^ M_M` ^M_` WMXU Mc`ZMZ ¥MPM NMZP`X PU^QN`_ E;F?D:; !5"$ ^QPMZSWMZ R]QW`QZ^U NQ]NMZPUZS _Q]NMXUW PQZSMZ ¥Q]U[PQ& GQOM]M YM_QYM_U^$ PU_`XU^ 5 ( ) < M_M` < ( ) 5 !*g-+" AQ_Q]MZSMZ2 5 4 ¥Q]U[PQ !^QW[Z" < 4 R]QW`QZ^U !TQ]_d 4 >d" 5. Gaya Pemulih pada Pegas dan Bandul :MXMY SQ]MW TM]Y[ZUW ^QPQ]TMZM$ NQWQ]VM ]Q^`X_MZ SMcM cMZS M]MTZcM ^QXMX` YQZ`V` _U_UW WQ^Q_UYNMZSMZ$ SMcM UZU PU^QN`_ =7M7 E;BIA?>$ NQ^M]ZcM NQ]NMZPUZS X`]`^ PQZSMZ ¥[^U^U NQZPM _Q]TMPM¥ _U_UW WQ^Q_UYNMZSMZ& EQ]TM_UWMZ 3>H?>K &#&,& EQSM^ PMXMY _USM WQP`P`WMZ$ Y`XM%Y`XM NQZPM ¥MPM ¥[^U^U ^Q_UYNMZS PU 1$ WQY`PUMZ PU_M]UW WQ NMbMT ^QVM`T gM" XMX` NQZPM PUXQ¥M^WMZ& 8Q]^MYMMZ PQZSMZ ^MM_ ¥QSM^ PU_M]UW$ NQWQ]VM ^QN`MT SMcM ! aQ]_UWMX WQ M_M^ NQ]_MZPM ¥[^U_UR PMZ NQZPM YQXQbM_U _U_UW WQ^Q_UYNMZSMZ TUZSSM YQZOM¥MU _U_UW _Q]_UZSSU #M$ ¥MPM ¥[^U^U _Q]^QN`_ NQZPM NQ]TQZ_U ^Q^MM_ !" 4 ("& EMPM ¥[^U^U UZU ¥`XM$ ¥MPM NQZPM NQWQ]VM SMcM ¥QY`XUT ! aQ]_UWMX WQ NMbMT YQZ`V` _U_UW WQ^Q_UYNMZSMZ& IZ_`W WQP`M WMXUZcM$ NQZPM MWMZ YQZ`V` _U_UW _Q]QZPMT XMSU& EMPM ^MM_ ¥[^U^U _Q]QZPMT$ WQOQ¥M_MZ NQZPM WQYNMXU NQ]ZUXMU YUZU% Y`Y !J 4 ("& :QYUWUMZ ^Q_Q]`^ZcM$ SQ]MW TM]Y[ZUW ¥MPM ¥QSM^ NQ]% XMZS^`ZS ^QOM]M NQ]`XMZS%`XMZS& @MPU$ SQ]MW TM]Y[ZUW ¥MPM ¥QSM^ MPMXMT Gambar 2.27 Periode dan frekuensi pada (a) pegas, (b) bandul, dapat ditentukan dari besar simpangannya. Gambar 2.28 Arah gaya pemulih pada pegas selalu berlawanan tanda dengan simpangan. gerak kertas pegas yang naik turun Gambar 2.26 Percobaan untuk menghasilkan grafik simpangan terhadap waktu. +y –y P –y F –F +y !M" !N" !O" !M" garis setimbang A B B O garis setimbang A !N" O O& EMPM ^MM_ H 4 * ^QW[Z YMWM 6 4 * ^UZ ! * . ! ! " 4 * ^UZ +1(e 4 ) Y J c 4 *! O[^ ! * . ! ! " 4 *! O[^ +1(e 4 -$,, Y'^ 7c 4 g *! * ^UZ ! * . ! ! " 4 )1$/* ^UZ +1(e 4 1$0. Y'^* P& :M]U ¥Q]^MYMMZ ^UY¥MZSMZ ¥MPM N`_U] !M"$ PU¥Q][XQT J B ( ' ) ( *! < ) ( .$*0 Y'^& 7B ( '& ) ( ,! & < * ) ( )1$/* Y'^* &

Gaya 55 SQ]MW cMZS NQ]`XMZS MWUNM_ SMcM ¥QY`XUT cMZS M]MTZcM ^QXMX` YQZ`V` _U_UW WQ^Q_UYNMZSMZ& 8Q^M] SMcM ¥QY`XUT ^QNMZPUZS PQZSMZ VM]MW NQZPM WQ _U_UW ^Q_UYNMZS M& GQOM]M YM_QYM_U^$ SMcM ¥QY`XUT ¥MPM ¥QSM^ PU_`XU^ , 4 @M !Z[_M^U ^WMXM]" ! 4 O@$# !Z[_M^U aQW_[]" !*g-," =McM ¥QY`XUT ^QXMX` NQ]XMbMZMZ M]MT PQZSMZ M]MT ^UY¥MZSMZ& AQ_UWM M]MT NQZPM WQ NMbMT$ SMcM ¥QY`XUT WQ M_M^& :QYUWUMZ V`SM ^MM_ NQZPM NQ]SQ]MW WQ M_M^$ M]MT SMcM ¥QY`XUT MPMXMT aQ]_UWMX WQ NMbMT& GQN`MT NMZP`X NQ]YM^^M B PUT`N`ZSWMZ PQZSMZ ^Q`_M^ _MXU cMZS ¥MZVMZSZcM A ^Q¥Q]_U _MY¥MW ¥MPM 3>H?>K &#&-& 8MZP`X PU_M]UW ^QVM`T G ^QTUZSSM YQYNQZ_`W ^`P`_ % & EMPM NMZP`X NQWQ]VM P`M SMcM$ cMU_` SMcM _QSMZSMZ _MXU 5 PMZ SMcM NQ]M_ NMZP`X !B=" cMZS M]MTZcM aQ]_UWMX WQ NMbMT& A[Y¥[ZQZ SMcM NQ]M_ !B=" cMZS NQWQ]VM ¥MPM NMZP`X MPMXMT B=O[^% & =McM UZU ^QXMX` ^QUYNMZS _Q]TMPM¥ SMcM _QSMZS _MXU 5 ^QTUZSSM NMZP`X NQ]SQ]MW _Q_M¥ ¥MPM XUZ_M^MZZcM& A[Y¥[ZQZ SMcM XMUZZcM MPMXMT B=^UZ% & =McM _Q]^QN`_ ^QXMX` YQZ`V` _U_UW WQ^Q_UYNMZSMZ Mc`ZMZ PMZ _QSMW X`]`^ _Q]TMPM¥ _QSMZSMZ _MXU& =McM cMZS M]MTZcM ^QXMX` YQZ`V` _U_UW WQ^Q_UYNMZSMZ MPMXMT SMcM ¥QY`XUT& 8Q^M] SMcM ¥QY`XUT ¥MPM Mc`ZMZ ^QPQ]TMZM PM¥M_ PUZcM_MWMZ PQZSMZ ¥Q]^MYMMZ ,4 O B = ^UZ% !*g--" AQ_Q]MZSMZ2 , 4 NQ^M] SMcM ¥QY`XUT !C" = 4 NQ^M] ¥QOQ¥M_MZ S]MaU_M^U !Y'^* " B 4 YM^^M NQZPM !WS" % 4 ^`P`_ ^UY¥MZSMZ a. Periode Gerak Harmonik pada Pegas EQ]U[PQ SQ_M]MZ ¥MPM ¥QSM^ PM¥M_ PU_QZ_`WMZ PQZSMZ YQZSS`ZMWMZ >`W`Y ?? CQb_[Z$ cMU_` 2 ( B>M PQZSMZ ZUXMU ¥Q]OQ¥M_MZ SQ]MW NQZPM 7M ( O 2 ' M& =McM ¥QY`XUT ¥MPM ¥QSM^ MPMXMT 2 ( O@$# ^QTUZSSM VUWM PUQXUYUZM^UWMZ MZ_M]M ¥Q]^MYMMZ >`W`Y ?? CQb_[Z PMZ ¥Q]^MYMMZ SMcM ¥QY`XUT$ PU¥Q][XQT @ $P 4 B >M ( @ M ( B !O * ' M" @ 4 B * ' ( * ' 4 @ B ( ' 4 @ B DXQT WM]QZM WQOQ¥M_MZ ^`P`_ ' 4 * 5 ! YMWM 5 4 *! B @ !*g-." <]QW`QZ^U ¥QSM^ NQ]NMZPUZS _Q]NMXUW PQZSMZ ¥Q]U[PQ ¥QSM^ ^QTUZSSM NQ^M] R]QW`QZ^U ¥QSM^ PUZcM_MWMZ PQZSMZ ¥Q]^MYMMZ < 4 ) *! @ B !*g-/" AQ_Q]MZSMZ2 < ( R]QW`QZ^U SQ_M]MZ ¥QSM^ !>d" B 4 YM^^M NQNMZ !WS" 5 4 ¥Q]U[PQ !^QW[Z" @ 4 _Q_M¥MZ ¥QSM^ !C'Y" Gambar 2.29 Gaya pemulih pada ayunan selalu menuju titik kesetimbangan. T m B mg 0 % mg cos% Gambar 2.30 Sebuah pegas ditarik hingga merenggang sejauh y. y m g garis seimbang mg sin%

56 Mudah dan Aktif Belajar Fisika untuk Kelas XI b. Periode Ayunan Bandul Sederhana 7c`ZMZ NMZP`X ^QPQ]TMZM YQYUXUWU NQ^M] SMcM ¥QY`XUT , ( OB= ^UZ% & @UWM ^`P`_% YQZPQWM_U Z[X$ ZUXMU ^UZ% 4 M YQZPQWM_U M & :M]U >`W`Y ?? CQb_[Z$ NQ^M] , ( B 7M ^QTUZSSM MWMZ PU¥Q][XQT ¥Q]U[PQ Mc`ZMZ NMZP`X ^QPQ]TMZM ^QNMSMU NQ]UW`_& , ( OB = ^UZ % B 7M 4 gB = M DXQT WM]QZM 7M ( O * ' M YMWM g * ' M 4 g= M ( * ' 4 = M_M` ' 4 = & :QZSMZ ' 4 * 5 ! $ PUPM¥M_ * 5 ! 4 = ^QTUZSSM 5 4 *! = !*g-0" AQ_Q]MZSMZ2 5 4 ¥Q]U[PQ SQ]MW NMZP`X !^" = 4 NQ^M] ¥Q]OQ¥M_MZ S]MaU_M^U !Y'^* " 4 ¥MZVMZS _MXU !Y" IZ_`W XQNUT YQYMTMYU ¥Q]U[PQ ¥MPM NMZP`X ^QPQ]TMZM$ XMW`WMZXMT MW_UaU_M^ NQ]UW`_& Aktivitas Fisika 2.3 Gerak Harmonik Sederhana Tujuan Percobaan Mengamati pengaruh panjang tali dan massa bandul terhadap periode getaran atau frekuensi getar pada gerak harmonik sederhana. Alat-Alat Percobaan 1. Tiga buah anak timbangan, masing-masing 50 g, 100 g, dan 200 g 2. Benang secukupnya Langkah-Langkah Percobaan 1. Rangkai alat seperti pada gambar di samping. Panjang tali yang digunakan = 50 cm dan massa anak timbangannya m = 50 g. 2. Berikan sudut simpangan pada anak timbangan sebesar % = 15° atau kurang, lalu lepaskan. Hitung periode dan frekuensinya untuk getaran selama 10 sekon. 3. Lakukan langkah 1 sampai 2 untuk massa anak timbangan 100 g dan 200 g. 4. Dari langkah 1–3, kesimpulan apa yang Anda peroleh tentang pengaruh massa bandul terhadap perioda atau frekuensi getar pada gerak harmonik sederhana? 5. Lakukan langkah 1–3 dengan massa bandul tetap m = 100 g dan panjang tali bervariasi, yaitu 50 cm, 75 cm, dan 100 cm. 6. Dari langkah 5, kesimpulan apa yang Anda peroleh tentang pengaruh panjang tali terhadap perioda atau frekuensi getar pada gerak harmonik sederhana? 7. Diskusikan bersama guru dan teman Anda, mengapa sudut simpangan yang digunakan pada gerak harmonik sederhana harus 15°? @UWM ¥Q]U[PQ Mc`ZMZ NMZP`X ^QPQ]TMZM cMZS ¥MZVMZSZcM ).( OY MPMXMT *$-- ^QW[Z$ _QZ_`WMZ NQ^M] ¥Q]OQ¥M_MZ S]MaU_M^U PU X[WM^U Mc`ZMZ _Q]^QN`_& Contoh 2.18 m % Gerak harmonik sederhana pada ayunan bandul akan terjadi jika besar sudut simpangan ayunan kurang dari atau sama dengan 15° karena pada sudut-sudut tersebut nilai sin% = tan % . Ingatlah

Gaya 57 )& :M]U S]MRUW ^UY¥MZSMZ _Q]TMPM¥ bMW_` ^Q¥Q]_U _MY¥MW ¥MPM SMYNM]$ _QZ_`WMZ2 M& MY¥XU_`P[3 N& ¥Q]U[PQ3 PMZ O& R]QW`QZ^U SQ_M]MZ& 5>O>?. M& 7Y¥XU_`P[ MPMXMT ^UY¥MZSMZ YMW^UY`Y PM]U SM]U^ YQZPM_M]$ cMU_` 7 4 - Y& N& EQ]U[PQ !5" MPMXMT ^QXMZS bMW_` cMZS PU¥Q]X`WMZ `Z_`W YQYNQZ_`W _USM _U_UW ¥[_[ZS NQ]`]`_MZ ¥MPM ^`YN`-H PQZSMZ H 4 )* ^QW[Z& O& <]QW`QZ^U !<" SQ_M]MZ2 < 4 ) 5 4 ) )* >d *& EMPM ^`YN`-M PMZ ^`YN`-H cMZS ^MYM$ X`WU^XMT P`M S]MRUW M g H SQ]MW TM]Y[ZUW$ PQZSMZ ¥Q]U[PQ SQ_M]MZ !*" ^Q_QZSMT ¥Q]U[PQ SQ_M]MZ !)"$ PMZ MY¥XU_`P[ SQ_M]MZ !*" ^Q_QZSMT MY¥XU_`P[ SQ_M]MZ !)"& 5>O>?. @UWM `Z_`W S]MRUW M g H SQ]MW TM]Y[ZUW !)" PUMYNUX MY¥XU_`P[ )) $ ¥Q]U[PQ 5) $ PMZ R]QW`QZ^U < ) $ YMWM `Z_`W S]MRUW M O H SQ]MW TM]Y[ZUW !*" NQ]XMW`2 MY¥XU_`P[ )* 4 ) * )) 3 ¥Q]U[PQ 5* 4 ) * 5) 3 PMZ R]QW`QZ^U < * 4 * < ) & =]MRUW SQ]MW M g H SQ]MW TM]Y[ZUW !)" PUZcM_MWMZ [XQT SM]U^ `_`T PMZ S]MRUW M g H SQ]MW TM]Y[ZUW !*" PUZcM_MWMZ [XQT SM]U^ ¥`_`^%¥`_`^ ^Q¥Q]_U ¥MPM SMYNM] NQ]UW`_& Contoh 2.19 5>O>?. :UWQ_MT`U2 ¥MZVMZS _MXU ! " 4 ).( OY 4 )$. Y& ¥Q]U[PQ !5" 4 *$-- ^QW[Z EQ]OQ¥M_MZ S]MaU_M^U PU¥Q][XQT PQZSMZ 9AKL>H>>I !&Q(*"2 5 4 *! = ( = 4 * * , 5 ! ( ! ! ! * * , +$), )$. Y *$-- ^ 4 1$/ Y'^* @MPU$ ¥Q]OQ¥M_MZ S]MaU_M^U PU _QY¥M_ _Q]^QN`_ MPMXMT 1$/ Y'^ * & 5. Energi pada Gerak Harmonik Sederhana =Q]MW TM]Y[ZUW ^QPQ]TMZM PM]U ^QN`MT Mc`ZMZ NMZP`X PU¥Q]XUTM_WMZ ¥MPM 3>H?>K &#'%& EMPM WQMPMMZ MbMX$ ¥[^U^U NQZPM PU ^UY¥MZSMZ _Q]% VM`T$ cMU_` PU _U_UW 7& EMPM ¥[^U^U _Q]^QN`_$ NQ^M] QZQ]SU ¥[_QZ^UMX NMZP`X YMW^UY`Y$ ^QNMXUWZcM NQ^M] QZQ]SU WUZQ_UW NMZP`X YUZUY`Y& AQ_UWM Gambar 2.31 Perubahan energi terjadi saat bandul bergerak dari A menuju B yaitu energi potensial ke energi kinetik dan sebaliknya dari B ke C. Y Ek = 0 B Ep = 0 Ekmaks = 1 2 mv2 maks Ek = 0 Epmaks = 1 2 kA2 q Epmaks = 1 2 kA2 C A – 5 5 0 3 6 9 12 15 18 21 24 y t simpangan (y) Grafik gerak harmonik (1) Amplitudo A1 , periode T1 Frekuensi f 1 waktu (t) T1 A2 T2 A1 Grafik gerak harmonik (2) Amplitudo A2 , periode T2 Frekuensi f 2

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62 Mudah dan Aktif Belajar Fisika untuk Kelas XI Setelah mempelajari bab ini, tentu Anda dapat mengetahui jenis-jenis gaya yang sering Anda temukan dalam kehidupan sehari-hari. Anda juga tentu dapat menjelaskan perbedaan antara jenis gaya yang satu dan gaya yang lainnya. Dari materi bab ini, bagian mana yang dianggap sulit? Coba diskusikan dengan teman atau guru Fisika Anda. Refleksi Pada bab ini, Anda dapat mempelajari gaya gesek. Kita dapat berjalan atau mobil dapat melaju karena adanya gaya gesek. Ternyata, banyak manfaat dengan adanya gaya gesek, meskipun memang ada kerugiannya pada kasus-kasus tertentu. Coba Anda cari manfaat lain mempelajari bab ini. =McM =Q^QW =McM =]MaU_M^U =McM =Q^QW G_M_U^ =McM =Q^QW AUZQ_UW Peta Konsep =Q]MW >M]Y[ZUW GQPQ]TMZM =]MaU_M^U IZUaQ]^MX EQ]OQ¥M_MZ =]MaU_M^U =McM GQZ_]U¥Q_MX AQXMV`MZ D]NU_ GM_QXU_ EQ]U[PQ D]NU_ GM_QXU_ 3>P> A[Z^_MZ_M ¥QSM^ EQSM^ PMZ 8MZP`X =McM ¥QY`XUT EQ]U[PQ ;ZQ]SU >`W`Y AQWQWMXMZ ;ZQ]SU BQWMZUW YQYNMTM^ ;XM^_U^U_M^ ¥MPM EQSM^ YQZSS`ZMWMZ >`W`Y >[[WQ YQZOM]U ¥MPM NQ]XMW` _Q]NMSU M_M^ PU MZ_M]MZcM ¥MPM YQYUXUWU

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Gaya 65 *)& GQN`MT ¥QSM^ cMZS ¥MZVMZSZcM +( OY _Q]SMZ_`ZS _MZ¥M NQNMZ& AQY`PUMZ$ `V`ZS NMbMT ¥QSM^ PUSMZ_`ZSU NQNMZ )(( S ^QTUZSSM ¥MZVMZS ¥QSM^ YQZVMPU +- OY& @UWM NQNMZ _Q]^QN`_ PU_M]UW WQ NMbMT ^QVM`T - OY$ PMZ ¥Q]OQ¥M_MZ S]MaU_M^U 8`YU 4 )( Y'^* $ QZQ]SU ¥[_QZ^UMX QXM^_UW ¥QSM^ MPMXMT &&&& M& ($(*- V[`XQ N& ($(- V[`XQ O& ($) V[`XQ P& ($*- V[`XQ Q& ($- V[`XQ !;49187/:= %-,(" **& @UWM VM]U%VM]U 8`YU 4 .$, h )(. OY$ WQXMV`MZ XQ¥M^ ^`M_` ][WQ_ cMZS PUX`ZO`]WMZ aQ]_UWMX PM]U ¥Q]Y`WMMZ 8`YU MPMXMT &&&& M& , * WY'^ N& . * WY'^ O& 0 * WY'^ P& )( * WY'^ Q& )* * WY'^ !=79<8 &$$%" *+& GQN`MT ¥QSM^ cMZS YQYUXUWU ¥MZVMZS )- OY PUSMZ_`ZS ^QOM]M aQ]_UWMX& AQY`PUMZ$ YQZPM¥M_WMZ SMcM _M]UW ($- C PMZ ¥MZVMZSZcM NQ]_MYNMT )* OY& EMZVMZS ¥QSM^ VUWM PU_M]UW PQZSMZ SMcM ($. C MPMXMT &&&& M& +*$, OY P& *1$( OY N& +)$, OY Q& *0$- OY O& *1$, OY *,& GQN`MT ¥QSM^ PUSMZ_`ZSU NQNMZ NQ]YM^^M +(( S$ WQY`PUMZ PU_M]UW ^QTUZSSM YQYUXUWU R]QW`QZ^U SQ]MW TM]Y[ZU^ ¥QSM^ ^QNQ^M] * >d& BM^^M NQZPM cMZS TM]`^ PU_MYNMTWMZ MSM] R]QW`QZ^U SQ]MW TM]Y[ZU^ ¥QSM^ YQZVMPU )$- >d MPMXMT &&&& M& )-( S P& ,)0 S N& *++ S Q& -++ S O& +,0 S *-& EMPM SQ]MW TM]Y[ZUW ¥QSM^$ VUWM YM^^M NQNMZ cMZS PUSMZ_`ZS ¥MPM `V`ZS NMbMT ¥QSM^ ) WS$ ¥Q]U[PQ SQ_M]MZZcM * ^QW[Z& @UWM YM^^M NQNMZ PU_MYNMT TUZSSM YQZVMPU , WS$ ¥Q]U[PQ SQ_M]MZZcM MPMXMT &&&& M& ) , ^QW[Z N& ) * ^QW[Z O& ) ^QW[Z P& , ^QW[Z Q& 0 ^QW[Z !=79<8 %-,-" )& EMPM ^`^`ZMZ NQZPM%NQZPM ^Q¥Q]_U ¥MPM SMYNM]$ YM^^M NQZPM 7 PMZ 8 ^MYM$ cMU_` - WS& @UWM W[QRU^UQZ SMcM SQ^QW WUZQ_UW MZ_M]M NQZPM 7 PMZ NUPMZS YU]UZS $k 4 ($* PMZ _MZ $ 4 + , $ NQ]M¥MWMT ¥Q]OQ¥M_MZ ^Q_UM¥ NQZPM VUWM WQP`M NQZPM PUXQ¥M^WMZ6 *& GQN`MT NQZPM cMZS NQ]YM^^M 0 WS _Q]XQ_MW ¥MPM NUPMZS PM_M] PQZSMZ W[QRU^UQZ SQ^QWMZ ^_M_U^ZcM ($0& M& HQZ_`WMZ SMcM YUZUYMX `Z_`W YQZSSQ]MWWMZ NQZPM _Q]^QN`_& N& @UWM NQZPM _Q]^QN`_ PU¥QZSM]`TU SMcM ^QNQ^M] -, C cMZS ^QVMVM] PQZSMZ M]MT NUPMZS$ NMSMUYMZM WQMPMMZ NQZPM _Q]^QN`_6 +& :`M NQZPM _Q]^`^`Z ^Q¥Q]_U SMYNM]& BM^^M NQZPM ? 4 . WS PMZ YM^^M NQZPM ?? 4 , WS& A[QRU^UQZ SQ^QWMZ WUZQ_UW NQZPM ? PQZSMZ NUPMZS ^MYM PQZSMZ ($*- PMZ ¥Q]OQ¥M_MZ S]MaU_M^UZcM 4 )( Y'^* & >U_`ZSXMT ¥Q]OQ¥M_MZ WQP`M NQZPM PMZ _QSMZSMZ _MXU ¥QZST`N`ZS WQP`M NQZPM& ,& :`M NQZPM 7 PMZ 8 PUT`N`ZSWMZ PQZSMZ _MXU ]UZSMZ$ ^Q¥Q]_U ¥MPM SMYNM]& BM^^M 7 4 . WS PMZ YM^^M 8 4 0 WS != 4)( Y'^* "& @UWM SMcM , YQZPM_M] ^QNQ^M] -. C PMZ W[QRU^UQZ SQ^QWMZ NQZPM PQZSMZ XMZ_MU ($*$ _QZ_`WMZ2 M& ¥Q]OQ¥M_MZ cMZS _UYN`X3 PMZ N& _QSMZSMZ _MXU& 0# 5>O>?G>C JAKM>IP>>I ?AKDFNM DID @AIB>I MAJ>M# F A B I II A = 5 kg B = 5 kg $

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67 A. Gaya Dapat Melakukan Usaha B. Energi dan Usaha C. Gaya Konservatif dan Hukum Kekekalan Energi Mekanik D. Daya >]T`VX aP]VPb SXQcbcWZP] ¥P]caXP SP[P¥ ¥T[PZcZP] PZbXdXbPa]gP aTWP`X(WP`X) ;P]gPZ PZbXdXbPa(PZbXdXbPa _`X¥T` ¥P]caXP gP]V ¥T¥QcbcW( ZP] T]T`VX' aT_T`bX ¥T¥PaPZ' ¥T]RcRX _PZPXP]' SP] aTQPVPX ac¥QT` _T]T`P]VP] _PSP ¥P[P¥ WP`X) KT[PX] PZbXdXbPa _`X¥T`' QP]gPZ PZbXdXbPa [PX]]gP gP]V ¥T¥QcbcWZP] T]T`VX' SX P]bP`P]gP ^[PW`PVP) IPSP VP¥QP` SX PbPa' aT^`P]V Pb[Tb aTSP]V ¥T]VP]VZPb QTQP] gP]V aP]VPb QT`Pb) :b[Tb bT`aTQcb WP`ca SP_Pb ¥T]VcZc`' P_PZPW XP ¥P¥_c PbPc bXSPZ ¥T]VP]VZPb QTQP] bT`aTQcb) KT[P¥P _`^aTa [PbXWP]' Pb[Tb bT`aTQcb WP`ca ¥T]VWXbc]V QT`P_P QP]gPZ ZP[^`X gP]V WP`ca XP Z^]ac¥aX ac_PgP SP[P¥ _T`[^¥QPP] XP SP_Pb ¥T]VP]VZPb QTQP] gP]V SXX]VX]ZP]) =P[P¥ QPQ X]X' PZP] SXQPWPa bT]bP]V caPWP' T]T`VX' SPgP' SP] WcQc]VP] P]bP`P ZTbXVP]gP) D^]aT_ ?XaXZP bT]bP]V caPWP' T]T`VX' SP] SPgP X]X QP]gPZ aTZP[X P_[XZPaX]gP SP[P¥ ZTWXSc_P] aTWP`X(WP`X) Usaha, Energi, dan Daya Pada saat atlet angkat besi mengangkat beban, sebetulnya ia sedang melakukan kerja pada beban yang disimpan sebagai energi potensial. Sumber: Fundamentals of Physics,2001 • menganalisis hubungan antara usaha, perubahan energi dan hukum kekekalan energi mekanik; • menerapkan hukum kekekalan energi mekanik untuk menganalisis gerak dalam kehidupan sehari-hari. Setelah mempelajari bab ini, Anda harus mampu: menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik. Hasil yang harus Anda capai: Bab 3

68 Mudah dan Aktif Belajar Fisika untuk Kelas XI A. Gaya Dapat Melakukan Usaha :VP` :]SP [TQXW ¥T¥PWP¥X _T]VT`bXP] caPWP SP[P¥ ZTWXSc_P] aTWP`X(WP`X' _T[PYP`X ¥PbT`X QT`XZcb X]X) 1. Pengertian Usaha IPSP aPPb SX ZT[Pa' :]SP QT`caPWP QT[PYP` ¥PZaX¥P[ c]bcZ ¥T¥_T`^[TW ]X[PX bX]VVX) DTbXZP QT[PYP`' :]SP ¥T]VVc]PZP] bT]PVP SP] _XZX`P]) =P[P¥ ZTWXSc_P] aTWP`X(WP`X' caPWP SXSTUX]XaXZP] aTQPVPX _TZT`YPP] gP]V SX[PZcZP] c]bcZ ¥T¥_T`^[TW bcYcP] gP]V SXX]VX]ZP]) FT]c`cb :]SP' P_PZPW _T]VT`bXP] caPWP SP[P¥ UXaXZP aP¥P ST]VP] _T]VT`bXP] caPWP SP[P¥ ZTWXSc_P] aTWP`X(WP`X bT`aTQcb9 MaPWP SP[P¥ UXaXZP aT[P[c QT`WcQc]VP] ST]VP] b`P]aUT` T]T`VX SP] VPgP) KX¥PZ[PW R^]b^W QT`XZcb) KTQcPW ¥^QX[ ¥^V^Z SXS^`^]V ^[TW L^VP` ST]VP] VPgP 5 aTWX]VVP ¥^QX[ QT`_X]SPW bT¥_Pb aTYPcW S SP`X _^aXaX PeP[]gP) DTbXZP L^VP` ¥T]S^`^]V ¥^QX[ bT`aTQcb aTWX]VVP ¥^QX[ QT`VT`PZ' L^VP` ¥T[PZcZP] caPWP' gPXbc ¥T]b`P]aUT` T]T`VX ¥T[P[cX VPgP S^`^]V _PSP ¥^QX[ aTWX]VVP ¥^QX[ QT`VT`PZ SP] QT`_X]SPW aTYPcW S) ;TaP` caPWP #9$ gP]V SX[PZcZP] L^VP` c]bcZ ¥T]S^`^]V ¥^QX[ ^[TW VPgP aP¥P ST]VP] WPaX[ ZP[X VPgP 5 ST]VP] _T`_X]SPWP] S) 9 , 5 ' S #.j,$ DTbT`P]VP]5 9 , caPWP #Y^c[T$ 5 8 VPgP #G$ S 8 _T`_X]SPWP] #¥$ MaPWP PSP[PW QTaP`P] aZP[P`' eP[Pc_c] VPgP 5 SP] _T`_X]SPWP] S ¥T`c_PZP] dTZb^`) FT]c`cb _T`ZP[XP] dTZb^` #)$' WPaX[]gP WP`ca QT`c_P aZP[P`) MaPWP gP]V SX[PZcZP] ^[TW VPgP Z^]abP] 5 gP]V ¥T¥QT]bcZ acScb & bT`WPSP_ P`PW _T`_X]SPWP] QT]SP' aT_T`bX bT`[XWPb _PSP 6CNDCR )%(' QTaP` caPWP]gP PSP[PW 9 , 1 K R^a & #.j-$ NTZb^` 5 SP_Pb SXc`PXZP] ¥T]YPSX ScP Z^¥_^]T] VPgP gP]V aP[X]V bTVPZ [c`ca' gPXbc Z^¥_^]T] 5 R^a& gP]V aTP`PW ST]VP] P`PW _T`_X]SPWP] QT]SP SP] 5 aX]& gP]V bTVPZ [c`ca ST]VP] P`PW _T`_X]SPWP]) LT`]gPbP' WP]gP Z^¥_^]T] VPgP gP]V aTP`PW ST]VP] _T`_X]SPWP] gP]V ¥T]VWPaX[ZP] caPWP' gPXbc aTQTaP` 5 K R^a&) ;T`XZcb X]X QTQT`P_P ZTPSPP] XabX¥TeP gP]V SXWPaX[ZP] =GRSCNCCO !)Z(") P) & 8 +i5 M]bcZ & 8 +i' P`PW VPgP aTP`PW ST]VP] P`PW _T`_X]SPWP] aTWX]VVP SX_T`^[TW 9 , 1 K R^a +i 9 , 1 K #.j.$ ,) CT[PaZP] ST]VP] QPWPaP :]SP aT]SX`X _T]VT`bXP] caPWP SP] T]T`VX) -) :_PZPW _PSP aTQcPW Q^[P gP]V PZP] SXbT]SP]V bT`SP_Pb T]T`VX _^bT]aXP[9 ?GDGMUN NGNQGMCKCRJ LPOSGQ ASCIC# 4OGRHJ# FCO 3CYC# LGRKCLCOMCI SPCM$SPCM DGRJLUT FCMCN DULU MCTJICO% Gambar 3.1 Togar melakukan usaha(W) dengan mentransfer energi melalui gaya dorong F sehingga mobil berpindah sejauh s. F s .) KTQcbZP] R^]b^W(R^]b^W _T]T`P_P] AcZc¥ DTZTZP[P] >]T`VX gP]V PSP SX aTZXbP` :]SP) /) :_P _T`QTSPP] SPgP SP] T]T`VX9 Tes Kompetensi Awal Gambar 3.2 (a) Usaha oleh gaya F yang membentuk sudut & terhadap perpindahan benda s. (b) Penguraian vektor F menjadi komponen-komponennya. F sin& F cos& F #Q$ & arah perpindahan F s & #P$

Usaha, Energi, dan Daya 69 KTQcPW VPgP bTbP_ aTQTaP` -0 G QTZT`YP _PSP aTQcPW QT]SP gP]V QT`¥PaaP / ZV) CXZP acScb gP]V SXQT]bcZ P]bP`P VPgP 5 SP] QXSP]V SPbP` PSP[PW .2i' QT`P_P caPWP gP]V SX[PZcZP] VPgP Xbc bT`WPSP_ QT]SP aT[P¥P / STbXZ9 9CWCD0 =XZTbPWcX5 1 8 -0 G6 F 8 / ZV6 & 8 .2i) 1 <HK & 8 F : : , 1 R^a F & 8 #-0 G$R^a .2 / ZV $ 8 0 ¥*aQ) & 8 4+i5 M]bcZ & 8 4+i' P`PW VPgP 1 bTVPZ [c`ca ST]VP] P`PW _T`_X]SPWP] aTWX]VVP SX_T`^[TW 9 , 1 K R^a 4+i 9 , + #.j/$ CXZP 9 , +' QT`P`bX VPgP bT`aTQcb bXSPZ ¥T[PZcZP] caPWP) =T]VP] ZPbP [PX]' VPgP gP]V bTVPZ [c`ca ST]VP] P`PW _T`_X]SPWP] QT]SP' P`bX]gP VPgP bT`aTQcb bXSPZ ¥T[PZcZP] caPWP) R) & 8 ,3+i5 DTPSPP] X]X ¥T]gPbPZP] QPWeP P`PW VPgP QT`[PeP]P] ST]VP] P`PW _T`_X]SPWP] aTWX]VVP SX_T`^[TW 9 , 1 K R^a ,3+i 9 , 1 K #j,$ 9 , S 1 K #.j0$ <^]b^W caPWP ]TVPbXU' gPXbc aT^`P]V _T]VT]SP`P aT_TSP gP]V aTSP]V ¥T¥PRc aT_TSP]gP' bXQP(bXQP ¥T]VT`T¥ aT_TSP]gP) MaPWP gP]V SX[PZcZP] ^[TW VPgP VTaTZ gP]V bT`YPSX P]bP`P ZTScP QP] aT_TSP ST]VP] YP[P]' QT`]X[PX ]TVPbXU ZP`T]P VPgP VTaTZ QT`[PeP]P] P`PW ST]VP] P`PW _T`_X]SPWP] aT_TSP) ;TaP`]gP caPWP ]TVPbXU bT`aTQcb aTQP]SX]V ST]VP] VPgP VTaTZ SP] _T`_X]SPWP] gP]V SXbT¥_cW aT_TSP aT[P¥P VPgP VTaTZ QTZT`YP) =T]VP] ST¥XZXP]' aT_TSP ¥T]VP[P¥X VT`PZ SX_T`[P¥QPb) S) IT`_X]SPWP] QT]SP K , +5 IPSP 6CNDCR )%)' ?PS[X aTSP]V QT`SX`X aP¥QX[ ¥T]VVT]S^]V bPa) LPa bT`aTQcb ¥T¥X[XZX VPgP QT`Pb aTQTaP` O ST]VP] P`PW ZT QPePW) ;TaP` VPgP bP`XZ bP[X bPa ^[TW _c]VVc]V ?PS[X #5$ aP¥P ST]VP] QTaP` VPgP QT`Pb bPa W aTWX]VVP bPa SP[P¥ ZTPSPP] aTbX¥QP]V) @PgP `TPZaX ZT PbPa ^[TW _c]VVc]V ?PS[X _PSP bP[X bPa bT`aTQcb bXSPZ SXWXbc]V aTQPVPX caPWP ZP`T]P bXSPZ PSP _T`_X]SPWP] _PSP bPa PZXQPb VPgP `TPZaX) =P`X =GRSCNCCO !)Z("' SXSP_PbZP] QPWeP 9 , 1 K R^a & 9 , 1#+$ R^a& 9 , + <^]b^W [PX] PSP[PW aT^`P]V P]PZ gP]V QT`aP]SP` _PSP SX]SX]V #6CNDCR )%*$) =X]SX]V bXSPZ QT`VTaT` ZP`T]P VPgP gP]V SX[PZcZP]]gP bXSPZ RcZc_ ZcPb c]bcZ ¥T]VVTaT` SX]SX]V) =T]VP] ST¥XZXP]' caPWP gP]V SX[PZcZP] ^[TW VPgP S^`^]V]gP aP¥P ST]VP] ]^[) IT`[c :]SP ZTbPWcX' aPbcP] caPWP PSP[PW Y^c[T #SXaX]VZPb C$' 7:LM CHME> =B=>?BGBKBD:G K>;:@:B ;>K:J MK:A: Q:G@ =BE:DMD:G HE>A @:Q: K>;>K:J K:LM G>OLHG MGLMD F>FBG=:AD:G ;>G=: K>C:MA K:LM F>L>J) F Gambar 3.3 Fadli sedang menggendong tas. w Gambar 3.4 Seorang anak sedang bersandar pada dinding. F Contoh 3.1 F F cos& & s

70 Mudah dan Aktif Belajar Fisika untuk Kelas XI KTQcPW QT]SP QT`¥PaaP 3 ZV bT`[TbPZ SX PbPa QXSP]V SPbP` ZPaP` ST]VP] Z^TUXaXT] VTaTZ ZX]TbXZ +'-) ;T]SP bT`aTQcb SXbP`XZ aTYPcW 1 ¥TbT` ST]VP] [PYc bTbP_) ;T`P_PZPW caPWP gP]V SXWPaX[ZP] ^[TW VPgP bP`XZ bT`aTQcb YXZP bP`XZP]]gP aTYPYP` ST]VP] [P]bPX9 #SXZTbPWcX @8,+ ¥*a- $ 9CWCD0 =XZTbPWcX5 F 8 3 ZV6 K 8 1 ¥ ? Z 8 +'-6 ' 8 ,+ ¥*a- ;TaP`]gP caPWP ^[TW VPgP bP`XZ PSP[PW 9 8 1 'S , 1 R^a& K H[TW ZP`T]P & , +R ¥PZP QTaP` caPWP PSP[PW 9 8 1 K ;TaP` VPgP 1 ¥PaXW QT[c¥ SXZTbPWcX) H[TW ZP`T]P [PYc QT]SP bTbP_ ¥PZP QTaP` `Tac[bP] VPgP %1 8 + 1P S ?D8 + #_PSP ac¥Qc-P$ SP] 1Q$4S O 8 + #_PSP ac¥Qc-Q$ aTWX]VVP 1 R^a +i S &D 4 , ( )))#,$ 1 aX] +i $ 4 S O , ( * 48 9 )))#-$ KcQabXbcaXZP] #,$ ZT #-$' SX_T`^[TW 1 S &D O ,( * 1 , &D F@ 1 , #+'-$#3 ZV$#,+ ¥*a- $8 ,1 G) ¥PZP 9 8 1 K , #,1 G$#1 ¥$ 841 C) CPSX' caPWP gP]V SX[PZcZP] VPgP bT`aTQcb PSP[PW 41 C) James Prescott Joule (1824–1907) James Prescott Joule lahir di Salford, Inggris. Ia adalah fisikawan kenamaan Inggris yang berperan dalam perumusan Hukum Kekekalan Energi. Pada 1840, Joule mendeklarasikan sebuah hukum, yang dikenal sebagai Hukum Joule, yaitu tentang panas yang diproduksi dalam konduktor listrik. Untuk menghormati jasajasanya, nama Joule digunakan sebagai satuan energi dan usaha. Tokoh Sumber:Jendela Iptek, 1997 Contoh 3.2 Contoh 3.3 F N f k s w K 8 1 2 : L - 8 1 2 #0 ¥*a- $#/ a$- 8 /+ ¥ 9 , 1 K R^a& 8 #-0 G$#/+ ¥$#+'3$ 8 3++ C CPSX' caPWP gP]V SX[PZcZP] VPgP 1 PSP[PW 3++ Y^c[T) FPaaP aT^`P]V _T]VT]SP`P ¥^b^` SP] aT_TSP ¥^b^`]gP PSP[PW -++ ZV) KT_TSP ¥^b^` X]X ¥T[c]Rc` ST]VP] ZT[PYcP] /+ ¥*a) DT¥cSXP]' ¥^b^` SX`T¥ WX]VVP QT`WT]bX aTbT[PW 3 STbXZ) LT]bcZP] caPWP gP]V SX[PZcZP] aT[P¥P _T]VT`T¥P] QT`[P]Vac]V) 9CWCD0 =XZTbPWcX5 F 8 -++ ZV6 N + 8 /+ ¥*a6 L 8 3 STbXZ) KT_TSP ¥^b^` QT`WT]bX5 N b , + N b 8 N + & : L + 8 /+ ¥*a & : #3 a$ : 8 j0 ¥*aK , N( L & , - : L - 8 #/+ ¥*a$#3 a$ & , - #j0 ¥*a- $#3 a$- 8 #.-+ ¥ j ,1+ ¥$ 8 ,1+ ¥ 9 8 1 K #ZP`T]P P`PW VPgP aTYPYP` ST]VP] _T`_X]SPWP] QT]SP$ 9 8 F : K 8 #-++ ZV$#j0 ¥*a$#,1+ a$ 8 j,1+)+++ C) CPSX' caPWP gP]V SX[PZcZP] aT[P¥P _T]VT`T¥P] PSP[PW j,1+ ZC)

Usaha, Energi, dan Daya 71 KT_^b^]V QP[^Z ZPgc gP]V ¥PaaP]gP / ZV bT`[TbPZ SX PbPa QXSP]V SPbP`) DT¥cSXP]' QP[^Z ZPgc bT`aTQcb ¥T]VP[P¥X VT`PZ [c`ca gP]V SXaTQPQZP] ^[TW VPgP gP]V QTaP`]gP QT`cQPW(cQPW bT`WPSP_ ZTScScZP] QP[^Z' aT_T`bX bP¥_PZ _PSP VP¥QP`) LT]bcZP] b^bP[ caPWP gP]V SX[PZcZP] VPgP _PSP QP[^Z WX]VVP QT`_X]SPW aTYPcW 2 ¥) 9CWCD0 ,) 9:;<=, [cPa b`P_TaXc¥ :;<= 8 ! := ;< :; / - /+ ! - - " " # # ,-+ Y^c[T -) 9=> , [cPa => 8 + .' 9>?@ , [cPa aTVXbXVP >?@ 8 , - #>@ m @?$ 8 , - #- m #j/+$$ 8 j/+ C CPSX' caPWP b^bP[ c]bcZ + 7 P 7 2PSP[PW 9b^bP[ 8 9:;<= & 9=> & 9>?@ , #,-+ $ + j /+$ C 8 3+ C Gambar 3.6 Grafik gaya (F) terhadap perpindahan (s) dengan gaya (F) tidak konstan atau berubahubah. F (N) B C D E G A 2 4 5 7 s F –40 40 Gambar 3.7 Usaha merupakan luas daerah arsir di antara s1 dan s2 pada kurva antara gaya F dan perpindahan s. 2. Menentukan Usaha dari Grafik Gaya Terhadap Perpindahan IPSP c`PXP] aTQT[c¥]gP' VPgP 1 gP]V SXVc]PZP] QT`]X[PX Z^]abP] c]bcZ ¥T]VWPaX[ZP] caPWP _PSP QT]SP gP]V QT`_X]SPW aTYPcW K' CXZP :]SP ¥T¥QcPb V`PUXZ 1#b$ bT`WPSP_ K #_T`_X]SPWP]$ _PSP VPgP Z^]abP] 1' :]SP PZP] ¥T¥_T`^[TW V`PUXZ aT_T`bX _PSP 6CNDCR )%+) ;T`SPaP`ZP] V`PUXZ bT`aTQcb' QTaP` caPWP gP]V SXWPaX[ZP] ^[TW VPgP Z^]abP] 5 aTWX]VVP QT]SP QT`_X]SPW aTYPcW "S aP¥P ST]VP] [cPa SPT`PW SX QPePW Zc`dP 1#b$) M]bcZ caPWP gP]V SXWPaX[ZP] VPgP 5 gP]V QTaP`]gP QT`cQPW(cQPW' PZP] SXSP_PbZP] aTQcPW V`PUXZ aT_T`bX _PSP 6CNDCR )%,) EcPa SPT`PW gP]V SXP`aX` QT`PSP SX P]bP`P VP`Xa ac¥Qc(K SP] VP`Xa ac¥Qc(1' MaPWP b^bP[ gP]V bT`YPSX _PSP 6CNDCR )%, ¥T`c_PZP] _T]Yc¥[PWP] aTbXP_ caPWP SP`X K , aP¥_PX ST]VP] K - ) CPSX' SP_Pb SXbc[XaZP] - , K LHL:E K 9 1 # "K #.j1$ IT]STZPbP] bT`QPXZ PSP[PW ST]VP] RP`P ¥T¥_T`ZTRX[ "K aP¥_PX ¥T]STZPbX ]^[ PbPc + [X¥ " $K ) H[TW ZP`T]P Xbc' aTRP`P ¥PbT¥PbXa =GRSCNCCO !)Z-" ¥T]YPSX - , + [X¥ K LHL:E K K 9 1 K " $ # " #.j2$ PbPc - - , , + [X¥ K K K K K 1 K 1=K " $ " # ! #.j3$ :`bX X]bTV`P[ _PSP =GRSCNCCO !)Z." PSP[PW [cPa SPT`PW gP]V SXP`aX` SX P]bP`P Zc`dP QTaP` VPgP 1 SP] QTaP` _T`_X]SPWP] K' Contoh 3.4 "s s1 s2 s F Kata Kunci • usaha negatif • usaha nol • usaha positif Gambar 3.5 Pada besar F konstan, W = luas daerah di bawah kurva F(t). s "s 1 s2 F s F = s F(t) s1 s2 s F 2 1 s s Fds !

72 Mudah dan Aktif Belajar Fisika untuk Kelas XI B. Energi dan Usaha IT`]PWZPW :]SP ¥T[XWPb aTTZ^` ZcSP gP]V aTSP]V ¥T]P`XZ VT`^QPZ gP]V _T]cW ST]VP] ¥cPbP]9 DTbXZP ZcSP aTSP]V ¥T]P`XZ VT`^QPZ SP[P¥ ePZbc gP]V RcZc_ [P¥P' QXPaP]gP ]P_Pa ZcSP bT`[XWPb bT`aT]VP[(aT]VP[) FT]VP_P ST¥XZXP]9 DcSP bT`aTQcb bT[PW ¥T]VT[cP`ZP] T]T`VX gP]V SX( Vc]PZP] c]bcZ ¥T[PZcZP] caPWP) =T]VP] ST¥XZXP]' >G>J@B :=:E:A KM:LM D>F:FIM:G MGLMD F>E:DMD:G MK:A:) 1. Energi Kinetik dan Teori Usaha-Energi LT[PW :]SP _T[PYP`X _PSP acQQPQ aTQT[c¥]gP QPWeP caPWP SP_Pb bT`YPSX _PSP VPgP Z^]abP] PbPc VPgP gP]V QT`cQPW(cQPW' DTScP YT]Xa caPWP bT`aTQcb ¥T¥X[XZX ZTaP¥PP]' gPXbc PSP]gP VPgP gP]V QTZT`YP _PSP QT]SP aTWX]VVP QT]SP QT`VT`PZ' [PYc]gP Z^]abP]' PbPc ¥T¥X[XZX _T`RT_PbP]) KTZP`P]V PZP] SXQPWPa ZTPSPP] ST]VP] `Tac[bP] VPgP 1 Z^]abP]) @PgP bT`aTQcb QTZT`YP _PSP QT]SP QT`¥PaaP F SP] PZP] ¥T]VWPaX[ZP] _T`RT_PbP] :) FT]c`cb AcZc¥ BB GTeb^]' QTaP` _T`RT_PbP] bT`aTQcb PSP[PW 1 : F # ) :SP_c] _T`aP¥PP] QTaP` _T`_X]SPWP]]gP PSP[PW ! - - + , - L K NN : # # ) MaPWP gP]V SX[PZcZP] ^[TW VPgP bT`aTQcb PSP[PW 981K8F:K , ! ! # - - + , - F: N N L : 9 , - - + , , - - FN FN L # #.j4$ ,) KT^`P]V aXaeP ¥T]S^`^]V aTQcPW ¥TYP ST]VP] VPgP 3+ G) ;T`P_PZPW caPWP gP]V SX[PZcZP] ^[TW VPgP S^`^]V PVP` ¥TYP QT`_X]SPW aTYPcW - ¥9 -) ;T`P_PZPW caPWP gP]V SX[PZcZP] c]bcZ ¥T]VP]VZPb aTQcPW ¥TaX] bXZ gP]V ¥PaaP]gP / ZV WX]VVP ZTbX]VVXP] - ¥ #@ 8 4'3 ¥*a- $9 .) KTQcPW QT]SP gP]V ¥PaaP]gP - ZV ¥T[c]Rc` ST]VP] ZTRT_PbP] ,+ ¥*a) H[TW ZP`T]P PSP _T]VP`cW VPgP VTaTZ P]bP`P [P]bPX SP] QT]SP' QT]SP QT`WT]bX aTbT[PW QT`VT`PZ 0 STbXZ) LT]bcZP] caPWP gP]V SX[PZcZP] ^[TW VPgP VTaTZ _PSP QT]SP bT`aTQcb) /) KTQcPW QT]SP QT`¥PaaP 0 ZV SXbP`XZ ZT PbPa _PSP QXSP]V ¥X`X]V ZPaP` ^[TW VPgP /+ G aTP`PW ST]VP] QXSP]V) KcScb ZT¥X`X]VP] QXSP]V bT`WPSP_ W^`Xh^]bP[ PSP[PW ' ' / 1 3 5 # 0 2 . bP] / aTWX]VVP QT]SP QT`_X]SPW Tes Kompetensi Subbab A :GRKCLCOMCI FCMCN DULU MCTJICO% aTYPcW / ¥) CXZP Z^TUXaXT] VTaTZP] P]bP`P QT]SP ST]VP] QXSP]V +'- SP] . bP] / ' # ' WXbc]V[PW caPWP gP]V SX[PZcZP] ^[TW VPgP QT`Pb SP] VPgP VTaTZ ZX]TbXZ) 0) KTQcPW VPgP 1 gP]V QT`cQPW(cQPW QTZT`YP _PSP aTQcPW QT]SP aTWX]VVP QT]SP ¥T]VP[P¥X _T`cQPWP] aT_T`bX V`PUXZ _PSP VP¥QP` QT`XZcb) AXbc]V caPWP gP]V SX[PZcZP] ^[TW VPgP 1 _PSP QT]SP c]bcZ YP`PZ aTYPcW 3 ¥) 2 4 6 8 F (N) 4 – 4 x (cm) 7

Usaha, Energi, dan Daya 73 :]SP bT[PW ¥T]VTbPWcX QPWeP caPWP PSP[PW _`^aTa b`P]aUT` T]T`VX ¥T[P[cX VPgP aTWX]VVP QT]SP QT`VT`PZ) DTbXZP QT]SP QT`VT`PZ' QT]SP ¥T¥X[XZX ZTRT_PbP] SP] ¥T]VWPaX[ZP] T]T`VX ZX]TbXZ) ;T`SPaP`ZP] =GRSCNCCO !)Z/"' T]T`VX ZX]TbXZ QT]SP SX]gPbPZP] ST]VP] 0D 8 , - FN- #.j,+$ DTbT`P]VP]5 0D 8 T]T`VX ZX]TbXZ #C$ F 8 ¥PaaP QT]SP #ZV$ N 8 ZT[PYcP] QT]SP #¥*a$ =T]VP] ST¥XZXP]' 9 8 0Z- S 0Z, #.j,,$ CPSX' caPWP gP]V SXWPaX[ZP] VPgP `Tac[bP] _PSP _P`bXZT[ bT`aTQcb aP¥P ST]VP] _T`cQPWP] T]T`VX ZX]TbXZ _P`bXZT[ 9 8 " 0Z #.j,-$ =GRSCNCCO !)Z'(" SXZT]P[ ST]VP] bT^`T¥P caPWP(T]T`VX c]bcZ _P`bXZT[) Tugas Anda 3.1 Amatilah perubahan energi yang terjadi di sekitar Anda. Diskusikanlah hal tersebut bersama teman Anda, apakah perubahan energi yang terjadi akan memengaruhi usaha yang dilakukan? Gambar 3.8 Besar usaha yang dilakukan oleh pengemudi becak sama dengan besar gaya yang bekerja pada becak dikalikan dengan besar perpindahannya. Vt V0 F s A B KTQcPW ZT[T`T]V QT`¥PaaP -+ V) H[TW ZP`T]P _T]VP`cW VPgP' ZT[T`T]V QT`VT`PZ ST]VP] ZT[PYcP] bTbP_ /+ R¥*a) LT]bcZP] T]T`VX gP]V SX¥X[XZX ZT[T`T]V bT`aTQcb) 9CWCD5 =XZTbPWcX5 F 8 -m,+j- ZV N 8 /+ R¥*a 8 +'/ ¥*a 0D 8 , - FN- 8 , - #-m,+j- ZV$#+'/ ¥*a$- 8 ,'1 m ,+j. C) CPSX' T]T`VX ZX]TbXZ gP]V SX¥X[XZX ZT[T`T]V PSP[PW ,'1 m ,+j. C) Contoh 3.5 IPZc QT`¥PaaP 0 V bT`[T_Pa SP`X bP]VP] aT^`P]V bcZP]V ZPgc) DTbXZP _PZc ¥T]gT]bcW bP]PW' ZT[PYcP]]gP .+ ¥*a) CXZP VPgP VTaTZ _PZc bT`WPSP_ bP]PW aTQTaP` /0 G' WXbc]V[PW ZTSP[P¥P] _PZc gP]V ¥T]P]RP_ SP[P¥ bP]PW) 9CWCD0 =XZTbPWcX5 F 8 0 V N , 8 .+ ¥*a 1 8 /0 G 9 8 ! 2 2 2 1 , - # # m N N 1 K 8 #j , - $#0 m ,+j. ZV$#+ j .+- ¥*a- $ /0 K 8 -'-0 *K, +'+0 ¥) CPSX' ZTSP[P¥P] _PZc gP]V ¥T]P]RP_ SP[P¥ bP]PW PSP[PW +'+0 ¥) Contoh 3.6 s F

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76 Mudah dan Aktif Belajar Fisika untuk Kelas XI Gambar 3.13 (a) Keadaan awal benda dalam posisi seimbang. (b) Pegas ditarik sejauh simpangan y2 . (c) Posisi benda kembali ke titik setimbang karena gaya pegas F = –ky2 . ;T`P_PZPW T]T`VX _^bT]aXP[ gP]V SX¥X[XZX ^[TW /++ ¥. PX` gP]V QT`PSP _PSP ZTbX]VVXP] 4+ ¥' YXZP ¥PaaP YT]Xa PX` ,)+++ ZV*¥. SP] _T`RT_PbP] V`PdXbPaX SX bT¥_Pb bT`aTQcb ,+ ¥*a9 9CWCD0 :X` bT`Yc] bT`aTQcb ¥T¥X[XZX ¥PaaP F , ( 8 8 #,)+++ ZV*¥. $#/++ ¥. $ 8 / m ,+0 ZV >]T`VX _^bT]aXP[ gP]V SX¥X[XZX PX` bT`Yc] PSP[PW 0I 8 F @ A , #/ m ,+0 ZV$#,+ ¥*a- $#4+ ¥$ 8 .'1 m ,+3 C CPSX' T]T`VX _^bT]aXP[ gP]V SX¥X[XZX PX` bT`Yc] PSP[PW .'1 m ,+3 Y^c[T) b. Energi Potensial Elastis Pegas >]T`VX _^bT]aXP[ T[PabXa _TVPa QT`QTSP ST]VP] T]T`VX _^bT]aXP[ _PSP c¥c¥]gP) >]T`VX _^bT]aXP[ _TVPa PSP[PW T]T`VX gP]V SX¥X[XZX _TVPa PZXQPb PSP]gP _T`cQPWP] _P]YP]V PbPc `TVP]VP] _TVPa) @PgP gP]V QTZT`YP _PSP _TVPa ¥T¥c]VZX]ZP] _TVPa c]bcZ ¥T`TVP]V) IT`WPbXZP] 6CNDCR )%')) IPSP 6CNDCR )%')!C"' ¥c[P(¥c[P _TVPa SP[P¥ ZTPSPP] aTbX¥QP]V' >]T`VX _^bT]aXP[ _TVPa SP] T]T`VX ZX]TbXZ]gP ]^[) IPSP 6CNDCR )%')!D" SP] 6CNDCR )%')!E"' _TVPa ¥T¥X[XZX aX¥_P]VP] aTYPcW Q * SP] Q * ! #_P]YP]V Q *, Q* "#) H[TW ZP`T]P PSP bP`XZP] aTQTaP` 1 8 DQ SP] _TVPa ¥T]P`XZ ZT¥QP[X QT]SP aTacPX AcZc¥ BBB GTeb^]' "_TVPa8 jD''' ;TaP`]gP caPWP gP]V SX[PZcZP] _TVPa SP`X ZTPSPP] Q , 8 + ZT Q - 8 Q aP¥P QTaP` ST]VP] _T`cQPWP] T]T`VX _^bT]aXP[ _TVPa P]bP`P Q , 8 + SP] Q - 8Q) 9? _TVPa 8 1"S6 "K 8 QTaP` _T`_X]SPWP] _^aXaX QT]SP) 8 - + # # # ) ! Q Q Q 1 =Q 8 ! + # # ! Q DQ =Q 8 , - - DQ =T]VP] ST¥XZXP]' QTaP`]gP caPWP gP]V SX[PZcZP] ^[TW VPgP _TVPa SX]gPbPZP] ST]VP] _T`aP¥PP] 9? _TVPa 8 #"0_ _TVPa ST]VP] 0_ _TVPa 8 , - - DQ #.j-+$ DTbXZP _TVPa SX[T_PaZP]' _TVPa PZP] ¥T[PZcZP] VT`PZ WP`¥^]XZ) KT[P¥P _T`VT`PZP]]gP' _TVPa ¥T]VP[P¥X _T`cQPWP] T]T`VX ZX]TbXZ ¥T]YPSX T]T`VX _^bT]aXP[ _TVPa' PbPc aTQP[XZ]gP) LXSPZ aT[P¥P]gP _TVPa ¥T[PZcZP] VT`PZ WP`¥^]XZ' _T]VP`cW VPgP [cP` PZP] ¥T¥QcPb _TVPa QT`WT]bX _PSP _^aXaX ZTaTbX¥QP]VP]) #P$ #Q$ #R$ y2 ' y2 y1 =0 Contoh 3.8 P) IT`cQPWP] T]T`VX _^bT]aXP[5 "Ep 8 F@#A. j A- $ 8 #- ZV$#,+ ¥*a- $#0 ¥ j -+ ¥$ 8 j.++ C) CPSX' _T`cQPWP] T]T`VX _^bT]aXP[ aTQTaP` .++ Y^c[T) Q) MaPWP gP]V SX[PZcZP] VPgP QT`Pb5 98 jF@ #A; j A: $ 8 j#- ZV$#,+ ¥*a- $#0 ¥ j -+ ¥$ 8 .++ C) MaPWP _^aXbXU ZP`T]P P`PW VPgP QT`Pb aTP`PW ST]VP] P`PW _T`_X]SPWP]) CPSX' caPWP gP]V SX[PZcZP] VPgP QT`Pb aTQTaP` .++ Y^c[T) Sumber: Fisika untuk Sains dan Teknik, 1998 Tantangan untuk Anda Perhatikan gambar di atas. Jika seorang ahli gizi menyatakan bahwa pada pizza isi daging dan keju tersebut mengandung energi 16 megajoule, bagaimana pendapat Anda jika dikaitkan dengan konsep Fisika? Bagaimana cara mendapatkan angka tersebut?

Usaha, Energi, dan Daya 77 Tes Kompetensi Subbab B :GRKCLCOMCI FCMCN DULU MCTJICO% ,) KTQcPW QPbc ZTRX[ QT`¥PaaP / V SX[T_PaZP] SP`X ZPbP_T[ aTWX]VVP QTaP` T]T`VX ZX]TbXZ gP]V SX¥X[XZX]gP PSP[PW ,3+ Y^c[T) AXbc]V ZT[PYcP] QPbc bT`aTQcb) -) F^QX[ QT`¥PaaP ,0+ ZV aTSP]V QT`VT`PZ ST]VP] ZTRT_PbP] 2- Z¥*YP¥' bXQP(bXQP SX`T¥ SP] QT`WT]bX aTbT[PW ¥T]T¥_cW YP`PZ -+ ¥) LT]bcZP][PW5 P) VPgP `T¥ _PSP ¥^QX[6 SP] Q) caPWP gP]V SX_T`^[TW SP`X _T]VT`T¥P]) .) DT`TbP ¥PX]P] gP]V ¥PaaP]gP / ZV SX[T_PaZP] SP`X _c]RPZ QXSP]V ¥X`X]V [XRX] ST]VP] acScb ZT¥X`X]VP] .+i bT`WPSP_ W^`Xh^]bP[) CXZP _P]YP]V [X]bPaP] QXSP]V ¥X`X]V ,- ¥ SP] @ 8 ,+ ¥*a- ' bT]bcZP] _T`cQPWP] T]T`VX _^bT]aXP[ SX : SP] ZT`TbP aTbT[PW ¥T]T¥_cW YP`PZ ,+ ¥) /) ;T]SP QT`¥PaaP +'- ZV SX[T_PaZP] SP`X ZTbX]VVXP] ,++ R¥) P) AXbc]V[PW caPWP gP]V SX[PZcZP] VPgP V`PdXbPaX _PSP QT]SP bT`aTQcb) Q) AXbc]V[PW QT`Zc`P]V]gP T]T`VX _^bT]aXP[ V`PdXbPaX QT]SP bT`aTQcb) 0) ;T]SP F QT`¥PaaP , ZV YPbcW ¥T]VVT[X]RX` SP`X PbPa QXSP]V ¥X`X]V ST]VP] acScb ZT¥X`X]VP] .2i) ;T]SP bT`aTQcb ¥T]c¥QcZ aTQcPW _TVPa gP]V bT`[TbPZ , ¥ SP`X [TbPZ F aT¥c[P) CXZP D 8 -++ G*¥ SP] _TVPa bT`bTZP] ¥PZaX¥c¥ aTYPcW ,+ R¥' WXbc]V Z^TUXaXT] VTaTZ P]bP`P QP[^Z F ST]VP] QXSP]V ¥X`X]V) Kata Kunci • energi kinetik • energi potensial ITVPa QT`bP¥QPW _P]YP]V ,+ R¥ ZTbXZP SXQT`X VPgP ,+ G) ;T`P_PZPW T]T`VX _^bT]aXP[ _TVPa YXZP VPgP _PSP _TVPa bT`aTQcb SXYPSXZP] -'0 ZP[X [X_Pb9 9CWCD0 =XZTbPWcX5 1, 8 ,+ G6 P, 8 ,+ R¥ 8 +', ¥) D 8 , , P F 8 ,+ G +', ¥ 8 ,++ G*¥) CXZP 1- 8 -'0 1, 8 #-'0$#,+ G$ * 1- 8 -0 G) P - 8 - - D F 8 -0G ,++ G*¥ 8 ,++ G*¥ 8 +'-0 ¥) 0I 8 , - DP- 8 , - #,++ G*¥$#+'-0 ¥$- 8 .',-0 C) CPSX' QTaP` T]T`VX _^bT]aXP[ T[PabXa _TVPa PSP[PW .',-0 C) Contoh 3.9 C. Gaya Konservatif dan Hukum Kekekalan Energi Mekanik IT`WPbXZP] 6CNDCR ))'*!C") KTQcPW _TVPa SX[TbPZZP] SX PbPa [P]bPX SP] aP[PW aPbc cYc]V]gP SXXZPbZP] _PSP SX]SX]V) DT¥cSXP]' aTQcPW QP[^Z QT`¥PaaP F ¥T[c]Rc` ST]VP] ZTRT_PbP] % bT_Pb ZT P`PW _TVPa) CXZP [P]bPX SPbP` SP] [XRX]' aT`bP _TVPa]gP XSTP[' aXabT¥ PZP] ¥T¥T]cWX AcZc¥ A^^ZT' 5 8 jDX' ST]VP] 5 PSP[PW VPgP _PSP _TVPa aPPb cYc]V QTQPa]gP QT`VTaT` aTYPcW &) DTPSPP] gP]V SXX]VX]ZP] _PSP aXabT¥ bT`aTQcb PSP[PW T]T`VX ZX]TbXZ bT`_caPb _PSP ¥PaaP QP[^Z aTWX]VVP T]T`VX ZX]TbXZ _TVPa SXPQPXZP]) :ZXQPb]gP' ¥PaaP _TVPa SXP]VVP_ aP]VPb ZTRX[ SP`X_PSP ¥PaaP QP[^Z) DTbXZP QP[^Z ¥T]gT]bcW _TVPa' [PYc QP[^Z QT`Zc`P]V aP¥_PX PZWX`]gP QT`WT]bX ZP`T]P VPgP _TVPa gP]V ¥T[PeP] VPgP S^`^]VP] SP`X QP[^Z) IT`WPbXZP] 6CNDCR ))'*!D") DT¥cSXP]' P`PW QP[^Z QT`QP[XZ PZXQPb VPgP _TVPa QTZT`YP) :ZXQPb]gP' QP[^Z ¥T¥_T`^[TW T]T`VX ZX]TbXZ]gP ZT¥QP[X aT_T`bX aPPb QP[^Z ¥T]gT]bcW _TVPa' eP[Pc_c] P`PW]gP QT`QTSP) ;P[^Z Gambar 3.14 Gaya pada pegas merupakan gaya konservatif. m m m x v v k #Q$ #R$ #P$ licin x1 x2 "x= x2 – x1 licin licin

78 Mudah dan Aktif Belajar Fisika untuk Kelas XI Tugas Anda 3.2 Sebutkan contoh-contoh gaya konservatif yang ada di sekitar Anda. Gambar 3.15 Seseorang sedang melakukan usaha memindahkan peti. ZTWX[P]VP] T]T`VX ZX]TbXZ]gP _PSP aP[PW aPbc P`PW VT`PZ]gP' bTbP_X ¥T¥_T`^[TW T]T`VX ZX]TbXZ]gP ZT¥QP[X _PSP P`PW VT`PZ gP]V [PX]' gPXbc ZTbXZP QP[^Z QT`QP[XZ ZT _^aXaX aT¥c[P #6CNDCR ))'*!E"$) IPSP _T`XabXeP bT`aTQcb' caPWP gP]V SX[PZcZP] VPgP _TVPa 5 8 DX bXSPZ ¥T]VcQPW T]T`VX ¥TZP]XZ aXabT¥ _TVPa) @PgP gP]V SX[PZcZP] ^[TW _TVPa bT`aTQcb QT`aXUPb Z^]aT`dPbXU) @PgP V`PdXbPaX YcVP QT`aXUPb Z^]aT`dPbXU' SP_PbZPW :]SP ¥T]YT[PaZP] ¥T]VP_P VPgP V`PdXbPaX QT`aXUPb Z^]aT`dPbXU9 =P`X acScb _P]SP]V gP]V [PX]' VPgP Z^]aT`dPbXU YcVP ¥T¥X[XZX RX`X QPWeP Yc¥[PW caPWP gP]V SX[PZcZP] VPgP _PSP _P`bXZT[ #QT]SP SXP]VVP_ aTQPVPX _P`bXZT[$ PSP[PW ]^[) IPSP ZTPSPP] aTbX¥QP]V #_^aXaX P 8 +$' VPgP _TVPa 5_ _PSP R^]b^W bT`aTQcb SX]gPbPZP] ST]VP] _T`aP¥PP] 5_ , DX #.j-,$ LPWcZPW :]SP caPWP gP]V SX[PZcZP] ^[TW VPgP _TVPa bT`aTQcb9 IT`WPbXZP] ZT¥QP[X 6CNDCR )%'*' ZTbXZP QT]SP QT`_X]SPW SP`X _^aXaX , gP]V ¥T¥X[XZX aX¥_P]VP] P , ZT _^aXaX - ST]VP] aX¥_P]VP] P - ' QTaP` caPWP gP]V SX[PZcZP] VPgP _TVPa bT`WPSP_ QT]SP SX]gPbPZP] ST]VP] _T`aP¥PP] 9,'- 8 j1I "P 9,'- 8 jDP "P #%$ LP]SP ]TVPbXU ¥T]gPbPZP] QPWeP P`PW VPgP _TVPa 1 I QT`[PeP]P] ST]VP] P`PW _T`_X]SPWP] "P ' -=:IMG KBFI:G@:G f =:I:L =BI>JHE>A =:JB GBE:B J:L:&J:L: =:JB KBFI:G@:G P, SP] P - ) =T]VP] ST¥XZXP]' _T`aP¥PP] #%$ SP_Pb SX]gPbPZP] ST]VP] 9,'- 8 jDP "P 9,'- 8 jD ! - , - , - P P P P / 1 " 3 5 # 0 2 9,'- , # ! - ,- , " ! # - D P PP P 9,'- , # # ! - - - , - D P P #%%$ ;T`SPaP`ZP] _T`aP¥PP] #%%$' YT[Pa[PW QPWeP caPWP gP]V SX[PZcZP] ^[TW _TVPa bXSPZ ¥T]VcQPW T]T`VX ¥TZP]XZ aXabT¥ SP] bXSPZ QT`VP]bc]V _PSP _^aXaX PeP[ SP] _^aXaX PZWX` QT]SP gP]V SXZT]PX VPgP _TVPa bT`aTQcb) IT`WPbXZP] 6CNDCR )%'+% KTQcPW _TbX SX_X]SPWZP] ZT bT¥_Pb [PX] aTbX]VVX A' MaPWP gP]V SX_T`[cZP] c]bcZ ¥T¥X]SPWZP] _TbX PSP[PW 9, 8 jF@A' LP]SP ]TVPbXU bX¥Qc[ ZP`T]P P`PW VPgP QT`Pb 9 QT`[PeP]P] ST]VP] P`PW VT`PZ _TbX) MaPWP ZTbXZP ¥T¥X]SPWZP] _TbX bXSPZ QT`VP]bc]V _PSP _P]YP]V [X]bPaP] gP]V SX[P[cX _TbX' bTbP_X QT`VP]bc]V _PSP QTaP` _T`cQPWP] bX]VVX _TbX SP`X ZTScScZP] PZWX` ZT ZTScScZP] PeP[]gP) CXZP _TbX SX_X]SPWZP] [PVX ZT _^aXaX PeP[]gP' caPWP gP]V SX[PZcZP]]gP PSP[PW 9- 8 F@A) KTRP`P ¥PbT¥PbXa' caPWP b^bP[ gP]V SX[PZcZP] c]bcZ ¥T¥X]SPWZP] _TbX SP`X QPePW ZT PbPa #9, $' [P[c SX_X]SPWZP] [PVX ZT QPePW #9- $ PSP[PW 9b^b 8 9- & 9, 8 #jF@A$ & #F@A$ 8 + ;TaP` caPWP _T¥X]SPWP] aTQcPW _TbX SP`X ZTScScZP] PeP[ WX]VVP ZT¥QP[X ZT ZTScScZP] PZWX`]gP QT`]X[PX ]^[) CPSX' SP_Pb SXaX¥_c[ZP] QPWeP caPWP gP]V SX[PZcZP] ^[TW VPgP Z^]aT`dPbXU PZP] QT`]X[PX ]^[' YXZP ZTScScZP] PZWX` QT]SP ZT¥QP[X ZT ZTScScZP] PeP[]gP)

Usaha, Energi, dan Daya 79 1. Perumusan Hukum Kekekalan Energi Mekanik =P[P¥ ¥TSP] V`PdXbPaX' Yc¥[PW T]T`VX _^bT]aXP[ SP] T]T`VX ZX]TbXZ acPbc QT]SP bTbP_ #YXZP WP]gP PSP VPgP V`PdXbPaX$) IT`]gPbPP] bT`aTQcb SXZT]P[ aTQPVPX AcZc¥ DTZTZP[P] >]T`VX FTZP]XZ) IT`WPbXZP] 6CNDCR )%',) KTQcPW QT]SP QT`¥PaaP F YPbcW QTQPa) IPSP _^aXaX ,' ZTbX]VVXP]]gP A) bT`WPSP_ PRcP] #[P]bPX$) KTaPPb ZT¥cSXP]' QT]SP QT`PSP _PSP _^aXaX - ST]VP] ZTbX]VVXP] A* bT`WPSP_ PRcP]) =XZPbPZP] QPWeP _PSP QT]SP bT`YPSX _T]Vc`P]VP] T]T`VX _^bT]aXP[ gP]V QTaP`]gP aP¥P ST]VP] caPWP gP]V SX[PZcZP] VPgP QT`Pb) 9 8 j #0_- S 0_,$ #.j--$ IPSP _^aXaX ,' ZTRT_PbP] QT]SP N ) ' ZT¥cSXP] QT]SP bc`c] WX]VVP _PSP _^aXaX - ST]VP] ZTRT_PbP] N * ' IPSP ZTPSPP] bT`aTQcb' ZTRT_PbP] QT]SP QT`bP¥QPW ZP`T]P _T]VP`cW _T`RT_PbP] V`PdXbPaX aTWX]VVP caPWP gP]V SX[PZcZP] QT]SP aP¥P ST]VP] _T`cQPWP] T]T`VX ZX]TbXZ' gPXbc 9 8 0Z- S 0Z, #.j-.$ ;T`SPaP`ZP] =GRSCNCCO !)Z((" SP] =GRSCNCCO !)Z()" SX_T`^[TW 0_, j 0_- 8 0Z- j 0Z, PbPc 0_, $ 0Z, 8 0_- & 0Z- #.j-/$ Gambar 3.16 Balok dijatuhkan dari ketinggian tertentu. v 1 1 v2 2 mg h2 h1 KTQcPW Q^[P QT`¥PaaP F SX[T¥_P`ZP] dT`bXZP[ ZT PbPa ST]VP] ZTRT_PbP] PeP[ aTQTaP` %+ ' LT]bcZP]5 P) bX]VVX ¥PZaX¥c¥ gP]V SXRP_PX6 SP] Q) ZTRT_PbP] ZTbXZP Q^[P ¥T]RP_PX bX]VVX aTbT]VPW ¥PZaX¥c¥) 9CWCD0 P) 0I, $ 0D, 8 0I-$ 0DF@A, & - , , - FN 8 F@A- & - - , - FN + & - , , - FN , F@A & + H[TW ZP`T]P N ) 8 N( ¥PZP - + , - FN 8 F@A * A 8 - + - N @ CPSX' bX]VVX ¥PZaX¥c¥ gP]V SXRP_PX PSP[PW A , - + - N @ ) Q) 0I, $ 0D, 8 0I-$ 0D- + & - + , - FN 8 F@ ! , - F:DK A & , - - FN - + , - FN 8 F@ - , + - - N @ / 1 3 5 0 2 & , - - FN - + , - FN 8 F - + , / N & , - - FN - + , / FN 8 , - - FN N - , - + , - N N - 8 - + , - N CPSX' ZTRT_PbP] Q^[P ZTbXZP ¥T]RP_PX bX]VVX aTbT]VPW bX]VVX ¥PZaX¥c¥ PSP[PW N 8 - + , - N ' Contoh 3.10 h m v2 = 0 h2 = h h1 = 0 v1 = v0 Ek2 ; Ep2 Ek1 ; Ep1

80 Mudah dan Aktif Belajar Fisika untuk Kelas XI KTQcPW QPbc QT`¥PaaP F bT`VP]bc]V _PSP aTcbPa bP[X gP]V _P]YP]V]gP SXQT`X VPgP ¥T]SPbP`) ;Pbc ¥c[PX QT`VT`PZ ST]VP] ZT[PYcP] PeP[ N + aT_T`bX _PSP VP¥QP`' ZTbXZP QPbc ¥T]gX¥_P]V ST]VP] acScb ' bX]VVX gP]V SXRP_PX Q^[P SP`X bXbXZ aTbX¥QP]V]gP PSP[PW A) LT]bcZP]5 P) bX]VVX ¥PZaX¥c¥ gP]V SXRP_PX QPbc6 SP] Q) QTaP` ZTRT_PbP] PeP[ QPbc #N + $) 9CWCD0 P) 0I: $ 0D: 8 0I;$ 0D; F@A: & , - N 2 m A 8 F@A; & , - - FN; + & , - N 2 m 0 8 F@A; & + N + 8 -@A $ A , - + - N @ CPSX' bX]VVX ¥PZaX¥c¥ gP]V SXRP_PX QPbc 8 - + - N @ ' Q) R^a A & # # A 8 j - + R^a - N @ & # j - + R^a - N @ & # N + 8 - , R^a @ ! # & h & v0 ;P[^Z : gP]V QT`¥PaaP 0 ZV ¥T]VVT[X]RX` SP`X PbPa aTQcPW QXSP]V ¥X`X]V gP]V acScb ¥X`X]V]gP .+i) ;P[^Z bT`aTQcb ZT¥cSXP] ¥T]c¥QcZ _TVPa gP]V bT`[TbPZ 3 ¥ SP`X _^aXaX aT¥c[P) CXZP Z^TUXaXT] VTaTZ P]bP`P QP[^Z : ST]VP] QXSP]V ¥X`X]V +'-0' QT`P_P ¥TbT` _TVPa bT`bTZP]9 =XZTbPWcX Z^]abP]bP _TVPa 8 0++ G*¥) 9CWCD0 MaPWP gP]V SX[PZcZP] VPgP _TVPa PSP[PW ]TVPbXU ZP`T]P _TVPa ¥T[PeP] VPgP bTZP] QP[^Z) :`bX]gP' ZTbXZP _TVPa bT`bTZP]' _TVPa ¥T[PeP] VPgP bTZP] aTWX]VVP VPgP _TVPa SP] P`PW _T`_X]SPWP] QT`[PeP]P] P`PW) IT`WPbXZP] VP¥QP` QT`XZcb) 9_TVPa 8 , - DP- 8 j , - D;- 9V`Pd , S " 0I , S F@#AR j AP $ 8 F@#K $ ;$ aX] .+i 8 +'0 F@#K $ ;$ MaPWP ^[TW VTaTZP] QT`]X[PX ]TVPbXU ZP`T]P P`PW QP[^Z QT`[PeP]P] ST]VP] P`PW VPgP VTaTZ) 9@>K>D , S ? Z #K $ ;$ 8 #&kF@ R^a .+i #K $ ;$ 8 , - . F@ #K $ ;$ Z & ha hb hc A B C b s 30° Contoh 3.11 Contoh 3.12 Tugas Anda 3.3 Apakah Anda tahu olahraga bungee jumping? Selidikilah Hukum Kekekalan Energi yang bekerja saat orang melakukan bungee jumping.

Usaha, Energi, dan Daya 81 Pembahasan Soal Dua buah benda A dan B yang bermassa masing-masing m, jatuh bebas dari ketinggian h meter dan 2h meter. Jika A menyentuh tanah dengan kecepatan v m/s, benda B akan menyentuh tanah dengan energi kinetik sebesar .... a. 3 2 mv2 d. 1 2 mv2 b. mv2 e. 1 4 mv2 c. 3 4 mv2 Soal UMPTN Tahun 1989 Pembahasan: hB = 2hA Berarti, EpB = 2 EpA Sesuai dengan Hukum Kekekalan Energi Mekanik maka EpB – EpA = EkA – EkB EkB = 2 EkA = 2 ! 1 2 2 mv = mv2 Jawaban: b FT`cYcZ _`X]aX_ T]T`VX SXZTbPWcX QPWeP 9LHL:E , "0D aTWX]VVP SX _T`^[TW 9I>@:K $ 9@J:N $ 9@>K>D , , - F #N < * S N : * $ j , - D;* $ , - F@#K $ ;$ j , - 3F@#K $ ;$ &k 8 , - F #+- j + - $ j , - D ;* $ , - F @ & / 1 3 5 # 0 2 k , +'0 . - ; S +'0 K & , - 3 k & K 8 + :]SP SP_Pb ¥T]gT[TaPXZP] _T`aP¥PP] ZcPS`Pb bT`aTQcb ST]VP] ¥T]VWXbc]V ; SP`X F , 0 ZV' D , 0++ G*¥' K , 3 ¥' k & 8 +'-0' SP] @ , ,+ ¥*a- ) ! ! ! - 0++ - 0 ZV ,+ ¥*a N/m ; * ¥- j ! , +'0 . +'-0 - / 1 / 1 3 5 # 3 5 0 2 0 2 ; S #+'0$#3 ¥$ & ! , - 3 #+'-0$#3 ¥$ 8 + 0 ; *¥- S +'-3-0 ; ¥j -'-13 ¥ 8 + ;,- 8 ! ! ! ! - +' -3-0 # +' -3-0$ -' -1-3 ,+ # # % ## # / 0 8 +' -3-0 /0' // ,+ % 8 +' -3-0 1'2/ ,+ % ;) , j+'10 ¥ #bXSPZ bT`_PZPX$ ;* , +'2 ¥ CPSX' _TVPa bT`bTZP] aTYPcW +'2 ¥) ;^[P SP_Pb QT`VT`PZ bP]_P VTaTZP] _PSP [X]bPaP] aT_T`bX VP¥QP` QT`XZcb) KPPb SX bXbXZ :' Q^[P QT`ZTRT_PbP] -++ R¥*a) ;T`P_P [PYc SX bXbXZ ; SP] <9 9CWCD0 IPSP aXabT¥ QT`[PZc DTZTZP[P] >]T`VX FTZP]XZ aTWX]VVP5 P) F @A: & , - FN: - 8 F @A; & , - FN; - #,+ ¥*a- $#+'3 ¥$ & , - #- ¥*a$- 8 + & , - N ; - N ; 8 -+ ¥*a 8 /'// ¥*a CPSX' ZT[PYcP] Q^[P SX bXbXZ ; PSP[PW /'// ¥*a) Q) F @A: & , - FN: - 8 F @A< & , - FN< - #,+ ¥*a- $#+'3 ¥$ & , - / 1 3 5 0 2 #- ¥*a$- 8 #,+ ¥*a- $#+'0 ¥$ & , - N < - N < 8 ,+ ¥*a 8 .',/ ¥*a CPSX' ZT[PYcP] Q^[P SX bXbXZ < PSP[PW .',/ ¥*a) A C B 80 cm 50 cm Contoh 3.13

82 Mudah dan Aktif Belajar Fisika untuk Kelas XI B A lintasan loop Gambar 3.17 Lintasan roller coaster. 2. Analisis Gerak pada Roller Coaster AP¥_X` aT¥cP bTZ]^[^VX SX bP¥P] WXQc`P] aT_T`bX /BKG>Q 2:G=' /BKG>Q 9HJE=' PbPc =c]XP ?P]bPaX aP]VPb ZPgP PZP] Z^]aT_ UXaXZP) =X P]bP`P aTYc¥[PW _T`¥PX]P] gP]V PSP' JHEE>J <H:KL>J PbPc gP]V QXPaP SXaTQcb WP[X[X]bP` SP_Pb ¥T]S^`^]V :]SP c]bcZ ¥T¥PWP¥X [TQXW SP[P¥ Z^]aT_ UXaXZP bT]bP]V VT`PZ) IT`WPbXZP] 6CNDCR )%'-) DT]SP`PP] bP]_P ¥TaX] ¥T]VVc]PZP] QP] QT`YP[P] #<HGN>QHJ ;>EL$ c]bcZ ]PXZ ZT _c]RPZ QcZXb : ¥T[P[cX [X]bPaP] gP]V bXSPZ bT`[P[c Rc`P¥) Ic]RPZ QcZXb : aT]VPYP SX`P]RP]V [TQXW bX]VVX SP`X_PSP _c]RPZ [^^_ ;' WP[ bT`aTQcb ¥T¥c]VZX]ZP] T]T`VX _^bT]aXP[ ZT]SP`PP] SX : gP]V [TQXW QTaP` aTWX]VVP ¥P¥_c QT`YP[P] ¥T[P[cX [X]bPaP] ¥T]cYc _c]RPZ ; ST]VP] QPXZ) EX]bPaP] [^^_ aT]VPYP SXQcPb aT_T`bX bTbTaP] PX` bT`QP[XZ) CXZP [^^_ QT`c_P [X]VZP`P] _T]cW' PZP] SX_T`^[TW Q^Q^b _T]c¥( _P]V T]P¥ ZP[X Q^Q^b ]^`¥P[]gP aPPb ZT]SP`PP] SX _^aXaX bT`T]SPW' Z^]SXaX X]X SP_Pb ¥T]gTQPQZP] _caX]V [P[c _X]VaP]) EX]bPaP] [^^_ gP]V aT_T`bX bTbTaP] PX` WP]gP ¥T¥QT`XZP] Q^Q^b ¥PZaX¥c¥ .'2 ZP[X Q^Q^b ]^`¥P[( ]gP' _PSP Q^Q^b bT`aTQcb _T]c¥_P]V ¥PaXW ¥T`PaPZP] ZT]gP¥P]P]) DTbXZP JHEE>J <H:KL>J QT`PSP SX bXbXZ bT`bX]VVX SP`X [X]bPaP] [^^_' gPXbc SX bXbXZ < aT_T`bX gP]V :]SP [XWPb _PSP 6CNDCR )%'.' VPgP aT]b`X_TbP[]gP PSP[PW `Tac[bP] SP`X 4< #VPgP bTZP]$ SP] QTaP` VPgP QT`Pb _T]c¥_P]V F@ aTWX]VVP 1a 8 4R & F@ 8 - N F 6 KgP`Pb ZT[PYcP] ¥X]X¥P[ SX bXbXZ < PSP[PW 4< 8 + aTWX]VVP SX_T`^[TW + $ F@ , - < N F 6 NCmin 8 @J DTbXZP JHEE>J <H:KL>J QT`PSP SX bXbXZ bT`T]SPW' gPXbc bXbXZ ;' 0I; , + 0D;$ 0I; , 0DR $ 0IR , - FN; - & F@A; 8 , - FN< - & F@A< DP[XZP] ZTScP `cPa _T`aP¥PP] bT`aTQcb ST]VP] - F aTWX]VVP SX_T`^[TW - @A; $ N; * , - @A< $ N< * H[TW ZP`T]P A; , + 6 A< , -66 SP] N < * , @6 ¥PZP _T`aP¥PP] ¥T]YPSX + & N ; * , - @#-6$ & @6 ;¥X] N 8 0@6 #.j-0$ DTbX]VVXP] PeP[ ¥X]X¥P[ [c]Rc`P] SX bXbXZ : SP_Pb :]SP WXbc]V ¥T[P[cX _T]T`P_P] AcZc¥ DTZTZP[P] >]T`VX FTZP]XZ SX bXbXZ : SP] < PVP` JHEE>J <H:KL>J ¥P¥_c ¥T[TePbX [^^_ ST]VP] P¥P]) Gambar 3.18 Lintasan roller coaster dengan loop berbentuk lingkaran. B C A Sumber: Dokumentasi Penerbit Nc mg

Usaha, Energi, dan Daya 83 KT_^b^]V QP[^Z QT`¥PaaP F ¥T[c]Rc` _PSP acPbc bP[P]V #[X]VZP`P] SP[P¥$ aT_T`bX bT`[XWPb _PSP VP¥QP`) CXZP VPgP VTaTZ P]bP`P QP[^Z SP] bP[P]V SXPQPXZP]' P) QT`P_PZPW ZTbX]VVXP] ¥X]X¥c¥ QP[^Z gP]V WP`ca SX[T_Pa PVP` VT`PZP]]gP SP_Pb ¥T]RP_PX _c]RPZ [X]VZP`P] #bXbXZ ;$96 SP] Q) bT]bcZP][PW QTaP` _T`RT_PbP] QP[^Z SX bXbXZ ;) 9CWCD0 P) @c]PZP] `c¥ca ZT[PYcP] ¥X]X¥c¥ _PSP bXbXZ bT`T]SPW' =GRSCNCCO !)Z(+") CPSX' ZT[PYcP] ¥X]X¥c¥ SX bXbXZ < QTaP`]gP N < ¥X] 8 0@6 aTWX]VVP P]bP`P bXbXZ : SP] < ST]VP] ¥T]VVc]PZP] WcZc¥ ZTZTZP[P] T]T`VX ¥TZP]XZ) 0I: & 0D: 8 0I< & 0D< F@A: & , - FN: - 8 F@A< & , - FN< - F@A: & + 8 + & , - F #0@6$ A: 8 -'0 6 CPSX' ZTbX]VVXP] ¥X]X¥c¥ PVP` QP[^Z ¥T]RP_PX bXbXZ ; PSP[PW -'0 6) Q) ;TaP` _T`RT_PbP] SX bXbXZ ; PSP[PW _T`RT_PbP] aT]b`X_TbP[) ;T`SPaP`ZP] VP¥QP`' SX bXbXZ ; 1a 8 4 & F@ F:K , F@' SX ¥P]P 4 8 + :K 8 @ CPSX' _T`RT_PbP] QP[^Z SX bXbXZ . PSP[PW :K 8 @) Contoh 3.14 Kata Kunci • energi mekanik • gaya konservatif • gaya sentripetal • kelajuan minimal • konstanta pegas Tes Kompetensi Subbab C :GRKCLCOMCI FCMCN DULU MCTJICO% ,) :_PZPW gP]V :]SP ZTbPWcX bT]bP]V VPgP Z^]aT`dPbXU SP] VPgP bXSPZ Z^]aT`dPbXU9 -) :_PZPW WcZc¥ ZTZTZP[P] T]T`VX ¥TZP]XZ QT`[PZc _PSP aTQcPW QT]SP' YXZP VPgP Z^]aT`dPbXU QTZT`YP _PSP QT]SP bT`aTQcb9 .) =cP QcPW QT]SP : SP] ; gP]V QT`¥PaaP ¥PaX]V(¥PaX]V F' YPbcW QTQPa SP`X ZTbX]VVXP] A ¥TbT` SP] -A ¥TbT`) CXZP : ¥T]gT]bcW bP]PW ST]VP] ZTRT_PbP] N ¥*a' bT]bcZP][PW T]T`VX ZX]TbXZ QT]SP ; aPPb PZP] ¥T]gT]bcW bP]PW) /) KTQcPW QP[^Z QT`¥PaaP 0 ZV ¥c[P(¥c[P SXP¥) ;P[^Z bT`aTQcb ZT¥cSXP] SXYPbcWZP] SP`X acPbc ZTbX]VVXP] 1'0 R¥ _PSP aTQcPW _TVPa gP]V Z^]abP]bP VPgP]gP ,++ G*¥) CXZP @ 8 4'3 ¥*a- ' QT`P_P ¥TbT` _TVPa bT`bTZP]9 0) L^[T ¥T¥X]SPWZP] QcZc SP`X [P]bPX ZT PbPa ¥TYP) ;T`P_P caPWP b^bP[ gP]V SXbT`X¥P ^[TW QcZc bT`aTQcb9 1) LXVP QPbc QPbP gP]V bTQP[]gP 3 R¥ SX[TbPZZP] SX PbPa aTQcPW ¥TYP) AXbc]V[PW caPWP c]bcZ ¥T]c¥_cZ ZTbXVP QPbc QPbP bT`aTQcb SP[P¥ aPbc bc¥_cZP] YXZP ¥PaaP aTbXP_ QPbc QPbP 8 ,'0 ZV) A v B NB mg R hA C

84 Mudah dan Aktif Belajar Fisika untuk Kelas XI 2) KTQcPW ZT[P_P YPbcW QTQPa SP`X ZTbX]VVXP] 1 ¥TbT`) CXZP ¥PaaP QcPW ZT[P_P -'0 ZV SP] @ 8 ,+ ¥*a- ' bT]bcZP][PW ZTRT_PbP] QcPW ZT[P_P aPPb ¥T]RP_PX ZTbX]VVXP] - ¥TbT` SP`X bP]PW SP] T]T`VX ZX]TbXZ QcPW ZT[P_P aTaPPb aTQT[c¥ ¥T]RP_PX bP]PW) 3) KTQcPW ZT`TbP ¥T[TePbX [X]bPaP] JHEE>J <H:KL>J ST]VP] SXP¥TbT` -+ ¥) :VP` ZT`TbP SP_Pb ¥T[X]bPa ST]VP] P¥P]' bT]bcZP][PW ZTRT_PbP] ¥X]X¥c¥ ZT`TbP bT`aTQcb) 4) KTQcPW QT]SP QT`¥PaaP +'20 ZV YPbcW QTQPa SP`X ZTbX]VVXP] 3 ¥TbT` SX PbPa bP]PW) CXZP @ 8 ,+ ¥*a- ' bT]bcZP][PW5 P) ZTRT_PbP] QT]SP aPPb bXQP SX bP]PW6 SP] Q) caPWP ^[TW VPgP QT`Pb aT[P¥P _T`_X]SPWP]) ,+) KTQcPW _T[c`c SXbT¥QPZZP] ¥X`X]V ZT PbPa ST]VP] acScb T[TdPaX /0i SP] T]T`VX ZX]TbXZ aTQTaP` ,0+ C) CXZP @ 8 ,+ ¥*a- ' bT]bcZP][PW T]T`VX ZX]TbXZ SP] T]T`VX _^bT]aXP[ QT]SP _PSP aPPb ¥T]RP_PX bXbXZ bT`bX]VVX) D. Daya :]SP bT[PW QT[PYP` bT]bP]V RP`P ¥T]VWXbc]V caPWP SP`X VPgP gP]V SX[PZcZP]) =XQP]SX]VZP] ¥T]VTbPWcX QTaP` caPWP' [TQXW ¥T]P`XZ ¥T]VT( bPWcX aTQT`P_P [PYc caPWP bT`aTQcb SXZT`YPZP]) LT]bc]gP QTaP`P] ePZbc SX SP[P¥ QPWPaP] X]X ¥T]YPSX aP]VPb QT`_T`P]) KPPb caPWP _T` aPbcP] ePZbc SXSTUX]XaXZP]' ¥c]Rc[[PW XabX[PW SPgP) IT`[c :]SP X]VPb QPWeP SPgP bXSPZ SXbT]bcZP] ^[TW QTaP` T]T`VX gP]V SX¥X[XZX acPbc QT]SP) M]bcZ [TQXW ¥T¥PWP¥X]gP' _T`WPbXZP] R^]b^W QT`XZcb) MR^Z SP] ;cbTb QT`¥PaaP aP¥P' gPXbc 0+ ZV' ¥T]PXZX [P]bPX ScP aTZ^[PW]gP aTbX]VVX . ¥TbT`) DTScP]gP ¥T¥X[XZX T]T`VX aP¥P QTaP` c]bcZ ¥T[PZcZP] caPWP ,)0++ Y^c[T) >]T`VX _^bT]aXP[ gP]V SX¥X[XZX ¥T`TZP aP¥P' eP[Pc_c] ZT]gPbPP]]gP MR^Z aP¥_PX SX [P]bPX ScP [TQXW RT_Pb) =P`X c`PXP] R^]b^W bT`aTQcb SXZTbPWcX QPWeP P`bX]gP caPWP QT[c¥ SP_Pb ¥T¥QT`XZP] X]U^`¥PaX [TQXW [T]VZP_ bT]bP]V _T`_X]SPWP] PZXQPb _T]VP`cW VPgP) =P[P¥ _T`XabXeP X]X' SP_Pb SXZPbPZP] QPWeP MR^Z ¥T¥X[XZX SPgP [TQXW QTaP` SP`X_PSP ;cbTb eP[Pc_c] ZTScP]gP ¥T¥X[XZX ZT¥P¥_cP] c]bcZ ¥T]V( WPaX[ZP] T]T`VX gP]V aP¥P) CPSX' SPgP PSP[PW QTaP`P] UXaXZP gP]V ¥T]gPbPZP] caPWP gP]V SX[PZcZP] ^[TW QT]SP aTbXP_ aTZ^]]gP PbPc [PYc T]T`VX gP]V SXQcbcWZP] QT]SP aTbXP_ aTZ^]]gP) =PgP #`PbP(`PbP$ 8 caPWP aT[P]V ePZbc 9 5 L # " PbPc 1 K 5 1 N L " # # " #.j-1$ DTbT`P]VP]5 9 8 caPWP gP]V SX[PZcZP] #Y^c[T$ "L 8 ePZbc gP]V SX_T`[cZP] #aTZ^]$ N 8 ZT[PYcP] `PbP(`PbP #¥*a$ =P[P¥ aXabT¥ KB' aPbcP] SPgP SXbc`c]ZP] SP`X aPbcP] caPWP' gPXbc C*a) KPbcP] bT`aTQcb aT`X]V SXaTQcb ePbb' SXbTbP_ZP] aTQPVPX _T]VWP`VPP] bT`WPSP_ X[¥ceP] KZ^b[P]SXP' gPXbc 9CNGS BCTT #,2.1j,3,4$) KPbcP] SPgP SP[P¥ ZT¥P¥_cP] aTQcPW ¥TaX] QXPaP ¥T]VVc]PZP] aPbcP] AHJK> IHO>J #AI$ PbPc SPgP ZcSP) , W_ 8 2/1 ePbb 8 +'2/1 ZO) , ZOW 8 , #ZO$#, YP¥$ 8 .'1 m ,+1 C) Tugas Anda 3.4 Sebutkan contoh alat-alat yang mencantumkan besaran daya yang ada di sekitar Anda.

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Usaha, Energi, dan Daya 87 +' MaPWP b^bP[ gP]V SX[PZcZP] ^[TW VPgP Z^]aT`dPbXU WP]gP ¥T¥_T`WPbXZP] ZTPSPP] PeP[ SP] ZTPSPP] PZWX` _^aXaX QT]SP' [X]bPaP] bXSPZ ¥T¥T]VP`cWX) 2) =PgP PSP[PW caPWP gP]V SX[PZcZP] ^[TW QT]SP aTbXP_ aTZ^] PbPc [PYc T]T`VX gP]V QT`cQPW ¥T]YPSX T]T`VX QT]bcZ [PX]) Setelah mempelajari bab ini, tentu Anda dapat memahami konsep usaha, energi, dan daya. Anda juga tentu dapat mengetahui hubungan antara usaha, energi, dan daya. Nah, dari materi-materi bab ini, bagian manakah yang Anda anggap sulit? Coba diskusikan dengan teman atau guru Fisika Anda. Refleksi Dengan mempelajari konsep usaha, Anda dapat menentukan usaha dengan menentukan lintasan yang lebih efisien untuk dilakukan. Hal tersebut adalah salah satu manfaat mempelajari bab ini. Coba Anda sebutkan manfaat lain setelah mempelajari bab ini. Peta Konsep >]T`VX DX]TbXZ >]T`VX I^bT]aXP[ ASCIC# 4OGRHJ# FCO 3CYC MaPWP >]T`VX =PgP MaPWP 8 IT`cQPWP] >]T`VX AcZc¥ DTZTZP[P] >]T`VX FTZP]XZ >]T`VX I^bT]aXP[ @`PdXbPaX >]T`VX I^bT]aXP[ ITVPa ¥T¥QPWPa WcQc]VP]]gP ¥T¥QPWPa ¥T¥QPWPa

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91 A. Momentum Linear B. Tumbukan C. Jenis Tumbukan D. Tumbukan Lenting Sebagian pada Benda Jatuh Bebas E. Ayunan Balistik F. Gaya Dorong Roket IWc`SZ]SZ :`VS _W`a`ea` bWceS`V[`YS` e[`¥f V[ KM9 K[`¥f _WcfbS]S` dS^SZ dSef a^SZcSYS iS`Y Uf]fb V[YW_Sc[( JWTSYS[ TW]S^ dSSe TWceS`V[`Y& dWacS`Y bWe[`¥f _W^Se[Z bf]f^S``iS dWUScS eWcSefc VS` [`eW`d[X( JWbWce[ iS`Y :`VS ^[ZSe bSVS YS_TSc V[ SeSd& dWacS`Y bWe[`¥f _W^Se[Z bf]f^S``iS bSVS dfSef dSdScS` VW`YS` _W_S]S[ dScf`Y e[`¥f( IWe[`¥f TWc^Se[Z dWUScS [`eW`d[X SYSc cWX^W]d VS` ]WUWbSeS` bf]f^S` dW_S][` _W`[`Y]Se( JW_S][` d[`Y]Se [`eWcS]d[ bf]f^S` VW`YS` dSdScS`& dW_S][` TS[] ]fS^[eSd bf]f^S`( IWc`SZ]SZ :`VS TWcb[][c& _W`YSbS bWe[`¥f ZScfd _W`YYf`S]S` dScf`Y e[`¥f9 :bS]SZ bW`YScfZ iS`Y V[cSdS]S` bWe[`¥f ]We[]S ^ShS``iS _W_f]f^ VW`YS` dScf`Y e[`¥f9 FW`YSbS bWe[`¥f V[ef`efe _W_[^[][ bf]f^S` dWUWbSe _f`Y][`9 IWceS`iSS`'bWceS`iSS` eWcdWTfe VSbSe :`VS ¥ShST ¥[]S :`VS VSbSe _W_SZS_[ [d[ TST [`[( Momentum, Impuls, dan Tumbukan Petinju secara rutin berlatih meningkatkan kecepatan pukulan dan berusaha mempersingkat interaksi dengan sasarannya. Petinju juga menggunakan sarung tangan ketika bertinju. menunjukkan hubungan antara konsep impuls dan momentum untuk menyelesaikan masalah tumbukan. Setelah mempelajari bab ini, Anda harus mampu: menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik. Hasil yang harus Anda capai: Sumber:www.savannah.com Bab 4