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PUSAT PERBUKUAN Departemen Pendidikan Nasional Hak Cipta Pada Departemen Pendidikan Nasional dilindungi oleh Undang-Undang Mudah dan Aktif Belajar Fisika untuk Kelas XI Sekolah Menengah Atas/Madrasah Aliyah Program Ilmu Pengetahuan Alam 530.07 DUD m Penulis Penyunting : : Pewajah Isi Ilustrator Pewajah Sampul : : : Dudi Indrajit Ahmad Fauzi Ahmad Saripudin Neni Yuliati S. Riyadi A. Purnama Ukuran Buku : 21 x 29,7cm DUDI Indrajit Mudah dan Aktif Belajar Fisika : untuk Kelas XI Sekolah Menengah Atas/ Madrasah Aliyah Program Ilmu Pengetahuan Alam / penulis, Dudi Indrajit ; penyunting, Ahmad Fauzi, Ahmad Saripudin, ; illustrator, S. Riyadi. . — Jakarta : Pusat Perbukuan, Departemen Pendidikan Nasional, 2009. vi, 218 hlm, : ilus. ; 30 cm Bibliografi : hlm. 218 Indeks ISBN 978-979-068-816-2 (No. Jil Lengkap) ISBN 978-979-068-818-6 1. Fisika-Studi dan Pengajaran I. Judul II. Ahmad Fauzi III. Ahmad Saripudin IV. S. Riyadi Hak Cipta Buku ini dibeli oleh Departemen Pendidikan Nasional dari Penerbit Setia Purna Inves, PT Diterbitkan oleh Pusat Perbukuan Departemen Pendidikan Nasional Tahun 2009 Diperbanyak oleh .... Kata Sambutan Puji syukur kami panjatkan ke hadirat Allah SWT, berkat rahmat dan karunia-Nya, Pemerintah, dalam hal ini, Departemen Pendidikan Nasional, pada tahun 2009, telah membeli hak cipta buku teks pelajaran ini dari penulis/penerbit untuk disebarluaskan kepada masyarakat melalui situs internet (website) Jaringan Pendidikan Nasional. Buku teks pelajaran ini telah dinilai oleh Badan Standar Nasional Pendidikan dan telah ditetapkan sebagai buku teks pelajaran yang memenuhi syarat kelayakan untuk digunakan dalam proses pembelajaran melalui Peraturan Menteri Pendidikan Nasional Nomor 22 Tahun 2007 tanggal 25 Juni 2007. Kami menyampaikan penghargaan yang setinggi-tingginya kepada para penulis/penerbit yang telah berkenan mengalihkan hak cipta karyanya kepada Departemen Pendidikan Nasional untuk digunakan secara luas oleh para siswa dan guru di seluruh Indonesia. Buku-buku teks pelajaran yang telah dialihkan hak ciptanya kepada Departemen Pendidikan Nasional ini, dapat diunduh (down load), digandakan, dicetak, dialihmediakan, atau difotokopi oleh masyarakat. Namun, untuk penggandaan yang bersifat komersial harga penjualannya harus memenuhi ketentuan yang ditetapkan oleh Pemerintah. Diharapkan bahwa buku teks pelajaran ini akan lebih mudah diakses sehingga siswa dan guru di seluruh Indonesia maupun sekolah Indonesia yang berada di luar negeri dapat memanfaatkan sumber belajar ini. Kami berharap, semua pihak dapat mendukung kebijakan ini. Kepada para siswa kami ucapkan selamat belajar dan manfaatkanlah buku ini sebaik-baiknya. Kami menyadari bahwa buku ini masih perlu ditingkatkan mutunya. Oleh karena itu, saran dan kritik sangat kami harapkan. Jakarta, Juni 2009 Kepala Pusat Perbukuan iii Kata Pengantar Fisika adalah salah satu rumpun ilmu sains yang mempelajari alam semesta. Ruang lingkup ilmu Fisika sangat luas, mulai dari atom yang berdimensi nanometer hingga jagat raya yang berdimensi tahunan cahaya. Dalam kehidupan sehari-hari, banyak ditemukan aplikasi ilmu Fisika, baik berupa fenomena-fenomena di alam atau rekayasa teknologi. Oleh karena itu, Fisika memiliki tingkat urgensitas yang tinggi karena merupakan dasar untuk penguasaan teknologi di masa depan. Sesuai dengan misi penerbit untuk memberikan kontribusi yang nyata bagi kemajuan ilmu pengetahuan maka penulis dan penerbit merealisasikan tanggung jawab tersebut dengan menyediakan buku bahan ajar Fisika yang berkualitas, sesuai dengan tuntutan kurikulum yang berlaku saat ini. Buku ini disusun dengan mengutamakan pendekatan secara inkuiri (eksperimen) dan disajikan secara sistematis, komunikatif, dan integratif, serta adanya keruntutan rangkaian (bab dengan subbab, antarsubbab dalam bab, antaralenia dalam subbab). Sebelum mempelajari materi, sebaiknya Anda terlebih dahulu membaca bagian Advanced Organizer yang terdapat pada halaman awal setiap bab agar Anda dapat mengetahui isi bab secara umum. Pada awal setiap bab, disajikan pula Tes Kompetensi Awal sebagai evaluasi materi prasyarat untuk mempelajari bab yang bersangkutan. Di akhir setiap bab, terdapat Rangkuman, Peta Konsep, dan Refleksi yang bertujuan lebih meningkatkan pemahaman Anda tentang materi yang telah dipelajari dengan memunculkan umpan balik untuk evaluasi diri. Buku ini dilengkapi juga dengan beberapa materi, tugas, dan soal pengayaan, di antaranya Informasi untuk Anda (Information for You), Tantangan untuk Anda, Mari Mencari Tahu, Tugas Anda, Pembahasan Soal, dan Tokoh yang dapat memperluas pengetahuan materi Fisika yang sedang dipelajari. Untuk menguji pemahaman Anda terhadap materi yang telah dipelajari, diberikan Tes Kompentensi Subbab pada setiap akhir subbab, Tes Kompetensi Bab pada setiap akhir bab, dan Tes Kompetensi Fisika Semester pada setiap akhir semester. Selain itu, pada akhir buku juga diberikan Tes Kompetensi Akhir untuk menguji pemahaman materi Fisika selama satu tahun ajaran. Semua tes kompetensi tersebut merupakan sarana mengevaluasi pemahaman dan melatih kemampuan menerapkan konsep/prinsip Fisika yang berkaitan dengan materi yang telah dipelajari. Adapun Kunci Jawaban (nomor ganjil) kami sajikan untuk memudahkan Anda dalam mengevaluasi hasil jawaban. Untuk menumbuhkan daya kreativitas, kemampuan psikomotorik, dan cara berpikir ilmiah, kami sajikan Aktivitas Fisika dan Proyek Semester yang menuntut peran aktif Anda dalam melakukan kegiatan tersebut. Demikianlah persembahan kami untuk dunia pendidikan. Bandung, Mei 2007 Penerbit Panduan untuk Pembaca Materi-materi pembelajaran pada buku ini berdasarkan kurikulum yang berlaku saat ini dan disajikan secara sistematis, komunikatif, dan integratif. Di setiap awal bab, dilengkapi gambar pembuka pelajaran, bertujuan memberikan gambaran materi pembelajaran yang akan dibahas, dan mengajarkan siswa konsep berpikir kontekstual sekaligus merangsang cara berpikir kontekstual. Selain itu, buku ini juga ditata dengan format yang menarik dan didukung dengan foto dan ilustrasi yang representatif. Penggunaan bahasa yang sederhana, sesuai dengan tingkatan kognitif siswa sehingga membuat pembaca lebih mudah memahaminya. Buku Fisika untuk Kelas XI ini terdiri atas delapan bab, yaitu Analisis Gerak, Gaya, Usaha, Energi dan Daya, Momentum, Impuls dan Tumbukan, Gerak Rotasi dan Kesetimbangan Benda Tegar, Fluida, Teori Kinetik Gas, dan Termodinamika. Untuk lebih jelasnya, perhatikan petunjuk untuk pembaca berikut. (1) Judul Bab, disesuaikan dengan tema materi dalam bab. (2) Hasil yang harus Anda capai, tujuan umum yang harus Anda capai pada bab yang Anda pelajari. (3) Setelah mempelajari bab ini, Anda harus mampu, kemampuan 4 yang harus Anda kuasai setelah mempelajari bab. 18 (4) Gambar Pembuka Bab, disajikan untuk mengetahui contoh manfaat dari materi yang akan dipelajari. (5) Advanced Organizer, uraian singkat tentang isi bab untuk 1 menumbuhkan motivasi belajar dan mengarahkan Anda agar lebih 2 fokus terhadap isi bab. 19 3 (6) Tes Kompetensi Awal, merupakan soal prasyarat yang harus Anda pahami sebelum memasuki materi pembelajaran. 20 5 (7) Materi Pembelajaran, disajikan secara sistematis, komunikatif, integratif, dan sesuai dengan perkembangan ilmu dan teknologi terkini (up to date). (8) Gambar dan Ilustrasi, sesuai dengan materi dalam bab yang disajikan secara proporsional dan harmonis. 6 21 (9) Contoh Soal, berisi contoh dan penyelesaian soal. (10) Tugas Anda, berisi tugas atau latihan soal yang berkaitan dengan materi tersebut. (11) Pembahasan Soal, berisi contoh soal yang berasal dari 7 Ebtanas, UAN, UMPTN, atau SPMB. 22 (12) Mari Mencari Tahu, tugas mencari informasi yang bertujuan 8 menumbuhkan rasa ingin tahu dan mendorong siswa untuk 23 mencari informasi lebih jauh. (13) Aktivitas Fisika, kegiatan yang dilakukan secara berkelompok untuk mengembangkan kecakapan hidup Anda. (14) Ingatlah, catatan atau hal-hal penting yang perlu Anda ketahui. (15) Informasi untuk Anda (Information for You), berisi pengayaan 10 mengenai informasi dan aplikasi materi, disajikan dalam 2 bahasa 9 (bilingual). (16) Tantangan untuk Anda, berisi soal-soal yang disajikan 11 dengan tingkat kesulitan lebih tinggi. 24 12 (17) Kata Kunci (18) Tokoh, berisi tokoh Fisika penggagas ide baru dan pekerja 13 keras sehingga akan menumbuhkan semangat inovatif/kreatif, etos kerja, dan mengembangkan kecakapan hidup Anda. (19) Tes Kompetensi Subbab, berisi soal-soal untuk mengevaluasi penguasaan materi subbab. (20) Rangkuman (21) Peta Konsep (22) Refleksi, sebagai umpan balik bagi siswa setelah 14 mempelajari materi di akhir pembelajaran tiap bab. (23) Tes Kompetensi Bab, berisi soal-soal untuk mengevaluasi 16 25 penguasaan materi bab. (24) Proyek Semester, kegiatan percobaan untuk meningkatkan 15 pemahaman konsep Fisika dan memotivasi Anda untuk menggali informasi, memanfaatkan informasi, dan menyelesaikan masalah. (25) Tes Kompetensi Fisika Semester, berisi soal-soal untuk 26 mengevaluasi penguasaan materi selama satu semester. 17 (26) Tes Kompetensi Akhir, berisi soal-soal untuk mengevaluasi penguasaan materi selama satu tahun ajaran. v Daftar Isi Kata Sambutan • iii Kata Pengantar • iv Panduan untuk Pembaca • v Bab 1 Analisis Gerak • 1 A. Persamaan Gerak Lurus • 2 B. Gerak Parabola • 14 C. Gerak Melingkar • 20 Rangkuman • 21 Peta Konsep • 22 Refleksi • 22 Tes Kompetensi Bab 1 • 23 Bab 2 Gaya • 25 A. Gaya Gesek • 26 B. Gaya Gravitasi • 35 C. Elastisitas dan Gaya Pegas • 44 D. Gerak Harmonik Sederhana • 51 Rangkuman • 61 Peta Konsep • 62 Refleksi • 62 Tes Kompetensi Bab 2 • 63 Bab 3 Usaha, Energi, dan Daya • 67 A. B. C. Gaya Dapat Melakukan Usaha • 68 Energi dan Usaha • 72 Gaya Konservatif dan Hukum Kekekalan Energi Mekanik • 77 D. Daya • 84 Rangkuman • 86 Peta Konsep • 87 Refleksi • 87 Tes Kompetensi Bab 3 • 88 Bab 4 Momentum, Impuls, dan Tumbukan • 91 A. B. C. D. Momentum Linear • 92 Tumbukan • 94 Jenis Tumbukan • 96 Tumbukan Lenting Sebagian pada Benda Jatuh Bebas • 100 E. Ayunan Balistik • 102 F. Gaya Dorong Roket • 104 Rangkuman • 105 Peta Konsep • 106 Refleksi • 106 Tes Kompetensi Bab 4 • 107 Proyek Semester 1 • 110 Tes Kompetensi Fisika Semester 1 • 111 vi Bab 5 Gerak Rotasi dan Kesetimbangan Benda Tegar • 115 Bab 7 Teori Kinetik Gas • 163 A. B. C. Kinematika Gerak Rotasi • 116 Dinamika Gerak Rotasi • 119 Kesetimbangan Benda Tegar • 132 Rangkuman • 135 Peta Konsep • 136 Refleksi • 136 Tes Kompetensi Bab 5 • 137 A. Gas Ideal • 164 B. Prinsip Ekuipartisi Energi • 167 C. Kecepatan Efektif Partikel Gas • 173 Rangkuman • 175 Peta Konsep • 176 Refleksi • 176 Tes Kompetensi Bab 7 • 177 Bab 6 Fluida • 139 Bab 8 Termodinamika • 179 A. Fluida Statis • 140 B. Viskositas Fluida • 150 C. Fluida Dinamis • 152 Rangkuman • 159 Peta Konsep • 160 Refleksi • 160 Tes Kompetensi Bab 6 • 161 A. Usaha pada Berbagai Proses Termodinamika • 180 B. Hukum I Termodinamika • 184 C. Kapasitas Kalor Gas dan Siklus Termodinamika • 187 D. Hukum II Termodinamika • 191 Rangkuman • 193 Peta Konsep • 194 Refleksi • 194 Tes Kompetensi Bab 8 • 195 Proyek Semester 2 • 198 Tes Kompetensi Fisika Semester 2 • 200 Tes Kompetensi Akhir • 204 Kunci Jawaban • 208 Apendiks • 212 Senarai • 215 Indeks • 216 Daftar Pustaka • 218 vii Bab 1 Sumber: Fundamentals of Physics, 2001 Meriam dengan peluru manusia ditembakkan dengan sudut kemiringan dan kecepatan awal tertentu agar peluru jatuh tepat pada sasaran. Analisis Gerak Hasil yang harus Anda capai: menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik. Setelah mempelajari bab ini, Anda harus mampu: menganalisis gerak lurus, gerak melingkar, dan gerak parabola dengan menggunakan vektor. (7C@3:=3: @63 ?7>;:3E 3EC3=D; ?7C;3? 67@93@ B7>FCF ?3@FD;3      *3>3: D3EF =7>A?BA= D;C=FD J3@9 E7C=7@3> 67@93@ 3EC3=D;   @J3 E3:F@  3@ 363>3: =7>A?BA= D;C=FD =7>F3C93 035:;@; (C7DE3D; ?7C7=3 J3@9 E7C53E3E D74393; C7=AC 6;>3=F=3@ A>7: ?3@F7>035:;@;E3:F@  *33E;EF;347C:3D;>E7C43@9?7>7H3E;E;93 4F3: =;@5;C 63@ ?7@63C3E 6; <3C;@9 D7<3F:  ? 63C; E;E;= B7@7?43=3@ (C7DE3D;87@A?7@3>B363=7<36;3@E7CD74FE?7CFB3=3@D3>3:D3EF4F=E; B7@7C3B3@ =3;63:=3;63: ;D;=3 63>3? :3> ;@; 363>3: 97C3= B3C34A>3 7@93@ =757B3E3@ 3H3> J3@9 DF63: 6;=7E3:F; 63@ DF6FE 7>7G3D; ?7C;3? E7C:363B :AC;KA@E3> DF63: 6;3EFC ?3=3 E;E;= ?3=D;?F? =7E;@99;3@ 63@ E;E;=E7C<3F:63B3E6;=7E3:F;'>7:=3C7@3;EF?7C7=363B3E?7@7@EF=3@ D7E;@99; 3B3 C;@E3@93@ J3@9 6;9F@3=3@ 63@ 6; ?3@3 :3CFD ?7>7E3==3@ <3C;@9@J3 +3:F=3: @63 43:H3 97C3= B3C34A>3 63B3E 6;3@3>;D;D ?7>3>F; B7CB36F3@ 6F3 97C3= >FCFD J3@9 E7>3: @63 B7>3<3C; 6; #7>3D / ,@EF= ?7?B7C?F63: 3@3>;D;D 97C3= B7CD3?33@ 97C3= 6;F43: 63>3? 47@EF= G7=EAC ,@EF= >74;: ?7?3:3?;@J3 B7>3<3C;>3: 434 ;@; 67@93@ 43;= A. Persamaan Gerak Lurus B. Gerak Parabola C. Gerak Melingkar 1 Tes Kompetensi Awal $!$*2++$+.$* ( /')-,0$., *'0'0$/ ))$/( ) ,* &0- *0- *!$/')21# * +!2)2* 1'& ,  (363DF4434(7CD3?33@7C3=$FCFD@633=3@ 43@J3=?7@99F@3=3@EFCF@3@63@;@E79C3> ;EF@9>3:@;>3;EFCF@3@3E3F;@E79C3>47C;=FE 3                  !        4 5   6               (36397C3=B3C34A>33DF?D;97C3=3B3J3@96;9F@3=3@ 63>3?3C3:DF?4F63@DF?4F  B3=3:B7C47633@=757B3E3@>;@73C63@=757B3E3@ DF6FE A. Persamaan Gerak Lurus y 1. Posisi dan Arah Partikel Berdasarkan Vektor j i x k z Gambar 1.1 Vektor satuan dalam sumbu-x, sumbu-y, dan sumbu-z. 3>3?;D;=3BAD;D;DF3EFB3CE;=7>D7>3>F6;EF>;D=3@63>3?DF3EFDF?4F =AAC6;@3E *F?4F =AAC6;@3E J3@9 D7C;@9 6;9F@3=3@ J3;EF =AAC6;@3E 53CE7D;FD=AAC6;@3ED;>;@67C63@=AAC6;@3E4A>3,@EF=B7?43:3D3@B363 434 ;@; DF?4F =AAC6;@3E J3@9 6;9F@3=3@ 363>3: =AAC6;@3E 53CE7D;FD 67@93@ BAD;D; B3CE;=7> 6;@J3E3=3@ 63>3? DF?4F- DF?4F-  63@ DF?4F-! ,@EF= ;EF =;E3 3B>;=3D;=3@ G7=EAC =3>; B7CE3?3 B363 97C3= >FCFD a. Vektor Satuan dan Vektor Posisi 3 y Py P = P i+ x j Py j 0 i Px x y 4 Py j *F3EFG7=EAC63>3?=AAC6;@3E53CE7D;FD?7?;>;=;=A?BA@7@6;DF?4F- DF?4F- 63@DF?4F-!(363D7E;3BDF?4FE7CD74FEE7C63B3EG7=EACD3EF3@ J3@947D3C@J3D3EF63@?7?;>;=;3C3:D3?367@93@3C3:DF?4F@J3(363 DF?4F- G7=EAC D3EF3@@J3 363>3: ' (363 DF?4F-  G7=EAC D3EF3@@J3 363>3: ( 63@ DF?4F-! G7=EAC D3EF3@@J3 363>3: ) *74393; 5A@EA: B7C:3E;=3@ +! /   -7=EACJ3@9E7C>7E3=B3634;63@9 63B3E 6;EF>;D=3@ 63>3? 47@EF= G7=EAC D74393; 47C;=FE  ' ( 63BF@F@EF=G7=EACJ3@9E7C>7E3=63>3?CF3@9 +! /  ! G7=EAC  63B3E 6;EF>;D=3@ 63>3? @AE3D; G7=EAC D74393; 47C;=FE P Px i Gambar 1.2 (a) Posisi partikel pada bidang xy. (b) Vektor P dalam ruang. y A r1 0 Dr B b. Vektor Perpindahan *74F3:B3CE;=7>J3@947C97C3=B363DF3EF4;63@963E3CJ3;EFE7C:363B DF?4F- 63@ DF?4F-  G7=EAC BAD;D;@J3 B363 DF3EF E;E;= 6;EF@?7>3=F=3@B7CB;@63:3@63C;BAD;D; /  =7 BAD;D; /  B7CB;@63:3@ BAD;D; E7CD74FE 6;@J3E3=3@ 67@93@ /  (7CB;@63:3@ D74F3: B3CE;=7> /  63B3E 6;B7CA>7: 67@93@ ?7@99F@3=3@ 3EFC3@ G7=EAC B7CB;@63:3@ J3;EF D74393; 47C;=FE // P/ r2 x Gambar 1.3 Perpindahan vektor posisi r . 2  P  67@93@   63@ ! ?7CFB3=3@ 47D3C3@ D=3>3C Pz k z  ' J( K) x  P  ";=3G7=EACBAD;D;/  ' (63@G7=EACBAD;D;/  ' ( B7CD3?33@ B7CB;@63:3@ / ?7@<36; / ' (P ' ( / P 'P P ( ";=3      63@    ?3=33=3@6;B7CA>7: Mudah dan Aktif Belajar Fisika untuk Kelas XI /   '   ( ,@EF= ?7@7@EF=3@ 47D3C G7=EAC B7CB;@63:3@ 63B3E 6;EF>;D /        P   P  63BF@ 3C3: B7CB;@63:3@ B3CE;=7> 63B3E 6;B7CA>7: ?7>3>F; 47D3C DF6FE J3@9 6;47@EF= E7C:363B DF?4F- J3;EF y y E3@   3E3F  3C5E3@ x x Ingatlah Penulisan notasi vektor yang benar adalah dengan tanda panah di atas atau dengan huruf tebal.  P = P. Dalam buku ini digunakan huruf tebal sebagai penanda vektor. Contoh 1.1 (AD;D;3H3>D74F3:B3CE;=7>363>3:/ 'P(?=7?F6;3@B3CE;=7>E7CD74FE47CB;@63: =7BAD;D;/  '(?+7@EF=3@>3:G7=EACB7CB;@63:3@47D3CG7=EACB7CB;@63:3@ 63@3C3:B7CB;@63:3@B3CE;=7>;EF y  4 ! 12 ;=7E3:F; / 'P(? /  '(? -7=EACB7CB;@63:3@ 7 Dr /   '  ( r2 Dr = r2 – r1 /  P'PP( 112,7° P' (? 8 x 7D3CG7=EACB7CB;@63:3@ 3 0 –5 /     C3:B7CB;@63:3@ 3C5E3@  N  c. r1     ? –5 y Menentukan Komponen-Komponen Vektor Jika Arah dan Besarnya Diketahui (7C:3E;=3@  +! /   (363 93?43C E7CD74FE G7=EAC  6;FC3;=3@ E7C:363B DF?4F- 63@ DF?4F-   363>3: =A?BA@7@ G7=EAC  B363 DF?4F- D763@9=3@   363>3: =A?BA@7@ G7=EAC  B363 DF?4F-  ";=3  363>3:DF6FEJ3@96;47@EF=A>7:G7=EACE7C:363BDF?4F-47D3C 63@   63B3E 6;:;EF@9 67@93@ ?7@99F@3=3@ B7CD3?33@ 47C;=FE     5AD  63@    D;@   P A Ay  0 Ax x Gambar 1.4 Ax dan Ay merupakan komponenkomponen vektor A pada sumbu-x dan sumbu-y. Contoh 1.2 7@93@?7@97@63C3;D7B763+3C;93@?7@9;=FE;J3@96;D7>7@993C3=3@D7=A>3:@J3 67@93@?7@7?BF:CFE7D7B7CE;6;EF@3?3C3: N=743C3E>3FE=7?F6;3@47C97C3==7=AE3 D7<3F: =?=7FE3C3+7@EF=3@BAD;D;=AE363@3C3:@J3E7C:363BD7=A>3:+3C;93@  4 ! y (km) -7=EACB7CB;@63:3@D7B7636;@J3E3=3@D74393;G7=EAC B U 63@#A?BA@7@G7=EAC T  5AD  N =?P P =? B R  D;@  N =?  =? #A?BA@7@G7=EAC A A  5AD N =?  =? 30° x (km)  D;@ N =?  =? Sekolah Tarigan Analisis Gerak 3 (AD;D;E;E;=63B3E6;EF>;D=3@D74393;47C;=FE  P =? =?P =?    =? =? =? (AD;D;E;E;=63B3E6;EF>;D63>3?@AE3D;G7=EACJ3;EF P ' (=? "36;3C3:B7CB;@63:3@=AE363C;D7=A>3:+3C;93@363>3: E3@     =F36C3@!!    3C5E3@   N  2. Perpindahan dan Jarak (363 FC3;3@ D747>F?@J3 E7>3: 6;<7>3D=3@ 43:H3 B7CF43:3@ BAD;D; ?7?F@5F>=3@B7CB;@63:3@ 3E3FD753C3?3E7?3E;D 6;EF>;D  / (AD;D;63@ B7CB;@63:3@=76F3@J3?7CFB3=3@47D3C3@G7=EAC*3@93EB7@E;@9F@EF= 6;;@93E 43:H3 8;D;=3 ?7?4763=3@ B7@97CE;3@ B7CB;@63:3@ 63@ <3C3= %;D3>@J3 !4F B7C9; 63C; CF?3: =7 B3D3C F@EF= 47>3@<3 *3EF <3? 47C;=FE@J3!4F=7?43>;>39;=7CF?3:%7@FCFEB7@97CE;3@B7CB;@63:3@ D7>3?3D3EF<3?E7CD74FE!4F?7@93>3?;B7CB;@63:3@@A>63BF@<3C3= J3@9 6;3>3?; !4F 363>3: EAE3> B3@<3@9 >;@E3D3@ D33E !4F 47C97C3= 4A>3= 43>;= 63C; CF?3: =7 B3D3C 3. Persamaan Kecepatan dan Kelajuan 7@63 3E3F D7D7AC3@9 6;=3E3=3@ 47C97C3= =3C7@3 BAD;D;@J3 47CF43: 3E3F ?7@93>3?; B7CB;@63:3@ *7>3;@ 47CB;@63: 97C3= ?7@93=;43E=3@ B7CF43:3@ H3=EF 3E3F D7>3@9 H3=EF 7@93@ 67?;=;3@ =7E;=3 47@63 47C97C3= E7C<36; B7CF43:3@ BAD;D; D7E;3B D33E 3CE;@J3 BAD;D; ?7CFB3=3@ 8F@9D;H3=EF(7C@J3E33@E7CD74FED753C3?3E7?3E;D63B3E6;EF>;DD74393; /E *33E 47@63 47CF43: BAD;D; 3E3F 47CB;@63: 63>3? D7>3@9 H3=EF E7C E7@EF?F@5F>>3:47D3C3@=757B3E3@47@63E7CD74FE 3>;@;?7@93=;43E =3@ =757B3E3@ 63B3E 6;EFCF@=3@ 63C; 8F@9D; BAD;D; y A, t1 Dr = r2 – r1 r1 B, t2 r2 x 0 Gambar 1.5 Kecepatan rata-rata v di antara A dan B searah dengan arah r . a. Kecepatan dan Kelajuan Rata-Rata #757B3E3@ C3E3C3E3 63C; D74F3: 47@63 J3@9 47C97C3= B363 D3EF 6;?7@D; D3?3 67@93@ B7CB;@63:3@ D74F3: 47@63 6;439; 67@93@ ;@E7CG3> H3=EF J3@9 6;9F@3=3@ D7>3?3 B7CB;@63:3@ E7CD74FE 3> E7CD74FE 3=F F@EF= 97C3= B363 6F3 6;?7@D; 63@ E;93 6;?7@D;*753C3?3E7?3E;D=757B3E3@C3E3C3E363B3E6;EF>;DD74393;47C;=FE    Ingatlah Penulisan vektor satuan yang benar adalah i, j, dan k atau i , j , dan k . 4  P #7E7C3@93@ 3  =757B3E3@ C3E3C3E3 ?D /  B7CB;@63:3@ 47@63 ?   D7>3@9 H3=EF D7=A@ ";=3 @63 B7C:3E;=3@ (7CD3?33@  P  63@  P 67@93@     63@    G7=EAC =757B3E3@ C3E3C3E3 63>3? 6F3 6;?7@D; 363>3:    3   '   (  P Mudah dan Aktif Belajar Fisika untuk Kelas XI #7E7C3@93@ 3  G7=EAC =757B3E3@ C3E3C3E3 ?D x  47D3C =757B3E3@ C3E3C3E3 B363 DF?4F- ?D  y  47D3C =757B3E3@ C3E3C3E3 B363 DF?4F-  ?D 7D3C =757B3E3@ C3E3C3E3 ?7?7@F:; B7CD3?33@      Ingatlah Laju adalah besaran skalar, sehingga ditulis dengan huruf v miring.  P #7>33 ;@; E7C<36; B363 97C3= D3EF 3C3:393;?3@3=7>3;= 3C3: =7 E7?B3E 3H3> "36; =7>3;D D74393; 47C;=FE >3<3C3= t Contoh 1.3 ;=7E3:F;G7=EACBAD;D;DF3EFB3CE;=7>J3@947C97C3=363>3:/ ' P  ( 67@93@63>3??7E7C63@63>3?D7=A@+7@EF=3@>3: 3 BAD;D;47@63B363D33E D7=A@ 4 =757B3E3@63@47D3C=757B3E3@C3E3C3E3D7>3?3D7>3@9H3=EF D7=A@:;@993  D7=A@  4 ! ;=7E3:F;/ ' P  ( 3 -7=EACBAD;D;B3CE;=7>B363D33E D7=A@363>3: /1  2'1  P   2('P( 4 -7=EACBAD;D;B3CE;=7>B363D33E D7=A@363>3: /1  2'1  P   2( 'P ( ?3=3=757B3E3@C3E3C3E3B3CE;=7>363>3: 3  /    /     /     Tugas Anda 1.1 Berilah sebuah contoh persamaan kecepatan sebagai fungsi dari waktu yang berorde 2.  i  (  ?  '   (  ?    D ( '  () ?  'P (?D D 63BF@47D3C=757B3E3@C3E3C3E3@J3363>3:  | v | v       ?D 3E3F v  C       ?D  b. Kecepatan dan Kelajuan Sesaat #7E;=3 @63 47C3@9=3E =7 D7=A>3: 43;= 67@93@ 47C<3>3@ 47CD7B763 3E3F 67@93@ ?7@3;=; =7@63C33@ 4393;?3@3 @;>3; =757B3E3@ 97C3= @63 +7@EF@J3E;63=D7B3@<3@9B7C<3>3@3@?7?;>;=;@;>3;=757B3E3@J3@9D3?3 &;>3; =757B3E3@ D7>3>F 47CF43: D7E;3B D33E #757B3E3@ D7D33E 3E3F =757B3E3@D3<3363>3:=757B3E3@97C3=47@636;DF3EFE;E;=B363>;@E3D3@ @J3 7@93@ =3E3 >3;@ =757B3E3@ D7D33E 63C; DF3EF 47@63 J3@9 47C97C3= 363>3:=757B3E3@J3@96;?;>;=;47@63B363;@E7CG3>H3=EF?7@67=3E;@A> Analisis Gerak 5 (363 +! / <;=3E;E;=?7@67=3E;BAD;D;E;E;=G7=EACB7CB;@ 63:3@ /3=3@47C;?B;E67@93@93C;DD;@99F@9B363>;@E3D3@6; "36; 3C3: =757B3E3@ D7D33E 3 D3?3 67@93@ 93C;D D;@99F@9 >;@E3D3@ 6; E;E;=  *753C3 ?3E7?3E;D =757B3E3@ D7D33E 6;EF>;D y A, t1 B'', t2'' v r'' r1 r2'' B', t2' r' r r2' B, t2 r2 x 0 Gambar 1.6 Ketika B makin dekat dengan A atau  lim  , kecepatan sesaat v di A t 0 menyinggung lintasan di A. x v 3  >;?  /  d /  P 3 >;?     t dt *753C3 ?3E7?3E;D D7DF3; 67@93@ E38D;C3@ 97A?7EC;D F@EF= EFCF@3@ EFCF@3@ B7CE3?3 63C; DF3EF 8F@9D; B363 DF3EF E;E;= 363>3: 9C36;7@ 93C;D D;@99F@9 =FCG3 6; E;E;= E7CD74FE 7@93@ 67?;=;3@ =757B3E3@ D7D33E 63C; DF3EF E;E;= ?3E7C; 63B3E 6;E7@EF=3@ D753C3 9C38;= 3B34;>3 6;=7E3:F; 9C38;= B7CB;@63:3@ E;E;= ?3E7C; E7C:363B H3=EF (7C:3E;=3@  +! /  ,@EF= 9C38;= B7CB;@63:3@  E7C:363B H3=EF  63>3?97C3=D3EF6;?7@D;63B3E6;=7E3:F;47D3C=757B3E3@D7D33E47@63";=3 93C;D D;@99F@9 =FCG3 6; DF3EF E;E;= ?7?47@EF= DF6FE   E7C:363B DF?4F- 47D3C =757B3E3@ D7D33E 47@63 E7CD74FE 63B3E 6;EF>;D D74393; 47C;=FE garis singgung y = x(t) E3@  P   +! /  ?7?B7C>;:3E=3@ D74F3: E;E;= ?3E7C; B363 4;63@9   -7=EAC =757B3E3@ D7D33E@J3 363>3: 3  '    ( D763@9=3@ 47D3C@J3 ?7@<36; =7>337: 67@93@ B7CD3?33@ v sesaat         P  t 0 Gambar 1.7 Kecepatan sesaat suatu benda dapat diperoleh dari garis singgung kurva lintasan benda untuk satu dimensi. y vy 63BF@ 3C3: =757B3E3@ D7D33E B363 4;63@9 67@93@ ?7>;:3E =757B3E 3@B363DF?4F-363>3:63@=757B3E3@B363DF?4F- 363>3: D7:;@993 3=3@ 6;B7CA>7:  E3@   P   "36; =7>33: v 5AD  63@ D;@  v sin   v cos   P  #7E7C3@93@ =7>333?3C3: NE7C:363B3C3: :AC;KA@E3>+7@EF=3@>3:=A?BA@7@=A?BA@7@=7>33?G7=EACD3EF3@  4 ! $F=;D>3: E7C>74;: 6F>F G7=EAC =757B3E3@ 63@ =A?BA@7@=A?BA@7@ =757B3E3@ E7C:363BDF?4F-63@DF?4F- 393C?F63:6;B3:3?; #7>333: 3 ' (  ' (?D 6 Mudah dan Aktif Belajar Fisika untuk Kelas XI y v = 20 m/s vy j 37° 0 vx i x Contoh 1.5 x (m) 60 B Tantangan C 30 A 0 3 6 8 10 D 14 15 t (s) 3?43C6;D3?B;@9363>3:9C38;=B7CB;@63:3@ D74F3:D7B763J3@947C97C3=E7C:363BH3=EF +7@EF=3@=757B3E3@D7B763B363D33E 3  D7=A@ 4 D7=A@63@ 5  D7=A@  4 ! *7B3@<3@99C38;=97C3=P97C3=D7B7636;439;63>3?E;9393C;D>FCFDJ3;EF93C;D 93C;D63@93C;D 3 (363D33E D7=A@9C38;=97C3=PD7B76347C363B36393C;D>FCFD 7D3C=757B3E3@D7B3@<3@993C;DE7CD74FE363>3:  ?    ?D E3@    D   4 (363D33ED7=A@9C38;=97C3=PD7B76347C363B36393C;D>FCFD 7D3C=757B3E3@@J3363>3:  E3@     D7B763E;63=47C97C3= D   5 (363D33E D7=A@D7B76347C363B36393C;D>FCFD#757B3E3@D7B763 ?7CFB3=3@=7?;C;@93@93C;DJ3;EF   ?  P ?D E3@      D  +3@63@793E;8?7@F@;=3C3: untuk Anda Pada saat balapan A1-GP, pembalap Indonesia, Ananda Mikola memantau kecepatannya melalui speedometer. Menurut Anda, bagaimanakah cara kerja speedometer? Gunakan bahasa Anda sendiri untuk menerangkan cara kerja speedometer. Contoh 1.6 *74F3:B3CE;=7>47C97C3=67@93@B7CD3?33@>;@E3D3@/  P ?67@93@ 63>3??7E7C63@63>3?D7=A@+7@EF=3@=757B3E3@B3CE;=7>=7E;=3 D7=A@  4 ! #757B3E3@6;B7CA>7:63C;6;87C7@D;3>B7CD3?33@BAD;D;7@93@?7?3DF==3@H3=EF  6;B7CA>7: /      P '  '?D     '   ''?D c. Menghitung Posisi dari Kecepatan +7>3: @63 =7E3:F; 43:H3 =757B3E3@ ?7CFB3=3@ EFCF@3@ B7CE3?3  63C; 8F@9D; BAD;D; J3;EF 3  /    '  (  *753C3 ?3E7?3E;D BAD;D;    D74F3: B3CE;=7> 63B3E 6;B7CA>7: 63C; 8F@9D; =757B3E3@@J3 ?7>3>F; BCAD7D ;@E79C3D; 7D3C =757B3E3@ 63>3? 3C3: DF?4F-                 P                 P  Analisis Gerak 7 7D3C =757B3E3@ 63>3? 3C3: DF?4F-                P                 P  Contoh 1.7 *77=AC=7>;@5;47C<3>3@6;3E3DCF?BFEB3634;63@9 $7E3=3H3>=7>;@5;B363 =AAC6;@3E  ?#A?BA@7@=757B3E3@@J3363>3: 63@    ";=3 63@ 63>3??D63@63>3?D7=A@E7@EF=3@>3: 3 G7=EACBAD;D;=7>;@5;63@ 4 BAD;D;=7>;@5;B363D33E D7=A@  4 ! 3 #AAC6;@3E3H3>  ?63@47D3C=A?BA@7@=757B3E3@@J3363>3:  63@    D7:;@993                        -7=EACBAD;D;=7>;@5;363>3: /' (   '   ( 4 #AAC6;@3E=7>;@5;B363D33E D7=A@363>3:      ? ? ?       ? ?? ? "36;G7=EACBAD;D;B363D33E D7=A@363>3: / ?' ?( d. Menghitung Perpindahan dan Jarak dari Grafik Kecepatan terhadap Waktu v (t) C38;= =757B3E3@ E7C:363B H3=EF 63C; 97C3= DF3EF 47@63 63B3E 6;>;:3EB363 +! /  *753C39C38;=>F3D637C3:J3@96;3CD;CJ3;EF 637C3: J3@9 6;43E3D; 9C38;= 47D3C =757B3E3@ D74393; 8F@9D; H3=EF  67@93@ DF?4F :AC;KA@E3>  363>3: BAD;D; 63C; 47@63 ";=3D74F3:47@6347C97C3=?7@7?BF:93C;D>FCFDE3@B347C43>;=3C3: 47D3CB7CB;@63:3@D7>3>FD3?367@93@<3C3=J3@96;E7?BF:47@63=3@ E7E3B; F@EF= 47@63 J3@9 47C97C3= >FCFD 63@ D7D33E =7?F6;3@ 47C43>;= 3C3: 3=3@ ?7?;>;=; 47D3C <3C3= J3@9 47C4763 67@93@ 47D3C B7CB;@63:3@ (7C:3E;=3@ 93?43C  +! / ! $F3D 637C3: J3@9 6;3CD;C ?7@F@=3@ B7CD3?33@ 93C;D@J3 6;B7CA>7: 47D3C <3C3= D74393; 47C;=FE a (t) t2  t v(t)dt 1 0 t1 t t2 3 v t2 0 t1 t3 t                  4 Gambar 1.9 (a) Grafik fungsi kecepatan (v) terhadap waktu (t). (b) Grafik v–t untuk gerak benda yang berbalik arah. 8  +3@63?FE>3=6;9F@3=3@F@EF=?7?3DE;=3@43:H347D3C<3C3=D7>3>F 47CE3@63 BAD;E;8 63BF@ F@EF= ?7@9:;EF@9 47D3C B7CB;@63:3@@J3 6;9F@3=3@ B7CD3?33@ 47C;=FE  Mudah dan Aktif Belajar Fisika untuk Kelas XI         Contoh 1.8 v (m/s) v = 3t2 – 6t – 9 8 #757B3E3@B3CE;=7>J3@947C97C3=>FCFD?7?7@F:;B7CD3?33@3  PP' 67@93@47D3C63>3??D63@63>3?D7=A@+7@EF=3@B7CB;@63:3@63@<3C3=J3@9 6;E7?BF:B3CE;=7>F@EF=D7>3@9H3=EF3@E3C3 D7=A@63@ D7=A@  4 ! 3?43C=3@9C38;=   PPE7C>74;:63:F>F67@93@B7C:;EF@93@47C;=FE O +;E;=BAEA@9E7C:363BDF?4F-6;B7CA>7:63C;   PP  P P  P    63@P O +;E;=BF@53=9C38;=        D7:;@993=757B3E3@6; D363>3:   P PP ?D ,@EF=D7>3@9H3=EF D7=A@:;@993 D7=A@6;B7CA>7: O O "3C3=  P            P                   5 4 3 2 –4 –3 –2 –1 t (s) –2 –3 –4 –5 –6 –7 –8 –9 –10 –11 –12  1 2 3 4 5 –1  P              1 0 6 (7CB;@63:3@       PP         P   P P P   P  ? 7   P                P      ? Tugas Anda 1.2 4. Percepatan *7E;3B 47@63 J3@9 ?7@63B3E 93J3  3=3@ ?7@93>3?; B7CF43:3@ =757B3E3@ D7:;@993 47@63 E7CD74FE ?7?;>;=; B7C57B3E3@ *3?3 :3>@J3 67@93@ =757B3E3@ B363 B7C57B3E3@ 6;=7@3> 3: B7C57B3E3@ C3E3 C3E363@B7C57B3E3@D7D33E'>7:=3C7@3=757B3E3@E7C?3DF=47D3C3@G7=EAC ?3=3B7C57B3E3@3;@J3?7CFB3=3@ EFCF@3@ B7CE3?3 63C; =757B3E3@ ,@EF= 47@63 J3@9 47C97C3= G7CE;=3> =7 3E3D B7C57B3E3@ J3@9 6;?;>;=; 363>3: B7C57B3E3@ 9C3G;E3D; 63@ 47C@;>3; @793E;8 D763@9=3@ F@EF= 97C3= <3EF: B7C57B3E3@@J3 47C@;>3; BAD;E;8 a. Percepatan Rata-Rata (7C57B3E3@C3E3C3E3B36397C3=6F36;?7@D;?7?;>;=;B7@97CE;3@D3?3 67@93@ B7C57B3E3@ C3E3C3E3 B363 97C3= D3EF 6;?7@D; J3;EF :3D;> 439; B7CF43:3@ =757B3E3@ E7C:363B ;@E7CG3> H3=EF  +! /   ?7?B7C>;:3E=3@ 9C38;= :F4F@93@ =757B3E3@ E7C:363B H3=EF (363 D33E   47@63 47C363 6; E;E;=  67@93@ =757B3E3@ J3@9 6;?;>;=;  (363 D33E  47@63 47C363 6; E;E;=  67@93@ =757B3E3@ J3@9 6;?;>;=;   (7C57B3E3@ C3E3C3E3 47@63 63C;  D3?B3;  363>3:         #7E7C3@93@  B7C57B3E3@ C3E3C3E3 ?D    B7CF43:3@ =757B3E3@ ?D   D7>3@9 H3=EF D  P  Diskusikan dengan teman sebangku Anda, apa perbedaan antara jarak dan perpindahan? Bagaimana Anda menerangkan konsep jarak dan perpindahan ini pada kasus mobil F1 yang sedang balapan di sirkuit? Pada balapan F1, garis start dan finish berada di tempat yang sama, dan mobil hanya bergerak mengelilingi sirkuit. v v2 B a= v1 A v t v t t1 t2 t Gambar 1.10 Percepatan rata-rata. Analisis Gerak 9 -7=EAC B7C57B3E3@ D74F3: 47@63 J3@9 47C97C3= B363 4;63@9 J3;EF B363DF?4F:AC;KA@E3>DF?4F-63@DF?4FG7CE;=3>DF?4F- @;>3;@J3 363>3:  a' a (  P  63BF@ 47D3C B7C57B3E3@ C3E3C3E3 ?7?7@F:; B7CD3?33@  a x 2  a y 2  P  #7E7C3@93@  B7C57B3E3@ C3E3C3E3 ?D  a  47D3CB7C57B3E3@B363DF?4F-?D  a 47D3CB7C57B3E3@B363DF?4F- ?D  b. Percepatan Sesaat *7B7CE;B363=757B3E3@D7D33EB7C57B3E3@D7D33E97C3=D74F3:B3CE; =7> ?7?4FEF:=3@ D7>3@9 H3=EF   J3@9 D3@93E D;@9=3E J3;EF   ?7@67=3E;@A>"36;B7C57B3E3@D7D33E?7CFB3=3@EFCF@3@B7CE3?363C; B7CD3?33@ =757B3E3@ F@EF= D7>3@9 H3=EF ?7@67=3E; @A> y v a t v2 3 d 3  >;?  >;?      t dt v2 v1 t2 t1 v1 x 0 3 +3:F=3: @63 53C3 ?7@F@;?;E 63>3? ?7@7@EF=3@ B7C57B3E3@D7D33E47C63D3C=3@9C38;=,@EF=?7@97E3:F;@J3B7C:3E;=3@  +! /   v a t v2 v1 t2 t1 (7C57B3E3@D7D33E?7CFB3=3@EFCF@3@=76F363C;8F@9D;BAD;D;=3C7@3 3 / '>7:=3C7@3;EF     3    /     P        y v2 v1 x (363  +! /    63@  +! /  ! G7=EAC 3  63@ 3  ?7CFB3=3@ G7=EAC =757B3E3@ B363 D33E   63@   D763@9=3@ 3 ?7CFB3=3@ B7CF43:3@ =757B3E3@   6;4F3E E7E3B D763@9=3@   6;4F3E ?7@67=3E;  D7:;@993    7C63D3C=3@ 678;@;D; 0 4 a v x 0 5 Gambar 1.11 v t merupakan percepatan pada saat t2 – t1 menuju nol atau t menuju nol. Percepataan sesaat a = lim t 0 3    ?7?;>;=; 3C3: J3@9 D3?3 ";=3B3CE;=7>47C97C3=B3634;63@9 6;63B3E=A?BA@7@=A?BA@7@ B7C57B3E3@ 47C;=FE ;@;  d 3  d   '   ( dt dt dv dv    x '  y (   '  ( dt dt   @63 E7@EF E7>3: ?7@97E3:F; 43:H3    63@                7@93@ 67?;=;3@     63@              D7:;@993 10  67@93@ 3 '>7: =3C7@3 ;EF  ?7?;>;=; 3C3: J3@9 D3?3 67@93@ 3 =7E;=3   ?7@67=3E; @A> (363 D33E   6;53B3; D7B7CE; 6;EF@3>F ?7@<36; D;D; >7@9=F@9 >;@E3D3@ E;E;= ?3E7C; D763@9=3@ G7=EAC =757B3E3@ 3 E7E3B ?7@J;@99F@9 >;@E3D3@ 6;  y t  P  Mudah dan Aktif Belajar Fisika untuk Kelas XI 2 d2y  d 2x '  2 ( dt dt  P  63BF@ 47D3C B7C57B3E3@ D7D33E 363>3:  Tugas Anda 1.3     P  Jika Anda naik mobil dan duduk di sebelah sopir, coba perhatikan bagaimana gerakan speedometer mobil. Diskusikan bersama teman Anda bagaimana pengaruhnya terhadap percepatan mobil. 63BF@ 3C3: B7C57B3E3@ D7D33E E7C:363B DF?4F- 63B3E 6;E7@EF=3@ E3@   67@93@ B7CD3?33@   P  Contoh 1.9 *74F3:B3CE;=7>47C97C3=67@93@B7CD3?33@=7>33??D63@63>3?D7=A@+7@EF=3@>3: 3 47D3CB7C57B3E3@C3E3C3E397C3=B3CE;=7>F@EF= DD3?B3;67@93@ D 4 47D3CB7C57B3E3@3H3>B3CE;=7>63@ 5 47D3CB7C57B3E3@B3CE;=7>B363D33E D7=A@  4 ! 3 (7CD3?33@=757B3E3@363>3:  P  ,@EF=  D    P   ?D ,@EF=  D    P   ?D   a      ?D     4 (7CD3?33@B7C57B3E3@6;B7CA>7:63C;EFCF@3@B7CE3?3B7CD3?33@=757B3E3@J3;EF d    P  P dt 7D3CB7C57B3E3@3H3>B3CE;=7>B363D33E 363>3: P  P P ?D 5 7D3CB7C57B3E3@B3CE;=7>B363D33E D7=A@363>3: P  P  ?D c. Persamaan Kecepatan dari Percepatan Fungsi Waktu ,@EF=97C3=47@63B363D3EF4;63@9=757B3E3@6;678;@;D;=3@D74393; B7CF43:3@ BAD;D; 63>3? D7>3@9 H3=EF E7CE7@EF '>7: =3C7@3 B7C57B3E3@ 63@ =757B3E3@ ?7CFB3=3@ 47D3C3@ G7=EAC ?3=3 =757B3E3@ 63B3E 7: 63C; 8F@9D; B7C57B3E3@ 67@93@ ?7EA67 ;@E79C3D; 47C;=FE  a d 3 3E3F v  t dt v0 d 3 0 dt P   t 0  P   P  dt t #7E7C3@93@ =757B3E3@ 47@63 B363 D33E  D7=A@ ?D =757B3E3@3H3>47@63B363D33E ?D  B7C57B3E3@ 47@63 ?D  C38;= 47D3C B7C57B3E3@ E7C:363B H3=EF 63C; 97C3= D74F3: 47@63 63B3E6;>;:3EB363 +! /  $F3D637C3:J3@96;3CD;CJ3;EF637C3: J3@9 6;43E3D; A>7: 9C38;= 47D3C B7C57B3E3@ D74393; 8F@9D; H3=EF 3 67@93@ DF?4F :AC;KA@E3>  363>3: B7CF43:3@ =757B3E3@ 97C3= 47@63 ";=3 D74F3: 47@63 47C97C3= B363 6F3 6;?7@D; J3;EF B363 4;63@9 :AC;KA@E3> 63@ 4;63@9 G7CE;=3> 47D3C =A?BA@7@=A?BA@7@ =757B3E3@ E7C:363B DF?4F 63@ DF?4F  ?7?7@F:; B7CD3?33@ 47C;=FE      x dt 63@    y dt  a dt 0 t 0 t Gambar 1.12 Grafik fungsi percepatan (a) terhadap waktu (t).  P  Analisis Gerak 11 Contoh 1.10 *74F3:B3CE;=7>47C97C3=D7B3@<3@9DF?4F67@93@B7CD3?33@B7C57B3E3@  ";=3 B363 ?7?;>;=;47D3C=757B3E3@  ?DE7@EF=3@=7>3B363D33E 3  D63@ 4  D  4 ! #7>3B3CE;=7>  ?D?3=3B7CD3?33@47D3C=7>33B3CE;=7>B363D33E J3;EF?D (363D33E D?3=3        ?D "36;=7>3B3CE;=7>B363D33E D363>3: ?D Contoh 1.11 *74F3:4A>36;>7?B3C=3@B3634;63@9 #A?BA@7@B7C57B3E3@4A>3B3633C3: :AC;KA@E3>363>3:  '?D 63@=A?BA@7@B7C57B3E3@63>3?3C3:G7CE;=3>  P (?D (363D33E 4A>347C3636;BFD3E=AAC6;@3E  67@93@ =A?BA@7@=A?BA@7@=757B3E3@3H3>@J3363>3:3 I'?D63@3 J(?D 3 +F>;D=3@G7=EAC=757B3E3@63@G7=EACBAD;D;D74393;8F@9D;H3=EF 4 7C3B3E;@99;?3=D;?F?J3@96;53B3;4A>3 5 +7@EF=3@<3C3=E7C<3F:J3@96;53B3;4A>3  4 ! 3 -7=EAC=757B3E3@63B3E6;B7CA>7:67@93@B7CD3?33@        '   '  '?D           (      ( P (?D -7=EAC=757B3E3@@J3363>3: ' (L  ' P (M?D -7=EACBAD;D;6;B7CA>7:63C;B7CD3?33@ Information for You  On September 26th, 1993, Dave Munday a diesel mechanic went over the Canadian edge of Niagara Falls for the second time. Freely falling 48 m to the water (and rocks) below. On this attempt, he rode in a steel ball with a hole of air. Munday keep on surviving this plunge that had killed four other stuntman, had done considerable research on the physics (motion along a straight line) and engineering aspects of the plunge.   4 5       (        (  P  (   /' (    '      ( +;@99;?3=D;?F?J3@96;53B3;=7E;=3  363>3:   P  P  7@93@B7C:;EF@93@?3E7?3E;=36;B7CA>7:D+;@99;?3=D;?F?6;B7CA>7: ?7>3>F;B7CD3?33@ D  P    P   ? A>3=7?43>;=7E3@3:47C3CE;     P    P     P   PP   7@93@B7C:;EF@93@?3E7?3E;=36;B7CA>7: D7=A@"3C3=E7C<3F:63B3E 6;:;EF@9?7>3>F;B7CD3?33@  D        ?  Sumber: Fundamental of Physics, 2001 12       '       '  '   Mudah dan Aktif Belajar Fisika untuk Kelas XI      5. Perpaduan Dua Vektor Tugas Anda 1.4 (7CB36F3@ 3@E3C3 6F3 G7=EAC 3=3@ ?7@9:3D;>=3@ G7=EAC B7CB36F3@ 3E3F G7=EAC C7DF>E3@ A@EA: G7=EAC B7CB36F3@ 3E3F G7=EAC C7DF>E3@ ;@; 63B3E@63=3@=757B3E3@3>;C3@DF@93;6;@J3E3=3@67@93@ 63@=757B3E3@ B7C3:F 6;@J3E3=3@ 67@93@  D7B7CE; 6;EF@FCFD 47C3EFC3@ E7CD74FE ?7?47@EF= C7DF>E3@ 6F3 G7=EAC J3;EF  1  2 7D3C C7DF>E3@ =757B3E3@@J3 363>3:       5AD Buatlah kelompok diskusi kecil. Apakah Anda dan teman-teman dapat memprediksi gerak seperti apa yang dihasilkan oleh perpaduan dua buah gerak lurus berubah beraturan? Setelah selesai diskusi, kemukakan pendapat kelompok Anda di depan kelas.  P  v2 (kecepatan perahu) 63BF@<3C3=J3@96;E7?BF:B7C3:F=3C7@3C7DF>E3@=757B3E3@@J3363>3:   #7E7C3@93@   47D3C C7DF>E3@ =757B3E3@ =76F3 97C3= ?D   <3C3= ?   H3=EF E7?BF: D  v1 (aliran sungai) Gambar 1.13 v adalah vektor resultan dari v1 (kecepatan aliran sungai) dan v2 (kecepatan perahu). Contoh 1.12 *74F3:B7C3:F:7@63=?7@J747C3@9;DF@93;67@93@=757B3E3@ ?D63@?7?47@EF= DF6FE NE7C:363B3C3:3CFDDF@93;J3@9?7@93>;C67@93@=757B3E3@ ?D 3 3?43C=3@>;@E3D3@B7C3:F 4 +7@EF=3@C7DF>E3@=757B3E3@B7C3:F 5 7C3B3=3:B7CB;@63:3@B7C3:FD3?B3;=7D747C3@9D7E7>3:D7=A@  4 ! ;=7E3:F; .  ?D   N   ?D 3 $;@E3D3@B7C3:F vp  4  >743CDF@93; 3. =757B3E3@B7C3:F 3 3.30 v s vs 3 =757B3E3@C7DF>E3@ 30 =757B3E3@3>;C3@DF@93; Kata Kunci         5AD   5       1   5AD   2   1  2   ?D "36;47D3CC7DF>E3@=757B3E3@B7C3:F363>3: ?D  ?DQD  ? "36;B3@<3@9>;@E3D3@J3@96;E7?BF:B7C3:FD7E7>3:D7=A@363>3:  ? • • • • • • • • • arah vektor besar vektor jarak kecepatan kelajuan percepatan perpindahan posisi vektor satuan Analisis Gerak 13 v Tes Kompetensi Subbab A $/( ) ,* &# * +!2)2* 1'& ,     *74F3:B3CE;=7>47CB;@63:63C;BAD;D;/ =7BAD;D;/  ";=3 BAD;D; /   ' P ( 63@ BAD;D; /   '  ( E7@EF=3@>3: 3 G7=EACB7CB;@63:3@@J363@ 4 47D3CB7CB;@63:3@@J3 *74F3:B3CE;=7>47C97C3=47C63D3C=3@8F@9D;=757B3E3@   67@93@63>3??D63@63>3? D7=A@";=3=A@DE3@E3  ?D P ?D 63@ ?DE7@EF=3@>3: 3 B7C57B3E3@C3E3C3E3B3CE;=7>F@EF=D7>3@9H3=EF  D7=A@D3?B3;D7=A@ 4 B7C57B3E3@3H3>B3CE;=7>63@ 5 B7C57B3E3@B3CE;=7>B363D33ED7=A@ (7CD3?33@97C3=D74F3:B3CE;=7>6;@J3E3=3@A>7:8F@9D;   67@93@63>3??7E7C63@63>3?D7=A@ 3 ;EF@9>3: B7C57B3E3@ C3E3C3E3 63>3? D7>3@9 H3=EF D7=A@D3?B3;67@93@ D7=A@ 4 ;EF@9>3:=757B3E3@D7D33EB363D7=A@ 5 ;EF@9>3:B7C57B3E3@D7D33EB363D7=A@ (AD;D;D74F3:47@636;@J3E3=3@A>7:/ P '    (67@93@/63>3??7E7C63@63>3?D7=A@ 3   +7@EF=3@G7=EACBAD;D;63@<3C3=47@6363C;E;E;= 3D3>B363D33E D7=A@ 4 +7@EF=3@B7CB;@63:3@63@=757B3E3@C3E3C3E3 47@6363>3?D7>3@9H3=EF D7=A@D3?B3;67@93@ D7=A@ 5 +FCF@=3@B7CD3?33@F?F?=757B3E3@47@63 6 +7@EF=3@=7>37?B3C=3@G7CE;=3>67@93@B7CD3?33@  P  67@93@ 63>3??7E7C63@63>3? D7=A@+7@EF=3@ 3 47D3CB7C57B3E3@43EF63@ 4 E;@99;?3=D;?F?J3@96;53B3;43EF *74F3:CA=7E47C97C3=B3634;63@9 (7C57B3E3@ CA=7E?7?;>;=;=A?BA@7@  ?D 63@  P E?D 67@93@63>3?D7=A@(363D33E CA=7E 47C3636;E;E;=BFD3E=AAC6;@3E  67@93@=A?BA@7@ =757B3E3@3H3>  ?D63@ ?DD7:;@993 D753C3G7=EAC6;EF>;D=3@  '(?D 3 &J3E3=3@ G7=EAC =757B3E3@ 63@ BAD;D; D74393; 8F@9D;63C;H3=EF 4 7C3B3E;@99;?3=D;?F?J3@96;53B3;CA=7E 5 7C3B3<3C3=E7C<3F:J3@96;53B3;CA=7E B. Gerak Parabola bola (A) bola (B) Sumber: Physics for Scientist & Engineers, 2000 Gambar 1.14 Dua buah bola dilepaskan dari ketinggian yang sama dengan perlakuan yang berbeda. 14 +3:F=3:@63J3@96;?3=DF667@93@97C3=B3C34A>3%7@FCFE3>;>7A 97C3=B3C34A>363B3E6;B3@63@9D74393;:3D;>B7CB36F3@97C3=>FCFD47C3EFC3@ B363 DF?4F :AC;KA@E3> DF?4F- 63@ 97C3= >FCFD 47CF43: 47C3EFC3@ B363 DF?4F G7CE;=3> DF?4F-  D753C3 E7CB;D3: *7E;3B 97C3= E;63= D3>;@9 ?7?7@93CF:; 34F@93@ 63C; =76F3 97C3= E7CD74FE 47CFB3 97C3= B3C34A>3 7C3=B3C34A>36;D74FEFCF3>3?=7:;6FB3@D7:3C; :3C; :3> E7CD74FE 63B3E @63 @J3 =7E;=3 @63 ?7@7@63@9 4A>367@93@DF6FEE7@63@93@E7CE7@EF3E3F NE7C:363B4;63@9:AC;KA@E3> ?3=3 >;@E3D3@ 97C3= 4A>3 3=3@ 47C47@EF= B3C34A>3 (7C:3E;=3@ +! /  6F34F3:4A>36;>7B3D=3@63C;=7E;@99;3@ E7CE7@EF A>3  6;>7B3D=3@ 63C; =73633@ 6;3? 3>3? :3> ;@; 97C3= 4A>3  363>3: 97C3= <3EF: 4743D J3@9 6;B7@93CF:; A>7: B7C57B3E3@ 9C3G;E3D; F?; (363 D33E J3@9 47CD3?33@ 4A>3  6;47C; 93J3 :AC;KA@E3> 67@93@ B793D $;@E3D3@ 4A>3  D7B7CE; B363  +! /   47CFB3 B3C34A>3(3633H3>@J3=76F34A>3E7C>7E3=B363=7E;@99;3@J3@9D3?3 =7?F6;3@ 6;>7B3D=3@ B363 D33E J3@9 D3?3 3B3E=3: @63 ?7@743= 4A>3?3@3J3@9?7@J7@EF:E3@3:>74;:57B3E +7C@J3E3 H3=EF J3@9 6;4FEF:=3@ A>7: =76F3 4A>3 :;@993 ?7@J7@EF: E3@3: 363>3: D3?3 7@93@ 67?;=;3@ =757B3E3@ ?7@63E3C 3=;43E 363@J3 93J3E7C:363B4A>3E;63=?7@<36;=3@4A>3?7@J7@EF:E3@3:>74;:57B3E 7C3= 47@63 J3@9 D7C;@9 6;<36;=3@ D74393; 5A@EA: 97C3= B3C34A>3 363>3: 97C3= B7>FCF J3@9 3C3:@J3 ?7?47@EF= DF6FE 7>7G3D; E7CE7@EF E7C:363B B7C?F=33@ F?; Mudah dan Aktif Belajar Fisika untuk Kelas XI (7C:3E;=3@ 93?43C 47C;=FE y vy vy = 0 v vx vx vx vy v0 v0 sin  Gambar 1.15 v Lintasan gerak parabola. Nilai a selalu negatif karena ditetapkan arah positif adalah arah ke atas, dan arah gravitasi selalu ke bawah. ay = –g vx  O(0,0) v0 cos  vy x v (363 +! /  E7C>;:3E=757B3E3@B363DF?4F-J3;EF367@93@ 3C3:63@47D3C@J3D7>3>F=A@DE3@63BF@=757B3E3@B363DF?4F- J3;EF 3  3C3: 63@ 47D3C@J3 6;B7@93CF:; A>7: B7C57B3E3@ 9C3G;E3D;  -7=EAC C7DF>E3@ =757B3E3@ 3 D7E;3B D33E 6; =AAC6;@3E   ?7CFB3=3@ C7DF>E3@ 63C;=A?BA@7@G7=EAC 63@  ";=3 47D3C =757B3E3@ 3H3> B7>FCF 363>3:   47D3C =757B3E3@ 63>3? 3C3: DF?4F- 363>3:  63@ 47D3C =757B3E3@ B363 DF?4F-  363>3:   6;B7CA>7: B7CD3?33@B7CD3?33@ 47C;=FE ;@;  (7CD3?33@ B363 DF?4F- 7D3C =757B3E3@ B363 DF?4F- 363>3:   5AD   P  "3C3= B363 DF?4F- 363>3:  5AD    Tokoh Galileo Galilei (1564–1642)  P  (7CD3?33@ B363 DF?4F-  7D3C =757B3E3@ B363 DF?4F-  67@93@   P 363>3:   D;@  "   P  "3C3= B363 DF?4F-  363>3: Sumber: Conceptual Physics, 1998  D;@  " 1  2  P  #7E7C3@93@   47D3C =757B3E3@ B363 DF?4F-  ?D   47D3C =757B3E3@ B363 DF?4F- ?D A  47D3C =757B3E3@ 3H3> ?D   47D3C B7C57B3E3@ 9C3G;E3D; ?D    DF6FE 7>7G3D;   <3C3= E7?BF: ?7@63E3C ?  <3C3= E7?BF: G7CE;=3> ? 7C63D3C=3@ B7CD3?33@B7CD3?33@ E7CD74FE 63B3E 6;D;?BF>=3@ 43:H3=A?BA@7@97C3=B363DF?4F- G7CE;=3>D3@93E6;B7@93CF:;A>7: B7C57B3E3@ 9C3G;E3D; F?; D763@9=3@ 47D3C =757B3E3@ 63>3? 3C3: ?7@63E3C D7>3>F E7E3B 7C3= B363 DF?4F-  363>3: 97C3= >FCFD 47CF43: 47C3EFC3@ 63@ DF?4F- 363>3: 97C3= >FCFD 47C3EFC3@ Galileo Galilei lahir di kota Pisa, Italia, pada 15 Februari 1564. Ia belajar kedokteran di Universitas Pisa. Oleh karena ia lebih tertarik dengan ilmu alam, ia tidak melanjutkan belajar kedokterannya, tetapi belajar matematika. Ia meninggalkan Pisa untuk belajar di Universitas Padua. Ia adalah pendukung teori Heliosentris yang menyatakan bahwa Matahari adalah pusat tata surya. Penemuan Galileo yang terkenal adalah teleskop dan menemukan pegunungan di Bulan serta satelit di Yupiter. Oleh karena hobinya mengamati benda-benda langit termasuk Matahari, ia menderita kebutaan pada usia 74 tahun. Ia meninggal dunia 4 tahun kemudian pada usia 78 tahun. Analisis Gerak 15 Contoh 1.13 *7AC3@9D;DH3?7>7?B3C4A>367@93@=757B3E3@ ?DB3633C3:J3@9?7?47@EF= DF6FE NE7C:363BE3@3:D;@  +7@EF=3@ 3 47D3C=757B3E3@4A>3D7E7>3: D63@ 4 47D3C=76F6F=3@4A>3D7E7>3: D<;=3B7C57B3E3@9C3G;E3D; ?D   4 ! ;=7E3:F;  ?D   N D;@  D;@ N  5AD    ?D 3 7D3C=A?BA@7@=757B3E3@B363D33E D7=A@363>3:   D;@    5AD   ?D ?D  ?D ?D 7D3C=757B3E3@B363D33E D7=A@363>3:   ?D   P E ?DP ?D  D ?D 4   tx 2  ty 2   m/s  m/s    ?D "36;47D3C=757B3E3@4A>3D33E D363>3: ?D #76F6F=3@4A>3D33E D7=A@363>3:    ?D D ?  P   ?D DP  ?D D  P  ? ? "36;=76F6F=3@4A>3B363D33E D363>3:B363=AAC6;@3E ? ? 1. Tinggi Maksimum dan Jarak Terjauh ,@EF= ?7@7@EF=3@ E;@99; ?3=D;?F? 63@ <3C3= E7C<3F: J3@9 63B3E 6;53B3; A>7: 47@63 J3@9 47C97C3= 67@93@ >;@E3D3@ B3C34A>3 B7C>F 6;E7@EF=3@63:F>FH3=EFJ3@96;B7C>F=3@F@EF=?7@53B3;E;E;=E7CE;@99; 63@ <3C3= E7C<3F:@J3 a. Waktu untuk Mencapai Tinggi Maksimum #7E;=3 ?7@53B3; E;@99; ?3=D;?F? 47D3C =757B3E3@ 47@63 J3@9 47C97C3= B3C34A>3 B363 3C3: G7CE;=3> D3?3 67@93@ @A>     CE;@J3 47@63D7?B3E47C:7@E;4747C3B3D33ED747>F?3=:;C@J3EFCF@"36;H3=EF E7?BF: 47@63 D33E ?7@53B3; E;@99; ?3=D;?F? 363>3:   D;@ "  D;@  P  D;@   P   ?3=D  b. Waktu untuk Mencapai Jarak Terjauh (36397C3=B3C34A>33C3=E7C<3F:363>3:<3C3=J3@96;E7?BF:47@63 D33E =7?43>; =7 B7C?F=33@ E3@3: (363 =A@6;D; E7CD74FE <3C3= ?7@FCFE DF?4F-  63@<3C3=?7@FCFE DF?4F-363>3:?3=D;?F?'>7:=3C7@3 ;EF 6;9F@3=3@ =A@6;D; =76F3 J3;EF    "36; H3=EF F@EF= ?7@53B3; <3C3= E7C<3F: 363>3: 16 Mudah dan Aktif Belajar Fisika untuk Kelas XI    D;@       D;@     D;@   I?3=D    P  c. Tinggi Maksimum +;@99; ?3=D;?F? J3@9 63B3E 6;53B3; A>7: 47@63 J3@9 ?7>3=F=3@ 97C3=B3C34A>363B3E6;53C;67@93@?7@99F@3=3@H3=EFF@EF=?7@53B3; E;@99;?3=D;?F?=7B7CD3?33@97C3=63>3?DF?4F- 7@93@?7>3=F=3@ DF4DE;EFD;$/0 + , 6 =763>3?$/0 + , 6 6;B7CA>7:E;@99; ?3=D;?F? D74393; 47C;=FE ?3=D   D;@     D;@   "          D;@    Tantangan untuk Anda  D;@   D;@  P   ?3=D  D;@     P  Apakah tendangan bebas yang biasa dilakukan oleh pemain sepakbola seperti David Beckham termasuk gerak parabola? d. Jarak Terjauh pada Sumbu-x 7@93@?7>3=F=3@DF4DE;EFD;$/0 + , 6 =763>3?$/0 + ,  6  ?3=3 6;B7CA>7: <3C3= E7C<3F: B363 DF?4F- D74393; 47C;=FE  ?3=D  5AD  ?3=D   D;@        5AD     y jarak vertikal (m)  ( D;@ 5AD   ?3=D   D;@    P  2. Jarak Terjauh dan Pasangan Sudut Elevasi (7C:3E;=3@  +! /   J3@9 ?7@F@;@E3D3@ B3C34A>3 J3@9 6;E7?BF: D74F3: 47@63 67@93@ =7>3 J3@9 D3?3 E7E3B; 67@93@ DF6FEDF6FE 7>7G3D; J3@9 47C4763 @63 63B3E ?7@J;?BF>=3@ 43:H3B3D3@93@DF6FE7>7G3D;J3@947C3: NJ3;EFN63@ ND7CE3  N 63@ N 3=3@ ?7@9:3D;>=3@ <3C3= E7C<3F: J3@9 D3?3 (363 93?43C E7CD74FE E7C>;:3E 43:H3 <3C3= E7C<3F: ?7@53B3; :3C93 ?3=D;?F? F@EF= DF6FE7>7G3D; N7C63D3C=3@B7CD3?33@B7CD3?33@97C3=B3C34A>3<3C3= E7C<3F:6;B7CA>7:<;=3D;@   3E3F   N 75° 60° 45° 30° 15° x jangkauan (meter) Gambar 1.16 Grafik lintasan sebuah benda dengan sudut elevasi berbeda dan kecepatan awal yang sama. Contoh 1.14 *74F3:47@636;>7B3D=3@63C;B7D3H3EE7C43@9J3@9D763@9E7C43@9?7@63E3C67@93@ =757B3E3@ ?D63@47C363B363=7E;@99;3@ ?6;3E3DE3@3:";=3 ?D  47C3B3=3: 3 H3=EFJ3@96;B7C>F=3@47@63:;@993E;436;E3@3: 4 <3C3=?7@63E3C<3EF:@J347@6363@ 5 =757B3E3@47@63D747>F??7@J7@EF:E3@3: Analisis Gerak 17 Tantangan untuk Anda Buktikan bahwa jika kecepatan awalnya sama, pasangan sudut elevasi yang hasil jumlahnya 90° akan menghasilkan jarak terjauh yang sama. Kemudian, apakah waktu tempuh keduanya sama?  4 ! 3 7C3=G7CE;=3>47@63D3?367@93@97C3=<3EF:4743D   "   ?  ?D   ? ?D   D "36;47@63E;436;E3@3:D7E7>3: D7=A@ 4 "3C3=?7@63E3C6;B7CA>7:?7>3>F;B7CD3?33@    ?D D  ? "36;<3C3=?7@63E3C47@63 ? 5 #757B3E3@47@63D747>F??7@J7@EF:E3@3:63B3E6;B7CA>7:67@93@CF?FD G7=EACC7DF>E3@=757B3E3@J3;EF   ?D  P ?D  DP ?D          ?D   ?D  ?D "36;47D3C=757B3E3@47@63D747>F??7@J7@EF:E3@3: ?D Contoh 1.15 F34F3:B7>FCF67@93@<3@9=3F3@ ?7?4FEF:=3@H3=EF 63@ F@EF=?7@53B3; =7E;@99;3@D7?F>3B7>FCF=7?43>;=7E3@3:F=E;=3@43:H3      4 ! 5AD 3E3F5AD     D;@ 3E3FD;@       7@93@?7?3DF==3@:3C93D;@ 63@5AD B363CF?FD5AD  D;@    @633=3@?7?B7CA>7:  P      ,@EF=?7@63B3E=3@@;>3; 63@ @63:3CFD?7@53C;@;>3;3=3C3=3CB7CD3?33@ E7CD74FE67@93@?7@99F@3=3@CF?FD47C;=FE Ingatlah Untuk mencari nilai akar-akar dari y = ax2 + bx + c digunakan rumus abc berikut ini. x1,2 = b  b 2  4 ac 2a       t  t         t         t t   18                          E7C4F=E;  Mudah dan Aktif Belajar Fisika untuk Kelas XI     3 4P  5 ) Contoh 1.16 Kata Kunci *74F3:B7>FCF6;E7?43==3@67@93@DF6FE7>7G3D; N+7@EF=3@B7C43@6;@93@3@E3C3 E;@99;?3=D;?F?63@<3C3=E7C<3F:J3@96;53B3;B7>FCF  4 ! 3C;B7CD3?33@E;@99;?3=D;?F?63@<3C3=:AC;KA@E3>E7C<3F:6;B7CA>7:   • jarak terjauh • sudut elevasi • tinggi maksimum  D;@   D;@ 2    D;@  : D;@  D;@  : D;@ 60o   2     1 1:    :  :  "36;B7C43@6;@93@@J3363>3:1:  Tes Kompetensi Subbab B $/( ) ,* &# * +!2)2* 1'& ,      *74F3:47@636;>7?B3C=3@67@93@DF6FE7>7G3D; N 63@ =757B3E3@ 3H3>@J3  ?D ";=3    ?D E7@EF=3@>3: 3 H3=EFE7?BF:47@636;F63C3 4 E;@99;?3=D;?F?J3@96;53B3;63@ 5 <3C3=?7@63E3CE7C<3F: F=E;=3@ 43:H3 47@63 J3@9 6;>7?B3C=3@ 67@93@ DF6FE 7>7G3D;   3=3@ ?7@53B3; E;E;= E7C<3F: <;=3   N *74F3:47@636;>7?B3C=3@67@93@DF6FE7>7G3D; N 63@=757B3E3@ ?D ;EF@947D3C63@3C3:=757B3E3@ D7E7>3: D7=A@63@ 3 4 D7=A@ (AD;D;4FCF@9E7C>7E3=B363=AAC6;@3E ?*7AC3@9 3@3=?7>A@E3C=3@43EF67@93@?7@99F@3=3@=3E3 B7>@J3 B363 DF6FE 7>7G3D; N =7 3C3: 4FCF@9 7C3B3=3:=757B3E3@J3@9:3CFD6;47C;=3@393C43EF ?7@97@3;4FCF@9E7CD74FE 3>3?B7C?3;@3@D7B3=4A>3(FEF?7@7@63@94A>3 67@93@DF6FE7>7G3D;  D7:;@993?7@53B3;=7E;@9 9;3@?3=D;?F? ?7E7C7C3B3>3?34A>3:3CFD6; EF@99F:;@993E;43=7?43>;6;E3@3: ?D   *74F3:D3D3C3@E7C>7E3=B363<3C3= ?63@B363 =7E;@99;3@ ?7C3B3DF6FE7>7G3D;B7>FCF393C E7?43=3@@J3E7B3E?7@97@3;D3D3C3@<;=3=757B3E3@ 3H3>@J3 ?D 10 m 100 m   *74F3:D3D3C3@E7C>7E3=B363=AAC6;@3E  ? *7D7AC3@9?7>7?B3C=3@43EF67@93@DF6FE N=7 3C3:D3D3C3@E7CD74FE63C;BFD3E=AAC6;@3E7C3B3=3: =757B3E3@J3@9:3CFD6;47C;=3@393C43EF;EFE7B3E ?7@97@3;D3D3C3@ *74F3:B7D3H3EE7?BFC47C97C3=67@93@=757B3E3@ ?D63@3C3:@J3?7?47@EF=DF6FE N67@93@ 4;63@963E3C#7E;=347C363B363=7E;@99;3@ ? 63C;3C3:G7CE;=3>D74F3:4A?6;>7B3D=3@63C; B7D3H3EE7CD74FE";=34A?<3EF:6;E;E;=E7@EF=3@ <3C3= 60° 800 m A B Analisis Gerak 19 y C. Gerak Melingkar v  P yP  xP x 3 y vy v  ;#7>3D/@63E7>3:?7?B7>3<3C;97C3=?7>;@9=3C47C3EFC3@(363 DF4434 ;@; 3=3@ 6;43:3D 97C3= ?7>;@9=3C D753C3 F?F? 67@93@ ?7@99F@3=3@ =3;63: G7=EAC (7C:3E;=3@  +! /    *74F3: B3CE;=7> 47C97C3= ?7>;@9=3C B363 4;63@9   67@93@ <3C;<3C;  E7C:363B BFD3E =AAC6;@3E @63 E7@EF E7>3: ?7@97E3:F; 43:H3 63>3? 97C3= ?7>;@9=3CG7=EAC=757B3E3@97C3=B3CE;=7>3D7>3>F?7@J;@99F@9>;@E3D3@ 97C3= B3CE;=7> 63@ E793= >FCFD <3C;<3C; >;@E3D3@ B3CE;=7> ; E;E;= ( G7=EAC =757B3E3@ 3 ?7?47@EF= DF6FE   E7C:363B 93C;D G7CE;=3> 63@ 47D3C@J3 D3?3 67@93@ DF6FE   J3@9 6;47@EF= A>7: <3C;<3C; /63@DF?4F'>7:=3C7@3;EF=A?BA@7@G7=EAC36;@J3E3=3@67@93@ B7CD3?33@ 3' ( vx 3PD;@  '5AD  ( x  P  63BF@BAD;D;B3CE;=7>B3634;63@9 6;@J3E3=3@67@93@B7CD3?33@ /' (  P  7@93@ 67?;=;3@ G7=EAC =757B3E3@ 3 63B3E 6;@J3E3=3@ 67@93@ B7CD3?33@    3     4 y   (   P  @63 E7@EF ?7@97E3:F; 43:H3 B7CD3?33@ 97C3= B3CE;=7> 6;63B3E=3@ 63C;EFCF@3@B7CE3?3B7CD3?33@=757B3E3@3E3FEFCF@3@=76F3B7CD3?33@ BAD;D;B3CE;=7>'>7:=3C7@3;EFB7CD3?33@B7C57B3E3@>;@73C63>3?97C3= ?7>;@9=3C 6;@J3E3=3@ 67@93@ B7CD3?33@ ay a     '     ax x  3             ' (          3C;$/0 + , 6 @;>3; 5 Gambar 1.17 Sebuah partikel bergerak melingkar. (a) Posisi dan kecepatan partikel pada saat tertentu. (b) Komponen-komponen vektor kecepatan. (c) Percepatan gerak partikel dan komponen-komponennya. 63>3? 3C3: DF?4F-  63@  P    ?7CFB3=3@=A?BA@7@=757B3E3@     ?7CFB3=3@ =A?BA@7@ =757B3E3@ 63>3?  3C3: DF?4F- (7C:3E;=3@  +! /  ! 3C; 93?43C E7CD74FE @63 3=3@ ?7@97E3:F; 43:H3 P D;@   63@   D;@   7@93@ 67?;=;3@ $/0 + ,  6  63B3E 6;@J3E3=3@ 67@93@ B7CD3?33@          5AD   '    D;@   (        P  -7=EAC B7C57B3E3@ 63@ =A?BA@7@ G7=EAC B7C57B3E3@ 63>3? 97C3= ?7>;@9=3C 6;EF@7:  +! /  " D763@9=3@ 47D3C G7=EAC B7C57B3E3@ 6;@J3E3=3@ 67@93@ B7CD3?33@       5AD   D;@       P  ,@EF= ?7@7@EF=3@ 3C3:  63B3E @63 E7@EF=3@ ?7>3>F; DF6FE   D7B7CE; 6;EF@;@9=3C3@  +! /  " (7C57B3E3@ E7CD74FE 6;@3?3=3@      Tes Kompetensi Subbab C $/( ) ,* &# * +!2)2* 1'& ,  *74F3:B3CE;=7>47C97C3=?7>;@9=3C67@93@=757B3E3@ =A@DE3@63>3?4;63@9 #7E;=3B3CE;=7>47C3636;BAD;D;   P  ? =757B3E3@@J3 P  ?D( +7@EF=3@>3: =757B3E3@63@B7C57B3E3@B3CE;=7>B363BAD;D;  ?  *74F3: D3E7>;E F?; 47C97C3= B363 AC4;E@J3 J3@9 47C<3C3=   =? 6; 3E3D B7C?F=33@ F?; 67@93@ B7C;A67?7@;E+7@EF=3@>3:=757B3E3@63@47D3C B7C57B3E3@D7@EC;B7E3>63C;D3E7>;EE7CD74FE  *7AC3@93DECA@3FE47C97C3=63>3?>;@E3D3@?7>;@9=3C 47C<3C;<3C;? 3 +7@EF=3@=757B3E3@97C3=3DECA@3FE<;=347D3C B7C57B3E3@D7@EC;B7E3>@J3  4 7C3B3=3: 3: BFE3C3@ J3@9 6;:3D;>=3@ 47C63D3C=3@B7C57B3E3@E7CD74FE 5 +7@EF=3@B7C;A6763C;97C3=3DECA@3FEE7CD74FE Rangkuman  -7=EACBAD;D;?7@F@63C;E;E;= 3D3>=7BAD;D;B3CE;=7>E7CD74FEJ3;EF /' ( (7CB;@63:3@?7CFB3=3@B7CF43:3@G7=EACBAD;D; / D7>3?3D7>3@9H3=EF    // P/   '  ( 67@93@   P 63@   P  #757B3E3@C3E3C3E3363>3:47D3C@J3B7CB;@63:3@ 63>3?D7>3@9H3=EFE7CE7@EF / /  /  3     #757B3E3@D7D33E363>3:=757B3E3@C3E3C3E3F@EF= D7>3@9H3=EF  ?7@67=3E;@A> / /  3  >;? 3  >;?       -7=EACBAD;D;63B3E6;E7@EF=3@63C;=757B3E3@D7D33E 67@93@53C3;@E79C3D;    v  67@93@ 363>3:G7=EACBAD;D;B363   (7C57B3E3@C3E3C3E3363>3:B7CF43:3@=757B3E3@ 63>3?D7E;3BD3EF3@H3=EF 3 3  3       (7C57B3E3@D7D33E363>3:B7C57B3E3@C3E3C3E3F@EF= D7>3@9H3=EF  ?7@67=3E;@A> 3 3  >;?  >;?        #757B3E3@D7D33E63B3E6;E7@EF=3@63C;B7C57B3E3@ D7D33E67@93@53C3;@E79C3D;     67@93@ 363>3:=757B3E3@B363 D33E   7C3=B3C34A>3?7CFB3=3@B7CB36F3@63C;$B363 DF?4F-63@$B363DF?4F- D7:;@993  E7E3B63@     63@     67@93@ P  (36397C3=B3C34A>3E;E;=E7CE;@99;6;53B3;B363D33E     7@93@ ?7?3DF==3@ DJ3C3E ;@; 63B3E 6;E7@EF=3@  D;@   ?3=D   D;@    ?3=D   +;E;=B3>;@9<3F:6;53B3;B363D33E  7@93@ ?7@99F@3=3@D;83ED;?7EC;B3C34A>36;B7CA>7:  D;@  ?3=D  ?3=D   D;@  ?3=D    (36397C3=?7>;@9=3C47D3CB7C57B3E3@D7@EC;B7E3> 6;@J3E3=3@67@93@B7CD3?33@    63BF@DF6FEJ3@96;47@EF=3C3:G7=EACB7C57B3E3@ D7@EC;B7E3>6;@J3E3=3@67@93@B7CD3?33@ E3@    (7C57B3E3@ D7@EC;B7E3> 363>3: B7C57B3E3@ 97C3= B3CE;=7> J3@9 47C97C3= ?7>;@9=3C 63@ 3C3:@J3 ?7@F;@9=3C3@ Analisis Gerak 21 Peta Konsep $/ )$,# 63B3E 47C47@EF= 7C3=(3C34A>3 7C3=$FCFD 7C3=%7>;@9=3C ?7?43:3D D753C3 G7=EAC ?7?43:3D D753C3 G7=EAC (AD;D; #757B3E3@ )3E3C3E3 (7C57B3E3@ )3E3C3E3     #757B3E3@ *7D33E (7C57B3E3@ *7D33E (AD;D; #757B3E3@ (7C57B3E3@ ?7?43:3D DF?4F- DF?4F- 7C3=$FCFD 7C3EFC3@$ 7C3=$FCFD7CF43: 7C3EFC3@$ B363 B363 +;E;=+7C<3F:?3=D .3=EF*3?B3;6; +;E;=+7C<3F:?3=D +;E;=+7CE;@99;  ?3=D .3=EF*3?B3;6; +;E;=+7CE;@99; ?3=D Refleksi Setelah mempelajari bab ini, Anda tentu dapat membedakan antara besaran vektor dan besaran skalar yang ada pada konsep gerak. Anda juga dapat menentukan persamaan besaran fisika dari persamaan yang diketahui dengan menggunakan operasi integral dan diferensial. Dari materi bab ini, bagian manakah yang Anda anggap sulit? 22 Mudah dan Aktif Belajar Fisika untuk Kelas XI Dengan mempelajari bab ini, Anda dapat menentukan bentuk lintasan gerak suatu benda. Pada gerak parabola, titik terjauh dan titik tertinggi dapat ditentukan dari persamaan gerak dan waktunya. Nah, sekarang coba Anda sebutkan manfaat lain mempelajari bab ini. Tes Kompetensi Bab 1  '*'&* &0 * &0 12( 4 ! ,5 ,%. *',%1$. 1# ,)$/(  (363D33E  D77=AC4FCF@9?7?;>;=;BAD;D;6; =AAC6;@3E ? ?63@B363D33E  D?7?;>;=; =AAC6;@3E??3>3?D7>3@9H3=EFE7CD74FE 47D3C=757B3E3@C3E3C3E34FCF@9363>3: 3  ?D 6  ?D 4  ?D 7  ?D 5  ?D  (7CD3?33@ G7=EAC BAD;D; D74F3: ?3E7C; 6;@J3E3=3@ 67@93@/ P  '  (";=3D3EF3@/63>3? ?7E7C63@63>3?D7=A@47D3CB7C57B3E3@?3E7C;E7B3E D7E7>3: D7=A@63C;3H3>B7@93?3E3@363>3: 3 ?D 6 ?D 4 ?D 7 ?D 5 ?D !1 , 0   *74F3:B7>FCFJ3@96;E7?43==3@67@93@DF6FE7>7G3D; E7CE7@EF?7?;>;=;B7CD3?33@G7=EACBAD;D; / '    (67@93@63>3?D7=A@63@ /63>3??7E7C"3C3=E7C<3F:J3@963B3E6;53B3;A>7: B7>FCF63>3?3C3:DF?4F363>3: 3 ? 6  ? 7  ? 4  ? 5  ?     (AD;D;D74F3:47@63J3@96;>7?B3C=3@G7CE;=3>=73E3D 6;@J3E3=3@67@93@B7CD3?33@  P 67@93@ 63>3??7E7C63@63>3?D7=A@#757B3E3@3H3>63@ E;@99;?3=D;?F?J3@963B3E6;53B3;47@63?3D;@9 ?3D;@9363>3: 3 ?D63@ ? 6 ?D63@ ? 4 ?D63@ ? 7  ?D63@  ? 5 ?D63@ ? (7C:3E;=3@93?43C47C;=FE 4 0 vx 2 6 t –2 *74F3: B3CE;=7> J3@9 47C97C3= D7B3@<3@9 DF?4F- ?7?;>;=;9C38;==757B3E3@E7C:363BH3=EFD7B7CE; E3?B3=B36393?43CE7CD74FE";=3B363D33E D7=A@B3CE;=7>47C363B363 ?BAD;D;B3CE;=7>B363 D33ED7=A@47C363B363 3 P ? 6 P ? 4  ? 7  ? 5  ?  *74F3: B3CE;=7> 47C97C3= >FCFD 63C; =73633@ 6;3? 67@93@ B7CD3?33@ B7C57B3E3@       7D3C =757B3E3@B3CE;=7>D7E7>3: D7=A@363>3: ) ,* &. # !2)2* 1'& , 3 ?D 6 ?D 4 ?D 7 ?D 5 ?D  *74F3:B3CE;=7>47C97C3=D7B3@<3@9DF?4F-67@93@ 47D3CB7C57B3E3@  67@93@ 63>3??D ";=3 B363D33E =757B3E3@ ?D=757B3E3@B3CE;=7> B363D33E D363>3: 3 ?D 6 ?D 4 ?D 7 ?D 5 ?D  *74F3:B3CE;=7>47C?F3E3@>;DEC;=?F>3?F>347C97C3= >FCFD 63@ ?7?;>;=; =757B3E3@  ?D (3CE;=7> ?7@93>3?; B7C57B3E3@ J3@9 6;@J3E3=3@ 67@93@ B7CD3?33@  P ?D 67@93@363>3:H3=EF >3?3@J393J3>;DEC;=47=7C<3#757B3E3@B3CE;=7>D7E7>3: 93J347=7C<3D7>3?3 D7=A@363>3: 3 ?D 6 ?D 4 ?D 7 ?D 5 ?D  (7C:3E;=3@9C38;=47C;=FE 2 6 ax (m/s ) y = –t + 6 3 0 3 6 t (s) (363D33E D74F3:B3CE;=7>47C363B363 ? 63@47C97C3=67@93@=757B3E3@3H3> ?D67@93@ 3C3: DF?4F- BAD;E;8 (7C57B3E3@ B3CE;=7> 47CF43: E7C:363BH3=EFD7B7CE;E3?B3=B36393?43C(AD;D; 47@63B363D7=A@363>3: 3 ? 6 ? 4 ? 7 ? 5  ?  (7C3:F?AEAC<;=347C97C3=D73C3:67@93@3C3:3CFD DF@93;?7?;>;=;=7>3FCFDE7C:363B3C3: 3CFDB7C3:F?F@9=;@:3@J3?3?BF47C97C3=67@93@ =7>3F=3@H3=EF ?7@;EF@EF=?7 @J747C3@9;63@3FJ3@9>743C@J3 ?7E7C63@3F E;63=47C3CFD.3=EFJ3@96;4FEF:=3@B7C3:FF@EF= ?7@J747C3@9; 63@3F <;=3 6; 63@3F E;?4F> 3CFD 3;C 47C=757B3E3@ ?7E7C?7@;EE793=>FCFDE7C:363B3C3: B7C3:F363>3: Analisis Gerak 23 3 ?7@;E 6 ?7@;E 4 ?7@;E 7 ?7@;E 5 ?7@;E  (7C43@6;@93@3@E3C3<3C3=E7?43=3@6F34F3:B7>FCF J3@96;E7?43==3@63C;D74F3:D7@3B3@67@93@DF6FE 7>7G3D; N63@ N363>3: 3 6  3 :1 4 1 : 3 7  5   *74F3:4A>36;E7@63@9?7@9;=FE;97C3=B3C34A>3";=3 E;@99;?3=D;?F?J3@963B3E6;53B3;363>3: ?63@  ?D H3=EFJ3@96;B7C>F=3@A>7:4A>3D7>3?36; F63C3363>3: 3 D7=A@ 6 D7=A@ 4 D7=A@ 7 D7=A@ 5 D7=A@  (7>FCF6;E7?43==3@63C;E3@3:63E3C67@93@=757   B3E3@3H3> ?D*F6FE7>7G3D;   E3@   63@   B7C57B3E3@9C3G;E3D; ?D 7D3C=757B3E3@B7>FCF D7E7>3: D7=A@63C;E7?43=3@363>3: 3   ?D 6 ?D 4 ?D 7 ?D 5  ?D      *74F3:43EF6;>7?B3C67@93@=757B3E3@3H3> ?D B363DF6FE7>7G3D;  5AD   63@ ?D   (363DF3EFD33E=757B3E3@43EF=73C3:DF?4F- 363>3: ?D#7E;@99;3@43EFB363D33EE7CD74FE363>3: 3 ? 6  ?D 4  ?D 7  ?D 5 ?D  F3B7>FCF6;E7?43==3@63C;D74F3:D7@3B3@"3C3= E7?43=3@3=3@D3?3<;=3DF6FE7>7G3D;@J3     24  4 !* &.$/1 ,5 ,!$/')21','#$,% ,1$. 1 *74F3:B3CE;=7>47C97C3=67@93@B7CD3?33@8F@9D; =757B3E3@  67@93@63>3??D63@ 63>3?D7=A@";=3  ?D P ?D 63@?D E7@EF=3@>3: 3 B7C57B3E3@C3E3C3E3B3CE;=7>F@EF=D7>3@9H3=EF  D7=A@D3?B3;D7=A@ 4 B7C57B3E3@3H3>B3CE;=7>63@ 5 B7C57B3E3@B3CE;=7>B363D33ED7=A@ (7CD3?33@97C3=DF3EFB3CE;=7>6;@J3E3=3@A>7:8F@9D;   67@93@63>3??7E7C63@63>3?D7=A@  3 +7@EF=3@ =757B3E3@ C3E3C3E3 63>3? D7>3@9 H3=EF D7=A@D3?B3;67@93@ D7=A@ 4 ;EF@9=757B3E3@D7D33EB363D33E D7=A@ (7>FCF?7C;3?6;E7?43==3@67@93@=757B3E3@3H3>  ?D63@DF6FE7>7G3D;  67@93@ 5AD   ";=3  B7C57B3E3@9C3G;E3D; ?D E7@EF=3@>3: 3 =757B3E3@B7>FCF?7C;3?D7E7>3: D7=A@ 4 BAD;D;B7>FCF?7C;3?D7E7>3: D7=A@ Mudah dan Aktif Belajar Fisika untuk Kelas XI   3 N63@ N 6 N63@ N 4 N63@ N 7 N63@N 5 N63@ N *74F3:B7>FCF6;E7?43==3@67@93@DF6FE7>7G3D; N 63@=757B3E3@3H3>@J3 ?D*7E7>3:?7@53B3;E;E;= BF@53==757B3E3@B7>FCF?7@<36; 3 6  ?D 4 ?D 7 ?D 5 ?D (7D3H3EB7?4A?E7C43@9C7@63: ?63C;3E3D B7C?F=33@E3@3:67@93@=757B3E3@  =?<3? (7D3H3E E7CD74FE ?7>7B3D=3@ D74F3: 4A? "3C3= :AC;KA@E3>J3@96;E7?BF:A>7:4A?D747>F?E;436; E3@3:363>3: ?D  3 ? 6  ? 4 ? 7  ? 5  ? (36397C3=B3C34A>36;E;E;=BF@53= 3 B7C57B3E3@47@63363>3:@A> 4 =757B3E3@47@63363>3:@A> 5 B7C57B3E3@63@=757B3E3@47@63E;63=363>3:@A> 6 =757B3E3@47@63D7D33E363>3:@A> 7 =7>3363>3:@A>    7@6363@6;<3EF:=3@63C;=7E;@99;3@J3@9D3?3 D753C347CD3?33@=3@E7E3B;47@636;<3EF:=3@ D753C34743D63@47@636;<3EF:=3@D753C3:AC;KA@E3> 67@93@ =757B3E3@ 3H3> .3=EF J3@9 6;4FEF:=3@ =76F347@63F@EF=?7@53B3;E3@3:363>3:97D7=3@ 67@93@F63C36;343;=3@ 3  6   4  7   5  5 E;@99;?3=D;?F?63@ 6 <3C3=E7?43=3@?3=D;?F? *74F3:B7>FCF6;E7?43==3@63C;3E3B976F@9J3@9 E;@99;@J3 ?7E7C67@93@=757B3E3@3H3> ?D 5A@6A@9 =7 3E3D 67@93@ DF6FE 7>7G3D;  6; ?3@3 5AD   ";=3 ?D E7@EF=3@  3 H3=EFJ3@96;4FEF:=3@B7>FCFF@EF=D3?B3;6; E3@3:63@ 4 <3C3=E7C<3F:J3@96;53B3;B7>FCF63C;63D3C976F@9 D33E?7@53B3;E3@3: (363B7C?3;@3@D7B3=4A>3D7AC3@93@3=?7@7C;?3 63@?7@7CFD=3@4A>367@93@?7@99F@3=3@=7B3>3 A>3?7@;@993>=3@=7B3>33@3=E7CD74FE67@93@>37G3D;E7C:363B:AC;KA@E3>363>3:  6;?3@3 E3@   ";=34A>3D3?B3;6;E3@3:B363 <3C3=  ?7E7C47C3B3E;@99;3@3=;EF ?D  Bab 2 Sumber: F1F1 Racing, Mei 2003 Sumber: Racing, Mei 2003 Tikungan pada sirkuit balapan F1 dibuat kasar dan miring ke dalam agar pembalap dapat melintas dengan aman. Gaya Hasil yang harus Anda capai: menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik. Setelah mempelajari bab ini, Anda harus mampu: • • • menganalisis keteraturan gerak planet dalam tata surya berdasarkan hukumhukum Newton; menganalisis pengaruh gaya pada sifat elastisitas bahan; dan menganalisis hubungan antara gaya dengan gerak getaran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aya Gesek B. Gaya Gravitasi C. Elastisitas dan Gaya Pegas D. Gerak Harmonik Sederhana 25 Tes Kompetensi Awal # #)1**#*-#)'.&(,+/#-4(#.'(+)%/,)/,) #.&(10")* 1(1)0&%+ "57-:0-91:6-?@47-:>1.@-4-<180-:>1.@-4-:33@= 0-=5 71?5:335-: D-:3 >-9- 0-8-9 =@-:3 A-/@9 91:3-<- B-7?@ 6-?@4 710@- .@-4 D-:3 .1=-?:D.1=.10-?1=>1.@?>-9-  $1:3-<-?1=6-05<->-:3>@=@?<-0--5=8-@? -3-59-:-7-47;:>?-:?-<13->3-.@:3-:0-=5<13-> <13->D-:305>@>@:>1/-=->1=50-:<-=-=18 A. Gaya Gesek Gambar 2.1 Ban mobil dibuat bergerigi untuk memperbesar gaya gesek sehingga mobil tidak slip. piston ring piston stang piston poros engkol Gambar 2.2 Gaya gesek pada mesin bersifat merugikan. rem cakram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aya Gesek Statis dan Gaya Gesek Kinetik Gambar 2.3 Rem cakram pada sepeda motor menerapkan konsep gaya gesek. 26 -D- 31>17 D-:3 ?59.@8 <-0- .1:0- D-:3 >10-:3 .1=31=-7 05>1.@? 3-D- 31>17 75:1?57 7 >10-:37-: 3-D- 31>17 <-0- .1:0- 05-9 -?-@ .1:0- D-:3 ?1<-? -7-: .1=31=-7 05>1.@? 3-D- 31>17 >?-?5>  >  +:?@7 81.54 618->:D- <18-6-=58-4 @=-5-: .1=57@? Mudah dan Aktif Belajar Fisika untuk Kelas XI a. Gaya Gesek Statis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fs w Gambar 2.4 Gaya gesek statis fs mempertahankan keadaan balok agar tetap diam.  %   %   G  #1?1=-:3-: %  3-D- 31>17 >?-?5> %  >  7;125>51: 31>17 >?-?5>  .1>-=3-D-:;=9-8% *-:0- >-9- 01:3-:  .1=8-7@ 657- % .1=:58-5 9-7>59@9 -3-59-:- 91:31?-4@5 .1>-=:D- 3-D- :;=9-8 '1=4-?57-: * .   "57- 4-:D- -0- .1>-= 3-D- .1=-? ) 0-: ?50-7 -0- 3-D- 8-5: <-0- -=-4 >@9.@ A1=?57-8 .1>-= 3-D- :;=9-8  >-9- 01:3-: .1>-= 3-D- .1=-? .1:05?@ >1:05=5 5:3-? @7@9 !!! %1B?;:  &814 7-=1:- 5?@ #./*+  5  0-<-? 05?@85>7-:  %  %   G  Tantangan Contoh 2.1 )1.@-4.-8;7.1=9->>- 73?1=81?-705-?->.50-:30-?-=7->-= -8;705.1=53-D-?-=57 >1.1>-=%91:0-?-=>1<1=?5<-0-3-9.-= "57-7;125>51:31>17-:>?-?5>-:?-=-.-8;7 0-:8-:?-5 ?1:?@7-: - .1>-=3-D-31>17>?-?5>9-7>59@90-: N . .1>-=3-D-31>17D-:39191:3-=@45.1:0- F=4N 3  fs 571?-4@5  73 w %  %     9 > - >9-7>  >   >    73 9 > % "-053-D-31>17>?-?5>9-7>59@9<-0-.-8;7-0-8-4% . -D-8@-=D-:39191:3-=@45.1:0-4-:D- % 1>-=3-D-?1=>1.@?81.54 71/580-=5<-0-3-D-31>17>?-?5>>145:33-.-8;79->54?1?-<05-9 -8-97->@> 5:5.1>-=:D-3-D-31>17>-9-01:3-:.1>-=:D-3-D-8@-=>G % "-053-D31>17>?-?5>D-:3.1=2@:3>5<-0-.1:0--0-8-4>1.1>-=% untuk Anda Mengapa koefisien gesek (  ) tidak memiliki satuan? Gaya 27 b. N =m gs in  fs  m g cos  mg  Gambar 2.5 Sebuah balok tepat akan bergerak pada suatu bidang miring. Koefisien Gaya Gesek Statis Benda pada Bidang Miring )1.@-4 .-8;7 01:3-: .1=-? ) ?1=81?-7 05 -?-> .50-:3 95=5:3 7->-= 01:3-: >@0@? 7195=5:3-:  ?1=4-0-< 4;=5E;:?-8  '-0- >--? .-8;7 ?1<-? -7-: .1=31=-7 <1=>-9--: 7;125>51: 31>17:D- -0-8-4 >1.-3-5 .1=57@? 1>-=3-D-:;=9-8 /;>  1>-=3-D-31>17>?-?5>> 9-7> >5:  >5: f%  >5:   ?-:  /;>  /;> N "-05 7;125>51: 31>17 >?-?5> 9-7>59@9 -:?-=- .-8;7 01:3-: .50-:3 95 =5:3 <-0- >--? ?1<-? -7-: .1=31=-7 -0-8-4  >  >?-:  c.  G Gaya Gesek Kinetik +:?@7 919-4-95 <1=.10--: -:?-=- 3-D- 31>17 >?-?5> > 0-: 3-D31>17 75:1?57 7 8-7@7-:8-4 -7?5A5?-> .1=57@? Aktivitas Fisika 2.1 Gaya Gesek Tujuan Percobaan Membedakan antara gaya gesek statis dan gaya gesek kinetik Alat-Alat Percobaan 1. Balok kayu 2. Katrol 3. Tali 4. Neraca pegas/Dinamometer Langkah-Langkah Percobaan 1. Susunlah alat-alat percobaan seperti pada gambar. 2. Tarik balok sehingga balok tepat akan bergerak. 3. Catatlah skala yang ditunjukkan neraca pegas. 4. Tarik kembali balok tersebut dengan gaya tarik yang lebih besar daripada gaya tarik pertama sehingga balok bergerak. 5. Pada saat balok bergerak, catatlah kembali skala yang ditunjukkan neraca pegas. 6. Apa yang dapat Anda simpulkan? N N F F fs fs Gambar 2.6 "57- 3-D- ?-=57 .1=?-9.-4 <-0- >--? D-:3 >-9- 3-D- 31>17 >?-?5> 6@3- .1=?-9.-4 >-9<-5 9-7>59@9  )-9<-5 >--? ?1=>1.@? .-8;7 .18@9 .1=31=-7 7-=1:- 3-D- 31>17 >18-8@ 0-<-? 91:359.-:35 3-D- ?-=57  "-05 .-8;79->5405-9 '-0->--?.-8;7.1=31=-7.1>-=3-D-?-=57918-9<-@5  %   -D- 31>17 75:1?57 9191:@45 4@7@9 19<5=5> >-9- >1<1=?5 3-D31>17>?-?5> &8147-=1:-5?@.1>-=3-D-31>1775:1?570-<-?05=@9@>7-: >1.-3-5 .1=57@?  G 7   7 (a) Balok diam, F < fs maks. (b) Balok tepat akan bergerak, F = fs maks. (c) Balok mengalami percepatan, F > fk. (d) Balok bergerak dengan kecepatan konstan, a = 0. '-0-@9@9:D-  7  >>145:33-<-0->--?9@8-5.1=31=-7.-8;7 >19<-?91:3-8-95<1=/1<-?-: '-0-.-8;7D-:3.1=31=-7?-:<-<1=/1<-?-: .-8;7 ?1=@> .1=31=-7 01:3-: 71/1<-?-:7;:>?-: 0-: .1>-= 7 w w - N . N a F F fk w / 28 w v a=0 fk 0 Mudah dan Aktif Belajar Fisika untuk Kelas XI d. Koefisien Gaya Gesek Kinetik Benda pada Bidang Miring )1.@-4.-8;701:3-:.1=-?).1=31=-771.-B-405-?->.50-:395=5:3 7->-= D-:3 91958575 7195=5:3-:   ?1=4-0-< 4;=5E;:?-8  '1=>-9--: 7;125>51: 31>17:D- 0-<-? 05?@=@:7-: 0-=5 @7@9 !! %1B?;:    >5:  G  7   >5:  G  7 /;>    7  /;>      >5:  G   >5:   a  7  /;> >5:  a  7  /;> N fk  mg sin   mg cos  mg Gambar 2.7 Sebuah balok bergerak di atas bidang miring.  G 1:3-:019575-:7;125>51:31>1775:1?570-<-?0571?-4@501:3-:91:3@7@= <1=/1<-?-: D-:3 05-8-95 ;814 .1:0-  "57- 7;125>51: 31>17 75:1?57 0571?-4@5 .1>-= <1=/1<-?-: .1:0- 0-<-? 0571?-4@5 01:3-: 91:33@:-7-: <1=>-9--: >5:  G  7/;>    G Contoh 2.2 )1.@-4.1:0-.1=9->>-73?1=81?-7<-0-.50-:395=5:301:3-:>@0@?7195=5:3-:  01:3-:>5:   "57-7;125>51:31>1775:1?57-:?-=-.-8;70-:.50-:3   ?1:?@7-:.1>-=<1=/1<-?-:.-8;7?1=>1.@? untuk Anda 3  571?-4@5 73>5:  7   -D-3-D-D-:3.171=6-<-0-.1:0-?1=81.540@8@05@=-57-: 1>-=3-D-31>17-:75:1?57  7   7  7 /;>   73 9 >  %  >5:   73 9 >  % 1>-=<1=/1<-?-:.-8;705<1=;8140-=5 @7@9!!%1B?;:   Tantangan N m f k= g . sin  Perhatikan gambar berikut. m1  m2 m g . cos  mg   F  f   %   % 9 >  "-05.-8;7918@:/@=<-0-.50-:395=5:301:3-:<1=/1<-?-:9 > Ketika gerobak diam, balok bermassa m akan bergerak ke arah balok bermassa m2 karena pengaruh gaya berat m2g. Berapa gaya dorong F minimum yang harus diberikan pada gerobak supaya sistem berada dalam keadaan setimbang? Contoh 2.3 )1.@-4.1:0-73?1=81?-705-?->.50-:30-?-= #;125>51:31>1775:1?57.1:001:3-:<1=9@7--:.50-:30-?-=-0-8-4  1:0-05?-=57;8143-D->1.1>-= >1<1=?5<-0-3-9.-= )@<-D-.1:0-.1=31=-701:3-:71/1<-?-:7;:>?-:.1=-<-7-4 .1>-=3-D- D-:34-=@>05.1=57-: 9 >  F 3  571?-4@5 73 37°  7     9 > -D-3-D-D-:3.171=6-<-0-.1:0-05@=-57-:?1=81.540@8@ 1:0-.1=31=-78@=@>.1=-?@=-:.1=-=?5 Gaya 29 Pembahasan Soal Sebuah balok yang beratnya w ditarik sepanjang permukaan mendatar dengan kelajuan konstan v oleh gaya F yang bekerja dengan arah membentuk sudut  terhadap bidang horizontal. Besar gaya normal yang bekerja pada balok oleh permukaan adalah .... a. w + F cos  b. w + F sin  c. w – F sin  d. w – F cos  e. w Soal UMPTN 2000 Pembahasan: F  >5:F   G >5:F 73 9> G G    %G  1>-=3-D-0-8-9-=-4>@9.@-*  *  /;>FG7 F sin  F N  37° F cos  fk  G  7  mg  G  %G    G %      %   % "-05-3-=.1:0-.1=31=-701:3-:71/1<-?-:7;:>?-:4-=@>05.1=53-D-?-=57>1.1>-=  % F sin  N  F cos  w Gaya tarik F jika diuraikan atas komponen searah sumbu-x dan sumbu-y adalah Fy = Fsin  Fx = Fcos  Besar gaya normal:  Fy  0 F sin  + N = w N = w – F sin  Jawaban: c Contoh 2.4 @-.@-4.1:0-.1=9->>- 0-: 054@.@:37-:01:3-:>1@?->?-85918-8@5>1.@-4 7-?=;8 1:0-.1=9->>- ?1=81?-705-?->916->10-:37-:.1:0-.1=9->>- ?1=3-:?@:3<-0-?-85>1<1=?5<-0-3-9.-= $->>-.1:0-9->5:39->5:3730-: 73 1>-=<1=/1<-?-:3=-A5?->5 9 > "57-7;125>51:31>1775:1?57-:?-=-.1:0.1=9->>- 0-:-8->:D- ?1:?@7-:<1=/1<-?-:710@-.1:0-?1=>1.@?  3  a #10@-.1:0-.1=31=-701:3-:<1=/1<-?-:D-:3>-9T 7-=1:- 710@- .1:0- 054@.@:37-: ;814 >1@?-> ?-85 m 1 '1=4-?57-:3-9.-=.1=57@? 571?-4@5 T a 73 m  73 2   9 >  -8;7  73 9 >  % -8;7 )   73 9 >  % -=5.-8;7 0-: 05<1=;814 ) G  7   m2 g  7 %G  %   %  9 > "-05.1>-=<1=/1<-?-:710@-.-8;7>-9-D-5?@ 9 > Tugas Anda 2.1 Amatilah sebuah tabung pejal yang berada di puncak suatu bidang miring. Jika tabung mulai bergerak di sepanjang bidang miring tersebut, bagaimanakah gerakannya? Jika bidang miring tersebut diberi oli sehingga licin, apa yang akan terjadi pada tabung tersebut? Jelaskan fenomena tersebut di depan teman-teman Anda. 30 N fk m1 T T w1 m2 w2 2. Penerapan Gaya Gesek pada Jalan Menikung a. Tikungan Mendatar "-8-:D-:3.->-4>1=5:391:D1.-.7-:71:0-=--:9@0-4?1=3185:/5=-<- 8-35657-71:0-=--:918-6@71:/-:3<-0-6-8-:91:57@:3 +:?@791:345:0-=5 >185< 6-8-: 0-?-= ?1=>1.@? 4-=@> 05.@-? 7->-= >145:33- 71?57- 71:0-=--: 91:57@:3 -7-: ?59.@8 3-D- 31>17  -D- 31>17 ?1=>1.@? .1=2@:3>5 >1.-3-5 3-D- >1:?=5<1?-8 D-:3 >18-8@ 91:@6@ 71 <@>-? 85:?->-: 85:37-=-:  * .  91:33-9.-=7-: 3-D- 31>17 D-:3 91:@6@ <@>-? 85:37-=-: Mudah dan Aktif Belajar Fisika untuk Kelas XI N Gambar 2.8 Sebuah mobil sedang melaju pada lintasan melingkar dan datar. fgesek R Tugas Anda 2.2 w Perhatikan gambar berikut. <-7-4:0-91:31?-4@561:5>3-D-31>17D-:3.171=6-<-0-7->@> 5:5"57-9;.58919.18;70-8-971-0--:.-:9->54.1=<@?-=3-D-D-:3 .171=6- -0-8-4 3-D- 31>17 >?-?5>  *1?-<5 71?57- 9;.58 918@:/@= >185< 3-D- 31>17 D-:3 .171=6- -0-8-4 3-D- 31>17-: 75:1?57  1>-= 71/1<-?-: 9-7>59@99;.58D-:39185:?-><-0-?57@:3-:6-8-:7->-=91:0-?-=-3-= ?50-7 >185< 9191:@45 <1=>-9--: >1.-3-5 .1=57@? T a B w Diskusikan dengan teman Anda, apakah benar percepatan sistem tersebut adalah: ><% ( 9-7>  %   $ T A ( 9-7>   %   $ (9-7>  $ • Jika permukaan bidang datar licin,  G mB   g a=   mA  mB  • Jika permukaan bidang datar kasar, mB   k . mA  a=  m m  g A b   Contoh 2.5 )1<10-9;?;=918-6@<-0-6-8-:9185:37-=01:3-:6-=56-=585:37-=-::D- 9 "573-D-31>179-7>59@9D-:3.171=6--:?-=-.-:0-:6-8-: %9->>-9;?;=01:3-: <1:@9<-:3:D- 73?1:?@7-:718-6@-:9-7>59@9D-:30-<-?05/-<-5;814 9;?;=-3-=?50-7>185< 3  571?-4@5 ><  %  73   9 #18-6@-:05<1=;81401:3-:91:33@:-7-:<1=>-9--:.1=57@? ( ><   2  % 73 (  9 ( 9-7>  9 > (9-7>  9 > "-05-3-=?50-7>185<718-6@-:9-7>59-89;?;=4-=@>>1.1>-= 9 > b. Tikungan Miring Licin '1=4-?57-:* .  )1.@-49;.58>10-:3.1=31=-705.18;7-:95=5:3 05 85:?->-: 85/5:  )@0@? 7195=5:3-: 6-8-: ?1=4-0-< .50-:3 4;=5E;:?-8 -0-8-4  -D-:;=9-871:0-=--:D-:3.171=6-<-0-7;9<;:1:4;=5E;:?-8 >5:  -7-:919.1=57-:3-D->1:?=5<1?-8D-:305<1=8@7-:9;.58-3-= 0-<-? 91:57@:3 Gaya 31 N N cos   N sin  R Gambar 2.9 Sebuah mobil sedang melaju pada lintasan melingkar yang miring dan licin. w &8147-=1:-.1>-=3-D-31>17>?-?5>>>-9-01:3-::;805<1=;814 <1=>-9--: 3-D- :;=9-8 >1.-3-5 .1=57@?  +  /;>  G   /;>     G -D- D-:3 91:@6@ <@>-? 85:37-=-: 91=@<-7-: 3-D- >1:?=5<1?-8 D-5?@ >5:   >< >5:   ( $  G 1:3-:919.-35#./*+ 501:3-:#./*+ 505<1=;814 (  >5:   $  /;>  Informasi untuk Anda Pernahkah Anda menonton balap motor di TV? Jika Anda perhatikan, pada setiap tikungan, pembalap motor selalu memiringkan badannya. Apakah Anda tahu alasannya? Jika pembalap motor itu menikung dengan kecepatan yang cukup tinggi, dia membutuhkan gaya sentripetal yang lebih besar. Gaya sentripetal tersebut berupa gaya gesek dan gaya normal. Untuk mendapatkan gaya normal yang arahnya menuju pusat lingkaran, pembalap tersebut harus memiringkan badannya. Information for You Have you watched motorcycle racing on TV? If you watch it, you can see that the riders always put their bodies at an angle with road in each corners. Do you know what is their reason? If the riders come in the corner at high velocity, they need bigger centripetal force which are from friction and normal force. To get normal force which has direction to the center of circle, the riders should put their bodies at an angle. 32 ( ?-:   $g  G  #18-6@-: 9-7>59@9 9;.58 -3-= 0-<-? .1=31=-7 05:D-?-7-: 01:3-: (9-7> $ g ?-:   G  #1?1=-:3-:   >@0@? 7195=5:3-: .18;7-: ?1=4-0-< 4;=5E;:?-8 (9-7>  718-6@-: 9-7>59@9 9 > $  6-=56-=5 ?57@:3-: 9   <1=/1<-?-: 3=-A5?->5 9 >  *-4@7-4:0-?17:;8;359;.58?1=.-=@D-:3<-85:39@?-745=)5>?19 7;9<@?1=5>->5 D-:3 ?1=<->-:3 <-0- 9;.58 0-<-? 91:3-?@= <5854-: 0-D/1:371=-9=19=;0-D-:3<-85:305.@?@47-:71?57-9;.58918-6@056-8-: 91:57@:3  )1/-=- ;?;9-?5> 7-9<-> =19 <-0- >1?5-< =;0- 0-<-? .171=6>1>@-5.1>-=71/58:D-0-D-/1:371=-9>1?5-<.-:9;.58?1=4-0-<6-8-:=-D- c. Tikungan Miring dan Kasar '-=- -485 91:01>-5: 6-8-: ?57@:3-: 95=5:3 01:3-: 919<1=45?@:37-: 6-=56-=5 ?57@:3-: $ <1=/1<-?-: 3=-A5?->5  7195=5:3-: 6-8-:   >1=?:58-5 717->-=-: 6-8-:  "57- :0- <1=4-?57-: #./*+  5  >19-75: .1>-= >@0@? 7195=5:3-: 6-8-: >19-75: .1>-= 6@3- 718-6@-: 9-7>59@9 71:0-=--: D-:3 05<1=.;8147-: @:?@7 9181B-?5 ?57@:3-: ?1=>1.@? Mudah dan Aktif Belajar Fisika untuk Kelas XI -3-59-:-7-4/-=-91:345?@:3.-?->718-6@-:<-0-?57@:3-:6-8-: D-:395=5:30-:7->-='1=4-?57-:* .   *1=0-<-?0@-7;9<;:1: 3-D- 0-8-9 -=-4 =-05-8 71 <@>-? ?57@:3-: 6-8-: D-5?@ 7;9<;:1: 3-D:;=9-8>5: 0-:7;9<;:1:3-D-31>17-:>?-?5>%/;> (1>@8?-:710@3-D-?1=>1.@?.1=2@:3>5>1.-3-53-D->1:?=5<1?-8 #18-6@-:9-7>59@99;.58 -3-= ?50-7 >185< 0-<-? 05<1=;814 >1.-3-5 .1=57@? ( 9-7> >  r ( 9-7> >5:  >/;>  r ( 9-7> >5:    >/;>  r ( 9-7> r >5:    >/;>    N cos  N  fs cos   N sin  fs sin  fs Gambar 2.10 Diagram gaya pada mobil yang sedang melaju pada lintasan melingkar yang miring dan kasar.  G  $;.58 ?50-7 .1=31=-7 <-0- >@9.@-+ >145:33 +  -9.58-=-471-?-><;>5?52 /;>  G ,% >5:   /;>  G  >>5:    /;>  G  >>5:      G  "57- #./*+  5  05.-35 01:3-: #./*+  5  05<1=;814     /;> >5:    % ( 9-7> /;>  g $ /;>   % >5:  /;>  %  ?-:  (9-7> g$   ?-:  %  G  -=5 <1=>-9--: ?1=>1.@? 0-<-? 05>59<@87-: .-4B- >@0@? 7195=5:3-: 6-8-: 0-:717->-=-:6-8-:  >.1=<1:3-=@4?1=4-0-<8-6@9-7>59@9 9;.58 @:?@7 919.18;7 -3-= ?50-7 ?1=6-05 >185< Kata Kunci • gaya gesek kinetik • gaya gesek statis • koefisien gaya gesek Contoh 2.6 $;.589181B-?5?57@:3-:6-8-:D-:36-=56-=57181:37@:3-::D- 9 "57->@0@? 7195=5:3-:6-8-: F?1:?@7-:71/1<-?-:9-7>59@99;.58D-:305<1=.;8147-: @:?@77;:05>5 - 6-8-:85/5:7-=1:-.1=-5=31>17-:05-.-57-: . 6-8-:71=5:301:3-:7;125>51:31>17-:>?-?5>  -9.58 9 >  3  - +:?@77;:05>56-8-:85/5:3@:-7-:<1=>-9--: (9-7>  $ ?-:  9 >  9  ?-: (9-7>      9 > Gaya 33 . Tantangan untuk Anda (9-7> g $ Sebuah benda bermassa m meluncur pada bidang miring kasar. Sudut kemiringan bidang tersebut adalah  . Jika benda berhenti setelah berpindah sejauh x akibat gaya gerak, buktikan bahwa: w +:?@77;:05>56-8-:-:7->-=3@:-7-:<1=>-9--: (9-7>  mg x  %  ?-:   ?-:        % ?-:    ?-:  9 >  9       9 > Mari Mencari Tahu 1   cos -8-9-7?5A5?->25>57-D-:3?18-4:0-8-7@7-:05>@..-.5:5:0-0-<-?91:1:?@7-: >1/-=-8-:3>@:33-D-31>17>?-?5>>@-?@.1:0- #19@05-:01:3-:918-7@7-:>@. >?5?@>5:58-5?1=>1.@?710-8-9<1=>-9--:%  % :0-0-<-?7-::58-5 s?1=>1.@? )17-=-:3=-:/-:38-4>@-?@<1=/;.--:>101=4-:-@:?@791:0-<-?7-::58-5 *@85>7-:8-4 =-:/-:3-:<1=/;.--:?1=>1.@?0-:7@9<@87-:71<-0-3@=@:0- Tes Kompetensi Subbab A #.'(+)%")* 1(1)0&%+   1:0-.1=9->>-73?1=81?-705-?->.50-:30-?-= 1>-=7;125>51:31>17-:>?-?5>-:?-=-.1:0-0-:-8-> -0-8-4  "57- 9 > .1=-<-.1>-=3-D-D-:3 05.@?@47-:@:?@791:-=57.1:0-71?57-?1<-?-7-: .1=31=-7 -8;7.1=9->>- 73?1=81?-705-?->8-:?-57->-= '-0.-8;70571=6-7-:3-D-91:0-?-= %-3-=.-8;7?1<-? -7-:.1=31=-7 )1?18-4.-8;7.1=31=-705<1=8@7-:3-D%45:33-.-8;7.1=31=-701:3-:71/1<-?-:?1?-< 5?@:37;125>51:31>17-:>?-?5><-0-.-8;70-:8-:?-5 1:0-.1=9->>-73?1=81?-7<-0->1.@-4.50-:30-?-= '-0-.1:0-.171=6-3-D-4;=5E;:?-8>1.1>-= % "577;125>51:31>17-:75:1?57-:?-=-.1:0-0-:.50-:3  .1=-<-7-4<1=/1<-?-:D-:305-8-95.1:0- -8;7.1=9->>- 73?1=81?-705-?->8-:?-50-:05?-=57 ;8143-D-%95=5:371-?->0-:919.1:?@7>@0@? F 01:3-: -=-4 4;=5E;:?-8  "57- 7;125>51: 31>17-: 75:1?57 0-: >?-?5> 9->5:39->5:3   0-: >1=?<1=/1<-?-:3=-A5?->5 9 > ?1:?@7-:3-D-31>17-: D-:3.171=6--:?-=-.-8;70-:8-:?-5  m B mA = 2 kg  37° 34 1:0-.1=9->>- 73?1=81?-7<-0-.50-:37->-=      -=571-0--:05-9.1:0-05.1=53-D?1?-<%>18-9- >17;: )1?18-491:19<@46-=-7   9 71-0--: .50-:3 9@8-5 85/5: >19<@=:- 1=-<-7-4<1=<5:0-4-:.1:0- Mudah dan Aktif Belajar Fisika untuk Kelas XI =8 kg  )--?0581<->7-:710@-.1:0-91958575<1=/1<-?-:  9 > "57->5:  .1=-<-7;125>51:31>17-:?-= .1:0-0-:.50-:3 *53-.@-4.1:0-05>@>@:>1<1=?5<-0-3-9.-= A B 4 kg 3 kg 3 kg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aya Gravitasi -D- D-:3 919.@-? .1:0- 6-?@4 71 ?-:-4 -0-8-4 3-D- D-:3 >-901:3-:3-D-D-:3919.@-?<8-:1?<8-:1??1=@>91:35?-=5$-?-4-=5 /! #30,+5-8-4;=-:3<1=?-9-D-:391:31?-4@54-85:5 '-0-?-4@:  %1B?;: 918-8@5 .@7@:D- $!# 91:618->7-: .-4B- <8-:1?<8-:1? 91:35?-=5 $-?-4-=5 7-=1:- -0-:D- 3-D- 3=-A5?->5 D-:3 91:-=57 <8-:1? <8-:1? 71-=-4 $-?-4-=5  %1B?;: 6@3- 0-<-? 91:@:6@77-: .-4B- .1>-= 3-D- 3=-A5?->5 -:?-=- $-?-4-=5 0-: <8-:1? .1=3-:?@:3 <-0- 6-=-7 -:?-=710@-:D-  )19-75: 6-@4 6-=-7 <8-:1? 0-=5 $-?-4-=5 3-D- 3=-A5?->5 D-:3 .171=6- >19-75: 71/58  %1B?;: 6@3- 0-<-? 91:@:6@77-: .-4B- 3-D?-=573=-A5?->5-:?-=-0@-.@-4.1:0-.1=3-:?@:3<-0-9->>-710@-:D- )19-75: .1>-= 9->>- .1:0- >19-75: .1>-= <@8- 3-D- ?-=57:D- 1. Hukum Gravitasi Universal Newton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m1 F F m2 r Gambar 2.11 Gaya tarik menarik pada dua benda bermassa m1 dan m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aya 35 posisi kesetimbangan tali torsi m' m B m' m A Gambar 2.12 %1=-/- -A1:05>4 ?1=.@-? 0-=5 .-?-:3  =5:3-: >1<1=?5 <-0* .   '-0- @6@:3@6@:3  0-:  ?1=0-<-? .;8-.;8- 71/58 0-=5 19-> -?-@ <8-?5:- D-:3 9->>-:D- >-9- D-5?@  #10@- .;8- ?1=>1.@? 0-<-? .1=31=-7 01:3-: .1.->  -35-: ?1:3-4 .-?-:3 0557-? 01:3-: 91:33@:-7-: .1:-:3 4-8@> 0-: 053-:?@:3 A1=?57-8  1=95: 0-?-= 0581?-77-: <-0- .1:-:3 ?1=>1.@? 0-: 0-<-? 919-:?@87-: >5:-= <-0>@-?@ >7-8-  ;8-.;8- 71/58  0-:  9->5:39->5:3 05017-?7-: <-0.;8- -3-7 .1>-= D-:3 ?1=.@-? 0-=5 ?59-4 45?-9 D-:3 9->5:39->5:3 .1=9->>-   "-=-7 -:?-=- .;8- 71/58 0-: .;8- .1>-= 0@- <->-:3 05@>-4-7-:>-9- -D-3=-A5?->5D-:3?59.@8-:?-=- 0-: .-5705 9-@<@:0591:34->587-:7;<183-D-D-:3919@?-=.1:-:3 75.-?:D- /1=95: .1=<@?-= >145:33- 91:D1.-.7-: >5:-= <-0- >7-8- .1=31>1= 1=0->-=7-: <1:3-9-?-: 0-: <1:3@7@=-: 3-D- ?-=57 -:?-=- 0@9->>- .;8- 71/58 0-: 9->>- .;8- .1>-= >1/-=- >-7>-9- -A1:05>4 919<1=;814:58-5  H G %9 73 Skema neraca Cavendish. Contoh 2.7 Tantangan untuk Anda Berapakah massa dua benda pada jarak 1 meter agar memiliki gaya gravitasi sebesar 1 N? F  r2 F2 Resultan gaya gravitasi. Gaya gravitasi merupakan besaran vektor. 36 m2 Gambar 2.13 Ingatlah $ 73 73  H G%   9 '1=4-?57-: * .   '-0- >1.@-4 .1:0- .1=9->>-  .171=63-D-3=-A5?->5 0-: 1>-==1>@8?-:3-D-3=-A5?->5 0-: 9191:@45 <1=>-9--: .1=57@? 5:5 1>-=3-D-3=-A5?->50-=5 -0-8-4  $ 1>-=3-D-3=-A5?->50-=5 -0-8-4  $ 1>-= =1>@8?-: 3-D- 3=-A5?->5  0-:  -0-8-4 r1 M  H G %9 73  m1 F1 *1:?@7-:.1>-=3-D-3=-A5?->5-:?-=-0@-.1:0-.1=9->>-730-: 73D-:3?1=<5>-4 <-0-6-=-7 /9 3  m2 = 12 kg m1 = 8 kg 571?-4@5 F F 73  73 r = 0,25 m $  /9  9 H G %9 73 1>-=3-D-3=-A5?->505<1=;81401:3-:<1=>-9--:    /;>  G  )1<1=?5 ?18-4 05.-4-> <-0- .-35-: -B-8 >@..-. 5:5 01:3-: 91:33@:-7-: @7@9 =-A5?->5 +:5A1=>-8 %1B?;: 5:5 :0- 0-<-? 91:345?@:3 9->>- <8-:1?<8-:1? 0-: 9->>- $-?-4-=5 a. Menghitung Massa Bumi :0-<->?5?18-491:31?-4@5.-4B->1?5-<.1:0-05<1=9@7--:@95 D-:3.1=9->>- -7-:91:0-<-?<1=/1<-?-:3=-A5?->5>145:33-.1=-?.1:0?1=>1.@?D-:36@3-05<1:3-=@453-D-?-=57@950-:9191:@45<1=>-9--: Mudah dan Aktif Belajar Fisika untuk Kelas XI "57- 9->>- >1.@-4 .1:0-  0-: 9->>- @95  >10-:37-: 6-=-7 .1:0-?1=4-0-<<@>-?@95-0-8-4$.1=-=?5.1:0-.1=-0-05<1=9@7--: @95 .1=-? .1:0- -7-: 9191:@45 <1=>-9--: .1=57@?  G  ) $ 1:3-: 918-7@7-: >@.>?5?@>5 0-=5 .1>-= #./*+  5  71 #./*+  5  -7-: 054->587-: 3 $ "57-6-=56-=5@95>-9-01:3-:  790-:.1>-=3-D-3=-A5?->5 .@959 > 9->>-@9505:D-?-7-:01:3-:  Tokoh  G  3 $ $  H 73H 73  G  b. Menghitung Massa Matahari )18-5:91:345?@:39->>-@959->>-$-?-4-=5<@:0-<-?0545?@:3 01:3-:91:33@:-7-:<1=>-9--:<1=>-9--:31=-7>--?@9591:318585:35 $-?-4-=5 #1>159.-:3-:31=-7@95<-0-;=.5?:D-05>1.-.7-:;8140@3-D- D-:3 .171=6- <-0- @95 D-5?@ .1>-= 3-D- ?-=57 $-?-4-=5  0-: .1>-= 3-D- >1:?=5<1?-8 @95 >< 1>-= 3-D- ?-=57 $-?-4-=5 ?1=4-0-< @95 -0-8-4  G   $ 1:3-: 91:3-:33-< .-4B- 85:?->-: 31=-7 @95 .1=@<- 85:37-=-: .1=8-7@ <1=>-9--: 31=-7 9185:37-= D-5?@ Isaac Newton (1642–1777) Sumber: Fisika untuk Sains dan Teknik, 1998 Isaac Newton lahir di Inggris tahun 1642. Ia kuliah di Universitas Cambridge selama 5 tahun. Selama menjadi mahasiswa, ia tidak terlalu menonjol dalam bidang akademis. Pada waktu wabah pes menyerang Inggris, ia mengasingkan diri di pedesaan. Di tempat itulah, legenda tentang apel jatuh itu terjadi. Ia memperhatikan dan terus memikirkan mengapa apel jatuh ke bawah, gaya itulah yang kemudian disebut gaya gravitasi. Selain gaya gravitasi, ia juga menemukan prinsipprinsip dasar kalkulus. (  G  $ #./*+ 5 05>@.>?5?@>57-:71#./*+ 5 91:34->587-: %  $    $ ( $  G  @95 91:318585:35 $-?-4-=5 0-8-9 >-?@ <1=5;01  91:19<@4 85:?->-:>-?@<@?-=-:<1:@4  = "-05 718-6@-: <1=<@?-=-:@95-0-8-4 ( 6-=-7?19<@4  $  B-7?@?19<@4   G  "57- :0- >@.>?5?@>57-: #./*+  5  71 #./*+  5  4->58:D- -0-8-4     $   $  $    G  #1?1=-:3-:  9->>- $-?-4-=5 73 $  6-=-7 @95 0-=5 $-?-4-=5 9  <1=5;01@95> H G %9 73 Gaya 37 $->>-$-?-4-=50-<-?0545?@:3.1=0->-=7-:B-7?@10-=@95>18-9 ?-4@: "-=-7-:?-=-@950-:$-?-4-=5-0-8-4 H 9>145:339->>- $-?-4-=5 -0-8-4  $  =       9 = H  %9 73  H  > =  H  73 2. Kuat Medan Gravitasi  #)  %58-5'1=/1<-?-:=-A5?->505 1=.-3-5*19<-? #*-0 #.!#-0+ .2&0/&*/  #@?@.+?-==11:8-:0 )?;/74;89 =@>>18> %1B,;=7 1:A1= )-:=-:/5>/; #4-?@85>?5B-            Sumber: Physics for Scientists and Engineers with Modern Physics, 2000  #)  #1.1=3-:?@:3-:%58-5'1=/1<-?-: =-A5?->501:3-:#1?5:335-: #0&+$$&+ (* */                Sumber: Physics for Scientists and Engineers with Modern Physics, 2000 38 )19@- .1:0- 05 >175?-= <1=9@7--: @95 -7-: 05<1:3-=@45 ;814 910-: 3=-A5?->5 @95 >145:33- 91958575 3-D- .1=-? D-:3 .1>-=:D>1.-:05:3 01:3-: <1=/1<-?-: 3=-A5?->5 05 ?19<-? ?1=>1.@?  '1=/1<-?-: 3=-A5?->5@9505>@-?@?19<-?-7-:>19-75:71/58657-6-=-7-:?-=-<@>-? @95 71 ?19<-? ?1=>1.@? >19-75: 6-@4  =?5:D- >19-75: 6-@4 81?-7 >1.@-4 .1:0- 0-=5 <@>-? @95 >19-75: 71/58 3-D- 3=-A5?->5 @95 D-:3 05-8-95;814.1:0-?1=>1.@?  #)  91:@:6@77-:<1=/1<-?-:3=-A5?->5 05 .1.1=-<- ?19<-? $1:@=@? 917-:57- %1B?;: 3-D- .1=-? 3-D- 3=-A5?->5 >1.@-4 .1:0- 9191:@45 <1=>-9--:    01:3-:  05>1.@? <1=/1<-?-: 3=-A5?->5 D-:3 6@3- 91=@<-7-: 3-D- <1= >-?@-: 9->>- D-:3 058-7@7-: @95 ?1=4-0-< >1?5-< .1:0- 0-: 05>1.@? 910-: 3=-A5?->5 @95 "57- 9->>- @95  0-: 9->>- >1.@-4 .1:0- D-:3 .1=-0- 05 <1=9@7--:@95 .1:0-.1=9->- ?1=>1.@?-7-:91:0-<-?7-:3-D3=-A5?->5 D-:3 .1>-=:D )  $ >145:33- -7-: 05<1=;814   G  $ #1?1=-:3-:   7@-? 910-: 3=-A5?->5 9 >   7;:>?-:?- 3=-A5?->5 @:5A1=>-8 %9 73  $  6-=-7 .1:0- ?1=4-0-< <@>-? @95 9 #./*+  5  ?1=>1.@? -0-8-4 <1=>-9--: D-:3 91:D-?-7-: .1>-= <1=/1<-?-: 3=-A5?->5 @95 D-:3 05-8-95 ;814 >@-?@ .1:0- D-:3 .1=6-=-7 $ 0-=5 <@>-? @95 0-: 91:0-<-? 7@-? 910-: 3=-A5?->5 3 0-: 91=@<-7-:7;:>?-:?-0-:.1>-=-:.1=.-:05:3?1=.-857 01:3-: 6-=-7 >@-?@ .1:0- ?1=4-0-< <@>-? @95  "-05 >19-75: 6-@4 81?-7 >@-?@ .1:0- $ >19-75: 71/58 <1=/1<-?-: 3=-A5?->5 D-:3 05-8-95 >@-?@ .1:0- Contoh 2.8 @-.1:0-0-:9->5:39->5:3.1=9->>-730-:730581?-77-:?1=<5>-4<-06-=-7 /9 59-:-7-4?5?57'4-=@>05?19<-?7-:-3-=7@-?910-:3=-A5?->505 ?19<-??1=>1.@?>-9-01:3-::;8 3  571?-4@5 73  73    /9 9 Mudah dan Aktif Belajar Fisika untuk Kelas XI $5>-8:D-81?-7?5?570-=5.1:0--0-8-4* 3-=7@-?910-:3=-A5?->505?5?57>-901:3-::;89-7mA = 4 kg mB = 9 kg  gA A (       g2 P B   x *  50 cm     *        *    * *    * *     *   G** G ** * * 9  "-05?5?57'4-=@>05?19<-?7-:<-0-6-=-7 90-=5.1:0-     m1 r1 )1<1=?5 4-8:D- 3-D- 3=-A5?->5 <1=/1<-?-: 3=-A5?->5 6@3- 91=@<-7-: .1>-=-:A17?;= "-05.1>-==1>@8?-:<1=/1<-?-:3=-A5?->5D-:3.171=6-<-0>1.@-4?5?57-75.-?910-:3=-A5?->5D-:3054->587-:;8140@-.@-4.1:0.1=9->>-  0-:  4-=@> 0545?@:3 <@8- >1/-=- A17?;=  '1=4-?57-: * .  1>-==1>@8?-:710@-<1=/1<-?-:3=-A5?->5?1=>1.@?-0-8-4         /;> g  $   G  Resultan percepatan gravitasi 0-: g  $ Pembahasan Soal Contoh 2.9 5m @-.@-4.1:0-.1=9->>-730-: 73 *1=0-<-?>1.@-4?5?57D-:3.1=6-=-7>-90-=5.1:0- 0-:.1:0- D-5?@9D-:3919.1:?@7>@0@? F>1<1=?5<-0-3-9.-= "577;:>?-:?-3=-A5?->5 H G %9 73 ?1:?@7-:7@-?910-:3=-A5?->505?5?57 3  m1 = 5 kg 571?-4@5 $ $ 9 73  73 g1  g   73 9   $       $     73 9 #@-?910-:3=-A5?->505<1=;8140-=5<1=>-9--: O Perbandingan antara jari-jari sebuah planet (Rp) dan jari-jari Bumi (Rb) adalah 2 : 1, dan perbandingan massanya 10 : 1. Jika berat Butet di Bumi 100 N, di planet tersebut beratnya menjadi .... a. 100 N b. 200 N c. 250 N d. 400 N e. 500 N Soal UMPTN Tahun 1990 Pembahasan: 60° g2 5m Percepatan gravitasi g = m1 = 15 kg         /;>  m2 r2 g2 Gambar 2.14 #1?1=-:3-: g g1                         /;>                                   H G % 73    "-057@-?910-:3=-A5?->5H G % 73 M R2 2  Rb   M p   =    gb  R p   Mb  gp 2  1   10   = 2,5 2  1  =    gp = 2,5 gb maka wp= 2,5 wb w = 2,5 (100 N) = 250 N Jawaban: c Gaya 39 3. Hukum-Hukum Kepler Tantangan untuk Anda Banyak penelitian menunjukkan bahwa ada beberapa tempat yang rendah, tetapi percepatan gravitasinya lebih kecil daripada tempat yang lebih tinggi. Menurut Anda, faktor-faktor apa yang menyebabkan hal tersebut? y M b a F1 F2 x Gambar 2.15 Dua titik fokus pada elips. Gambar 2.16 (a) Lintasan planet yang eliptis dengan Matahari di salah satu titik fokusnya. Titik P, dinamakan perihelion, dan titik A dinamakan aphelion. (b) Luas daerah yang ditempuh dalam waktu yang sama adalah sama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a P A Matahari - A2 b planet A1 . $1:@=@?#1<81=8@->0-1=-4 0-: <-0-3-9.-=?1=>1.@?-0-8-4 >-9-  1:3-: 019575-: 71/1<-?-: ;=.5? <8-:1? 81.54 .1>-= <-0- >--? 6-=-7 -:?-=- <8-:1? 0-: $-?-4-=5 017-?  #1?57- 6-=-7 -:?-=- <8-:1? 0-: $-?-4-=5 6-@4 71/1<-?-: ;=.5? <8-:1? -7-: 918-9.-?  #1>59<@8-: ?1=>1.@? 0-<-? 6@3- 05.@7?57-: >1/-=- 9-?19-?5> D-5?@ 01:3-: 91:3 3@:-7-:7;:>1< @7@9#1717-8-:$;91:?@9)@0@? '19.-4->-:0-: <1:@=@:-: =@9@>:D- 0-<-? :0- <18-6-=5 <-0- -.  40 Mudah dan Aktif Belajar Fisika untuk Kelas XI @7@9!!!#1<81=91:D-?-7-:.-4B-7@-0=-?<1=5;01>1?5-<<8-:1? >1.-:05:3 01:3-: <-:37-? ?53- 6-=-7 <8-:1? ?1=>1.@? 0-=5 $-?-4-=5 1:?@7 9-?19-?5> 0-=5 @7@9 !!! #1<81= 5:5 -0-8-4   $  G  #1?1=-:3-:   <1=5;01 $  6-=-7 -:?-=- <8-:1? 0-: $-?-4-=5   7;:>?-:?- Contoh 2.10 Ingatlah "-=-7=-?-=-?-<8-:1?,@<5?1=0-:$-?-4-=5-0-8-4 >- 1=-<-7-4<1=5;01<8-:1? ,@<5?1=?1=>1.@? 3  571?-4@5 @95 ?-4@: $@95  >$,@<5?1= >- 1 sa = 1,5 × 1011 m 5?-:D-7-: ,@<5?1=  ,@<5?1= $ ,@<5?1=   ,@<5?1=   @95 $ @95 $ ,@<5?1= $ @95   @95  >-   >-   ?-4@:     9-7 ,@<5?1=      ?-4@: *-4@7-4 :0- .1=-<- :58-5 7;:>?-:?-  <-0- @7@9 !!! #1<81= ?1=>1.@? '-0- ,+0,%   :0- 0-<-? 91:33@:-7-: <1=>-9--: @7@9 !!! #1<81= ?-:<- 9191=8@7-: :58-5 7;:>?-:?-   7-: ?1?-<5 @:?@7 .1.1=-<- 7->@> ?-:<- -0- 0-?- <19.-:05:3 :58-5 7;:>?-:?-  -7-: >-:3-? 919.-:?@ -8-9 >-?@-: ->?=;:;95 >- 7    :0?1:?@5:35:91:31?-4@5:58-50-=57;:>?-:?-?1=>1.@? &8147-=1:-5?@ 57@?58-4 8-:37-48-:37-4 .1=57@? 5:5 '-0- 31=-7 <8-:1? D-:3 91:318585:35 $-?-4-=5 ?1=0-<-? 3-D>1:?=5<1?-8 D-:3 -=-4:D- 91:@6@ $-?-4-=5 >1.-3-5 <@>-? 0-=5 31=-7 9185:37-=  -D- >1:?=5<1?-8 ?1=>1.@? ?50-7 8-5: -0-8-4 3-D- 3=-A5?->5 '-0--. :0-?18-4.18-6-=?1:?-:331=-79185:37-= 1>-=<1=/1<-?-: >1:?=5<1?-8 <-0- 31=-7 9185:37-= 0-<-? 05?@85>7-: >1.-3-5 .1=57@? > $  01:3-:   >145:33   $ $ >   )1>@-5 01:3-: @7@9 !! %1B?;: .1>-= 3-D- >1:?=5<1?-8:D- -0-8-4 >  >   >   $   Tugas Anda 2.3 Hitunglah nilai konstanta k. Dengan menggunakan nilai k yang sudah Anda dapatkan, hitung kembali berapa periode planet Yupiter jika jaraknya terhadap Matahari 5,2 sa. Gaya 41 1=0->-=7-: :58-5   <-0- #./*+  5  <1=>-9--:  0-<-? 05?@85>7-: 91:6-05 >   $  )1<1=?5 ?18-4 0571?-4@5 <-0- <19.-4->-: >1.18@9:D- 3-D- >1:?=5<1?-8 >1?-=- 01:3-: 3-D- 3=-A5?->5 >145:33 3=-A5?->5  >1:?=5<1?-8     $ $    G  #1?1=-:3-:   7;:>?-:?- <-0- @7@9 !!! #1<81=  7;:>?-:?- 3=-A5?->5 @:5A1=>-8 %9 73   9->>- $-?-4-=5 73 )17-=-:3 :0- ?1:?@ >@0-4 0-<-? 91:345?@:3 :58-5 7;:>?-:??1=>1.@?  *1=:D-?- ?50-7 >@85? @:?@7 91:@=@:7-: <1=>-9--: ?1=>1.@? 4. Kelajuan Orbit Satelit 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? 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? 0- 0@- 9-/-9 >-?185? D-:3 0571:-8 D-5?@ >-?185? -8-95 0-: >-?185? .@-?-: )-?185?-8-9595>-8:D-@8-:>10-:37-:>-?185?.@-?-:95>-8:D>-?185? *#"$$ '%0-: % )-?185?.@-?-:D-:3<1=?-9-.1=4->58 91:3;=.5? @95 -0-8-4 >-?185? #'&!  058@:/@=7-: ;814 +:5 );AD1? <-0-&7?;.1=  )-?185?5:591:318585:35@950-8-9B-7?@ 6-9 01:3-: 718-6@-:   79 6-9 !:0;:1>5- 91958575 >-?185? 7;9@:57->5 <1=?-9- .1=:-9- # )-?185??1=>1.@?053@:-7-:@:?@7919.1=5<18-D-:-:7;9@:57->5=-05; 0-: ?181A5>5 71<-0- >1.-35-: .1>-= <1:0@0@7 !:0;:1>5-  -47-: .1.1=-<- :13-=- ?1?-:33- 91:D1B-:D- @:?@7 71<1=8@-: D-:3 >-9- )@9.1= 1:1=35 @:?@7 91:3;<1=->57-: >-?185? -0-8-4 .-?1=-5 >18 $-?-4-=5D-5?@>18>5857;:D-:391:3@.-4>5:-=$-?-4-=591:6-051:1=35 85>?=57  )@9.1= 1:1=35 8-5: D-:3 053@:-7-: -0-8-4 31:1=-?;= D-:3 8-:3>@:3 91:34->587-: 1:1=35 85>?=57 0-=5 ?1:-3- -?;9 >145:33- >-?185? 0-<-? .1=31=-7 <-0- ;=.5?:D- 91:318585:35 @95 01:3-: 718-6@-: ?1?-< -D-3=-A5?->5@95.1=2@:3>5>1.-3-53-D->1:?=5<1?-8>145:33->-?185? ?1?-< .1=-0- <-0- ;=.5?:D- @:?@7 91:318585:35 @95  "57- 9->>- >-?185?  .1=31=-7 01:3-: 718-6@-: ( 0-8-9 ;=.5? 85:37-=-: .1=6-=56-=5 $ 9-7-7-: 05<1=;814 <1=>-9--: .1=57@? 5:5 (  $ $ >145:33- 718-6@-: >-?185? -3-= ?1?-< .1=-0- <-0- ;=.5?:D- -0-8-4 ( $ #1?1=-:3-:  9->>- @95 73 $  6-=56-=5 ;=.5? >-?185? 9  7;:>?-:?- 3=-A5?->5 @:5A1=>-8 %9 73  42 Mudah dan Aktif Belajar Fisika untuk Kelas XI  G  Contoh 2.11 '-0-718-6@-:.1=-<-7-4>-?185?.@-?-:4-=@>91:3;=.5?@95<-0-71?5:335-: 0-=5 <1=9@7--:@95657-0571?-4@59->>-@95H 730-:6-=56-=5:D-H 9 3  571?-4@5 "-=-7>-?185?0-=5<1=9@7--:@95  1:3-:019575-:6-=-7>-?185?71<@>-? @95-0-8-4$  H G %9 73 H 73 H 9 01:3-:919->@77-::58-5  0-:9-7 (    $     H 73     %9 73      H  9     9 >05.@8-?7-:91:6-05 9 > "-05>-?185?4-=@>91:3;=.5?01:3-:71/1<-?-: 9 > 5. Periode Satelit pada Orbitnya (Materi Pengayaan) <-7-4 :0- 9->54 5:3-? @7@9 !!! #1<81= #1<81= 91:D-?-7-: .-4B- 7@-0=-? <1=5;01 =1A;8@>5 <8-:1? ?1=4-0-< $-?-4-=5 >1.-:05:3 01:3-:<-:37-??53-6-=-7<8-:1??1=>1.@?0-=5$-?-4-=5 #;:>1<?1=>1.@? 0-<-? 05?1=-<7-: 6@3- @:?@7 >-?185?  "-05 :0- 0-<-? 91:1:?@7-: <1=5;01 >1.@-4 >-?185? 01:3-: <1=>-9--: .1=57@?   $  $  G   &8147-=1:-   9-7      $  G  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? #1?1=-:3-:   <1=5;01 ;=.5? >-?185? >  7;:>?-:?- 3=-A5?->5 %9 73   9->>- @95 73 $  6-=-7 >-?185? 71 <@>-? @95 9 Contoh 2.12 '1=5;01$1=7@=5@>91:318585:35$-?-4-=5-0-8-44-=5>10-:37-:<1=5;01@95 91:318585:35$-?-4-=5-0-8-44-=5 "57-6-=-7@9571$-?-4-=5-0-8-4 H 9 ?1:?@7-:8-46-=-7$1=7@=5@>71$-?-4-=5 3  571?-4@54-=5$4-=5$$ H 9 Gaya 43 Kata Kunci • • • •   $      kelajuan orbit konstanta gravitasi universal percepatan gravitasi periode orbit $$    $$$  $ $   $  $$  $$  $   $$  $$      H 9H 796@?-79 "-056-=-7$1=7@=5@>71$-?-4-=5-0-8-46@?-79 Tes Kompetensi Subbab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lastisitas dan Gaya Pegas 5)$':0-?18-4919<18-6-=5>52-?>52-?.1:0-B-8-@<@:05.-?->5 4-:D-<-0-B@6@0:D- 1=0->-=7-:B@6@0:D-.1:0-05.-3591:6-05?539-/-9 D-5?@ <-0-? /-5= 0-: 3-> 1:0-<-0-?-0-8-4.1:0-D-:391958575.1:?@7A;8@91?1?-<>1=?91958575 >52-? 18->?5>  %&%&% -0-8-4   #'! ! '!&'    !&' % ' & + +! $ # ! &$%'& &! )-8-4 >-?@ .1:0- D-:3 91958575 >52-? 18->?5> D-:3 /@7@< ?5:335 -0-8-4 7-=1? 44 Mudah dan Aktif Belajar Fisika untuk Kelas XI (29.6; :2:69686 ?63.@ 29.?@6? /2;1. =.1.@ 7A4. :2:69686 ?63.@ =9.?@6? D.6@A82@68.4.D.D.;4/282>7.=.1./2;1.16@6.1.8.;:.8./2;1.@61.8 1.=.@ 82:/.96 82 /2;@A8 ?2:A9. (63.@ =9.?@6? @6:/A9 768. 4.D. D.;4 16/2>68.; :292/656 /.@.? 29.?@6?6@.? /2;1. 2/2>.=. 0<;@<5 /2;1. D.;4 :2:69686 ?63.@ =9.?@6? D.;4 0A8A= /2?.> .;@.>. 9.6; @.;.5 92:=A;4 1.; =9.?@6?6; "21A. ?63.@ 29.?@6? 1.; =9.?@6? @2>?2/A@ 16:69686 <925 ?2@6.= /2;1. =.1.@ 8.; @2@.=6 8.1.> 821A. ?63.@ @2>?2/A@ A;@A8 ?2@6.= /2;1. /2>/21./21. ".>2@ :2:69686 ?63.@ =9.?@6? D.;4 ?.;4.@ >2;1.5 1.; ?63.@ 29.?@6?D.;4?.;4.@@6;446%9258.>2;.6@A8.>2@?.;4.@0<0<8164A;.8.; ?2/.4.6 /.5.; =2:/A.@ /.; 82;1.>..; 1. Tegangan dan Regangan karet karet 0  F karet ditarik . F (N) gaya tarik *;@A8 92/65 :2:.5.:6 29.?@6?6@.? ?A.@A /2;1. =2>5.@68.; ) ,  &.1.4.:/.>@2>?2/A@@2>965.@?2A@.?8.>2@D.;4:2:69686=.;7.;4 :A9.:A9.   ".>2@ @2>?2/A@ 16@.>68 12;4.; 4.D. ?2/2?.>  ?256;44. 8.>2@ :2;4.9.:6 =2>@.:/.5.; =.;7.;4 ?2/2?.>  1 "2@68. @.>68.;;D. 1692=.?8.>2@82:/.9682=.;7.;4?2:A9. ;6/2>.>@68.>2@:.?65/2>.1. 1.9.: 1.2>.5 29.?@6?6@.?;D. "2:A16.;/2?.>4.D.@.>68.;=.1.8.>2@16=2>/2?.>:2;7.16 1.; 8.>2@ :2;4.9.:6 =2>@.:/.5.; =.;7.;4 ?2/2?.>  2  "2@68. 4.D. @.>68.; 1692=.? @2>;D.@. 8.>2@ 82:/.96 82 =.;7.;4 ?2:A9. ;6 /2>.>@6 8.>2@ @2>?2/A@ /2>.1. 1.9.: 1.2>.5 29.?@6? (2@6.= /2;1. :2:69686 /.@.? 29.?@6?6@.? @2>@2;@A 768. 4.D. D.;4 16/2>68.; =.1. /2;1. :292C.@6 /.@.? 29.?@6?6@.?;D. /2;1. @2>?2/A@ .8.; :2;4.9.:6 =2>A/.5.; /2;@A8 123<>:.?6!68./2?.>4.D.@.>68.;=.1.8.>2@6;616=2>/2?.>9.46:2;7.16  :.8. 8.>2@ .8.; =A@A? ;6 /2>.>@6 4.D. @.>68.; =.1. 8.>2@ @29.5 :2;0.=.6 @6@68 =A@A?;D. *;@A8 92/65 729.?;D. ?69.58.; ;1. A9.;46 9.46 :2:/.0. 69A?@>.?6 6;6 ?.:/69 :2965.@ ) ,    .9.: =2:/.5.?.; :2;42;.6 29.?@6?6@.? ;1. .8.; :2;2:A8.; =2;42>@6.; ()'(( @24.;4.; 1.; ()' $ >24.;4.; .D. D.;4 /282>7. =2>?.@A.;9A.?=2;.:=.;416?2/A@@24.;4.;(20.>.:.@2:.@6?@24.;4.; 1.=.@ 16@A96? ?2/.4.6 /2>68A@ F   H  "2@2>.;4.;   @24.;4.; .@.A ?@>2?? $:  /2?.>4.D.@.>68$ 9A.?=2;.:=.;4:  &2>/.;16;4.; .;@.>. =2>@.:/.5.; =.;7.;4 1.; =.;7.;4 :A9.:A9. 16?2/A@ ()' $ .@.A >24.;4.; (20.>. :.@2:.@6? 1.=.@ 16@A96? ?2/.4.6 /2>68A@    H   "2@2>.;4.;  >24.;4.;()' $   =2>@.:/.5.; =.;7.;4 :   =.;7.;4 .C.9 : ba t as el t as isi ta s titik putus F3 F2 F1 daerah elastis pertambahan panjang  (m) / Gambar 2.17 (a) Besar gaya tarik F menyebabkan karet bertambah panjang. (b) Grafik F –  seutas karet yang ditarik dengan besar gaya F. Gaya 45 2. Modulus Elastisitas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x  H  "2@2>.;4.; 2?.>4.D.=2:A965=24.?$ ! "<;?@.;@.=24.?$:   x ?6:=.;4.;=.1.=24.?: *;@A892/65:2:.5.:6/2?.>8<;?@.;@.29.?@6?6@.?=24.?!9.8A8.; 9.5 8246.@.; /2>68A@ 6;6 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. 46 Mudah dan Aktif Belajar Fisika untuk Kelas XI 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. Contoh 2.13 (2A@.?8.C.@=.;7.;4;D. 0:1.;9A.?=2;.:=.;4;D. 0: (2/A.54.D. $ /282>7.=.1.8.C.@@2>?2/A@?256;44.8.C.@/2>@.:/.5=.;7.;4:2;7.16 0: 6@A;49.5 . >24.;4.;()' $8.C.@ / @24.;4.;()'((8.C.@1.; 0 :<1A9A?29.?@6?6@.?8.C.@ 0  682@.5A6   0: :   0:I H :  $   0:  I H : . '24.;4.;  I  :    I   I  : / )24.;4.;  $      :  I $: 0 #<1A9A?29.?@6?6@.?  I $:    I $: I  !.16/2?.>>24.;4.;@24.;4.;1.;:<1A9A?29.?@6?6@.?/.@.;4@2>?2/A@/2>@A>A@@A>A@ .1.9.5 I H  I $: 1.; I $:  4. Susunan Beberapa Pegas ).5A8.5 ;1. /2/2>.=. =2;44A;..; =24.? 1.9.: 82561A=.; ?25.>6 5.>6 9.@.9.@ D.;4 ;1. 4A;.8.; :A9.6 1.>6 .9.@ ?212>5.;. ?.:=.6 .9.@ D.;4:2;44A;.8.;@28;<9<46:<12>;/.;D.8:2;44A;.8.;=24.?!68.;1. :2;44A;.8.;/<9=<6;:28.;68;1..8.;:2;2:A8.;=24.?161.9.:;D. &24.? 1.9.: /<9=<6; :28.;68 /2>3A;4?6 A;@A8 :2;4.@A> 829A.> :.?A8;D. :.@. /<9=<6; .9.: /61.;4 <@<:<@63 =24.? =A; /.;D.8 164A;.8.; ;1. .8.;:2;2:A8.;=24.?=.1.?2=21.:<@<>.@.A=A;: 1.; : .@.A :5.@68.;9.5 ) ,   Gambar 2.18 (a) Sepeda motor yang menggunakan monoshockbreaker (b) Sepeda motor yang menggunakan double shockbreaker Sumber: Dokumentasi Penerbit . / Gaya 47 k1 %!'!' =.1. ?2=21. :<@<> .1. D.;4 :2;44A;.8.; ?6?@2: #%$%(%!'!' 1.; %*" (%!'!' #2;A>A@ ;1. ?6?@2: :.;.8.5 D.;4 1.=.@ :2:/2>68.; 82;D.:.;.; /.46 =2;42;1.>. ?2=21. :<@<> ?6?@2: #%$%(%!'!' .@.A %*" (%!'!' 1.8.5 5A/A;4.;;D.12;4.;4.D.D.;4/282>7.=.1.?2@6.=(%!'!'@2>?2/A@ (2=21. :<@<> D.;4 :2;44A;.8.; ?6?@2: #%$%(%!'!' 1.=.@ 16.;.9<468.; 12;4.; ?6?@2: ?.@A =24.? 1.; ?.@A /2/.; ?21.;48.; ?6?@2: %*"(%!'!'1.=.@16.;.9<468.;12;4.;?6?@2:1A.=24.?D.;416?A?A; ?20.>. =.>.929 12;4.; ?.@A /2/.; .4.6:.;.8.5 =2>56@A;4.; 4.D. 1.; 8<;?@.;@.=24.?=.1.821A.?6?@2:=24.?@2>?2/A@2>68A@6;6.8.;16/.5.? @2;@.;4 ?6?@2: =24.? D.;4 16?A?A; ?20.>. ?2>6 =.>.929 1.; ?2>6=.>.929 a. Pegas Disusun secara Seri &2>5.@68.; ) ,  A. /A.5 =24.? 16?A?A; ?20.>. ?2>6 1.; ?2@6.= =24.? :2:69686 8<;?@.;@. =24.? !  1.; !  !68. =.1. A7A;4 =24.? D.;4 16?A?A; ?2>6 @2>?2/A@ 16/2>6 4.D.  821A. =24.? @2>?2/A@ .8.; :2;2>6:.4.D.D.;4?.:.D.6@A.>6=24.? 1.;=24.? .8.;16=2><925 =2>?.:..; k1 k2 k2 F Gambar 2.19 Pegas disusun seri.  ! -  ! - &2>@.:/.5.;=.;7.;4=24.?@<@.9 x ?.:.12;4.; x1 x 2 ?256;44. =.1. =24.? D.;4 16?A?A; ?2>6 /2>9.8A  !  -  - ?   !? ! !   !? ! ! !?  ! ! !  !  H  "2@2>.;4.; !? .1.9.5 8<;?@.;@. =24.? A;@A8 =24.? D.;4 16?A?A; ?2>6 b. Pegas Disusun secara Paralel A. /A.5 =24.? 16?A?A; ?20.>. =.>.929 ?2=2>@6 =.1. ) ,  ?2@6.= =24.? :2:69686 8<;?@.;@. ! 1.; ! !68. =.1. A7A;4 =24.? D.;4 @2>?A?A; ?20.>. =.>.929 @2>?2/A@ 16/2>68.; 4.D.  /2?.> 4.D.  16/.46 :2;7.16 1A. =.1. 821A. =24.? @2>?2/A@ :6?.9;D.  1.;  k1 F  ! -  ! - k2 F1  F  ! -  ! - F2 F Gambar 2.20 Pegas disusun paralel. &.1. =24.? D.;4 16?A?A; =.>.929 /2>9.8A    ! & - &  ! -  ! - &2>@.:/.5.;=.;7.;4=24.?@<@.9?.:.12;4.;=2>@.:/.5.;=.;7.;4?2@6.= =24.?.@.A x1  x 2 x p?256;44.=2>?.:..;8<;?@.;@.=24.?=.>.929 :2;7.16 !&! ! 48 Mudah dan Aktif Belajar Fisika untuk Kelas XI  H  2;4.; 12:686.; =.1. ?2=21. :<@<> D.;4 :2;44A;.8.; ?6?@2: %*" (%!'!' @2>7.16 =2:/.46.; 4.D. <925 821A. (%!'!' ?21.;48.; =.1. ?6?@2: #%$%(%!'!' 4.D. 5.;D. /282>7. =.1. ?.@A (%!'!' Contoh 2.14 )64./A.5=24.?16?A?A;?2>6?2@6.==24.?:2:696868<;?@.;@.=24.??2/2?.>  $:  $:1.; $:"2@64.=24.?@2>?2/A@16/2>64.D.?2/2?.> $2>.=.8.5! @<@.9=24.?=24.?@2>?2/A@ 0  682@.5A6 !   $:!   $:!   $:          !)%)" ! ! !    ! @<@.9  $: 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? !.16/2?.>!@<@.9=24.?@2>?2/A@.1.9.5 $: Contoh 2.15 A./A.5=24.?16?A?A;?20.>.=.>.929?2@6.==24.?:2:696868<;?@.;@.=24.? $: !68.=.1.?A?A;.;=.>.929=24.?@2>?2/A@16/2>64.D./2>.@ $56@A;49.5=2>@.:/.5.; =.;7.;4=24.? 0  682@.5A6  $ !  $: !  $: !  $: ! @<@.9 ! !  $: $: $: !@<@.9 x $ $: x  x   : 0: !.16=2>@.:/.5.;=.;7.;4=24.?@2>?2/A@?2/2?.> 0: k1 k2 k3 F Gambar 2.21 Susunan pegas secara paralel-seri. c. Pegas Disusun secara Paralel-Seri )64./A.5=24.?16?A?A;?20.>.=.>.929?2>6?2=2>@6=.1.) , ?2@6.= =24.? :2:69686 8<;?@.;@. =24.? !  !  1.; !  &.1. A7A;4 =24.? D.;4 @2>?A?A; ?20.>. =.>.929?2>6 @2>?2/A@ 16/2>68.; 4.D. ?2/2?.>  2;4.; :2;44A;.8.; >A:A?.; 8<;?@.;@. =24.? =.1. ?A?A;.; ?2>6 1.; ?A?A;.; =.>.929 8<;?@.;@. =24.? @<@.9 1.=.@ 16@2;@A8.; .>.;D. 12;4.; :2;D212>5.;.8.; ?A?A;.; =24.? =.1. ) ,  &2>@.:.8<;?@.;@.=24.?! 1.;! 16.;44.=:2;7.16=24.??A?A;.; =.>.929 @.;=. 4.;44A.; 1.>6 =24.? 82  %925 8.>2;. 6@A =2>?.:..; 8<;?@.;@. =24.? !  1.; !  :2;7.16 !&! ! "2:A16.; ;69.6 8<;?@.;@. =24.? @2>?2/A@ 164./A;48.; ?20.>. ?2>6 12;4.; =24.? 82  ?256;44. ! & !   !?2>6 ! & ! .@.A!?2>6 ! &  ! shockbreaker Sumber: Kamus Visual, 2004 Gambar 2.22  H  Sistem pegas yang digunakan pada shockbreaker mobil. Dapatkah Anda memperhitungkan gaya yang bekerja pada setiap shockbreaker? Gaya 49 Tugas Anda 2.6 Contoh 2.16 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? )2;@A8.; ;69.6 =2>/.;16;4.; =2>6<12 ?A?A;.; =24.? =.1. ) ,  1.;) ,   768. :.??. /2/.;;D. ?.:. D.6@A# k k k k y1 2k 6k . m k m / 0  (A?A;.;=24.?=.1.) ,@2>16>6.@.?@64./A.5=24.?D.;416?A?A; =.>.929!&!!! !!.16!& ! Kata Kunci • • • • • • gaya pulih konstanta pegas regangan susunan pararel susunan seri tegangan ! &!  !!  !.@.A!( ! ! &  ! !  ! (A?A;.;=24.?=.1.) , :2>A=.8.;=24.?D.;416?A?A;?20.>.=.>.929.@.A !=!! !!.16!& ! (A?A;.;?2>612;4.;=24.?!:.8.!?  ! &  !  ! !   !.@.A!(! !  ! ! &  ! &2>/.;16;4.;=2>6<12?A?A;.;=24.?=.1.) ,1.;?A?A;.;=24.?=.1. ) , .1.9.5 (A?A;.;?2>612;4.;=24.? !.1.9.5!?   # #   ! !   !  !  ! !   !.16 1: 2 Tes Kompetensi Subbab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udah dan Aktif Belajar Fisika untuk Kelas XI F (N) 6 3 0    B (40,6) A (20,3) 20 40 x (mm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erak Harmonik Sederhana (2/A.5 /2;1. 168.@.8.; /2>42>.8 5.>:<;68 768. /2;1. @2>?2/A@ :29.8A8.; 42>.8 ?20.>. /<9.8/.968 16 ?286@.> @6@68 82?2@6:/.;4.; :6?.9;D..DA;.;?212>5.;.D.;4/.;D.8167A:=.616.>2;./2>:.6;).:.; ".;.8".;.8 2>.8 /<9.8/.968 ?2/A.5 .DA;.; @2>A? /2>9.;4?A;4 768. 16/2>64.D.1<><;4?20.>./2>829.;7A@.;A;@A8:29.C.;4.D.42?282>.8 /<9.8/.968=.1..DA;.;16?2/A@7A4.42>.85.>:<;68?212>5.;.DA;.; .8.; /2>52;@6 16 @6@68 82?2@6:/.;4.; !68. 42>.8.; /<9.8/.968 @2>?2/A@ /2>9.;4?A;4 1.9.: ?29.;4 C.8@A D.;4 ?.:. 42>.8 @2>?2/A@ 16;.:.8.; 42>.8 =2>6<168 .9.: /./ 6;6 ;1. .8.; :2:/.5.? 42>.8 5.>:<;68 ?212>5.;. 12;4.; :2;4./.68.; .1.;D. 42?28.; D.;4 @2>7.16 <;@<542>.85.>:<;68?212>5.;.1.=.@;1.965.@=.1..DA;.;/.;1A9 ?212>5.;..@.A42@.>.;=.1.=24.?.6842@.>.;=24.?.@.A42>.8.;/<9.8 /.968 =.1. /.;1A9 ?212>5.;. .>.5;D. ?29.9A :2;A7A @6@68 82?2@6:/.;4.; 1. Simpangan Gerak Harmonik Sederhana &2>5.@68.;) , (2/A.5@6@68/2>42>.8:296;48.>/2>.@A>.; !68.C.8@AD.;416=2>9A8.;A;@A8/2>=6;1.51.>6=?A1A@D.;416@2:=A5@6@686@A.1.9.5   )  )   ) &>5.1.= ?A:/A-. .1.9.5 D  1.; =>5.1.=?A:/A--.1.9.5-?21.;48.;.1.9.57.>67.>696;48.>.; !68. ;1. =2>5.@68.; =>?2/A@ :2:69686?6:=.;4.;:.8?6:A: D.;416?2/A@.:=96@A1<2?.>=>42>.8 :A9.6 1.>6   ",-)* 2  1.=.@ 16@A96?   ?6;  )   ?6;  )    H  y P Py R x  Px Po Gambar 2.23 Sebuah titik bergerak dari posisi Po ke posisi P. "2@2>.;4.;  ?6:=.;4.;:   3>28A2;?6 E .:=96@A1<:  0  ?A1A@ .C.9 >.1 )  C.8@A ?28<;   3>28A2;?6 ?A1A@ >.1? 2?.>?A1A@D.;416@2:=A5?2/A.5@6@681.9.:3A;4?6?6;A?16?2/A@(**) 2 t ( 2?.> ?A1A@ 3.?2 .1.9.5     )         !68.     T )        16:.;. .1.9.53.?242@.>.;=2>?.:..;3.?242@.>.;;D.    Gaya 51 Informasi untuk Anda 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. Information for You 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. )    H    (2/A.5 @6@68 D.;4 /2>42>.8 5.>:<;68 ?212>5.;. /2>=6;1.5 1.>6 ) )  )  :2:69686 3.?2    1.; =.1. ?..@ )  :2:69686 3.?2        :.8./21.3.?2) 1.;)A;@A8) )  .1.9.5       H  &.1. 42>.8 5.>:<;68 ?212>5.;. /21. 3.?2 16;D.@.8.; <925 .;48. 1.>6;<9?.:=.612;4.;?.@A21.3.?2A;@A8/69.;4.;/A9.@@61.8=2>9A 16?2>@.8.; :6?.9;D.    1.; ?2@2>A?;D. 0A8A= 16@A96? /21. 3.?2;D. .1.9.5  ?.7. &9.C.;.; 3.?2 768. /21. 3.?2;D. ?2@2;4.5  (20.>. :.@2:.@6? 1.=.@ 16@A96? ?2/.4.6 /2>68A@  (23.?2 .@.A 2>9.C.;.; 3.?2        $    H      H  "2@2>.;4.;$ .1.9.5 /69.;4.; 0.0.5     1.; ?2@2>A?;D. .@.A Tokoh ) H )   $ 2. Kecepatan Gerak Harmonik Willems Gravesande (1688–1742) "202=.@.;42>.85.>:<;68?212>5.;.:2>A=.8.;@A>A;.;=2>@.:.1.>6 =2>?.:..; =5.1.= C.8@A 2;1. =.1. .C.9;D. /2>42>.8    . :.8. ;69.6 8202=.@.;;D. .1.9.5 + .      ?6;  ) ) ) +.  06 +.    !.16 8202=.@.; :.8?6:A: :2:2;A56 =2>?.:..; /2>68A@ +:   H  Sumber: research.leidenuniv.nl 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. 52 .>6 ",-)* 2  1.; 2  .8.; 16=2><925 +D+:0.;4 =42>.8 5.>:<;68 .1.9.5   ?6;  )    ?6;   )    0 06 ",-)* 2  1.; 2  82 1.9.: =2>?.:..;    00<925 +D   "2@2>.;4.; +D  8202=.@.; @2>5.1.= ?A:/A-. :? .:=96@A1<:   3>28A2;?6 ?A1A@ >.1?  ?6:=.;4.;: Mudah dan Aktif Belajar Fisika untuk Kelas XI  H  3. Percepatan Gerak Harmonik Sederhana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aY – x aY + Y– Gambar 2.24 Arah simpangan Y dan percepatan ay pada gerak harmonik sederhana selalu berlawanan. y ymak A t 0 a y . vy + A t 0 / ay – A Contoh 2.17 t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ambar 2.25 Grafik gerak harmonik sederhana: (a) simpangan terhadap waktu, (b) kecepatan terhadap waktu, dan (c) percepatan terhadap waktu.       -  06=2>?.:..;?6:=.;4.;=.1./A@6>.16=2><925 +#         :? #           :?   ?6;     4. Periode dan Frekuensi pada Gerak Harmonik B O garis setimbang A . A B O garis setimbang / Gambar 2.27 Periode dan frekuensi pada (a) pegas, (b) bandul, dapat ditentukan dari besar simpangannya. . / +y 0 –F +y P –y F –y Gambar 2.28 Arah gaya pemulih pada pegas selalu berlawanan tanda dengan simpangan. 54 2?.>?6:=.;4.;42>.85.>:<;68?212>5.;.=.1.=24.?1.;/.;1A9 1.=.@16@2;@A8.;12;4.;:2;4.:.@642>.8/<9.8/.968=.1.42@.>.;=24.? 1.;.DA;.;?212>5.;.;1..8.;:2:=2><925=2>6<1242@.>.;1.; 3>28A2;?6&2>6<1242@.>.;.1.9.5C.8@AD.;416=2>9A8.;/2/.;A;@A8 :29.8A8.;?.@A8.9642>.8/<9.8/.96842@.>.;>28A2;?642@.>.;.1.9.5 /.;D.8;D.42>.8/<9.8/.968D.;41.=.@169.8A8.;1.9.:C.8@A?.@A?28<; &2>6<12 D.;4 169.8A8.; <925 ?2/A.5 /2;1. =.1. ) ,  .1.9.5 C.8@A D.;4 16/A@A58.; /2;1. A;@A8 /2>42>.8 1.>6    &.1. ) ,   /2/.;16@.>68?256;44.=24.?:2:.;7.;4 ?.:=.6 82@6@68 &.1..DA;.;/2/.;) ,  42>.8/2;1.:2;D6: =.;4 56;44. @6@68  "2@68. 1692=.? /2/.; /2>42>.8 :2;A7A @6@68 82?2@6:/.;4.; 1.; :292C.@6;D. ?.:=.6 16 @6@68  "2:A16.; /2/.; /2>42>.8 82:/.96 82 @6@68 ?2:A9. D.6@A @6@68 ?2@29.5 :292C.@6 @6@68 82?2@6:/.;4.; A;@A8 821A. 8.96;D. 16 @6@68  !.16 /2>1.?.>8.; =2;4.:.@.; C.8@A D.;4 16/A@A58.; /2/.; A;@A8 :29.8A8.; ?.@A 8.96 42@.>.; =.1. =24.? .@.A ?.@A 8.96 .DA;.; =.1. /.;1A9 16?2/A@ &' %  ?21.;48.; 3>28A2;?6 /2>/.;16;4 @2>/.968 12;4.; =2>6<12 (20.>. :.@2:.@6? 16@A96?  H    .@.A  "2@2>.;4.;   =2>6<12 ?28<;  3>28A2;?652>@EE 5. Gaya Pemulih pada Pegas dan Bandul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udah dan Aktif Belajar Fisika untuk Kelas XI 42>.8 D.;4 /2>A9.;4 .86/.@ 4.D. =2:A965 D.;4 .>.5;D. ?29.9A :2;A7A @6@68 82?2@6:/.;4.; 2?.> 4.D. =2:A965 ?2/.;16;4 12;4.; 7.>.8 /2;1. 82 @6@68 ?2@6:/.;4 . (20.>. :.@2:.@6? 4.D. =2:A965 =.1. =24.? 16@A96?  !.;<@.?6?8.9.> 0!;<@.?6B28@<> H  .D.=2:A965?29.9A/2>9.C.;.;.>.512;4.;.>.5?6:=.;4.;"2@68. .>.5 /2;1. 82 /.C.5 4.D. =2:A965 82 .@.? 2:686.; 7A4. ?..@ /2;1. /2>42>.8 82 .@.? .>.5 4.D. =2:A965 .1.9.5 B2>@68.9 82 /.C.5 (2/A.5 /.;1A9 /2>:.??. # 165A/A;48.; 12;4.; ?2A@.? @.96 D.;4 =.;7.;4;D."?2=2>@6@.:=.8=.1.) ,.;1A916@.>68?27.A5( ?256;44.:2:/2;@A8?A1A@ &.1./.;1A9/282>7.1A.4.D.D.6@A4.D. @24.;4.; @.96  1.; 4.D. /2>.@ /.;1A9 # D.;4 .>.5;D. B2>@68.9 82 /.C.5 "<:=<;2; 4.D. /2>.@ # D.;4 /282>7. =.1. /.;1A9 .1.9.5 #05.1.= 4.D. @24.;4 @.96  ?256;44. /.;1A9/2>42>.8@2@.==.1.96;@.?.;;D."<:=<;2;4.D.9.6;;D..1.9.5 #?6;   .D. @2>?2/A@ ?29.9A :2;A7A @6@68 82?2@6:/.;4.; .DA;.; 1.; @24.89A>A?@2>5.1.=@24.;4.;@.96.D.D.;4.>.5;D.?29.9A:2;A7A@6@68 82?2@6:/.;4.; .1.9.5 4.D. =2:A965 2?.> 4.D. =2:A965 =.1. .DA;.; ?212>5.;. 1.=.@ 16;D.@.8.; 12;4.; =2>?.:..;  H 0# ?6;  "2@2>.;4.; /2?.>4.D.=2:A965$   /2?.> =202=.@.; 4>.B6@.?6 :?  #  :.??. /2;1. 84   ?A1A@ ?6:=.;4.; a. Periode Gerak Harmonik pada Pegas &2>6<12 42@.>.; =.1. =24.? 1.=.@ 16@2;@A8.; 12;4.; :2;44A;.8.; A8A:  $2C@<; D.6@A  #. 12;4.; ;69.6 =2>02=.@.; 42>.8 /2;1. .  0  2 . .D. =2:A965 =.1. =24.? .1.9.5   0! ?256;44. 768. 16296:6;.?68.;.;@.>.=2>?.:..;A8A: $2C@<;1.;=2>?.:..;4.D. =2:A965 16=2><925 ! 1 #. !. # 0  . ! ! !#      # #  %925 8.>2;. 8202=.@.; ?A1A@    :.8.    # !  T  m 0 B mg sin  mg cos  mg Gambar 2.29 Gaya pemulih pada ayunan selalu menuju titik kesetimbangan. garis seimbang y mg Gambar 2.30 Sebuah pegas ditarik hingga merenggang sejauh y.  H >28A2;?6 =24.? /2>/.;16;4 @2>/.968 12;4.; =2>6<12 =24.? ?256;44. /2?.> 3>28A2;?6 =24.? 16;D.@.8.; 12;4.; =2>?.:..;   ! #  H "2@2>.;4.;   3>28A2;?6 42@.>.; =24.? E # :.??./2/.;84   =2>6<12 ?28<; ! @2@.=.;=24.?$: Gaya 55 b. Periode Ayunan Bandul Sederhana DA;.; /.;1A9 ?212>5.;. :2:69686 /2?.> 4.D. =2:A965   0# ?6;   . . !68. ?A1A@  :2;128.@6 ;<9 ;69.6 ?6;    :2;128.@6  .>6 A8A:   $2C@<;/2?.>  # .?256;44..8.;16=2><925=2>6<12.DA;.;/.;1A9 ?212>5.;. ?2/.4.6 /2>68A@  0#  ?6;  . # .H#  .    %9258.>2;.. 0  .:.8.H  .H     .@.A   2;4.;     161.=.@        ?256;44.       H "2@2>.;4.;   =2>6<12 42>.8 /.;1A9 ?   /2?.> =2>02=.@.; 4>.B6@.?6 :?    =.;7.;4 @.96 : *;@A8 92/65 :2:.5.:6 =2>6<12 =.1. /.;1A9 ?212>5.;. 9.8A8.;9.5 .8@6B6@.? /2>68A@ Aktivitas Fisika 2.3 Ingatlah 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  . 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 m 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°? Contoh 2.18 !68.=2>6<12.DA;.;/.;1A9?212>5.;.D.;4=.;7.;4;D.  0:.1.9.5 ?28<; @2;@A8.;/2?.>=2>02=.@.;4>.B6@.?6169<8.?6.DA;.;@2>?2/A@ 56 Mudah dan Aktif Belajar Fisika untuk Kelas XI 0  682@.5A6 =.;7.;4@.96    0: : =2>6<12 ?28<; &2>02=.@.;4>.B6@.?616=2><92512;4.;",-)*2         :      :?     ?  !.16=2>02=.@.;4>.B6@.?616@2:=.@@2>?2/A@.1.9.5:?    Contoh 2.19  .>64>.368?6:=.;4.;@2>5.1.=C.8@A?2=2>@6@.:=.8=.1.4.:/.>@2;@A8.; . .:=96@A1< / =2>6<121.; 0 3>28A2;?642@.>.; y 5 0 3 6 9 12 15 18 21 24 t –5 0  . :=96@A1<.1.9.5?6:=.;4.;:.8?6:A:1.>64.>6?:2;1.@.>D.6@A: / &2>6<12.1.9.5?29.;4C.8@AD.;416=2>9A8.;A;@A8:2:/2;@A8@64. @6@68=<@<;4/2>A>A@.;=.1.?A:/A-)12;4.;) ?28<; 0 >28A2;?642@.>.;    E  &.1.?A:/A-.1.;?A:/A-)D.;4?.:.9A86?9.51A.4>.368.H)42>.85.>:<;68 12;4.;=2>6<1242@.>.; ?2@2;4.5=2>6<1242@.>.; 1.;.:=96@A1<42@.>.;  ?2@2;4.5.:=96@A1<42@.>.;  0  !68.A;@A84>.368.H)42>.85.>:<;68 16.:/69.:=96@A1< =2>6<12 1.; 3>28A2;?6 :.8.A;@A84>.368.0)42>.85.>:<;68 /2>9.8A .:=96@A1<  =2>6<12   1.;3>28A2;?6    >.36842>.8.H)42>.85.>:<;68 16;D.@.8.;<9254.>6?A@A51.;4>.368.H) 42>.85.>:<;68 16;D.@.8.;<9254.>6?=A@A?=A@A??2=2>@6=.1.4.:/.>/2>68A@ simpangan (y) Grafik gerak harmonik (1) Amplitudo A1, periode T1 Frekuensi f1 T2 A2 q A1 waktu (t) T1 Grafik gerak harmonik (2) Amplitudo A2, periode T2 Frekuensi f2 Y C Ek = 0 Epmaks = 5. Energi pada Gerak Harmonik Sederhana 2>.85.>:<;68?212>5.;.1.>6?2/A.5.DA;.;/.;1A916=2>965.@8.; =.1. ) ,  &.1. 82.1..; .C.9 = 7.A5D.6@A16@6@68&.1.=?2/A@ /2?.>2;2>46=<@2;?6.9/.;1A9 :.8?6:A: ?2/.968;D. /2?.> 2;2>46 86;2@68 /.;1A9 :6;6:A: "2@68. 1 2 kA 2 Gambar 2.31 B Ek = 0 A Epmaks = Ep = 0 Ekmaks = 1 2 kA 2 1 mv2maks 2 Perubahan energi terjadi saat bandul bergerak dari A menuju B yaitu energi potensial ke energi kinetik dan sebaliknya dari B ke C. Gaya 57 /.;1A9 1692=.? :2;A7A @6@68 82?2@6:/.;4.; 16  /2?.> 2;2>46 =<@2;?6.9 /2>.;4?A> :2;A>A; ?21.;48.; /2?.> 2;2>46 86;2@68;D. /2>@.:/.5 56;44. :2;0.=.6 :.8?6:A: 16 @6@68  .;1A9 @2>A? /2>42>.8 :2;A7A @6@68  &.1.42>.8.;/.;1A91.>6@6@6882@6@68.8.;:2;4.9.:6=2;A>A;.; /2?.> 2;2>46 86;2@68 1.; =2>@.:/.5.; /2?.> 2;2>46 =<@2;?6.9 6 @6@68  /2?.> 2;2>46 =<@2;?6.9 /.;1A9 82:/.96 :.8?6:A: ?21.;48.; /2?.> 2;2>46 86;2@68;D. 82:/.96 ;<9 !.16 ?29.:. 42>.8.; 5.>:<;68 ?212>5.;. =.1. .DA;.; /.;1A9 /2>9.;4?A;4 .8.; ?29.9A @2>7.16 =2>A/.5.; 2;2>46 =<@2;?6.9 :2;7.16 2;2>46 86;2@68 .@.A ?2/.968;D. !68. @61.8 .1. 4.D. 42?28 /2>9.8A 5A8A:82828.9.;2;2>46:28.;68?256;44./2?.>2;2>46@<@.9=.1.42>.8.; 5.>:<;68 16 ?2@6.= 96;@.?.; ?29.9A @2@.= (20.>. :.@2:.@6? /2?.> 2;2>46 86;2@68 /2;1. =.1. 42>.8 5.>:<;68 :2:2;A56 =2>?.:..;  .@.A   #+   !  #   046 =<@2;?6.9 42>.8 5.>:<;68 16 ?2@6.= ?6:=.;4.; .1.9.5       t   !   ! ?6;  & #   ?6;   t  &     H  ;2>46 @<@.9 .@.A 2;2>46 :28.;68 D.;4 :2>A=.8.; =2;7A:9.5.; 2;2>46 =<@2;?6.9 1.; 2;2>46 86;2@68 1.=.@ 16@A96? ?2/.4.6 /2>68A@ # & !      #  06?63.@@>64<;<:2@>6?6;   t  # Energi Ep = 21 kA2 Ep = E M +A Ep = 0 Energi E k = EM simpangan Y +A Gambar 2.32 2>1.?.>8.; ",-)* 2  1.=.@ 16@A96? Grafik energi potensial dan energi kinetik terhadap simpangan pada gerak harmonik sederhana. 58 #    # !  !  0  Ek Ek = 0 –A #   !  H   H  ;2>46 :28.;68 =.1. 42>.8 5.>:<;68 ?212>5.;. /2?.>;D. @61.8 /2> 4.;@A;4=.1.?6:=.;4.;42>.81.;;69.6;D.?29.9A@2@.=16?2@6.=@6@6896;@.?.; 2;4.; 12:686.; 2;2>46 :28.;68 1.9.: 42>.8 5.>:<;68 ?29.9A @2@.= ;2>46=<@2;?6.942>.85.>:<;68:2:2;A56=2>?.:..; &  !   &2>?.:..; @2>?2/A@ :2>A=.8.; 3A;4?6 8A.1>.@ @2>5.1.=  >.368 2;2>46 =<@2;?6.9@2>5.1.=?6:=.;4.;/2>/2;@A8=.>./<9.:29.9A6@6@68=A?.@   2:686.; =A9. 12;4.; 2;2>46 86;2@68 &2>5.@68.; ) ,  ;2>46 86;2@68 16=2><925 1.>6 ",-)* 2  D.6@A ! #H & ! H !  Ep –A .@.A Mudah dan Aktif Belajar Fisika untuk Kelas XI   # +   ! 0   H  + !  H   # !68.=.85.>:<;68 :2;0.=.6 :.8?6:A: ?256;44. ",-)* 2  :2;7.16 +:.8?  ! # Kata Kunci  H  • • • • • • amplitudo fase frekuensi getar gaya pemulih periode getar simpangan  H "2@2>.;4.; +:.8?  8202=.@.; :.8?6:A: :? .:=96@A1<: !  8<;?@.;@. =24.? $: #  :.??. /2;1. 84 Contoh 2.20 (2/A.5=24.?/2>@.:/.5=.;7.;4  :?..@16@.>6812;4.;/2;1./2>:.??.  84 D.;4164.;@A;4=.1.=24.?@2>?2/A@965.@4.:/.>"2:A16.;16@.>689.46?27.A5  : 1.>6@6@6882?2@6:/.;4.;1.;1692=.?8.; +y 0,150 m m 0,100 m m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aya 59 =24.?=.1.?..@) .1.9.5.   :?256;44.=2>?.:..;;D. .H  :02;.3A;4?605.>4. =.1.?..@) 0 1 2 3 .   ?6;  @ )  +:.8? +:.8? ?H   :  :? !.168202=.@.;?2@6.=?..@).1.9.5+   :??6; ) "202=.@.;?2@6.=?..@) + @<@ !   $:  :  I H ! .>6/161.=.@8.;.H  :06016=2><925+   :??6; ) !.162;2>46=<@2;?6.91.;86;2@68?2/.4.63A;4?61.>6C.8@A.1.9.5 = !.  I H !046=<@2;?6.91.;2;2>4686;2@68/.9<8.1.9.5 = !.   $:     I H ! 8 @<@H =I H H  I H ! I H ! Tes Kompetensi Subbab D ",&'*($!() /'/(.%$*  (2/A.5.DA;.;?212>5.;.?2=2>@6=.1.4.:/.>@2>/A.@ 1.>6/.;1A9/2>:.??.  84D.;41668.@?2A@.?@.96D.;4 =.;7.;4;D. 0:   80 cm r m= 0,3 kg 10 cm   60  !68.=2>02=.@.;4>.B6@.?6 :? @2;@A8.;/2?.> 4.D.=2:A965=.1./.;1A9 (2/A.5=24.?=.;7.;4;D. 0:!68.=24.?16/2>6 /2/.; 4=.;7.;4;D.:2;7.16 0:"2:A16.; /2/.;=.1.=24.?@2>?2/A@1642@.>8.;!68.1682@.5A6  :? @2;@A8.;9.5=2>6<1242@.>.;=24.? (2/A.5/2;1.#164.;@A;48.;=.1.?2/A.5=24.? D.;4/2>42@.>12;4.;3>28A2;?6  E"2@68. /2/.; D.;4 :.??.;D.   4 16@.:/.58.; =.1.# 3>28A2;?642@.>.;:2;7.16  E)2;@A8.;9.5 ;69.6# Mudah dan Aktif Belajar Fisika untuk Kelas XI  (2/A.5=24.?12;4.;8<;?@.;@.=24.?   $: 164.;@A;4B2>@68.9&.1.A7A;4;D.16/2>6/2/.;?2/2?.>  4>.:/2/.;16@.>6882/.C.59.9A1692=.?)2;@A 8.;9.5=2>6<1242@.>=24.?1.;3>28A2;?642@.>;D. !68..:=96@A1<42@.>.;.:=96@A1<42@.>.;@2@.=6 =2>6<12 =2>6<129A86?9.54>.368.H)1.>61A. 42>.85.>:<;68@2>?2/A@ (2/A.5/2;1.:29.8A8.;42>.85.>:<;68?212>5.;. ?2=.;7.;4?A:/A.&2>?.:..;?6:=.;4.;16;D.@.8.;  ?2/.4.6 ?6;  )   12;4.;.1.9.::2@2>1.; )1.9.:?28<;)2;@A8.; . .:=96@A1<3>28A2;?68202=.@.;1.;=2>02=.@.; / =2>?.:..;8202=.@.;1.;=2>02=.@.; 0 ?6:=.;4.;8202=.@.;1.;=2>02=.@.;=.1.?..@ )  ?28<; 1 8202=.@.;:.8?6:A:1.;=2>02=.@.;:.8?6:A:   Rangkuman       2>.842?28@6:/A9768.1A./A.5/2;1./2>?2;@A5.; .D.42?28?@.@6?/2>;69.6:A9.61.>6 56;44.:2;0.=.6  (  (:.8?6:A:  (  .D.42?2886;2@68/2>;69.68<;?@.;D.6@A ! !  2;1.D.;416?6:=.;16.@.?/2;1.:6>6;4:.8. 8<236?62;42?28?@.@6?D.;4@2>7.16.1.9.5  (  @.;  12;4.;  .1.9.5 ?A1A@ 82:6>6;4.; /61.;4 "202=.@.; :.8?6:.9 :/<9258.; :296;@.?.4.>.:.;1.;@61.8?296=.1.9.5?2/.4.6 /2>68A@ G &.1.@68A;4.;:2;1.@.> +:.8?  ' G &.1.@68A;4.;:6>6;49.6; +:.8? '  @.;  / &.1.@68A;4.;:6>6;48.?.>  (  @.;  +:.8?  ' 1   @.;  ( 12;4.; ?A1A@82:6>6;4.;7.9.;'7.>.8:5.1.==A?.@8292;48A;4.;@68A;4.; A. /A.5 /2;1. D.;4 /2>:.??. #  1.; #  D.;4 /2>.1.=.1.7.>.8'?.@A?.:.9.6;.8.;:2;4.9.:6 4.D.@.>684>.B6@.?616.;@.>.821A.;D.D.;4/2?.>;D. 16;D.@.8.;12;4.; #1 # 2  2  ' &2>02=.@.; 4>.B6@.?6 A:6 16;D.@.8.; 12;4.;  =2>?.:..;  2 ' 12;4.;'7.>.8=2>:A8..;A:6@2>5.1.==A?.@ A:6 A8A: "2=92>:2;D.@.8.;/.5C.?2:A.=9.;2@ /2>42>.81.9.:<>/6@296=?12;4.;#.@.5.>616?.9.5 ?.@A3<8A?;D. A8A:  "2=92> :2;D.@.8.; /.5C. 4.>6? D.;4 :2;45A/A;48.;.;@.>.=9.;2@1.;#.@.5.>6.8.; :2;D.=A9A.?1.2>.5D.;4?.:.=.1.C.8@AD.;4?.:.  4.>?.@296@@2@.=/2>.1.=.1.96;@.?.;;D.?.@296@ 5.>A?:2:696868202=.@.;42>.8?2/2?.>  ' 2;1.=.1.@:2:69686/2;@A8B<9A:2@2@.=?2>@. :2:=A;D.6?63.@29.?@6? )'((@24.;4.;=.1./2;1.16;D.@.8.;12;4.; =2>?.:..; +  )' $>24.;4.;=.1./2;1.16;D.@.8.;12;4.;   0 #<1A9A?29.?@6?6@.?#<1A9A?+.85.>:<;68?212>5.;./282>7.>2?A9@.; 4.D.D.;4?29.9A:2;A7A@6@6882?2@6:/.;4.;.D. @2>?2/A@16;.:.8.;.&#*"  .D.=2:A965=.1.=24.? H!. .D.=2:A965=.1..DA;.;?212>5.;. 0#?6;  &2>6<1242>.85.>:<;68=.1.=24.?16;D.@.8.;    # ! &2>6<12 .DA;.; /.;1A9 ?212>5.;. 16;D.@.8.; 12;4.;=2>?.:..;     ;2>46 :28.;68 =.1. ?2/A.5 42>.8 5.>:<;68 ?212>5.;.?29.9A@2@.=1.;@61.8/2>4.;@A;4=.1. ?6:=.;4.;42>.8 #    #   2 A8A: "2=92> 3 8<;?@.; ' 12;4.;=2>6<12'7.>.8.;@.>.=9.;2@1.; #.@.5.>6 Gaya 61 Peta Konsep 1 :2:/.5.? .D.2?28 .D.>.B6@.?6 .D.(2;@>6=2@.9 @2>/.46 .@.? 16 .;@.>.;D. =.1. .D.2?28 "6;2@68 .D.2?28 (@.@6? >.B6@.?6 *;6B2>?.9 "29.7A.;%>/6@ (.@296@ &2>02=.@.; >.B6@.?6 9.?@6?6@.? =.1.&24.? 2>.8.>:<;68 (212>5.;. :2;44A;.8.; =.1. A8A:<<82 &24.?1.;.;1A9 :2;0.>6 :2:69686 /2>9.8A &2>6<12 %>/6@(.@296@ A8A:"2828.9.; ;2>46#28.;68 "<;?@.;@.=24.? .D.=2:A965 &2>6<12 ;2>46 Refleksi 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. 62 Mudah dan Aktif Belajar Fisika untuk Kelas XI 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. Tes Kompetensi Bab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kg . / 0 1 2      A B 1 kg  !68.7.>67.>6A:61.;/2>.@/2;1.16=2>:A8..; A:6,/2>.@/2;1.@2>?2/A@=.1.82@6;446.;1.>6 =2>:A8..;A:6.1.9.5 . , / , 0 , 1  , 2  ,  !68.:.??.A9.; 8.96:.??.A:61.;7.>67.>6A9.;  8.967.>67.>6A:6=2>/.;16;4.;4.D.@.>68A:6  @2>5.1.=A9.;.1.9.5 .  /  0  1    2   Gaya 63  !68.=2>/.;16;4.;7.>67.>6A:61685.@A96?@6C.1.;16 8A@A/=2>/.;16;4.;=2>02=.@.;4>.B6@.?6A:6 1685.@A96?@6C.1.;168A@A/.1.9.5 .  2 / 2  0  1   2    !68.7.>67.>6A:6:21.;4>.B6@.?616=2>:A8..; A:6/2?.>;D.:21.;4>.B6@.?6=.1.82@6;446.; 1.>6=2>:A8..;A:6.1.9.5  .   /      0 1 2                 682@.5A6=2>/.;16;4.;7.>67.>6?2/A.5=9.;2@= 1.; 7.>67.>6 A:6   .1.9.5    ?21.;48.; =2>/.;16;4.;:.??.=9.;2@=1.;:.??.A:6 .1.9.5  !68./2>.@&A@A16A:6 $16=9.;2@ /2>.@&A@A:2;7.16 .  $ /  $ 0  $ 1  $ 2  $  !68.:21.;4>.B6@.?616=2>:A8..;A:6:?  /2?.>;D. :21.; 4>.B6@.?6 =.1. 82@6;446.;  1.>6 =2>:A8..;A:6.1.9.57.>67.>6A:6 . ;<9 /  :? 0  :? 1 :? 2 :?  (D.:?A9D.;4/2>:.??. 8416@6:/.;41.9.:?2/A.5 963@!.>A:@6:/.;4.;:2;A;7A88.;.;48.  ;2C@<; !68.=2>02=.@.;4>.B6@.?6A:6 :? 1.=.@16?6:=A98.; /.5C. . 963@?21.;4/2>42>.882.@.?12;4.;8202=.@.; @2@.= / 963@?21.;4/2>42>.882/.C.512;4.;8202=.@.; @2@.= 0 963@?21.;4/2>42>.882.@.?12;4.;=2>02=.@.; @2@.= 64 Mudah dan Aktif Belajar Fisika untuk Kelas XI 1 963@?21.;4/2>42>.882/.C.512;4.;=2>02=.@.; @2@.= 2 963@?21.;4/2>42>.882/.C.512;4.;=2>02=.@.; /2>A/.5  2;1.29.?@6?.1.9.5/2;1.D.;4768.1682;.64.D. . :A1.5=.@.5 / :2:69686/2;@A8D.;4/.>A 0 1.=.@82:/.9682/2;@A8?2:A9.768.4.D.16 569.;48.; 1 /2>@.:/.5=.;7.;4 2 /2;@A8;D.@61.8/2>A/.5  #2;A>A@A8A:<<82=2>@.:/.5.;=.;7.;4?2/A.5 /.@.;4D.;416@.>68<925?A.@A4.D. . /2>/.;16;49A>A?12;4.;/2?.>4.D.@.>68 / /2>/.;16;49A>A?12;4.;9A.?=2;.:=.;4/.@.;4 0 /2>/.;16;4 @2>/.968 12;4.; :<1A9A? +?2/A@ 1 /2>/.;16;4@2>/.96812;4.;=.;7.;4:A9.:A9. 2 /2>/.;16;49A>A?12;4.;=.;7.;4:A9.:A9.  (2/A.5=24.?=.;7.;4.C.9;D.  9A.?=2;.:=.;4 1.;:<1A9A?+;D.8<;?@.;@.4.D. =24.?!D.;416:69686<925=24.?@2>?2/A@.1.9.5 .  / 0 1 2      !68. :<1A9A?DA/.5.;=.;7.;41.; 9A.?=2;.:=.;4 =2>?.:..;/2>68A@D.;4/2;.>.1.9.5  .    /    0   1   2    (2/A.5=24.?D.;4=.;7.;4;D. 0:@2>4.;@A;4@.;=. /2/.; "2:A16.; A7A;4 /.C.5 =24.? 164.;@A;46 /2/.; 4?256;44.=.;7.;4=24.?:2;7.16 0: !68./2/.;@2>?2/A@16@.>6882/.C.5?27.A50:1.; =2>02=.@.;4>.B6@.?6A:6 :? 2;2>46=<@2;?6.9 29.?@68=24.?.1.9.5 .  767.>6A:6 I 0:829.7A.;92=.??A.@A ><82@D.;4169A;0A>8.;B2>@68.91.>6=2>:A8..;A:6 .1.9.5 . 8:? /  8:? 0  8:? 1 8:? 2 8:?   0 ($+",.*1* ",%'/.%*%!"*#*."+.  &.1.?A?A;.;/2;1./2;1.?2=2>@6=.1.4.:/.>:.??. /2;1.1.;?.:.D.6@A84 A=  (2/A.5=24.?D.;4:2:69686=.;7.;4 0:164.;@A;4 ?20.>.B2>@68.9"2:A16.;:2;1.=.@8.;4.D.@.>68 $1.;=.;7.;4;D./2>@.:/.5 0:&.;7.;4=24.? 768.16@.>6812;4.;4.D. $.1.9.5 .  0: 1  0: /  0: 2 0: 0  0:  (2/A.5 =24.? 164.;@A;46 /2/.; /2>:.??.  4 82:A16.;16@.>68?256;44.:2:696863>28A2;?642>.8 5.>:<;6?=24.??2/2?.> E#.??./2;1.D.;45.>A? 16@.:/.58.; .4.> 3>28A2;?6 42>.8 5.>:<;6? =24.? :2;7.16 E.1.9.5 .  4 1 4 / 4 2  4 0 4  &.1.42>.85.>:<;68=24.?768.:.??./2/.;D.;4 164.;@A;4 =.1. A7A;4 /.C.5 =24.?  84 =2>6<12 42@.>.;;D. ?28<;!68.:.??./2/.;16@.:/.556;44. :2;7.16 84=2>6<1242@.>.;;D..1.9.5 ?28<; . / ?28<; 0 ?28<; 1 ?28<; 2 ?28<;    A./2;1.@2>?A?A;?2=2>@64.:/.> I g 5k II   B = 5 kg !68.8<236?62;4.D.42?2886;2@68.;@.>./2;1.1.; /61.;4:6>6;4 k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aya 65    66 #.??.=9.;2@+A=6@2>.1.9.5 I 841.;:.??. #.@.5.>6.1.9.5  I 84!68.7.>.8>.@.>.@. .;@.>.#.@.5.>61.;+A=6@2>.1.9.5I : 1.;I H $: 84@2;@A8.; . 4.D.4>.B6@.?6#.@.5.>6=.1.=9.;2@+A=6@2>1.; / 9.7A96;2.><>/6@=9.;2@+A=6@2> 2>.@*;616A:6.1.9.5 $!68.7.>67.>6A:6  I ::.??.A:6 I 841.; 8<;?@.;@.4>.B6@.?6I H $: 84 /2>.=. /2>.@*;61682@6;446.;1.>6=2>:A8..;A:6 #.??./A9.; :.??.A:61.;7.>67.>6A9.; 7.>6  7.>6A:6!68.=2>02=.@.;4>.B6@.?616=2>:A8..;A:6 :? @2;@A8.;=2>02=.@.;4>.B6@.?616=2>:A8..; A9.; Mudah dan Aktif Belajar Fisika untuk Kelas XI  (2/A.5/2;1./2>:.???.  8416@6:/.;412;4.; ;2>.0.=24.?=24.?.8.;:2;D6:=.;4?2/2?.>0: )2;@A8.;/2?.>8<;?@.;@.4.D.=24.?1.>6;2>.0.=24.? @2>?2/A@ :?   (2/A.5=24.?:2:696868<;?@.;@.=24.?! $: (..@/2/.;/2>:.??. 84164.;@A;48.;=.1.A7A;4 =24.?@2>;D.@.=2;7.;4=24.?:2;7.160:!68. =2>02=.@.;4>.B6@.?6 :? /2>.=.8.5=.;7.;4 =24.?:A9.:A9.  &.;7.;4 ?2/A.5 =24.? /2>@.:/.5  0: 768. .;.8 @6:/.;4.;/2>:.??. 84164.;@A;48.;=.1.A7A;4 ;D.!68. :? /2>.=.8.58<;?@.;@.=24.? @2>?2/A@ Bab 3 Sumber: Fundamentals of Physics, 2001 Pada saat atlet angkat besi mengangkat beban, sebetulnya ia sedang melakukan kerja pada beban yang disimpan sebagai energi potensial. Usaha, Energi, dan Daya Hasil yang harus Anda capai: menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik. Setelah mempelajari bab ini, Anda harus mampu: • • menganalisis hubungan antara usaha, perubahan energi dan hukum kekekalan energi mekanik; menerapkan hukum kekekalan energi mekanik untuk menganalisis gerak dalam kehidupan sehari-hari. >5A79 B1>71C 492DCD8;1> =1>DB91 41<1= =5<1;D;1> 1;C9E9C1B>H1 B581A9 81A9  1>H1; 1;C9E9C1B 1;C9E9C1B @A9=5A =1>DB91 H1>7 =5=2DCD8 ;1> 5>5A79 B5@5AC9 =5=1B1; =5>3D39 @1;191> 41> B521719 BD=25A @5>5A1>71> @141 =1<1= 81A9  ,5<19> 1;C9E9C1B @A9=5A 21>H1; 1;C9E9C1B <19>>H1H1>7=5=2DCD8;1>5>5A79491>C1A1>H1?<18A171 *14171=21A49 1C1B B5?A1>7 1C<5C B541>7 =5>71>7;1C 2521> H1>7 B1>71C 25A1C  C<5C C5AB52DC81ADB41@1C=5>7D;DA1@1;1891=1=@D1C1DC941;=5>71>7;1C 2521> C5AB52DC  ,5<1=1 @A?B5B <1C981> 1C<5C C5AB52DC 81ADB =5>789CD>7 25A1@121>H1;;1781ADB91;?>BD=B9BD@1H141<1=@5A91 41@1C =5>71>7;1C 2521> H1>7 499>79>;1> 1<1= 212 9>9 1;1> 492181B C5>C1>7 DB181 5>5A79 41H1 41> 8D2D>71> 1>C1A1 ;5C971>H1  %?>B5@ 9B9;1 C5>C1>7 DB181 5>5A79 41> 41H1 9>9 21>H1; B5;1<9 1@<9;1B9>H1 41<1= ;5894D@1> B581A9 81A9 A. Gaya Dapat Melakukan Usaha B. Energi dan Usaha C. Gaya Konservatif dan Hukum Kekekalan Energi Mekanik D. Daya 67 Tes Kompetensi Awal (%(.6//(/2(.$,$3+-104(2"4$*$0(3)+'$0$:$-(3,$-$0.$*41$.41$.%(3+-65'$.$/%6-6.$5+*$0 $5<1B;1>45>71>2181B1>41B5>49A9@5>75AC91>DB181  ,52DC;1> 3?>C?8 3?>C?8 @5>5A1@1> "D;D= 41>5>5A79 %5;5;1<1>>5A79H1>714149B5;9C1A>41  @1;18 @141 B52D18 2?<1 H1>7 1;1> 49C5>41>7  @1@5A25411>41H141>5>5A79 C5A41@1C5>5A79@?C5>B91< A. Gaya Dapat Melakukan Usaha 71A >41 <5298 =5=181=9 @5>75AC91> DB181 41<1= ;5894D@1> B581A9 81A9 @5<1:1A9 =1C5A9 25A9;DC 9>9 1. Pengertian Usaha F s Gambar 3.1 Togar melakukan usaha(W) dengan mentransfer energi melalui gaya dorong F sehingga mobil berpindah sejauh s. *141B11C49;5<1B>4125ADB18125<1:1A=1;B9=1<D>CD;=5=@5A?<58 >9<19C9>779 %5C9;125<1:1A>41=5>77D>1;1>C5>17141>@9;9A1> 1<1= ;5894D@1> B581A9 81A9 DB181 494569>9B9;1> B521719 @5;5A:11> H1>7 49<1;D;1> D>CD; =5=@5A?<58 CD:D1> H1>7 499>79>;1>  '5>DADC >41 1@1;18@5>75AC91>DB18141<1=69B9;1B1=145>71>@5>75AC91>DB18141<1= ;5894D@1> B581A9 81A9 C5AB52DC .B181 41<1= 69B9;1 B5<171> 45>71> CA1>B65A 5>5A79 41> 71H1  ,9=1;<18 3?>C?8 25A9;DC  ,52D18 =?29< =?7?;494?A?>7?<58-?71A45>71>71H1B589>771=?29<25A@9>418C5=@1C B5:1D8 4 41A9 @?B9B9 1F1<>H1  %5C9;1 -?71A =5>4?A?>7 =?29< C5AB52DC B589>771=?29<25A75A1;-?71A=5<1;D;1>DB181H19CD=5>CA1>B65A5>5A79 =5<17 @141 =?29< B589>771 =?29< 25A75A1; 41> 25A@9>418 B5:1D8 4  5B1A DB181  H1>7 49<1;D;1> -?71A D>CD; =5>4?A?>7 =?29< ?<5871H1B1=145>71>81B9<;1<971H1 45>71>@5A@9>4181> 4   4 %5C5A1>71>   DB181 :?D<5  71H1( 4  @5A@9>4181> = .B181 141<18 25B1A1> B;1<1A F1<1D@D> 71H1  41> @5A@9>4181> 4 =5AD@1;1> E5;C?A  '5>DADC @5A;1<91> E5;C?A   81B9<>H1 81ADB 25AD@1 B;1<1A .B181H1>749<1;D;1>?<5871H1;?>BC1>H1>7=5=25>CD;BD4DC  C5A8141@1A18@5A@9>4181>25>41B5@5AC9C5A<981C@141 $/%$3   25B1A DB181>H1 141<18 arah perpindahan F  s 1 F sin   ,3?B  F  2 F cos  Gambar 3.2 (a) Usaha oleh gaya F yang membentuk sudut  terhadap perpindahan benda s. (b) Penguraian vektor F menjadi komponen-komponennya. K /5;C?A  41@1C 49DA19;1> =5>:149 4D1 ;?=@?>5> 71H1 H1>7 B1<9>7 C571;5>3?B H1>7B51A1845>71>1A18@5A@9>4181> 25>41 41>  B9>  H1>7 C571; 71> 1A18 @5A@9>4181>  -5A>H1C1 81>H1;?=@?>5>71H1H1>7B51A1845>71>@5A@9>4181>H1>7=5>781B9<;1> DB181 H19CD B525B1A  , 3?B  5A9;DC 9>9 2525A1@1 ;51411> 9BC9=5F1 H1>7 4981B9<;1> (34$/$$0  ;  1   J .>CD;   J 1A1871H1B51A1845>71>1A18@5A@9>4181>B589>771 49@5A?<58  , 3?B J  , 68 K  Mudah dan Aktif Belajar Fisika untuk Kelas XI K 2 3   J .>CD;     J 1A18 71H1  C571; 71> 1A18 @5A@9>4181> B589>771 49@5A?<58  ,3?B J   K $9;1    25A1AC9 71H1 C5AB52DC C941; =5<1;D;1> DB181  5>71> ;1C1 <19> 71H1 H1>7 C571; 71> 1A18 @5A@9>4181> 25>41 1AC9>H1 71H1 C5AB52DC C941; =5<1;D;1> DB181    J %51411> 9>9 =5>H1C1;1> 218F1 1A18 71H1 25A<1F1>1> 45>71> 1A18 @5A@9>4181> B589>771 49@5A?<58  ,3?B  J  ,K   4, K ?>C?8 DB181 >571C96 H19CD B5?A1>7 @5>75>41A1 B5@541 H1>7 B541>7 =5=13D B5@541>H1 C921 C921 =5>75A5= B5@541>H1  .B181 H1>7 49<1;D;1> ?<58 71H1 75B5; H1>7 C5A:149 1>C1A1 ;54D1 21> B5@541 45>71> :1<1> 25A>9<19 >571C96 ;1A5>1 71H1 75B5; 25A<1F1>1> 1A18 45>71> 1A18 @5A@9>4181> B5@541  5B1A>H1 DB181 >571C96 C5AB52DC B521>49>745>71>71H175B5;41>@5A@9>4181>H1>749C5=@D8B5@541 B5<1=171H175B5;25;5A:1 5>71>45=9;91>B5@541=5>71<1=975A1; 49@5A<1=21C 4 *5A@9>4181>25>41,   *141 $/%$3   14<9 B541>7 25A49A9 B1=29< =5>775>4?>7 C1B  -1B C5AB52DC =5=9<9;9 71H1 25A1C B525B1A 0 45>71> 1A18 ;5 21F18  5B1A 71H1 C1A9; C1<9 C1B ?<58 @D>77D>7 14<9  B1=1 45>71> 25B1A 71H1 25A1C C1B 8 B589>771 C1B 41<1= ;51411> B5C9=21>7  !1H1 A51;B9 ;5 1C1B?<58@D>77D>7 14<9@141C1<9C1BC5AB52DCC941;4989CD>7B521719 DB181;1A5>1C941;141@5A@9>4181>@141C1B1;921C71H1A51;B9 1A9 (34$/$$0  ;  4941@1C;1> 218F1  , 3?B    3?B    ?>C?8<19>141<18B5?A1>71>1;H1>725AB1>41A@14149>49>7$/%$3    9>49>7 C941; 25A75B5A ;1A5>1 71H1 H1>7 49<1;D;1>>H1 C941; 3D;D@ ;D1C D>CD; =5>775B5A 49>49>7  5>71> 45=9;91> DB181 H1>7 49<1;D;1> ?<58 71H1 4?A?>7>H1 B1=1 45>71> >?< *5A41 ;5C18D9 B1CD1> DB181 141<18 :?D<5 49B9>7;1C $ -. $).& # #(#,#%( ,!# ,+ .," 2(! #&%.%( )&" !2 ,,+ ,-. (0-)(.(-.%''#("%((,$.",-.'-+ Contoh 3.1 F w Gambar 3.3 Fadli sedang menggendong tas. F Gambar 3.4 Seorang anak sedang bersandar pada dinding. ,52D1871H1C5C1@B525B1A(25;5A:1@141B52D1825>41H1>725A=1BB1;7 $9;1 BD4DCH1>74925>CD;1>C1A171H141>2941>741C1A141<18J25A1@1DB181H1>7 49<1;D;1>71H19CDC5A8141@25>41B5<1=145C9; F $8$% 9;5C18D9 (';7 J  ), ' F cos  (3?B     3?B   = B s ;7 ' Usaha, Energi, dan Daya 69 1 1 ,  - = BB = 2 2  ,3?B  ( =  $ $149DB181H1>749<1;D;1>71H1141<18 :?D<5 Contoh 3.2 Tokoh James Prescott Joule (1824–1907) Sumber: Jendela Iptek, 1997 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. 70 ,52D1825>4125A=1BB1;7C5A<5C1;491C1B2941>741C1A;1B1A45>71>;?569B95> 75B5;;9>5C9;  5>41C5AB52DC49C1A9;B5:1D8=5C5A45>71><1:DC5C1@ 5A1@1;18 DB181H1>74981B9<;1>?<5871H1C1A9;C5AB52DC:9;1C1A9;1>>H1B5:1:1A45>71><1>C19 49;5C18D9! = B N $8$% 9;5C18D9 ';7 , = F fk     = B ; w 5B1A>H1DB181?<5871H1C1A9;141<18 s  4 3?B  , )<58;1A5>1  3=1;125B1ADB181141<18  , 5B1A71H1=1B98251<1:D25>41C5C1@=1;125B1AA5BD71H1   14 % @141BD=2D-1 41> 240 @141BD=2D-2 B589>771 3?B J4  %      B9> J40     ,D2BC9CDB9;1> ;549@5A?<58 4  % 0     % '!   ;7 = B ( =1;1 ,  (=$ $149DB181H1>749<1;D;1>71H1C5AB52DC141<18$ Contoh 3.3 '1BB1B5?A1>7@5>75>41A1=?C?A41>B5@541=?C?A>H1141<18 ;7 ,5@541=?C?A 9>9=53DA45>71>;5<1:D1> = B %5=D491>=?C?A49A5=89>77125A85>C9B5C5<18 45C9; -5>CD;1>DB181H1>749<1;D;1>B5<1=1@5>75A5=1>25A<1>7BD>7 $8$% 9;5C18D9 ' ;7/  = B-45C9; ,5@541=?C?A25A85>C9/C  / C /   = BB  K= B , / - -   = BB K= BB =K  =  =   , ;1A5>11A1871H1B5:1:1A45>71>@5A@9>4181>25>41  ',  ;7K= B  BK  $ $149DB181H1>749<1;D;1>B5<1=1@5>75A5=1>141<18K  ;$ Mudah dan Aktif Belajar Fisika untuk Kelas XI F 2. Menentukan Usaha dari Grafik Gaya Terhadap Perpindahan *141DA191>B525H171H1H1>7497D>1;1>25A>9<19;?>BC1>D>CD; =5>781B9<;1> DB181 @141 25>41 H1>7 25A@9>418 B5:1D8 , $9;1>41=5=2D1C7A169;CC5A8141@,@5A@9>4181>@14171H1 ;?>BC1>  >41 1;1> =5=@5A?<58 7A169; B5@5AC9 @141 $/%$3  5A41B1A;1>7A169;C5AB52DC25B1ADB181H1>74981B9<;1>?<5871H1;?>BC1> B589>77125>4125A@9>418B5:1D8  4B1=145>71>CD; DB181 H1>7 4981B9<;1> 71H1  H1>7 25B1A>H1 25AD218 D218 1;1> 4941@1C;1> B52D18 7A169; B5@5AC9 @141 $/%$3   &D1B 415A18 H1>7 491AB9A 25A141 49 1>C1A1 71A9B BD=2D , 41> 71A9B BD=2D  .B181C?C1<H1>7C5A:149@141$/%$3  =5AD@1;1>@5>:D=<181> B5C91@ DB181 41A9 ,  B1=@19 45>71> ,  $149 41@1C 49CD<9B;1> F=s F(t) s s1 s s2 Gambar 3.5 Pada besar F konstan, W = luas daerah di bawah kurva F(t). F ,  -)-&    , K s1 , *5>45;1C1> C5A219; 141<18 45>71> 31A1 =5=@5A;539<  ,  B1=@19 =5>45;1C9>?<1C1D <9= )<58;1A5>19CDB531A1=1C5=1C9B(34$/$$0 ,   ; =5>:149 , -)-&  <9=   , , , ,  , Gambar 3.6 Grafik gaya (F) terhadap perpindahan (s) dengan gaya (F) tidak konstan atau berubahubah. F  s2 s1 Fds , K , AC99>C57A1<@141(34$/$$0 ;141<187491AB9A 491>C1A1;DAE125B1A71H141>25B1A@5A@9>4181> , s1 s2 Gambar 3.7 Contoh 3.4 ,5@?C?>7 217 =1BB1>H1  ;7 C5A<5C1;491C1B2941>741C1A %5=D491> 2171<1=975A1;749B5212;1>?<5871H1H1>725B1A>H1 25AD218 D218C5A8141@;54D4D;1>21CD;1>C?C1< DB181 H1>7 49<1;D;1> 71H1 @141 2177125A@9>418B5:1D8= $8$%  CD; 1141<18 C?C1<  !      K $ $ s K , <9=   ,     , 1C1D s2 s Kata Kunci • usaha negatif • usaha nol • usaha positif Usaha, Energi, dan Daya 71 s Tes Kompetensi Subbab A (3,$-$0.$*'$.$/%6-6.$5+*$0    ,5?A1>7B9BF1=5>4?A?>7B52D18=5:145>71>71H1   (  5A1@1;18 DB181 H1>7 49<1;D;1> ?<58 71H1 4?A?>7171A=5:125A@9>418B5:1D8= 5A1@1;18DB181H1>749<1;D;1>D>CD;=5>71>7;1C B52D18=5B9>C9;H1>7=1BB1>H1;789>771;5C9>7791> =!= B ,52D1825>41H1>7=1BB1>H1;7=53DA45>71> ;535@1C1> = B )<58;1A5>1141@5>71AD871H1 75B5;1>C1A1<1>C1941>25>4125>4125A85>C9B5C5<18 25A75A1;45C9; -5>CD;1>DB181H1>749<1;D;1>?<58 71H175B5;@14125>41C5AB52DC ,52D18 25>41 25A=1BB1  ;7 49C1A9; ;5 1C1B @141 2941>7=9A9>7;1B1A?<5871H1 (B51A1845>71> 2941>7 ,D4DC;5=9A9>71>2941>7C5A8141@8?A9I?>C1<   141<18    C1>    B589>771 25>41 25A@9>418    B5:1D8  =  $9;1 ;?569B95> 75B5;1> 1>C1A1 25>41  45>71>2941>7 41> C1>   89CD>7<18DB181  H1>749<1;D;1>?<5871H125A1C41>71H175B5;;9>5C9; ,52D18 71H1  H1>7 25AD218 D218 25;5A:1 @141 B52D1825>41B589>77125>41=5>71<1=9@5AD2181> B5@5AC97A169;@14171=21A25A9;DC 4 F (N) 6 7 8 2 x (cm) 4 –4 "9CD>7 DB181 H1>7 49<1;D;1> ?<58 71H1  @141 25>41D>CD;:1A1;B5:1D8= B. Energi dan Usaha *5A>18;18>41=5<981CB55;?A;D41H1>7B541>7=5>1A9;75A?21; H1>7@5>D845>71>=D1C1>%5C9;1;D41B541>7=5>1A9;75A?21;41<1= F1;CD H1>7 3D;D@ <1=1 291B1>H1 >1@1B ;D41 C5A<981C C5AB5>71< B5>71< '5>71@1 45=9;91> %D41 C5AB52DC C5<18 =5>75 5>5A79 H1>7 49 7D>1;1> D>CD; =5<1;D;1> DB181  5>71> 45=9;91> (+!# &" ,.-. %''*.( .(-.% '&%.%( .," 1. Energi Kinetik dan Teori Usaha-Energi -5<18>41@5<1:1A9@141BD2212B525H1218F1DB18141@1CC5A:149 @14171H1;?>BC1>1C1D71H1H1>725AD218 D218%54D1:5>9BDB181C5AB52DC =5=9<9;9 ;5B1=11> H19CD 141>H1 71H1 H1>7 25;5A:1 @141 25>41 B589>771 25>41 25A75A1; <1:D>H1 ;?>BC1> 1C1D =5=9<9;9 @5A35@1C1> ,5;1A1>7 1;1> 492181B ;51411> 45>71> A5BD 71H1  ;?>BC1> !1H1 C5AB52DC 25;5A:1 @141 25>41 25A=1BB1 ' 41> 1;1> =5>781B9<;1> @5A35@1C1>   '5>DADC "D;D= ## (5FC?> 25B1A @5A35@1C1> C5AB52DC  141<18    41@D> @5AB1=11> 25B1A @5A@9>4181>>H1 141<18 '   , /-  /  .B181 H1>7 49<1;D;1> ?<58 71H1 C5AB52DC 141<18  ,',     ' /-  /         '/-   '/ 72 Mudah dan Aktif Belajar Fisika untuk Kelas XI K >41 C5<18 =5>75C18D9 218F1 DB181 141<18 @A?B5B CA1>B65A 5>5A79 =5<1771 25>41 25A75A1;  %5C9;1 25>41 25A75A1; 25>41 =5=9<9;9 ;535@1C1> 41> =5>781B9<;1> 5>5A79 ;9>5C9;  5A41B1A;1> (34$/$$0  ; 5>5A79 ;9>5C9; 25>41 49>H1C1;1> 45>71> % '/  K  V0 %5C5A1>71> %  5>5A79 ;9>5C9; $ '  =1BB1 25>41 ;7 /  ;5<1:D1> 25>41 = B 5>71> 45=9;91> Vt F ; 4; K  $149DB181H1>74981B9<;1>71H1A5BD@141@1AC9;5<C5AB52DCB1=1 45>71> @5AD2181> 5>5A79 ;9>5C9; @1AC9;5< A   ; Gambar 3.8 K  (34$/$$0  ;  49;5>1< 45>71> C5?A5=1 DB181 5>5A79 D>CD; @1AC9;5< Contoh 3.5 ,52D18;5<5A5>725A=1BB1 7 )<58;1A5>1@5>71AD871H1;5<5A5>725A75A1;45>71> ;5<1:D1>C5C1@ 3= B -5>CD;1>5>5A79H1>749=9<9;9;5<5A5>7C5AB52DC $8$% 9;5C18D9 'N K;7 / 3= B = B % '/ N K;7 = B    N K$ $1495>5A79;9>5C9;H1>749=9<9;9;5<5A5>7141<18 N K$ B s Besar usaha yang dilakukan oleh pengemudi becak sama dengan besar gaya yang bekerja pada becak dikalikan dengan besar perpindahannya. 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? Contoh 3.6 *1;D25A=1BB17C5A<5@1B41A9C1>71>B5?A1>7CD;1>7;1HD %5C9;1@1;D=5>H5>CD8 C1>18 ;5<1:D1>>H1   = B  $9;1 71H1 75B5; @1;D C5A8141@ C1>18 B525B1A  ( 89CD>7<18;541<1=1>@1;DH1>7=5>1>31@41<1=C1>18 $8$% F 9;5C18D9 ' 7 /  = B  ( s    m /22  /12  , K N K;7 K = B  ,  ,   = $149;541<1=1>@1;DH1>7=5>1>31@41<1=C1>18141<18  =   Usaha, Energi, dan Daya 73 2. Energi Potensial (+!# *)-(,#& &" (+!# 2(! -+,#'*( * ,.-. ( %#(-.%(2&-%(2-.%((2($#%%(''.(!%#(%((+!# -+,.-*-#'.(.&%( ?>C?8>H1C1<92DBDAH1>7B541>749C571>7;1> *141 ;51411> 9>9 C1<9 2DBDA =5=9<9;9 5>5A79 @?C5>B91<  $9;1 C1<9 2DBDA 49<5@1B;1> 1>1; @1>18 41@1C C5A<5=@1A 45>71> :1A1; C5AC5>CD  579CD :D71@141;1C1@5< >5A79@?C5>B91<=D>3D<;5C9;1;1A5C;1C1@5<49C571>7 ;1> ;5=D491> 89<1>7 ;5C9;1 ;1A5C ;1C1@5< 49<5@1B;1>  5>CD; 5>5A79 @?C5>B91< <19> H1>7 C5A41@1C 49 1<1= 141<18 5>5A79 @?C5>B91< 7A1E9C1B9 41> 5>5A79 @?C5>B91< @571B Gambar 3.9 Menegangkan tali panah dan katapel memunculkan energi potensial. F h mg Gambar 3.10 Usaha yang dibutuhkan Pak Simbolon untuk mengangkat ikan setinggi h adalah W = mgh. y2 s h Ftangan= mg Energi Potensial Gravitasi >5A79 C941; 41@1C 4939@C1;1> 41> C941; 41@1C 49=DB>18;1> C5C1@9 41@1C 25AD218 41A9 BD1CD 25>CD; =5>:149 25>CD; H1>7 <19>  5=9;91> :D71 5>5A79 @?C5>B91< 7A1E9C1B9 H1>7 B5A9>7 49C5=D;1> 41<1= ;5894D@1> B581A9 81A9 *5A81C9;1> 3?>C?8 25A9;DC  ,52D18 21CD ;5A9;9< 49<5=@1A;1> B531A1 E5AC9;1<  >5A79 @?C5>B91< C5A25B1A H1>7 49=9<9;9 21CD 141<18 ;5C9;1 21CD =5>31@19 ;5C9>7791> =1;B9=D=  ?>C?8 <19> B52D18 @5>B9< H1>7 C5A<5C1; 49 1C1B =5:1 =5=9<9;9 5>5A79 @?C5>B91< 7A1E9C1B9 H1>7 25B1A>H1 B521>49>7 45>71> =1BB1 41> C5=@1C ;54D4D;1> @5>B9< C5A8141@ <1>C19  %5C9;1 @5>B9< >41B5>CD841>>41291A;1>:1CD8;5<1>C1971H125A1C@5>B9<=5<1;D;1> DB181 B589>771 @5>B9< 25A@9>418 @?B9B9>H1 41A9 1C1B =5:1 ;5 <1>C19 5B1A 5>5A79 @?C5>B91< 7A1E9C1B9 H1>7 49=9<9;9 25>41 25>41 @141 3?>C?8 49 1C1B 25A71>CD>7 @141 ;54D4D;1> 25>41 C5AB52DC C5A8141@ 13D1> C5AC5>CD  *141 $/%$3  D>CD; =5>71>7;1C B55;?A 9;1> H1>7 25A1C>H10B5C9>779"DB181H1>749<1;D;1>*1;,9=2?141<18 " 1A18 71H1 B51A18 @5A@9>4181> 25>41 1C1D 49CD<9B  '!" *'!" y1 Gambar 3.11 Sebuah benda yang diangkat oleh gaya dorong Ftangan = mg dari posisi y1 ke y2. K  %5C5A1>71> '  =1BB1 25>41 ;7 !  25B1A @5A35@1C1> 7A1E9C1B9 = B "  C9>779 25>41 = 5>41H1>725A141@141;5C9>7791>"41A9C9C9;13D1>=5=9<9;95>5A79 @?C5>B91< D>CD; =5<1;D;1> DB181 B525B1A '!"  $149 25>41 =5=9<9;9 @?C5>B91< 7A1E9C1B9 H1>7 25B1A>H1 ' Fgravitasi=mg 74 a. K   6%60)$0$05$3$(0(3)+215(04+$.)3$7+5$4+'$064$*$ *5A81C9;1>$/%$3  A18E5AC9;1<;51C1BBD=2D-249C5C1@;1> B521719 1A18 @?B9C96 B541>7;1> 71H1 7A1E9C1B9 25A1A18 ;5 BD=2D-2 >571C96 ;5 21F18 %5C9;1 ;5 1C1B C1>71> C1>71>4  '!"  '!2  4 2  Mudah dan Aktif Belajar Fisika untuk Kelas XI .B181C5AB52DC494569>9B9;1>B521719@5AD2181>5>5A795;BC5A>1<C1>71> * 5;B  *5;B *4* 5;B' !2 42  K  ,11C ;5 21F18 7A1E9C1B9  7A1E9C1B9  '!2  4 2  4' !" .B181C5AB52DC494569>9B9;1>B521719@5AD2181>5>5A79@?C5>B91<7A1E9C1B9   * 7A1E  *7A1E *4* 47A1E' !2  42  K  >5A79 @?C5>B91< 7A1E9C1B9 @141 C9C9; 2 41A9 C9C9; 13D1> C5AC5>CD 2   49>H1C1;1> 45>71> @5AB1=11> * ' !21C1D* ' !" K  45>71> " =5AD@1;1> C9>779 25>41 C5A8141@ <1>C19  "4$*$:$0)'+.$-6-$01.(*)$:$2$'$%(0'$2$'$-(5+0))+$0 *5A81C9;1>$/%$3  $41>$/%$3  %  1A9441>,1=D5< B541>7 =5=9>418;1> 217 25A=1BB1 B1=1 ;5 ;5C9>7791> "  1A94 =5=9>418;1> 2177D>1;1> 2941>7 =9A9>7 B541>7;1> ,1=D5< =5=9>418;1> 2177D>1;1> ;1CA?<  '5>DADC >41 B1=1;18 DB181 H1>7 49<1;D;1> 1A94 41> ,1=D5< C5A8141@ 21:1>7 <9>C1B1> H1>7 49C5=@D8  , =5=25>CD;BD4DC  C5A8141@2941>78?A9I?>C1< 5>71>45=9;91>DB181 @141 <9>C1B1> =9A9>7  H1>7 49<1;D;1> 1A94 141<18  O4 '!,B9>  N F sin h mg A  s 1 h K  41@D> DB181 H1>7 49<1;D;1> ,1=D5< D>CD; =5=9>418;1> 217791> " =5>781B9<;1> <9>C1B1> E5AC9;1< B5@1>:1>7 "  5>71> 45=9;91> DB181 H1>7 49<1;D;1> ,1=D5< 141<18 " '!" K  5A41B1A;1>;54D13?>C?8C5AB52DC41@1C49B9=@D<;1>218F1DB181 H1>7 49<1;D;1> 25>41 25A71>CD>7 @141 ;5C9>7791> H1>7 4931@19 C941; 25A71>CD>7 @141 31A1 @5>71>7;1C1> 25>41 C5AB52DC 1C1D <9>C1B1> H1>7 49C5=@D8 B5<1=1 @5>71>7;1C1>  B "  '!   B9>  B9>   '!" g =m mg 2 Gambar 3.12 (a) Farid memindahkan balok ke ketinggian h menggunakan bidang miring, sedangkan (b) Samuel menggunakan katrol dengan lintasan vertikal. Samakah usaha yang dilakukan keduanya? Contoh 3.7 1CD25A=1BB1;7:1CD82521B41A9;5C9>7791> =491C1BC1>18 -5>CD;1>@5AD2181> 5>5A79@?C5>B91<41>DB181H1>749<1;D;1>71H125A1C21CDC5AB52DC@141B11C=5>31@19 ;5C9>7791>=491C1BC1>18 $8$% 9;5C18D9 ' ;7"  ="= Usaha, Energi, dan Daya 75 Tantangan 1 untuk Anda 2 *5AD2181>5>5A79@?C5>B91< E p '!"K";7 = B=K =K $ $149@5AD2181>5>5A79@?C5>B91<B525B1A :?D<5 .B181H1>749<1;D;1>71H125A1C K'!"K"K;7 = B=K = $ .B181@?B9C96;1A5>11A1871H125A1CB51A1845>71>1A18@5A@9>4181> $149DB181H1>749<1;D;1>71H125A1CB525B1A :?D<5 Contoh 3.8 Sumber: Fisika untuk Sains dan Teknik, 1998 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? 5A1@1;18 5>5A79 @?C5>B91< H1>7 49=9<9;9 ?<58   = 19A H1>7 25A141 @141 ;5C9>7791> =:9;1=1BB1:5>9B19A ;7 =41>@5A35@1C1>7A1E9C1B949C5=@1C C5AB52DC = B $8$% 9AC5A:D>C5AB52DC=5=9<9;9=1BB1 '   ;7 = =N ;7 >5A79@?C5>B91<H1>749=9<9;919AC5A:D>141<18  * '!" N ;7 = B =N $ $1495>5A79@?C5>B91<H1>749=9<9;919AC5A:D>141<18N :?D<5 b. Energi Potensial Elastis Pegas 1 2 3 y2' y1=0 y2 >5A79 @?C5>B91< 5<1BC9B @571B 25A2541 45>71> 5>5A79 @?C5>B91< @141 D=D=>H1 >5A79@?C5>B91<@571B141<185>5A79H1>749=9<9;9@571B1;921C 141>H1@5AD2181>@1>:1>71C1DA571>71>@571B !1H1H1>725;5A:1@141 @571B =5=D>7;9>;1> @571B D>CD; =5A571>7 *5A81C9;1>$/%$3  *141$/%$3  $=D<1 =D<1@571B41<1= ;51411>B5C9=21>7 >5A79 @?C5>B91< @571B 41> 5>5A79 ;9>5C9;>H1 >?<  *141 $/%$3  %41>$/%$3  &@571B=5=9<9;9B9=@1>71>B5:1D82 41> 2  @1>:1>7 2  2   )<58 ;1A5>1 141 C1A9;1> B525B1A   %2 41> @571B =5>1A9; ;5=21<9 25>41 B5BD19 "D;D= ### (5FC?> @571B K% 5B1A>H1DB181H1>749<1;D;1>@571B41A9;51411>2  ;522B1=1 25B1A45>71>@5AD2181>5>5A79@?C5>B91<@571B1>C1A12  41>22 ,25B1A@5A@9>4181>@?B9B925>41   @571B  4 2  2    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.  2 2 2      %2  2   %2  5>71> 45=9;91> 25B1A>H1 DB181 H1>7 49<1;D;1> ?<58 71H1 @571B 49>H1C1;1> 45>71> @5AB1=11>  @571B @ @571B @@571B %2 K   %5C9;1 @571B 49<5@1B;1> @571B 1;1> =5<1;D;1> 75A1; 81A=?>9; ,5<1=1 @5A75A1;1>>H1 @571B =5>71<1=9 @5AD2181> 5>5A79 ;9>5C9; =5>:149 5>5A79 @?C5>B91< @571B 1C1D B521<9;>H1  -941; B5<1=1>H1 @571B =5<1;D;1> 75A1; 81A=?>9; @5>71AD8 71H1  =5=2D1C @571B 25A85>C9 @141 @?B9B9 ;5B5C9=21>71> 45>71> 76 Mudah dan Aktif Belajar Fisika untuk Kelas XI Contoh 3.9 *571B25AC1=218@1>:1>7 3=;5C9;14925A971H1 ( 5A1@1;185>5A79@?C5>B91< @571B:9;171H1@141@571BC5AB52DC49:149;1>;1<9<9@1C $8$% 9;5C18D9   (1  3=  = % F (   ( =  = 1 $9;1  ( ( 1 F  (   ( = = ( = % Kata Kunci * %1  ( = = $   $14925B1A5>5A79@?C5>B91<5<1BC9B@571B141<18 $ Tes Kompetensi Subbab • energi kinetik • energi potensial B (3,$-$0.$*'$.$/%6-6.$5+*$0   ,52D1821CD;539<25A=1BB1749<5@1B;1>41A9;1C1@5< B589>77125B1A5>5A79;9>5C9;H1>749=9<9;9>H1141<18  :?D<5 "9CD>7;5<1:D1>21CDC5AB52DC '?29< 25A=1BB1   ;7 B541>7 25A75A1; 45>71> ;535@1C1>;= :1=C921 C92149A5=41>25A85>C9 B5C5<18=5>5=@D8:1A1; = -5>CD;1><18 1 71H1A5=@141=?29<41> 2 DB181H1>749@5A?<5841A9@5>75A5=1> %5A5C1 =19>1> H1>7 =1BB1>H1  ;7 49<5@1B;1> 41A9 @D>31;2941>7=9A9>7<939>45>71>BD4DC;5=9A9>71>  JC5A8141@8?A9I?>C1< $9;1@1>:1>7<9>C1B1>2941>7 =9A9>7 =41>! = BC5>CD;1>@5AD2181>5>5A79 @?C5>B91<4941>;5A5C1B5C5<18=5>5=@D8:1A1; =   5>4125A=1BB1 ;749<5@1B;1>41A9;5C9>7791> 3= 1 "9CD>7<18DB181H1>749<1;D;1>71H17A1E9C1B9 @14125>41C5AB52DC 2 "9CD>7<1825A;DA1>7>H15>5A79@?C5>B91<7A1E9C1B9 25>41C5AB52DC 5>41'25A=1BB1 ;7:1CD8=5>775<9>39A41A91C1B 2941>7=9A9>745>71>BD4DC;5=9A9>71>J 5>41 C5AB52DC=5>D=2D;B52D18@571BH1>7C5A<5C1; = 41A9<5C1;'B5=D<1 $9;1% ( =41>@571B C5AC5;1>=1;B9=D=B5:1D8 3=89CD>7;?569B95> 75B5;1>C1A12171>2941>7=9A9>7 C. Gaya Konservatif dan Hukum Kekekalan Energi Mekanik *5A81C9;1> $/%$3  $  ,52D18 @571B 49<5C1;;1> 49 1C1B <1>C19 41> B1<18 B1CD D:D>7>H1 499;1C;1> @141 49>49>7  %5=D491> B52D18 213DA45>71>;535@1C1>C5@1C;51A18@571B $9;1<1>C19 41C1A41><939>B5AC1@571B>H19451<B9BC5=1;1>=5=5>D89"D;D="??;5   K% 9 45>71>  141<18 71H1 @141 @571B B11C D:D>7 2521B>H1 25A75B5A B5:1D8   %51411> H1>7 499>79>;1> @141 B9BC5= C5AB52DC 141<18 5>5A79 ;9>5C9;C5A@DB1C@141=1BB1217715>5A79;9>5C9;@571B491219;1> ;921C>H1 =1BB1 @571B 491>771@ B1>71C ;539< 41A9@141 =1BB1 21H5>CD8@571B<1:D217B1=@191;89A>H1 25A85>C9 ;1A5>1 71H1 @571B H1>7 =5<1F1> 71H1 4?A?>71> 41A9 21$/%$3  % %5=D491>1A1821H1 215A79 ;9>5C9;>H1 ;5=21<9 B5@5AC9 B11C 21H5>CD8 @571B F1<1D@D> 1A18>H1 25A2541  171> 5>5A79 ;9>5C9;>H1 @141 B1<18 B1CD 1A18 75A1;>H1 C5C1@9 =5=@5A?<58 5>5A79 ;9>5C9;>H1 ;5=21<9 @141 1A18 75A1; H1>7 <19> H19CD ;5C9;1 217 49<1;D;1> 71H1 @571B   % 9 C941;=5>7D2185>5A79=5;1>9;B9BC5=@571B !1H1H1>749<1;D;1>?<58 @571BC5AB52DC25AB961C;?>B5AE1C96 !1H17A1E9C1B9:D7125AB961C;?>B5AE1C96 41@1C;18>41=5>:5<1B;1>=5>71@171H17A1E9C1B925AB961C;?>B5AE1C96 1A9BD4DC@1>41>7H1>7<19>71H1;?>B5AE1C96:D71=5=9<9;939A9218F1 :D=<18DB181H1>749<1;D;1>71H1@141@1AC9;5<25>41491>771@B521719 @1AC9;5<141<18>?< *141;51411>B5C9=21>7@?B9B91 71H1@571B @ @141 3?>C?8 C5AB52DC 49>H1C1;1> 45>71> @5AB1=11> @ %9 -18D;18 >41 DB181 H1>7 49<1;D;1> ?<58 71H1 @571B C5AB52DC *5A81C9;1> ;5=21<9 $/%$3   ;5C9;1 25>41 25A@9>418 41A9 @?B9B9 H1>7=5=9<9;9B9=@1>71>1 ;5@?B9B945>71>B9=@1>71>125B1ADB181 H1>749<1;D;1>71H1@571BC5A8141@25>4149>H1C1;1>45>71>@5AB1=11>  K* 1  K%1 1  -1>41 >571C96 =5>H1C1;1> 218F1 1A18 71H1 @571B * 25A<1F1>1> 45>71> 1A18 @5A@9>4181> 1  *.( ,#'*(!( G *- #*+)&" +# (#&#+-+-+#,#'*(!(1 41>1 5>71> 45=9;91> @5AB1=11>  41@1C 49>H1C1;1> 45>71>   K%1 1 1 1    K%     1  1     %      1  1  1  1   %     1  1     5A41B1A;1> @5AB1=11>  :5<1B<18 218F1 DB181 H1>7 49<1;D;1> ?<58@571BC941;=5>7D2185>5A79=5;1>9;B9BC5=41>C941;25A71>CD>7 @141@?B9B91F1<41>@?B9B91;89A25>41H1>749;5>1971H1@571BC5AB52DC *5A81C9;1>$/%$3  ,52D18@5C949@9>418;1>;5C5=@1C<19> B5C9>779 " .B181 H1>7 49@5A D>CD; =5=9>418;1> @5C9 141<18  K'!"-1>41>571C96C9=2D<;1A5>11A1871H125A1C25A<1F1>1> 45>71> 1A18 75A1; @5C9 .B181 ;5C9;1 =5=9>418;1> @5C9 C941; 25A71>CD>7 @141 @1>:1>7 <9>C1B1>H1>749<1CD>7@14125B1A@5AD2181>C9>779 @5C941A9;54D4D;1>1;89A;5;54D4D;1>1F1<>H1 $9;1@5C949@9>418;1> <179;5@?B9B91F1<>H1DB181H1>749<1;D;1>>H1141<18'!" ,531A1 =1C5=1C9B DB181 C?C1< H1>7 49<1;D;1> D>CD; =5=9>418;1> @5C9 41A9 21F18 ;5 1C1B   <1418;1> <179 ;5 21F18  141<18 C?C   K'!"  '!"  5B1A DB181 @5=9>4181> B52D18 @5C9 41A9 ;54D4D;1> 1F1< 89>771 ;5=21<9 ;5 ;54D4D;1> 1;89A>H1 25A>9<19 >?<  $149 41@1C 49B9=@D<;1> 218F1 DB181 H1>7 49<1;D;1> ?<58 71H1 ;?>B5AE1C96 1;1> 25A>9<19 >?< :9;1 ;54D4D;1> 1;89A 25>41 ;5=21<9 ;5 ;54D4D;1> 1F1<>H1  Gambar 3.15 Seseorang sedang melakukan usaha memindahkan peti. Tugas Anda 3.2 Sebutkan contoh-contoh gaya konservatif yang ada di sekitar Anda. 78 K  Mudah dan Aktif Belajar Fisika untuk Kelas XI  1. Perumusan Hukum Kekekalan Energi Mekanik 1<1= =541> 7A1E9C1B9 :D=<18 5>5A79 @?C5>B91< 41> 5>5A79 ;9>5C9; BD1CD25>41C5C1@:9;181>H114171H17A1E9C1B9 *5A>H1C11>C5AB52DC49;5>1< B521719 "D;D= %5;5;1<1> >5A79 '5;1>9;  *5A81C9;1> $/%$3  ,52D18 25>41 25A=1BB1 ' :1CD8 2521B  *141 @?B9B9  ;5C9>7791>>H1 " C5A8141@ 13D1> <1>C19  ,5B11C ;5=D491> 25>41 25A141 @141 @?B9B9  45>71> ;5C9>7791> "  C5A8141@ 13D1>  9;1C1;1> 218F1 @141 25>41 C5A:149 @5>7DA1>71> 5>5A79 @?C5>B91< H1>7 25B1A>H1 B1=1 45>71> DB181 H1>7 49<1;D;1> 71H1 25A1C K K@ 4@  *141 @?B9B9  ;535@1C1> 25>41 /  ;5=D491> 25>41 CDAD> 89>771 @141 @?B9B9  45>71> ;535@1C1> /  *141 ;51411> C5AB52DC ;535@1C1> 25>41 25AC1=218 ;1A5>1 @5>71AD8 @5A35@1C1> 7A1E9C1B9 B589>771 DB181 H1>7 49<1;D;1> 25>41 B1=1 45>71> @5AD2181> 5>5A79 ;9>5C9; H19CD ; 4; v1 1 v2 2 h1 h2 mg Gambar 3.16 Balok dijatuhkan dari ketinggian tertentu. K 5A41B1A;1> (34$/$$0  ;  41> (34$/$$0  ;  49@5A?<58 @ K@;K; @ ; @; 1C1D K Contoh 3.10 ,52D182?<125A=1BB1'49<5=@1A;1>E5AC9;1<;51C1B45>71>;535@1C1>1F1<B525B1A  -5>CD;1> 1 C9>779=1;B9=D=H1>74931@1941> 2 ;535@1C1>;5C9;12?<1=5>31@19C9>779B5C5>718=1;B9=D= v2 = 0 $8$% Ek2 ; Ep2 h2 = h 1 * % *% '!"  '/  '!" '/    '/  '!" h  /   )<58;1A5>1/ / =1;1 '/ '!" " !  $149C9>779=1;B9=D=H1>74931@19141<18"  2 * % /  ! Ek1 ; Ep1 m h1 = 0 v1 = v0 *%    '/  '! " '%,  '/      '/  '!  /   '/       !   '/  ' /  '/     '/   '/    /   /  / /   $149;535@1C1>2?<1;5C9;1=5>31@19C9>779B5C5>718C9>779=1;B9=D=141<18 / /   Usaha, Energi, dan Daya 79 Contoh 3.11 ,52D1821CD25A=1BB1'C5A71>CD>7@141B5DC1BC1<9H1>7@1>:1>7>H1  4925A971H1 =5>41C1A 1CD=D<1925A75A1;45>71>;5<1:D1>1F1</ B5@5AC9@14171=21A;5C9;1 21CD=5>H9=@1>745>71>BD4DC  C9>779H1>74931@192?<141A9C9C9;B5C9=21>7>H1 141<18" -5>CD;1> 1 C9>779=1;B9=D=H1>74931@1921CD41> 2 25B1A;535@1C1>1F1<21CD/  $8$% 1 *%*%  '!" m / 2A '!" '/    2  m/0 '!"  h /  /  !"   "  v0 ! $149C9>779=1;B9=D=H1>74931@1921CD 2 3?B   "  "  K   3?B   Tugas Anda 3.3 Apakah Anda tahu olahraga bungee jumping? Selidikilah Hukum Kekekalan Energi yang bekerja saat orang melakukan bungee jumping. /  !   K   3?B   /  ! /  ! /   !    3?B   Contoh 3.12 1725A=1BB1;7=5>775<9>39A41A91C1BB52D182941>7=9A9>7H1>7BD4DC =9A9>7>H1 J 1=5>D=2D;@571BH1>7C5A<5C1;=41A9 @?B9B9B5=D<1 $9;1;?569B95>75B5;1>C1A12171>2941>7=9A9>7 25A1@1 =5C5A@571BC5AC5;1>9;5C18D9;?>BC1>C1@571B ( = $8$% .B181H1>749<1;D;1>71H1@571B141<18>571C96;1A5>1@571B=5<1F1>71H1C5;1> 21H1;5C9;1@571BC5AC5;1>@571B=5<1F1>71H1C5;1>B589>77171H1 @571B41>1A18@5A@9>4181>25A<1F1>1>1A18 *5A81C9;1>71=21A25A9;DC @571B %1K %   s 7A1E 4  * 4'!"3K"1 A b '!,B9> J ha  '!, B .B181?<5875B5;1>25A>9<19>571C96 hb ;1A5>11A18211> hc C 30° 45>71>1A1871H175B5; !,% 4 ;,    k '!3?B J,   '!,  ;  80 Mudah dan Aktif Belajar Fisika untuk Kelas XI '5AD:D;@A9>B9@5>5A7949;5C18D9218F1 -)-&  % B589>77149@5A?<58 *!,!+/!,%  '/ 4/   K %  '!,K 3 '!, k  ' K      Pembahasan Soal   k  4 , 3  k , K %  '!           >4141@1C=5>H5<5B19;1>@5AB1=11>;D14A1CC5AB52DC45>71>=5>789CD>741A9 ' ;7%  ( =, =  k  41>!  = B  N/m ;7   = B       3      4 =  =      =K      =4 =K=                  3 mv2 2 d. 1 mv2 2 b. mv 2 e. 1 mv2 4 c. 3 2 4 mv Pembahasan: hB = 2hA Berarti, EpB = 2 EpA Sesuai dengan Hukum Kekekalan Energi Mekanik maka EpB – EpA = EkA – EkB EkB = 2 EkA    a. Soal UMPTN Tahun 1989          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 ....      1  = 2 2 mv = mv2   K =C941;C5A@1;19    = $149@571BC5AC5;1>B5:1D8 = 2 Jawaban: b Contoh 3.13 ?<141@1C25A75A1;C1>@175B5;1>@141<9>C1B1>B5@5AC971=21A25A9;DC ,11C49C9C9; 2?<125A;535@1C1> 3= B 5A1@1<1:D49C9C9;41> A C 80 cm 50 cm B $8$% *141B9BC5=25A<1;D%5;5;1<1>>5A79'5;1>9;B589>771 1 '!" '/'!" '/    = B = = B  /   /  = B= B $149;5<1:D1>2?<149C9C9;141<18= B 2 '!" '/'!" '/    = B =   = B = B = /   / = B = B $149;5<1:D1>2?<149C9C9;141<18 = B Usaha, Energi, dan Daya 81 2. Analisis Gerak pada Roller Coaster A lintasan loop B Sumber: Dokumentasi Penerbit Gambar 3.17 Lintasan roller coaster. A C N c mg B Gambar 3.18 Lintasan roller coaster dengan loop berbentuk lingkaran. "1=@9AB5=D1C5;>?892DA1>B5@5AC9 #,(2( #,(2 )+&1C1DD>91 1>C1B9B1>71C;1H11;1>;?>B5@69B9;1 91>C1A1B5:D=<18 @5A=19>1> H1>7 141 +)&&+ ),-+ 1C1D H1>7 291B1 49B52DC 81<9<9>C1A 41@1C =5>4?A?>7>41D>CD;=5=181=9<529841<1=;?>B5@69B9;1C5>C1>775A1; *5A81C9;1> $/%$3   %5>41A11> C1>@1 =5B9> =5>77D>1;1> 21> 25A:1<1>)(/2)+&-D>CD;>19;;5@D>31;2D;9C=5<1C1B1>H1>7 C941; C5A<131; 2D;9C  B5>71:1 49A1>31>7 <5298 C9>779 41A9@141 @D>31; 7;9>;1> 5>5A79 @?C5>B91< ;5>41A11> 49  H1>7 <5298 25B1A B589>771 =1=@D 25A:1<1> =5<1C1B1> =5>D:D @D>31;  45>71> 219;  &9>C1B1> 71:1 492D1C B5@5AC9 C5C5B1> 19A C5A21<9; $9;17;1A1>@5>D81;1>49@5A?<582?2?C@5>D= @1>75>1=;1<92?2?C>?A=1<>H1B11C;5>41A11>49@?B9B9C5A5>418;?>49B9 9>9 41@1C =5>H5212;1> @DB9>7 <17B1>  &9>C1B1> 7 B5@5AC9 C5C5B1> 19A 81>H1 =5=25A9;1> 2?2?C =1;B9=D=  ;1<9 2?2?C >?A=1< >H1 @141 2?2?C C5AB52DC @5>D=@1>7 =1B98 =5A1B1;1> ;5>H1=1>1> %5C9;1+)&&+),-+25A14149C9C9;C5AC9>77941A9<9>C1B1>7>41<981C@141$/%$3 71H1B5>CA9@5C1<>H1 141<18 A5BD 41A9  71H1 C5;1> 41> 25B1A 71H1 25A1C @5>D=@1>7 '! B589>771 /  ,H1A1C ;5<1:D1> =9>9=1< 49 C9C9;  141<18    B589>771 49@5A?<58 B3'! ' '!  ' /  / Cmin  !+ %5C9;1 +)&&+ ),-+ 25A141 49 C9C9; C5A5>418 H19CD C9C9;  *  %* %3*3 '/ '!"  '/'!"     %1<9;1> ;54D1 AD1B @5AB1=11> C5AB52DC 45>71>  B589>771 49@5A?<58 ' !"/  !"/ )<58;1A5>1"  " 41>/  !=1;1 @5AB1=11> =5>:149 /  !! /=9>  ! K %5C9>7791> 1F1< =9>9=1< 3DA1> 49 C9C9;  41@1C >41 89CD>7 =5<15A1@1> "D;D= %5;5;1<1> >5A79 '5;1>9; 49 C9C9;  41>  171A +)&&+ ),-+ =1=@D =5<5F1C9 71> 1=1> 82 Mudah dan Aktif Belajar Fisika untuk Kelas XI Contoh 3.14 ,5@?C?>7213DA@141BD1CDC1<1>7<9>7;1A1>41<1=B5@5AC9 C5A<981C@14171=21A $9;171H175B5;1>C1A121C1<1>7491219;1> 1 25A1@1;18;5C9>7791>=9>9=D=21781ADB49<5@1B171A75A1;1>>H141@1C =5>31@19@D>31;<9>7;1A1>C9C9;41> 2 C5>CD;1><1825B1A@5A35@1C1>211;1>AD=DB;5<1:D1>=9>9=D=@141C9C9;C5A5>418(34$/$$0 ;  $149;5<1:D1>=9>9=D=49C9C9;25B1A>H1/=9> ! B589>7711>C1A1C9C9; 41>45>71>=5>77D>1;1>8D;D=;5;5;1<1>5>5A79=5;1>9; *%*% ' ! " '/ ' ! " '/    ' ! "   2 '!  " $149;5C9>7791>=9>9=D=171A2131@19C9C9;141<18 5B1A@5A35@1C1>49C9C9;141<18@5A35@1C1>B5>CA9@5C1< 5A41B1A;1>71=21A 49C9C9; B'! ', '!49=1>1 ,! $149@5A35@1C1>217>41;5C18D9C5>C1>771H1;?>B5AE1C96 41>71H1C941;;?>B5AE1C96  @1;188D;D=;5;5;1<1>5>5A79=5;1>9;25A<1;D @141B52D1825>41:9;171H1;?>B5AE1C9625;5A:1@141 25>41C5AB52DC  D12D1825>4141>H1>725A=1BB1=1B9>7 =1B9>7 ':1CD82521B41A9;5C9>7791>"=5C5A41>"=5C5A $9;1=5>H5>CD8C1>1845>71>;535@1C1>/= B C5>CD;1><18 5>5A79 ;9>5C9; 25>41  B11C 1;1> =5>H5>CD8C1>18    ,52D182149:1CD8;1>41A9BD1CD;5C9>7791> 3=@141B52D18@571BH1>7;?>BC1>C171H1>H1 ( = $9;1!= B25A1@1=5C5A@571BC5AC5;1> -?<5 =5=9>418;1> 2D;D 41A9 <1>C19 ;5 1C1B =5:1 5A1@1DB181C?C1<H1>749C5A9=1?<582D;DC5AB52DC -97121CD21C1H1>7C521<>H13=49<5C1;;1>491C1B B52D18 =5:1  "9CD>7<18 DB181 D>CD; =5>D=@D; ;5C97121CD21C1C5AB52DC41<1=B1CDCD=@D;1>:9;1 =1BB1B5C91@21CD21C1 ;7 Usaha, Energi, dan Daya 83   ,52D18;5<1@1:1CD82521B41A9;5C9>7791>=5C5A $9;1 =1BB1 2D18 ;5<1@1  ;7 41> !   = B C5>CD;1><18;535@1C1>2D18;5<1@1B11C=5>31@19 ;5C9>7791>=5C5A41A9C1>1841>5>5A79;9>5C9;2D18 ;5<1@1B5B11CB52531@19C1>18 ,52D18;5A5C1=5<5F1C9<9>C1B1>+)&&+),-+45>71> 491=5C5A = 71A;5A5C141@1C=5<9>C1B45>71> 1=1> C5>CD;1><18 ;535@1C1> =9>9=D= ;5A5C1 C5AB52DC  ,52D18 25>41 25A=1BB1  ;7 :1CD8 2521B 41A9 ;5C9>7791>=5C5A491C1BC1>18 $9;1! = B C5>CD;1><18 1 ;535@1C1>25>41B11CC92149C1>1841> 2 DB181?<5871H125A1CB5<1=1@5A@9>4181> ,52D18@5=9A9>7;51C1B45>71> BD4DC5<5E1B9J41>5>5A79;9>5C9;B525B1A  $ $9;1! = BC5>CD;1><185>5A79;9>5C9;41>5>5A79 @?C5>B91<25>41@141B11C=5>31@19C9C9;C5AC9>779 D. Daya Tugas Anda 3.4 >41 C5<18 25<1:1A C5>C1>7 31A1 =5>789CD>7 DB181 41A9 71H1 H1>7 49<1;D;1>  921>49>7;1> =5>75C18D9 25B1A DB181 <5298 =5>1A9; =5>75 C18D9 B525A1@1 <1:D DB181 C5AB52DC 49;5A:1;1>  -5>CD>H1 25B1A1> F1;CD 49 41<1= 2181B1> 9>9 =5>:149 B1>71C 25A@5A1>  ,11C DB181 @5A B1CD1> F1;CD 494569>9B9;1> =D>3D<<18 9BC9<18 41H1 *5A419>71C218F141H1C941;49C5>CD;1>?<5825B1A5>5A79H1>7 49=9<9;9 BD1CD 25>41  .>CD; <5298 =5=181=9>H1 @5A81C9;1> 3?>C?8 25A9;DC  .3?; 41> DC5C 25A=1BB1 B1=1 H19CD   ;7 =5>19;9 <1>C19 4D1 B5;?<18>H1 B5C9>779  =5C5A  %54D1>H1 =5=9<9;9 5>5A79 B1=1 25B1A D>CD; =5<1;D;1>DB181  :?D<5 >5A79@?C5>B91<H1>749=9<9;9=5A5;1B1=1 F1<1D@D>;5>H1C11>>H1.3?;B1=@1949<1>C194D1<529835@1C 1A9DA191> 3?>C?8 C5AB52DC 49;5C18D9 218F1 1AC9>H1 DB181 25 9>6?A=1B9<5298<5>7;1@C5>C1>7@5A@9>4181>1;921C@5>71AD871H1 1<1= @5A9BC9F1 9>9 41@1C 49;1C1;1> 218F1 .3?; =5=9<9;9 41H1 <5298 25B1A 41A9@141 DC5C F1<1D@D> ;54D1>H1 =5=9<9;9 ;5=1=@D1> D>CD; =5>7 81B9<;1> 5>5A79 H1>7 B1=1 $149 41H1 141<18 25B1A1> 69B9;1 H1>7 =5>H1C1;1> DB181 H1>7 49<1;D;1>?<5825>41B5C91@B5;?>>H11C1D<1:D5>5A79H1>7492DCD8;1> 25>41 B5C91@ B5;?>>H1 1H1 A1C1 A1C1 Sebutkan contoh alat-alat yang mencantumkan besaran daya yang ada di sekitar Anda.  DB181 B5<1>7F1;CD  ,  1C1D  /  - K %5C5A1>71>   DB181 H1>7 49<1;D;1> :?D<5 -  F1;CD H1>7 49@5A B5;?> /  ;5<1:D1> A1C1 A1C1 = B 1<1=B9BC5=,#B1CD1>41H149CDAD>;1>41A9B1CD1>DB181H19CD$ B ,1CD1> C5AB52DC B5A9>7 49B52DC F1CC 49C5C1@;1> B521719 @5>781A711> C5A8141@ 9<=DF1> ,;?C<1>491 H19CD $/(4 #$55  K   ,1CD1> 41H1 41<1= ;5=1=@D1> B52D18 =5B9> 291B1 =5>77D>1;1> B1CD1> ")+, *)0+ "* 1C1D 41H1 ;D41 8@F1CC ;0 ;08 ;0 :1=N $ 84 Mudah dan Aktif Belajar Fisika untuk Kelas XI ;08 141<18 B1CD1> DB181 1C1D 5>5A79 2D;1> B1CD1> 41H1  ,1CD1> C5AB52DC21>H1;497D>1;1>D>CD;=5>H1C1;1>5>5A79<9BCA9; $9;1B5CA9;1 <9BCA9; =5=9<9;9 41H1   F1CC 5<5=5> B5CA9;1 C5AB52DC 5>5A79 <9BCA9; =5<1;D;1> ;5A:1 1C1D DB181   :?D<5 B5C91@ B5;?>>H1 Contoh 3.15 +9>C?H1>725A=1BB1 ;7=5>19;9C1>771;5<1>C19C971B5C9>779 =B5<1=1 =5>9C 5A1@1;1841H1A1C1 A1C1H1>749<1;D;1>+9>C? $8$% 9;5C18D9 ' ;7 " = - =5>9C   -    '!" -  ;7   = B   =   F1CC  B $149+9>C?=5>7541H1B525B1A F1CC Contoh 3.16 ,52D18=5B9>@?=@1B5>CA96D71<41@1C=5=9>418;1> ;719A;521;H1>7C9>779>H1 =5C5AB5<1=1=5>9C $9;1569B95>B9=5B9>@?=@1C5AB52DC81>H1 25A1@1;18 41H1A1C1 A1C1<9BCA9;H1>749@5A $8$% 9;5C18D9 '  ;7 " = - =5>9C  B 1H1H1>749@5AD>CD;=5=9>418;1>19A141<18  '!"       ;7   = B   =    F1CC  B 1H1H1>749@5A@?=@1D>CD;=5=@5A?<58DB181B525B1A  F1CC45>71> 569B95>B9=5B9> 141<18   F1CC  F1CC   F1CC    $14941H1@?=@1171A569B95>B9>H1 81ADBB525B1A F1CC Usaha, Energi, dan Daya 85 Tes Kompetensi Subbab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m = 2 kg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° 1 -5>CD;1>;535@1C1>215=@D8 :1A1;, =B5@1>:1>72941>7=9A9>7 "9CD>741H1H1>74925A9;1>?<5871H1 , =! = BBD4DC2941>7=9A9>7 J 2 Rangkuman .B181 141<18 25B1A>H1 71H1  B51A18 @5A @9>4181>B49;1<945>71>25B1A>H1@5A@9>4181> 3?B  ,1C1D,3?B  45>71>   141<18 BD4DC 1>C1A1 71H1 41> @5A@9>4181> .B18125A81A71>571C96=5>D>:D;;1>218F171H1 H1>725;5A:125A<1F1>1>45>71>1A18@5A@9>4181>  *1417A169;71H1C5A8141@@5A@9>4181>25B1ADB181 =5AD@1;1>7491AB9A F W1 s Wtotal = W1+W2 W2  >5A79 141<18 ;5=1=@D1> D>CD; =5<1;D;1> DB181 >5A79;9>5C9;141<185>5A79H1>749=9<9;9 ?<58B5C91@25>41H1>725A75A1; 86 Mudah dan Aktif Belajar Fisika untuk Kelas XI % '/  >5A79@?C5>B91<141<185>5A79H1>749=9<9;9?<58 B5C91@25>41;1A5>1;54D4D;1>>H1 $9;1;51411> =5=D>7;9>;1>5>5A79C5AB52DC41@1C49=D>3D<;1> *'!"D>CD;5>5A79@?C5>B91<7A1E9C1B9 *5<1BC9B  %1 D>CD;5>5A79@?C5>B91<@571B   .B181 =5AD@1;1> @5AD2181> 5>5A79 41A9 BD1CD 25>41  %4% D>CD;5>5A79;9>5C9;  *4* D>CD;5>5A79@?C5>B91<  "D;D= %5;5;1<1> >5A79 '5;1>9; L$9;1 @141 BD1CD B9BC5= H1>7 25;5A:1 81>H1 71H1 71H1 ;?>B5AE1C965>5A79=5;1>9;B9BC5=B5<1BC1> * %  *%  .B181C?C1<H1>749<1;D;1>?<5871H1;?>B5AE1C96 81>H1=5=@5A81C9;1>;51411>1F1<41>;51411> 1;89A@?B9B925>41<9>C1B1>C941;=5=5>71AD89  1H1 141<18 DB181 H1>7 49<1;D;1> ?<58 25>41 B5C91@B5;?>1C1D<1:D5>5A79H1>725AD218=5>:149 5>5A7925>CD;<19> Peta Konsep "4$*$0(3)+'$0$:$ =5=2181B .B181 >5A79 1H1 8D2D>71>>H1 .B181*5AD2181>>5A79 =5=2181B >5A79%9>5C9; >5A79*?C5>B91< "D;D=%5;5;1<1> >5A79'5;1>9; =5=2181B >5A79*?C5>B91< !A1E9C1B9 >5A79*?C5>B91< *571B Refleksi 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. 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. Usaha, Energi, dan Daya 87 Tes Kompetensi Bab 3 A. Pilihlah salah satu jawaban yang paling tepat dan kerjakanlah pada buku latihan. ,1CD1> B1CD1>25A9;DC9>9H1>7-#%C5A=1BD;B1CD1> DB181141<18 1 >5FC?>=5C5A 2 :?D<5 3 ;7= BK 4 ;7= B 5 ;7= B 5B1A1> 25B1A1>25A9;DC9>9-#%=5=9<9;9B1CD1>B1=1 141<18 1 DB181 5>5A79 2 DB181 5>5A79;9>5C9; 3 5>5A79@?C5>B91< 5>5A79;9>5C9; 4 C5>171 DB181 5 71H1 DB181 ,52D1825>41=1BB1>H1;741<1=;51411>491= %5=D491>25>41C5AB52DC4925A971H1C5C1@B525B1A   ( B5<1=1  45C9;  .B181 H1>7 49<1;D;1> 71H1 C5AB52DC141<18 1  $ 2 $ 3 $ 4  $ 5  $ D '9>1 =5=21F1 ;5A1>:1>7 25A=1BB1   ;7 41> 25A:1<1>B5:1D8 = $9;1@5A35@1C1>7A1E9C1B9 = B 25B1ADB181H1>749<1;D1>D'9>1141<18 1  $ 2 $ 3  $ 4 $ 5 >?< '?29< H1>7 =1BB1>H1   ;7 49A5= 45>71> 71H1  (B589>77125A85>C9@141:1A1;= 5B1ADB181 B11C@5>75A5=1>=?29<C5AB52DC141<18 1 N $ 2 N $ 3 N $ 4 N $ 5 N $ 5>4125A=1BB1 ;7C5A<5C1;@1412941>741C1A 5>41 C5AB52DC4925A971H1 (H1>7=5=25>CD;BD4DC J C5A8141@2941>741C1A $9;125>4125A@9>418B5:1D8= 25B1ADB181H1>749<1;D;1>25>41141<18      1 88  $ 2  $ 3   $ 4   $ 5   $ Mudah dan Aktif Belajar Fisika untuk Kelas XI  *1412941>7=9A9>741><939>49<5@1B;1>25>41 C1>@1;535@1C1>1F1<89>77125>4125A14149;1;9 2941>7=9A9>7B5:1D8= $9;1B9>  ;535@1C1> 25>41141<18 1   = B 2   = B 3   = B 4   = B 5  = B  ,52D1871H1+,(=5<1;D;1>DB18145>71> C9C9;C1>7;1@>H125A@9>418=5>DADC3+,= 41>E5;C?A+41>,25ACDADC CDADC141<18E5;C?AB1CD1> H1>7 B51A18 45>71> BD=2D 1 41> BD=2D 2 @141 ;??A49>1C1AC5B9DB $9;1DB181C5AB52DC25A>9<19$ >9<19B1=145>71> 1  2  3  4  5  "!  !5A?21;45>71>=1BB1 ;7C5A<5C1;@1412941>7 =9A9>7 H1>7 BD4DC ;5=9A9>71>>H1  J C5A8141@ 2941>78?A9I?>C1< $9;149;5C18D9@5A35@1C1>7A1E9C1B9 ! = B41>75A?21;25A75B5AB5:1D8=;51A18 21F18 DB181 H1>7 49<1;D;1> ?<58 71H1 25A1C 141<18 1  $ 2   $ 3  $ 4  $ 5  $ ,52D18 25>41 25A=1BB1  ;7 :1CD8 2521B 41A9 ;5C9>7791>  = $9;125B1A@5A35@1C1>7A1E9C1B9!B1=1 45>71>  = B ;535@1C1> 25>41 B11C 25A141 49 ;5C9>7791>=41A9C1>18141<18 1 = B 2 = B 3  = B 4  = B 5 = B 9AC5A:D>B5C9>779==5>71<9A;1> =19AB5C91@ B5;?> '1BB1:5>9B19A ;7 =41>@5A35@1C1> 7A1E9C1B9! = B $9;181>H1 5>5A79@?C5>B91< 19A H1>7 41@1C 49D218 =5>:149 5>5A79 <9BCA9; 25B1A 5>5A79<9BCA9;H1>741@1C4981B9<;1>B5C91@B5;?>>H1 141<18      1  ;$ 2 ;$ 3  ;$ 4  ;$ 5 ;$ ,52D18@?C:1CD82521B41A9C5=@1CH1>7C9>779>H1 = $9;15>5A79@?C5>B91<1F1<@?CB525B1A :?D<541>! = BC5@1CB52518;535@1C1>>H1 141<18 1  = B 2  = B 3 = B 4 = B 5  = B ,52D18@125A;535@1C1> = B =5>781>C1=B52D18@1;DB589>771@1;D=1BD;;5 41<1=;1HD3= 5B1A71H1C181>1>H1>749B5212;1> ;1HD141<18 1  ( 2  ( 3  ( 4  ( 5  (  " 9AC5A:D>B5C9>779 =45>71>4529CB525B1A = B 49=1>611C;1> D>CD; =5=DC1A CDA29> H1>7 =5>7 75A1;1>75>5A1C?A<9BCA9; $9;15>5A7919AC5A:D>41@1C 49D218=5>:149<9BCA9;41H1;5;D1C1>75>5A1C?AB5C91@ B5;?>>H1B1=145>71> 1  =0 2  =0 3 =0 4  =0 5  =0 $9;1>4125AB5@541=5>DAD>92D;9CC1>@1=5>71HD8 41>25B1A;535@1C1>>H1C5C1@C5A:149@5AD2181>5>5A79 41A9 1 ;9>5C9;=5>:149@?C5>B91< 2 @?C5>B91<=5>:149;9>5C9; 3 @?C5>B91<=5>:149;1:149@?C5>B91< 5 ;9>5C9;=5>:149;1CD>7;1> @141 D:D>7 C1<9 H1>7 @1>:1>7>H1 = ?<149C1A9;;5B1=@9>7B589>771 C1<9=5=25>CD;BD4DC JC5A8141@E5AC9;1< $9;12?<1 49<5@1B;1>;5<1:D1>2?<1@141;54D4D;1>C5A5>418 141<18 1 2 3 = B  = B = B 4  = B  = B 5  ,52D18 25>41 H1>7 25A=1BB1  ;7 =D<1 =D<1 491= ;5=D491>25A75A1;71>@5A35@1C1>= B .B181 H1>7=5>:1495>5A79;9>5C9;B5C5<1845C9;141<18 1 :?D<5 2 :?D<5 3 :?D<5 4 :?D<5 5 :?D<5  ,52D18@571B=5=9<9;9C5C1@1>% ( = $9;1@141 D:D>7 @571B C5AB52DC 4971>CD>7;1> 2521> H1>7 25A1C>H1 (5>5A79@?C5>B91<H1>749B9=@1>41<1= @571BC5AB52DC141<18 1  $ 2  $ 3  $ 4  $ 5 $  D125>4141>=1B9>7 =1B9>725A=1BB1':1CD8 2521B 41A9 ;5C9>7791> " =5C5A 41> " =5C5A  $9;1  =5>H5>CD8C1>1845>71>;535@1C1>/= B25>411;1> =5>H5>CD8C1>1845>71>5>5A79;9>5C9;B525B1A 1 2   '/  '/ 3  '/  4  '/  5 '/   ,52D18 @571B 49C1A9; 45>71> 71H1  ( 89>771 25AC1=218@1>:1>73= 5B1A5>5A79@?C5>B91<@571B C5AB52DC141<18 1 $ 2  $ 3 $ 4  $ 5 $ Usaha, Energi, dan Daya 89  $8$%.$*2(35$0:$$0%(3+-65+0+'(0)$05(2$5 ,52D1825>41H1>7=1BB1>H1;741A9;51411>491= 25A75A1;89>771;535@1C1>>H1=5>:149 = BB5<1=1 B5;?>;1A5>1@5>71AD871H1 5A1@1;1825B1A DB181H1>749<1;D;1>?<5871H1C5AB52DC ,52D1825>41=5=9<9;9=1BB1;741<1=;51411>491= %5=D491> 25A75A1; 71> ;535@1C1>  = B B5<1=145C9; ,1=1;1825B1ADB18141>@5AD2181> 5>5A79;9>5C9;H1>7C5A:149$5<1B;1> ,52D18@5E5AC9;1<;5 1C1B 45>71> ;535@1C1> 1F1<   = B  -9>779 H1>7 4931@19 @5H1 @5AD2181>5>5A79=5;1>9;=5>:1495>5A79@1>1B@141 @5A9BC9F1C5AB52DC! = B ,52D1825>4149C5=21;;1>E5AC9;1<;51C1B45>71> ;535@1C1>1F1</ -9>779=1;B9=D=H1>74931@19 141<18" (H1C1;1>;5C9>7791>25>4141<1="@141 B11C 5>5A79 @?C5>B91< 25>41 B1=1 45>71> 5>5A79 ;9>5C9;>H1 ,52D18+)&&+),-+49D>91 1>C1B9>3?<49B52DC 81<9<9>C1A=5>41;9;5;5C9>7791>=1;B9=D=>H1"  =491C1BC1>1845>71>;5<1:D1>/  = B %5=D491> +)&&+ ),-+ =53DA ;5 21F18 ;5 ;5C9>7791>=9>9=D=>H1"=B52541;9 ;5=21<9=5>D:D;5C9>7791>" =     A C lintasan roller coaster hA B hC hB $9;171H175B5;+)&&+),-+41><9>C1B1>>H1491219;1> C5>CD;1> ;5<1:D1> +)&&+ ),-+ @141 ;54D1 C9C9; C5AB52DC 90 Mudah dan Aktif Belajar Fisika untuk Kelas XI  ,52D1825>4125A=1BB1;74971>CD>745>71>B5DC1B C1<9H1>7@1>:1>7>H1= .:D>7C1<9H1>7<19>499;1C @141<1>79C <1>79C 5>4149@D;D<B589>77125A75A1; 45>71>;535@1C1>C5C1@   = B 5A1@1;1825B1A BD4DC=1;B9=D=H1>74925>CD;C1<9C5A8141@1A18 E5AC9;1<  ?<1H1>7=1BB1>H1 ;749<5=@1A;1>;51A188?A9 I?>C1<45>71>;535@1C1> = B41A9@D>31;=5>1A1 754D>7H1>7C9>779>H1  = v0 A 0 120 m vy gedung vx v B vx lantai gedung vy v "9CD>7<18 1 5>5A79;9>5C9;1F1< 2 5>5A79@?C5>B91<1F1< 3 5>5A79;9>5C9;2?<1;5C9;1=5>D=2D;C1>18 4 ;5<1:D1>2?<1;5C9;1=5>D=2D;C1>18  *141B52D18@571BC5A71>CD>72521>H1>7=1BB1>H1 ;7 *571BC5AB52DC25AC1=218@1>:1>73= "9CD>7<18 5>5A79@?C5>B91<@571B41>25A1@1;1825B1A5>5A79 @?C5>B91<@571B:9;12521>>H149C1=218;7 ! = B  ,52D182149:1CD8;1>41A9;5C9>7791> =@141 B52D18@571B -5A>H1C1@571BC5AC5;1>=1;B9=D= B525B1A 3= 5A1@1;18;?>BC1>C1@571BC5AB52DC ! = B 9AC5A:D>=45>71>4529C = B497D>1;1>D>CD; =5=DC1A75>5A1C?A<9BCA9; $9;149;5C18D9! = B 41> 81>H1  5>5A79 19A H1>7 25AD218 =5>:149 5>5A79 <9BCA9; 25A1@1 F1CC 41H1 H1>7 4981B9<;1> 75>5A1C?AC5AB52DC 5>5A79    @5CD>:D; 41H1 B5;?>  =5=9<9;9B1CD1>F1CC    Bab 4 Sumber: www.savannah.com Petinju secara rutin berlatih meningkatkan kecepatan pukulan dan berusaha mempersingkat interaksi dengan sasarannya. Petinju juga menggunakan sarung tangan ketika bertinju. Momentum, Impuls, dan Tumbukan Hasil yang harus Anda capai: menganalisis gejala alam dan keteraturan dalam cakupan mekanika benda titik. Setelah mempelajari bab ini, Anda harus mampu: menunjukkan hubungan antara konsep impuls dan momentum untuk menyelesaikan masalah tumbukan. *8DA4;>4; A74 @8ABAFBA C8DF4A74A E4?4; E4FG B?4;D4:4 J4A: 6G>GC 7<:8@4D<  +854:4< 58>4? E44F 58DF4A7G?4AAJ4 E864D4 F8D4FGD 74A G?4AAJ4 C474 EG4FG E4E4D4A 78A:4A @8@4>4< E4DGA: FE74A>868C4F4ACG>G?4AE8@4>4F  +8@4>4F E< CG>G?4A 78A:4A E4E4D4A E8@4> >G4?G?4A *8DA4;>4; A74 58DC<>4A E4DGA: F4; C8A:4DG; J4A: 74A C8F8F<>4 ?4I4AAJ4 @8@G>G? 78A:4A E4DGA: F< CG>G?4A E868C4F @GA:>4 A74 74C4F @8@4;4@< 4;E8F<4C58A74J4A:@8@<@B@8AFG@=G:4 @8@<8A8D:< $<>47G45G4;58A74@8@<8A8D:<>E4@458E4D F8F4C<@4EE4AJ458D587458A74@4A4J4A:@8@< @B@8AFG@?85<;58E4D C4J4A:7<@4>EG778A:4A>B89:58D:8D4>78A:4A>868C4F4A @ E B?458D@4EE4 >:58D:8D4>58D?4I4A4A4D4;F8D;474C 58A7478A:4A>868C4F4A@ E +8F8?4;58DFG@5G>4A >868C4F4A5B?4@8A=47<@ E 8D4C4>4;>868C4F4A 4>; 78A:4A >868C4F4A F8DF8AFG 74A @8@<@B@8AFG@ 8E4DAJ4@B@8AFG@E4A:4F58D:4AFGA:C474@4EE4 74A >868C4F4A 58A74 F8DE85GF  'B@8AFG@ J4A: 7<@< EG4FG 58A74 474?4;;4E4?<4A4AF4D4@4EE474A>868C4F4A58A74C474E44FF8DF8AFG *8DE4@44A @B@8AFG@ EG4FG 58A74 J4A: 58D@4EE4 # 74A 58D:8D4> 78A:4A >868C4F4A 1 E864D4 @4F8@4F4A E854:4< 58D<>GF Tugas Anda 4.1 Jika Anda bersepeda dengan kecepatan tinggi, manakah yang memiliki momentum lebih besar, sepeda atau Anda? Apakah hal tersebut dapat memberikan penjelasan, mengapa Anda akan terpelanting ke depan ketika sepeda berhenti mendadak? Ingatlah Kecepatan yang berada pada kerangka satu-dimensi, penulisan notasi vektornya dapat diganti dengan notasi skalar. ,#1 M  %8F8D4A:4A ,  @B@8AFG@ 58A74 >: @ E # @4EE458A74>: 1  >868C4F4A 58A74 @ E 'B@8AFG@474?4;E85G4;58E4D4AH8>FBDJ4A:4D4;AJ4E4@478A:4A 4D4; >868C4F4A 58A74  ( ,)%$ @8A:8@G>4>4A ;G>G@ :8D4> J4A: >87G4 7<>44A 78A:4A @B@8AFG@  #4 @8A:4F4>4A @B@8AFG@ E854:4< >G4AF  "G>G@ ## (8IFBA @8A:4F4>4A 54;I4 C8DG54;4A @B @8AFG@ 58A74 F<4C E4FG4A I4>FG E854A78D=4C47458A7474A58D4D4;E4@478A:4A4D4;:4J4F8DE85GF +864D4 @4F8@4FGF , M  ) "-.)*  4  E8F4D4 78A:4A 58AFG>   #  GAFG> E85G4; C4DF<>8? FGA::4? 78A:4A @4EE4 # >BAEF4A  *8D;4F<>4A ;G5GA:4AAJ4 74?4@ 58AFG> 58D<>GF 4A @8@C8?4=4D4 'B78DA"G>G@## (8IFBAGAFG>C4DF<>8?FGA::4?58AFG> #F<74>58D?4>GF8F4C<"G>G@##(8IFBA58AFG> , F8F4C58D?4>G ) 1. Hukum Kekekalan Momentum Linear $<>4C4DF<>8?@8A:4?4@<FBF4?:4J4?G4DAB?"-.)* 4 74C4F 7GF ,  4F4G,F8F4C ) 92 Mudah dan Aktif Belajar Fisika untuk Kelas XI M "-.)*  4  @8AJ4F4>4A 54;I4 =<>4 :4J4 ?G4D FBF4? C474 E85G4; C4DF<>8? 474?4; AB? @B@8AFG@ ?8A4? 78A:4A *!*# !!"$ %#$)*#  $' J4A: 74A 78A:4A ,4I4?  ,4>;FG 4I4? E4@4 78A:4A @B@8AFG@ ?FG 4>; H8>FBD  )?8; >4D8A4 4A )-   +85G4; @B5 C474 5<74A: 74F4D 58D:8D4> 78A:4A >868C4F4A 1  >8@G7<4A 7<58D< :4J4 F8F4C  E8;868C4F4AAJ4 58DG54; @8A=47< 1  E8?4@4  ) 4D< "G>G@ ## (8IFBA 7 ?GDGE 7G 1 1  ) M M 4D< "-.)*  4  74A "-.)*  4 7<74C4F>4A 1  1  M # ) '8AGDGF "G>G@ ## (8IFBA J4A: 7<>44A 78A:4A @B@8AFG@ ?4A 54;I4 :4J4  J4A: 7<58D<>4A C474 58A74 58E4DAJ4 E4@4 78A:4A C8DG54;4A @B@8AFG@ , 58A74 C8D E4FG4A I4>FG )  &<;4F , "-.)* 4 J44D8A4 4A "-.)*  4 A74 @8A:8F4;G< 54;I4 ;4E4?< :4J4  74A E8?4A: I4>FG ?4@4AJ4 :4J4 58>8D=4  )  E4@4 78A:4A C8DG54;4A @B@8AFG@ 4F4G E8?; :4J4  J4A: F8F4C (8A4?E854:4<<@CG?EJ4A:74A78A:4A 8A:4A 78@<><4A74C4F74A54;I4<@CG?EJ4A:58>8D=4C474EG4FG58A74 E4@4 78A:4A C8DG54;4A @B@8AFG@ J4A: F8D=47< C474 58A74 F8DE85GF %8F8D4A:4A  <@CG?E(E  :4J4( )  E8?4A: I4>FG E v2 v1 M  Sumber: Conceptual Physics,1998 Ia dilahirkan di Duisberg, Jerman. Ia mempelajari fisika teoritis di Munich, di tempat ini pun ia menjadi penggemar ski dan pendaki gunung. Hasil pemikirannya yang terkenal ialah prinsip ketidakpastian Heisenberg yang didasarkan pada konsep momentum, yaitu foton yang digunakan untuk mengamati posisi elektron memiliki momentum yang relatif sama. Oleh karena itu, ketika terjadi tumbukan antara foton dan elektron akan mengubah posisi elektron. Momentum, Impuls, dan Tumbukan 93 Contoh 4.1 Ingatlah +85G4;5B?458D@4EE4 :=4FG;74D<>8F?4AF4< 5B?4@8@4AFG?>8@54?<58D?4I4A4A78A:4A4D4;E8@G?478A:4A>8F?4AF4< h1 5 :4J4J4A:7<58D<>4A?4AF4<C4745B?4>8F<>45B?4 h2 @8AJ8AFG;?4AF4<E8?4@4  E 2 <>8F4;G< #  :N M >:   @   @ )   E -AFG>:8D4>=4FG;5854E58D?4>GC8DE4@44AE854:4<58D<>GF Impuls sebanding dengan perubahan momentum. Kata Kunci • impuls • momentum linear +1 =   = 4 5 Tes Kompetensi Subbab +2 =     = – m/s =      =  m/s 4D4;>854I4; M 4D4;>84F4E M & #+  N >:M @ EM >:@ E4D4;AJ4>854I4; & #+ N M >:@ E >:@ E4D4;AJ4>84F4E $47< @B@8AFG@ 5B?4 E858?G@ FG@5G>4A 474?4; M  >:@ E 74A E8F8?4; FG@5G>4A474?4; >:@ E #@CG?EJ4A:7<58D<>4A5B?4 & M&   MM  >:@ E !4J4J4A:7<>8D=4>4A?4AF4<C4745B?4E8?4@4 N M 78F<>474?4; >:@ E  (    )     E $47<:4J4J4A:7<58D<>4A?4AF4< (@8?4I4A4D4;:8D4>=4FG;5B?4 A "-&'*($!()0'0(/%$* +85G4;5B?4E8C4>58D@4EE4 >:7868C4F4A @ E ,8AFG>4A:4J4J4A:7<58D<>4AB?8;>4><C8A=4:4:4I4A: F8D;474C5B?4=<>4E8?4A:I4>FG>4><@8AJ8AFG;5B?4 4 N M E 5 N ME +8BD4A:E:74A @8?8@C4D>4AAJ4E864D4;BD868C4F4A 4I4? @ E B?4F8DE85GF@8@58AFGDF<4A:E8?4@4 N M EE8;4D4;78A:4A>868C4F4A @ E ,8AFG>4A 4 <@CG?EJ4A:7<58D<>4AF<4A:C4745B?4 5 :4J4J4A:7<58D<>4AF<4A:C4745B?474A 6 C8D68C4F4A5B?4C8@G>G?E8?4@458DE8AFG;4A B. Tumbukan Ingatlah Jika berlaku Hukum Kekekalan Momentum Linear, momentum linear awal sama dengan momentum linear akhir. 94 *8D4A 74C4F A74 F8@G< C474 7G4 58A74 J4A: E4?4AE4FGE4@4?44AE864D4?4A:EGA: C8D4A 474?4; C8D@44; A74 4FGD4A C8D@48F4;G< 54;I4 <@CG?E E4@4 78A:4A C8DG54;4A @B@8AFG@  8D<>GF 4A 7<=8?4E>4A C8DG54;4A @B@8AFG@J4A:F8D=47<C474E8F<4C58A74J4A:E4?4AE8DF4 >44AE8C8DF<C474 )-   58D<>GF vA vA vB vB Gambar 4.2 ketika tumbukan sebelum tumbukan vA Hukum Kekekalan Momentum Linear berlaku pada dua benda yang bertumbukan. vB FA setelah tumbukan %8D8F474A>8D8F4E858?G@58DFG@5G>4A@4E< @4EE4#74A#74A>868C4F4A74A %87G4>8D8F4F8DE85GF58D474 C474E4FG5<74A:74F4D74A@8@<4D4;:8D4>J4A:E4@4 $<>4>868C4F4A >8D8F4  ?85<; 58E4D 74D868C4F4A >8D8F4  >8D8F4  C474 E44F F8DF8AFG 4>4A @8A45D4> >8D8F4   %8F<>4 >8D8F4  @8A45D4> >8D8F4  E8EG4<78A:4A"G>G@###(8IFBA>8D8F44>4A@8@58D<>4A:4J44>E< E858E4D  74A >8D8F4  4>4A @8@58D<>4A :4J4 D84>E< E858E4D  4:4<@4A4 58E4D :4J4 D84>E< F8DE85GF C474 >8D8F4  $<>4 "G>G@ %8>8>4?4A 'B@8AFG@ &G C474 C8D4A 4AF4D4 >8D8F474A58E4D>87G4:4J4F8DE85GF4>4A E4@458E4D >4AF8F4C< 4D4; >87G4 :4J4 58D?4I4A4A 4D4; E8;4A E854:4< 58D<>GF ,4I4?  ,4>;;;4A #1 #1 =G@?4;@B@8AFG@E8EG74;FG@5G>4A BAFB;?44AJ4A:74C4F7G>4AC8A78>4F4A 78A:4A"G>G@%8>8>4?4A'B@8AFG@&BF4 58E4D C8D@4>4A B?8; 8A8D:< ? J4A: 77<4F4EAJ4 %868C4F4A@4>E<@G@E8F<4C@B54D8A4 8A8D:< ? J4A: 7 7< 4F4EAJ4 =G:4 E4@4 >4A F8F4C< 58D4F C8AG@C4A:AJ4 58D5874 >868C4F4A @B54 F8D=47< 58AFGD4A 4AF4D4 7G4 @B5 :GA64A:4A J4A: C4?8D4E4>4A786:58D4747<4F4EC8D4;G   >:  *8D4;G 58D:8D4> 78A:4A >8?4=G4A  @ E ,8AFG>4A>868C4F4AC8D4;G=<>4A8?4J4A@8?B@C4F 78A:4A>868C4F4A @ E78A:4A4D4; 4 >878C4AE84D4;78A:4A4D4;:8D4>C8D4;G 5 >8 58?4>4A: 58D?4I4A4A 78A:4A 4D4; :8D4> C8D4;G74A 6 >8 E4@C ?GDGE 78A:4A 4D4; :8D4> C8D4;G G45G4;>8?8D8A:74A@4E:74A >:58D:8D4>E84D4;78A:4A>868C4F4A  @ E74A @ E *BE8?8D8A:7<5G4FE878@<><4A E8;8?8D8A:  @8AG@5G> >8?8D8A:  74D< 58?4>4A:  +8F8?4; FG@5G>4A >87G4AJ4 58D:8D4> 58DE4@44A  ,8AFG>4A >868C4F4A >87G4 >8?8D8A: F8DE85GF A vA B vB A Momentum, Impuls, dan Tumbukan B vAB 95 C. Jenis Tumbukan 74F<:4@464@FG@5G>4AJ4A:7B>54;4E4AFG@5G>4A J44A?8AF4A?8AF4A F<74>?8AF4?< +G55454A 4AF4D4 7G4 58A74 J4A: ?87G4AJ4 58D474 C474 E4FG :4D8;<7GC4A AJ4F4 FG@5G>4A ?8AF C8DA4; F8D=47<>4D8A4E8F8?4;FG@5G>4A474E854:<4A8A8D:<J4A:58DG54;58AFG> @8A=47< 8A8D:< C4A4E 8A8D:< 5GAJ< 74A 8A8D:< ?44A F8F4C< 74?4@ C8@54;4E4A 4A ?8AF<4A E8D4A B?8; C4D4 94I4A GAFG> @8AJ878D;4A4>4A EG4FG @4E4?4; J4A: 7<=47<>4A E854:4< EG4FG ?4A74E4A F8BD< J4A: @8A74E4D< C8D4A ?44A ?8AFG "G>G@ %8>8>4?4A 'B@8A FG@ & FBF4? J4A: 7<@< 58A74 E858?G@ 74A E8EG74; FG@5G>4A474?4;F8F4C A8D:<CBF8AE<4?58A74F<74>74A>4D8A4 >87G458A7458D:8D4>74?4@E4FG5<74A:74F4D78A:4A>8F4A)-  G45G4;58A74C4745<74A:74F4D58D:8D4> 58D?4I4A4A  %8@G7<4A E8F8?4; F8D=47< FG@5G>4A >87G4 58A74 F8DE85GF 58D:8D4> 58D?4I4A4A 4D4; 74D< 4D4; E8@G?4  %868C4F4A E8F<4C 58A74 474?4; 1  74A 1   +8EG4< 78A:4A "G>G@ %8>8>4?4A 'B@8AFG@ &4A C8DE4@44A E854:4< 58D<>GF # 1 # 1 # 1 # 1  Tugas Anda 4.2 Anggota polisi sering menggunakan rompi anti peluru dalam melaksanakan tugasnya. Dalam beberapa kejadian, rompi tersebut bisa tembus oleh peluru. Mengapa hal tersebut bisa terjadi? # 1  /1 # 1  /1  M  '8AGDGF "G>G@ %8>8>4?4A A8D:< % 7<74C4F>4A C8DE4@44A 58D<>GF !  !  !  !  # +  # +  # +   # +   M  4D< "-.)*  4  4>4A 7GF # + # + # +  # +  # + /+  # +  /  # +  + +  /+ # + + + /+  M  $<>4 DG4E >4A4A "-.)*  4  7<54:< 78A:4A DG4E >4A4A "-.)*  4 74ADG4E>4A 7<;4E4A + + + +  + M+ M+  /+  4F4G 96 Mudah dan Aktif Belajar Fisika untuk Kelas XI +   +      +  +  M  "4D:4  C474 "-.)*  4 @8AJ4F4>4A !% ( $ '() )*(  GAFG> FG@5G>4A ?8AFB89G GAFG> E8@G4 =8A4A 2. Tumbukan Lenting Sebagian dan Tumbukan Tidak Lenting Sama Sekali "G>G@>8>8>4?4A@B@8AFG@58D?4>GGAFG>E8@G4=8A4A >4A F8F4C< ;G>G@ >8>8>4?4A 8A8D:< > ;4AJ4 58D?4>G C474 FG@5G>4A ?8AF4A ?8AF E8F8?4; FG@5G>4A4>4A58DG54;58AFG>@8A=47<8A8D:<?4 E8F8?4; FG@5G>4A 4>4A ?85<; >864A "4D:4 >B894A F<74> ?8AF4?< E854:<4A 58E4D 8A8D:< >AJ4 58DG54; 58AFG> E8; E858?G@ FG@5G>4A ?85<; 58E4D 74D4A 74A  *474 FG@5G>4A F<74> ?8AF4?< >87G4 58A74 58DE4FG E8F8?4; FG@5G>4A 74A 58D:8D4> 58DE4@4E4@4 78A:4A >868C4F4A E4@4 A74 74C4F @8@C8D;4F<>4A 4><54F ?44A =8A:74A>:58D:8D4>58D?4I4A4A4D4;78A:4A>868C4F4A @ E74A@ E ,8AFG>4A>868C4F4A>87G458A74E8F8?4;FG@5G>4A=<>4FG@5G>4A ?8AF4A?8AF8F4;G<#  >:# >:+ @ E+ M@ E *8D;4F<>4A  )?8; >4D8A4 >87G4 58A74 58D:8D4> 58D?4I4A4A 4D4; @4>4 >87G4 >868C4F4A;4DGE58D?4I4A4AF4A74 *4746BAFB;EB4?G@%8>8>4?4A'B@8AFG@7<74C4F # +# +# +# +  >:@ E>:M@ E >:+>:+ @ EM @ E ++ M @ E+ +@ E  *474FG@5G>4A?8AF4 + A ’ + B ’ + ’ +B ’  A    M   ( )   + + A B  /++  @ E 4D<8?<@4 M++  @ E +  @ E+ +  @ EM @ EM +  +  @ E   Ingatlah • • Pada tumbukan lenting sempurna, koefisien restitusinya adalah e = 1. Pada tumbukan lenting sebagian, koefisien restitusinya 0 < e < 1, sedangkan pada tumbukan tidak lenting sama sekali, koefisien restitusinya adalah e = 0. Momentum, Impuls, dan Tumbukan 97 Tugas Anda 4.3 Jika Anda sedang menggunakan sepatu, cobalah tendang sebuah bola sepak. Kemudian, bukalah sepatu dan tendang kembali bola tersebut. Jika diasumsikan gaya yang Anda berikan selama menyentuh sama besar, selidikilah tendangan mana yang membuat bola terlempar jauh? Apa hubungan kejadian ini dengan konsep impuls? 4D<C8DE4@44A7868C4F4A>87G458A74E8F8?4;FG@5G>4A?8AF868C4F4A @8A:4?4@< C8DG54;4A F4A74  DF87G4 58A74 F8DE85GF @8A:4?4@<C8DG54;4A4D4;:8D4> $<>4A74@8A74C4F>4AA868C4F4AF<74> 58DG54;4D4;E8F8?4;FG@5G>4A58D4DF<C8D;4A?8AFFG@5G>4A?8AF868C4F4A58A74E8F8?4;FG@5G>4A474?4; @ E74A>868C4F4A58A74474?4; @ E   Contoh 4.3 Tantangan untuk Anda Apakah Anda pernah menonton balapan? Mengapa di beberapa bagian sirkuit diberi pagar dari ban (tyre wall)? G45G4;58A74F8D?8F4>C474E4FG5<74A:74AE8:4D:74A58A74>87G4#  >: %87G458A7458D:8D4>58D?4I4A4A4D4;78A:4A >868C4F4A+  @ E74A+ M @ E ,8AFG>4A>868C4F4AE8F<4C58A74E8F8?4; F8D=47<FG@5G>4A 8D4C48A8D:<>J4A:58DG54;@8A=47<8A8D:<C4A4E=<>4F8D=47< 4 FG@5G>4A?8AF4A?8AF4AF<74>?8AF4?< m1 m2 2 sebelum tumbukan <>8F4;G< # >: #  >: v1 v2 +  @ E + M @ E m1 m2 4 -AFG>FG@5G>4A?8AFG@%8>8>4?4A'B@8AFG@7<74C4F>4A # + # +# + # +  >: @ E >:M @ E>:+  >:+  >:@ E >:+ >:+   -AFG>FG@5G>4A?8AF4A"-.)*>8"-.)*@8A:;4E4A + M @ E +  @ E *8DG54;4A8A8D:<> A8D:<>E858?G@FG@5G>4A !  !   # +  # +  >: @ E   >: @ E  $ A8D:<>E8F8?4;FG@5G>4A !  ! # +   # +   >:M @ E   >: @ E  $ 98 Mudah dan Aktif Belajar Fisika untuk Kelas XI 5 $47<C474FG@5G>4A?8AFE858?G@74AE8EG74; FG@5G>4A474?4;F8F4C -AFG>FG@5G>4A?8AFG@%8>8>4?4A'B@8AFG@7<74C4F;4E4A?8AF4A"-.)*>874?4@"-.)*E8;E8F8?4;FG@5G>4A !  !   # +   # +   >:M @ E   >:@ E     =BG?8 $47<8A8D:<>J4A:58DG54;@8A=47<C4A4E474?4; $' ! $) !("*#)*#*!$/$' ! $) !()")*#*!$  =BG?8M =BG?8 =BG?8 -AFG>FG@5G>4AF<74>?8AF4?<  m1 = 8 kg m1 m1 m2 m2 v' setelah tumbukan sebelum tumbukan Tantangan untuk Anda (*"/ )?8;>4D8A4  @4>4+ + +E8;4A@8A=47< + + + + @ E A8D:<>E8F8?4;FG@5G>4A !  !  #  # +  >: @ E  =BG?8 $47<54AJ4>AJ48A8D:<>J4A:58DG54;@8A=47<C4A4E474?4;  M =BG?8  =BG?8 Tes Kompetensi Subbab • tumbukan lenting sebagian • tumbukan lenting sempurna • tumbukan tidak lenting sama sekali Berikut ini ukuran diameter, massa jenis, dan periode rotasi dari planet-planet. m2 = 12 kg v 1 v2 Kata Kunci ') G@<    '4DE 1GC<@B@8AFG@  @8AG@5G> 74AF8DE85GF58DE<94F ?8AF?GDGE ,8AFG>4A?4; 58E4DAJ4C8DG54;4A@B@8AFG@5B?4 +85G4;58A7458D@4EE4>:F8D:4AFGA:C474E8GF4E F4?<J4A:C4A=4A:AJ4@ 8A74J4A:58D@4EE4>: @8AG@5G> 58A74  78A:4A >868C4F4A @8A74F4D E858E4D  @ E  $<>4 FG@5G>4A J4A: F8D=47< 8?4EFE<@G@ G45G4;58A74@4E:74A >:58D:8D4>58D?4I4A4A4D4; %868C4F4AE8F<4C 58A74 @ E *474EG4FGE44F>87G458A74F8DE85GF E4?4A 7< 4F4E ?4AF4< J4A: ?<64A>868C4F4AE8F<4C58A74E8F8?4;FG@5G>4A 74A 8A8D:< > J4A: 58DG54; @8A=47< 8A8D:< C4A4E=<>4F8D=47< 4 FG@5G>4A?8AF4A?8AF4AF<74>?8AF4?< +85G4;54?B>58D@4EE4 >:F8D?8F4>7<4F4E?4AF4< %B894A54?B>78A:4A?4AF4<474?4;  *8?GDG J4A: 58D@4EE4  :D4@ 7>4A >8 4D4; 54?B> ;58D:8E8DE8=4G; E4FG @8F8D  8D4C4>4; >868C4F4A C8?GDG E44F 4>4A @8A:8A4<54?B> @ E !GA4>4A>( #+  Momentum, Impuls, dan Tumbukan 99  +85G4;58A7458D@4EE4 >:J4A:58D:8D4>78A:4A >8?4=G4A@ E58DFG@5G>4A78A:4A58A7458D@4EE4 >:J4A:7<4@ +8F8?4;FG@5G>4A58A7458D:8D4> @GA7GD78A:4A>8?4=G4A @ E ,8AFG>4A 4 >868C4F4A58A74E8F8?4;FG@5G>4A 5 8A8D:<J4A:58DG54;4><54FFG@5G>4A74A 6 >B89FG@5G>4AF8DE85GF  +85G4;FDG>58D78A:4A>868C4F4A @ E@8A45D4>E85G4; @B54A>87G4AJ458D:8D4>78A:4A>868C4F4A+ ">4A74A58DE4D4A: C474E85G4;54?B>>4JG %8@G7<4AE 74A C8?GDG 58D:8D4> 78A:4A >868C4F4A  @ E 58D4C4>4;>868C4F4AC8?GDG>8F<>4@8A:8A4<54?B> @4EE454?B>>:  ,BABJ4A:58D@4EE4>:@8?BA64F78A:4A>868C4F4A @ E74D<E85G4;C8D4;G>86: 8D4C4>4;>868C4F4AC8D4;GE8F8?4; ,BAB@8?B@C4F  G4@B578A:4A >868C4F4A>@ =4@74?4@4D4;58D?4I4A4A74A 58DFG@5G>4AE864D4F<74>8?4EF4?< '4EE4 >87G4@B5:74A  >: "868C4F4A >87G4 @B54A 8D4C4>4;8A8D:<>J4A:;GF 54D4A: 58D@4EE4  >: 58D:8D4>C474D8?AJ478A:4A>868C4F4A@ E ,<54 F<5454D4A:E858D4FFBA74A74?4@:8D5BA: F8DE85GF F8:4> ?GDGE 4D4; :8D4> :8D5BA:  "868C4F4A:8D5BA:E8>4D4A: D. Tumbukan Lenting Sebagian pada Benda Jatuh Bebas v1 h1 ,G@5G>4A ?8AFG =G:4 C474 E85G4; 58A74 J4A: 58D:8D4>=4FG;5854E 4?4@>4EGEE854:4<58A74>87G4 474?4;?4AF4< *8D;4F<>4A)-  8A:4A78@<><4A>868C4F4A58A74 >87G4 E858?G@ 74A E8EG74; FG@5G>4A 474?4; AB? +85G4;5B?4=4FG;5854E74D<>8F?4AF4<@8@8AG;<C8DE4@44A v2 h2 Gambar 4.5 +  Tumbukan lenting sebagian pada benda jatuh bebas. M  %868C4F4A5B?4E858?G@74AE8EG74;@8AG@5G>?4AF4<@8@8AG;<C8DE4@44A +    74A+    M  ,4A74 A8:4F<9 C474 +  @8A4A74>4A 4D4; 5B?4 >8 54I4; 74A F4A74 CBE4A 4D4; 5B?4 >8 4F4E  %B894AC47458A74=4FG;>8?4AF4<74A >8@G7<4A @8@4AFG? 5858D4C4 >4?<  +854:4< 6BAFB; C8D;4F<>4A >4EGE C474 )-   *474 >4EGE F8DE85GF C8DE4@44A >B894A=4FG;5854E74D<EG4FGF* &B>4E<F*7>4A C474:4@54D B?458D:8D4>5854EE8C4A=4A:F4?4A:?<64?<@4EE4 %87G4AJ458DFG@5G>4AE864D4 8?4EF868C4F4A5B?4E8E44FE858?G@@8AG@5G> 5B?4 P A 5 "868C4F4A5B?4E8E44FE8F8?4; x 58DFG@5G>4A78A:4A5B?4  B R 6 8D4C4FE<@G@J4A:7<64C4<B?8;58A74  R +B4?'8AG=G)?<@C<478+44A:4@54D ,44A 5 A 1 F4?4A:E858?G@=4FG;474?4; F4A -F4A X B   2 4 @4EE45B?4## R R @4EE45B?4# # 4 %868C4F4A5B?4E8E44FE858?G@@8AG@5G> 5B?4E4@478A:4A>868C4F4AC474CBE4 #+ #-#F4A  2 +  F4A  5 %868C4F4A5B?4E8E44FE8F8?4;58DFG@5G>4A78A:4A5B?4@8@8AG;<"G>G@ %8>8>4?4A'B@8AFG@ #+#+ #+#+ #+ #+ #+ +  ++  F4A  ++  "G>G@%8>8>4?4AA8D:<'8>4A<> # +  #+  #+  #+   #+  #+ #+  #F4A   #+ #+ F4A   + +   4D<C8DE4@44A74A4>4A74A474?4;   F4A     +  F4A  F4A   +    Kata Kunci + • koefisien restitusi +  F4A  @ E   F4A @ E  ,E<@G@J4A:7<64C4<5B?4E8F8?4;FG@5G>4A74A<>7<CBEE<@G@5B?4E8F8?4;FG@5G>4A474?4;.   F4A   74D<74E4DF4?4A: $47<>868C4F4A5B?4E8F8?4;FG@5G>4A474?4;+ 6 Tes Kompetensi Subbab D "-&'*($!()0'0(/%$* +85G4;5B?474A74D<>8F?4AF4<74A74A >8@54?<  $<>4 >B894AAJ4  58D4C4>4;F4A +85G4;58A7474A74D<EG4FGF8@C4FE8=4G; @7<4F4E?4AF4< +8F8?4;@8A:8A4<?4AF4<5B?4 @8@4AFG?>8@54?<74A58A74A4<>?4:<E8FB894A58A74F8DE85GF  +85G4;5B?474A74D<:87GA:J4A:F4A>8@54?< *474C4AFG?4AC8DF4@45B?4@8A64C4< >8F87G4@8A64C4<>8F4A F<74> ?8AFG =G:4 C474 C8D J4 >4JG J4A: 7<<>4F>4A C474 E8GF4E F4?<  %8@G7<4A 7<:4AFGA:>4A E878@<><4A DGC4 4:4D 54?B> 74C4F 58D:8D4> 78A:4A 5854E  JGA4A E8C8DF< 4A E854:4< E4?4; E4FG64D4GAFG>@8A:G>GD>8?4=G4AC8?GDG *8?GDGJ4A:4>4A7GD>8?4=G 4AAJ47>4A74D<E85G4;E8A=4F4>84D4;54?B>F8DE85GF *8D;4F<>4A )-  '4A54?B>J4A:F8D:4AFGA:@8@<@4EE4#E874A:>4A C8?GDG F8DE85GF @8@< @4EE4 #*  *8?GDG J4A: 7>4A F8DE85GF 58DE4D4A: 74?4@ 54?B> 74A 58D:8D4> 58DE4@4E4@4 78A:4A >868C4F4A + E8; 58D4JGA 74A @8A64C4< >8FG@ %8>8>4?4A 'B@8AFG@ &G@ %8>8>4?4A A8D:< '8>4A<> 8A8D:< > J4A: 7<@<C8?GDG74A54?B>C474CBE< C8?GDG 74A 54?B> >8F<>4 @8A64C4< >8FE<@G@  +864D4 @4F8@4F84744A F8DE85GF 74C4F 74A E854:4< 58D<>GF #   # + # #    *  * M  +   4D< "-.)*  4  74A "-.)*  4  7: #   @4EE4 54?B> >: +*  >868C4F4A C8?GDG @ E +  >868C4F4A E8F8?4; C8?GDG 74A 54?B> 58DFG@5G>4A @ E +8CBFBA:54?B>>4JG58D@4EE4>:F8D:4AFGA:C474E8GF4EF4?< +85G4;C8?GDG J4A:@4EE4AJ4 :7>4A74D<E85G4;E8A4C4A>84D4;54?B>E8;F8DE85GF58D4JGA74AA4<>E8F87G7G>4AE8@G?4 $<>4C8D68C4F4A:D4H4A >868C4F4AC8?GDGE858?G@@8A:8A4<54?B>      >:  >: untuk Anda Gaya dorong pada roket dihasilkan akibat semburan gas panas dengan kecepatan tinggi. Gas panas tersebut dihasilkan dari proses pembakaran hidrogen cair dan oksigen cair. Untuk mengatasi pengaruh gravitasi Bumi, roket memiliki percepatan 3 kali percepatan gravitasi Bumi. Oleh karena itu, gaya dorong yang harus diberikan oleh roket harus lebih dari 3 × 107 N. Information for You Contoh 4.5 2 <>8F4;G< #* :  >: #>:  #  #    +  # Informasi Rocket propulsion is produced by hot gas expelled from the rear of the rocket at high velocity. The hot gas made from burning of liquid hydrogen and liquid oxygen. To abandon the earth’s gravitational force, rocket have to get acceleration three times faster than earth’s gravitational acceleration. So, rocket propulsion should be more 3 × 107 N.  @ E  6@ @    @ E    @ @ E $47<>868C4F4AC8?GDGE858?G@@8A:8A4<54?B>474?4; @ E Tes Kompetensi Subbab E "-&'*($!()0'0(/%$* +85G4;54?B>54=458D@4EE4 >:F8D:4AFGA:C474 E8GF4E F4?< C4A=4A:  4?B> F8DE85GF 7 B?8; E85GF868C4F4A @8A74F4D @ E $<>4FG@5G>4AAJ48?4EF8FE<@G@J4A:74C4F 7<64C4<54?B>F8DE85GF G4 5B?4 >86:74A >:7<:4AFGA:>4A C474E8GF4EF4?<  @ +8F<4C5B?4@G?4 @G?47<58D<4JGA4AE858E4D LF8D;474C :4D4?E8C8DF<C474:4@54D %8@G7<4A>87G45B?4  787G4AJ4 58DFG@5G>4A E864D4 8?4EF8A4<>4A>87G45B?4F8DE85GFE8F8?4;FG@5G>4A +85G4; 58A74 F8D:4AFGA: C474 E8GF4E F4?< J4A: C4A=4A:AJ4 6@ 8A74F8DE85GF7B?8; 58A74?44?<@4EE458A74E8@G?4 $<>4FG@5G>4AAJ48?4EF4; >868C4F4A 58A74 J4A: @8AG@5G> 4:4D 58A74J4A:F8D:4AFGA:F8DE85GF@8A64C4<FF8DF4A@8AG@5G>5B?4J4A:58D@4EE4  >:  $<>4 >B894A  58D4C4 @8F8D>4;5B?44>4AA4<>C4A=4A:F4?<  @ B?4J4A:@4EE4AJ4>:58D474C474CBE4D8F ?4?G F 78A:4A F4A:4A >8@G7<4A ?8C4E>4A  A74 4>4A @8?<;4F54?BA>4D8FF8DE85GFF8D7BDBA:B?8;G74D4J4A:>8?G4D74D<74?4@ 54?BA >4E8F  *D4A CD8D=4 DB>8F 'B@8AFG@54?BAE858?G@74A474?4;E4@478A:4AAB?>4D8A4 +   %8F<>4 54?BA 74A @B@8AFG@ 54?BA @8A=47< &  #54?BA+54?BA *8DG54;4A@B@8AFG@AJ4C8DE4FG4AI4>FG474?4;E4@478A:4A:4J47BDBA: J4A: 7G>4A 8@5GE4A G74D4 F8D;474C 54?BA J4A: 4D4;AJ4 58D?4I4A4A 78A:4A 4D4; >8?4=G4A 54?BA  )?8; >4D8A4 CD8FC8DG54;4A@B@8AFG@C474DB>8F74C4F74AE854:4< 58D<>GF   #+  &   M  ) ) %8F8D4A:4A :4J47BDBA:DB>8F( +>868C4F4ADB>8F@ E !4J4 7BDBA: J4A: 7G>4A :4E C474 54?BA 74C4F 7<4A4?B:<>4A E854:4< :4J4 7BDBA: 54;4A 54>4D C474 DB>8F Gambar 4.8 Gaya dorong pada balon. Tes Kompetensi Subbab F "-&'*($!()0'0(/%$* <>8F4;G<:4EC4A4EJ4A:>8?G4D74D<DB>8F@8@< >8?4=G4A @ E ,8AFG>4A58E4D:4J47BDBA:E85G4; DB>8FJ4A:@8E4A:4EC4A4E ;4E4D4A78A:4A>8?4=G4AC4A64D4A:4E  >: E 104 Mudah dan Aktif Belajar Fisika untuk Kelas XI '4EE4FBF4?E85G4;DB>8FF8D@4EG>54;4A54>4DAJ4 474?4; >: +8@5GD4A:4J4C4A4EJ4A:>8?G4D74D< DB>8F@8@<>8?4=G4A  @ E $<>47<;4D4C>4ADB>8F 74C4F@8?4=G78A:4AC8D68C4F4A @ E F8AFG>4A?4; >8?4=G4AC8DG54;4A@4EE4:4E7<74?4@DB>8FF8DE85GF Rangkuman    # + # + # + # +  + M+ M+ M+  4F4G>B894AF<74>?8AF4?<>87G4 58A74J4A:58DFG@5G>4A4>4A58DE4FG74A58D:8D4> 58DE4@4E8F8?4;FG@5G>4A *474=8A4AG@ %8>8>4?4A A8D:< % F<74> 58D?4>G 8A8D:<E854:<4A;4?BD8A8D:< 5GAJ<74A@8AJ8545>4AC8DG54;4AIG=G7C474 58A74 # + # + # # + *474FG@5G>4A?8AFGC8DE4@44A # + # + # + # +  'B@8AFG@J4A:7<@<EG4FG58A74474?4;;4E4?<4A 4AF4D4 @4EE4 74A >868C4F4A C474 E44F F8DF8AFG  'B@8AFG@ @8DGC4>4A 58E4D4A H8>FBD J4A:4D4;AJ4E4@478A:4A4D4;>868C4F4AAJ4 , #1 #@CG?E474?4;;4E4?<:4J474AE8?4A:I4>FGE8?4@4 :4J458>8D=4   ) #@CG?EJ4A:58>8D=4C474EG4FG58A7458E4DAJ4E4@4 78A:4AC8DG54;4A@B@8AFG@J4A:7<4?4@<58A74  # 1 #1 M#1 "G>G@%8>8>4?4A'B@8AFG@@8AJ4F4>4A54;I4 =G@?4;@B@8AFG@E858?G@74AE8EG74;FG@5G>4A 474?4;E4@4J4G@##(8IFBA@8AJ4F4>4A54;I4:4J4J4A: 7<58D<>4AC474EG4FG58A7458E4DAJ4E4@478A:4A C8DG54;4A @B@8AFG@ 58A74 E8F<4C E4FG E4FG4A I4>FG , # 1  # 1   ) ) %B89GD4A >8?8AF4A +   +       +  +  "G>G@%8>8>4?4A'B@8AFG@58D?4>GC474E8@G4 =8A4A *474FG@5G>4A?8AFG   +   +         +  +  8A74J4A:58D:8D4>=4FG;5854E@8DGC4>4A=8A4A?8AFGD 78A:4A 4JGA4A 54?78A:4A@8@4A944F>4ACD4AF<74> ?8AF4?<  #  #  +    #   Momentum, Impuls, dan Tumbukan 105 Peta Konsep +)"*/0)),0(.!*0)0'* @8@54;4E "G>G@%8>8>4?4A 'B@8AFG@ 58D?4>G 'B@8AFG@ #@CG?E 7<:GA4>4A GAFG> @8A:4A4?G C474 ,G@5G>4A =8A4A &8AF4A &8AF4A ,<74>&8AF4?< Refleksi Setelah mempelajari bab ini, tentu Anda dapat memahami konsep momentum, impuls, dan tumbukan. Anda juga tentu dapat menjelaskan jenis-jenis tumbukan yang mungkin terjadi dan hukum apa saja yang berlaku di dalamnya. Dari keseluruhan materi yang telah Anda pelajari, bagian manakah yang menurut Anda sulit? Coba Anda diskusikan dengan teman atau guru Fisika Anda. 106 Mudah dan Aktif Belajar Fisika untuk Kelas XI Dengan mempelajari bab ini, Anda dapat mengetahui bahwa untuk mengukur kecepatan peluru tidak harus memasang alat ukur pada peluru. Anda cukup menghitung jejak yang ditinggalkannya, seperti pada bandul balistik. Nah, coba sebutkan manfaat lain mempelajari bab ini. Tes Kompetensi Bab 4  %(%$($.($./0&2*3*#,(%*#/",/!*'"-&'*($,!0'0(/%$*    <@8AE<<@CG?E474?4; 4 2'32&32,3M 5 2'32&32,3M 6 2'32&3M 2,3M 7 2'32&3M 2,3 8 2'32&3 2,3 G458A74@8@<@4EE4J4A:E4@4E874A:>4A @B@8AFG@58A74C8DF4@47G4>4?<@B@8AFG@58A74 >87G4 *8D54A758A74C8DF4@474A 58A74>87G4F8DE85GF474?4; 4  5  6  7  8  !4@54D58D<>GF@8AGA=G>>4A:D49<>(/)74D<:8D4> E85G4;58A74J4A:@4EE4AJ4>: 'B@8AFG@58A74 s (m) F8DE85GF474?4; 4 >:@ E 24 5 >:@ E 6 >:@ E 7 >:@ E t (s) 8 >:@ E 8 +85G4; 5B?4 5 @8A::GA4>4A FBA:>4F 78A:4A:4J4 A8IFBA74?4@I4>FG @BA $<>4@4EE45B?4  >:>868C4F4A5B?4E8F8?4;7 474?4; 4  @ E 5 @ E 6 @ E 7  @ E 8  @ E !D49<>@B@8AFG@&F8D;474CI4>FG)74D<E85G4; 58A7458D@4EE4#J4A:7>4AH8DF<>4?>84F4E 474?4; 4 p t 5 p t 6 p t 7 p t 8 p t  +85G4;5B?474D<>84744A7<4@7G?78A:4A:4J4  A8IFBA;868C4F4A @ E $<>4@4EE45B?4 >:C8@G>G?4>4A@8AJ8AFG;5B?4 E8?4@4 4 N M E 5 N M E 6 N M E 7 N M E 8 N M E  !4J4J4A:74AGAFG>@8A:;8AF<>4A58A7458D @4EE4>:J4A:58D:8D4>78A:4A>868C4F4A @ E ;BA474?4; 4  A8IFBA 5  A8IFBA 6  A8IFBA 7  A8IFBA 8  A8IFBA  8A7458D@4EE4#@8@<@B@8AFG@&74A8A8D:< > $<>48A8D:<>58DG54;@8A=47<  @B@8AFG@AJ4@8A=47< 4 & 5 & 6 & 7 & 8 &  B?474A@8@<@B@8AFG@J4A:E4@474A @4EE4@4>4 4 >868C4F4A>868C4F4A 5 8A8D:<>8A8D:<> 6 8A8D:<>8A8D:<> 7 8A8D:<>8A8D:<> 8 >868C4F4A>868C4F4A Momentum, Impuls, dan Tumbukan 107 +8BD4A:4A4>J4A:@4EE4AJ4 >:E874A:58D7:J4A:E874A:@8?GA6GD>84D4; GF4D478A:4A>868C4F4A @ E ,<54F<544A4>F8DE85GF @8?BA64F >8 4D4; E8?4F4A 78A:4A >868C4F4A  @ E %868C4F4AC8D4;GF8DE85GF@8A=47< 4 @ E 8 @ E 5 @ E 7  @ E 6 @ E 8D74E4D>4AEB4?AB@BD =<>44D4;?BA64F4A4A4>>8 GF4D4>868C4F4AC8D4;G4>4A@8A=47< 4 @ E 5 @ E 6 @ E 7 @ E 8 @ E *474 FG@5G>4A ?8AFG ;G>G@ >8>8>4?4A 4 @B@8AFG@ 5 8A8D:<> 6 8A8D:<CBF8AE<4? 7 >8E8F<@54A:4A 8 8A8D:<>74A@B@8AFG@  +85G4;58A74=4FG;5854E74D<>8F4A >8@54?< E864D4 F8:4> ?GDGE $<>4>B898F4FG@5G>4A78A:4A?4AF4<8?4EFB89868C4F4AC4AFG?5B?4 E8F8?4;@8AG@5G>?4AF4<474?4; 4 @ E 5 @ E 6 @ E 7 @ E 8 @ E  +85G4;5B?4=4FG;5854E74D<>8F4>B8947<>8F4;G<58A7458A7458D<>GF7<;8AF<>4AB?8; 7FGJ4A:E4@47<4AF4D458A74 108 Mudah dan Aktif Belajar Fisika untuk Kelas XI  58A74 F8DE85GF J4A: @8A:4?4@< :4J4 F8D58E4D C474 I4>FG58DFG@5G>4A78A:4A7:58D:8D4>78A:4A ?4=G@ E 5 58A74J4A:58D@4EE4 >:58D:8D4>78A:4A ?4=G @ E 6 58A74J4A:58D@4EE4 >:58D:8D4>78A:4A?4=G @ E 7 58A74J4A:58D@4EE4 >:58D:8D4>78A:4A?4=G @ E 8 58A74J4A:58D@4EE4 >:58D:8D4>78A:4A?4=G  @ E +85G4;58A7458D@4EE4 >:58D:8D4>>8>4A4A78A:4A >868C4F4A@ E74A@8AG@5G>58A74?4:74A58D:8D4>>8>868C4F4A  @ E  $<>4 >87G4 58A74 E4?4F E8F8?4; FG@5G>4A>868C4F4A>87G458A74F8DE85GF474?4; 4 @ E>8>4A4A 5 @ E>8>8>4A4A 7 @ E>8> 78A:4A >868C4F4A E858E4D @ E74A@8A8@5GEE85G4;54?B>58D@4EE4 >:J4A:7<4@7<4F4E5<74A:74F4D?<6 474?4;  @ E %868C4F4A54?B>>4D8A4F8DF8@5GEC8?GDG474?4; 4  @ E 5 @ E 6 @ E 7  @ E 8  @ E +85G4;5B@74AH8DF<>4?>84F4E *474F F8DF@8A=47<7G454:<4A 78A:4A C8D54A7>868C4F4A54:<4A5B@J4A:58E4D @ E %868C4F4A54:<4A5B@J4A:>86: 58D:8D4>E4?868C4F4A@ E 74A@ E $<>4FG@5G>4AJ4A:F8D=47<?8AF868C4F4A58A7474A474?4; 4 @ E74A@ E 5 @ E74A@ E 6 @ E74A @ E 7 @ E74A @ E 8 @ E74A @ E  2($,"-/*3*"-%'0/%*%!"*#*/",/ +85G4; 58A74 58D@4EE4  >: 7<=4FG;>4A F4AC4 >868C4F4A4I4?74D<>8F4C8D68C4F4A :D4H4A?4;@B@8AFG@ 58A74E44F@8AG@5G>F4A4; +85G4; @B5: 58D:8D4> 78A:4A >8?4=G4A @ E "4A 4:4D@B5BA G45G4;58A7474A@8@<@4EE4 :74A : $<>4>868C4F4A58A74 6@ E74A>868C4F4A 58A74 6@ E74A:8D4>>87G458A74F8DE85GF 58D?4I4A4A4D4;F8AFG>4A>868C4F4AE8F<4C58A74 E8F8?4;FG@5G>4A=<>4 4 >87G458A74@8?8>4F@8A=47<E4FG74A 5 FG@5G>4AJ4A:F8D=47<?8AF: J4A: 58D:8D4> 78A:4A >868C4F4A @ E@8A45D4>5B?4?4E84D4;78A:4A>868C4F4A@ E74A58D@4EE4 >: +8F8?4;FG@5G>4A>87G45B?458D:8D4>58DE4@4 8D4C4>4;>8?4=G4A>87G45B?4E8F8?4;FG@5G>4A +85G4;5B@58D@4EE4>:7>4AH8DF<>4?>8 4F4E78A:4A>868C4F4A4I4? @ E +8F8?4; E 5B@@8?874>@8A=47<7G454:<4A@4E:74A>: +8E44FE8F8?4;@8?874>54:<4AJ4A: >86868C4F4A @ E58D:8D4>H8DF<>4?>84F4E 8D4C4>868C4F4A54:<4AJ4A:58E4D +85G4;58A7458D@4EE4>:58D:8D4>78A:4A>868 C4F4A @ E@8A:8A4<?4AF4<78A:4AEG7GF74F4A: L 74A74A>8@54?<78A:4AEG7GFC4AFG? L 4 ,8AFG>4A >B894A 58A74 F8DE85GF 5 ,8AFG>4A58E4DAJ4C8DG54;4A@B@8AFG@58A74 F8DE85GF      +85G4;54?B>58D@4EE4 >:F8D?8F4>7<4F4E?4AF4<?<6>4A ;BD 74A C8?GDG 7<4@ 7< 74?4@ 54?B> F8DE85GF 4?B>58D:8E8DE8=4G; @8F8D74?4@I4>FG 78F<> 8D4C4>4;>868C4F4AC8?GDG>8F<>4@8A:8A4< 54?B> @ E   *4A=<58D@4EE4 >:@8A4<><C8D4;G58D@4EE4 >: J4A:E874A:@8?GA6GD>8F<@GD78A:4A>868C4F4A E858E4D  @ E  ,<54F<54 *4A=< @8?BA64F 78A:4A >868C4F4A  @ E F8D;474C C8D4;G  8D4C4>4; >868C4F4AC8D4;GE8E44FE8F8?4;*4A=<@8?BA64F=<>4 4 4D4;?BA64F4A>8F<@GD74A 5 4D4;?BA64F4A>8GF4D4  *8D;4F<>4A:4@54D58D<>GF A P 1m 1m B B?474A@4E:7<<>4F 78A:4AE8GF4EF4?<J4A:C4A=4A:AJ4 @C474C4>G* ,4?<5B?47<4D4;>4A@8A74F4D>8@G7<4A74A @8AG@5G> 5B?4   8D4C4 FE<@G@ J4A: 7<64C4<5B?4=<>4 @ E 74AFG@5G>4A>87G4 5B?458DE<94F 4 ?8AF?8AF4?< +8:G@C4? C?4EF: 7>4A 78A:4A>868C4F4A @ E@8A:8A4<54?B>58D@4EE4 >:J4A:7<4@7<4F4E?4AF4<>4E4D $<>4C?4EF74A:4J4:8E8>4AF4D454?B> 74A?4AF4< (58D4C4>4;C4A=4A:C8D:8E8D4A54?B> Momentum, Impuls, dan Tumbukan 109 Proyek Semester 1 *474E8@8EF8DBAE8CF8AF4A:!8D4>74A!4J4 -AFG> ?85<; @8A4F>4A C8@4;4@4A F8AF4A: >BAE8C F8DE85GF A74 74A @8?4>G>4A>8:<4F4AE8@8EF8DE864D458D>8?B@CB>MBD4A: &4A:>4;>8:<4F4A J4A: ;4DGE A74 ?4>G>4A F8D64AFG@ 74?4@ FG:4E E8@8EF8D  +854:4< FG:4E 4>;8:<4F4AA7458DE4@4>8?B@CB>A7474A@8@5G4F?4CBD4A>8:<4F4AE8 @8EF8DJ4A:4>4A74A7<4>;G>4A Kereta Dinamika 0&0*"#%/* '8@C8?4=4D<"G>G@(8IFBA (/!*$* %8D8F474 *4C4A?4A74E4A  6@N 6@N 6@74A>4FDB?@8=458D7<4@8F8D6@   !') #'68?4;C4D5BA74A58A4A:AGD @4EE4 >8D8F4 74 74A 5854A :4AFGA:  $G@?4; @4EE4 >87G4AJ4 7<4A::4CE854:4<@4EE4EGF benang nilon katrol sisa beban kereta dinamika ticker timer pita beban gantung papan landasan   !GA4>4AE854:<4A5854A:4AFGA:GAFG>@8A::8D4>>4A>8D8F47474A E8D8F474 !8D4>>4A >8D8F4 74 58DE4@44A 78A:4A 7<;<7GC>4AAJ4 ) !' ) #' "8AF<>4A>8D8F474C474E44F5854A:4AFGA:F8C4F4>4AF<547<?4AF4<74A E8:8D4@4F<>4A) !') #' ,8?>8F<>4A) !') #'C474C8DF4E $<>4 EG74;54:GE;4E4A?4A:>4;58D<>GFAJ4 &4>G>4A ?4A:>4; >87G4 74A >8F<:4 7< 4F4E  >4?< 78A:4A 5854A :4AFGA: C8A::8D4>J4A:58D5874A4@GA78A:4A@4EE4E8DF4EC8D8F4745G4F?4; :D49<>+)GAFG>E8F<4CC8D6B544A ,8AFG>4AC8D68C4F4AE4A:D49<>J4A:A745G4FF8DE85GF G4F?4;:D49<>;G5GA:4A4AF4D4D8EG?F4A:4J478A:4AC8D68C4F4AE4; ;4EG@##(8IFBA8D<>4AC8A=8?4E4A  ,8AFG>4A58E4D:4J4:8E8>J4A:F8D=47<74?4@C8D6B544AF8DE85GF 110 Mudah dan Aktif Belajar Fisika untuk Kelas XI Tes Kompetensi Fisika Semester 1  %(%$($.($./0&2*3*#,(%*#/",/!*'"-&'*($,!0'0(/%$*    *8D68C4F4AE85G4;C4DF<>8?C474E44F)474?4;)%M& 'G?4@G?4C4DF<>8?58D:8D4>78A:4A>868C4F4A % .8>FBD>868C4F4AC4DF<>8?C474E44F)474?4; 4  )%M)& 5  M) %)& 6  ) %M)& 7 M ) %)& 8  ) %M)& +85G4;C4DF<>8?58D:8D4>E8EG4<78A:4AC8DE4@44ACBE 8E4D>868C4F4A58A74C474E44F) 78F<> 474?4; 4 @ E 5 @ E 6  @ E 7 @ E 8  @ E G45G4;58A7474A@4E: 74A>:7<;G5GA:>4A78A:4AF4?<@4EE4F4?<7<454<>4A @8?4?G<E85G4;>4FDB?58D@4EE4 >:74A58D=4D<=4D< 6@ $<>458A7458DCGF4D78A:4AF4?<C8D68C4F4AE8F<4C58A74 474?4;  @ E  4 @ E 5  @ E 6  @ E 7 @ E 8  @ E +85G4;C4DF<>8?@G?4@G?47<4@>8@G7<4A74D78A:4A=4D<=4D< @@8AGDGF C8DE4@44AC8D68C4F4A) M) *8DE4@44A>868 C4F4AE8AFD:@8?GA6GD78A:4A >868C4F4A >@ =4@>8@G7<4A74>B89>4AF4D4DB7474A=4?4A  >8@G7<4A 58D;8AF< E8F8?4;  78F<> 58E4D :4J4 C8A:8D8@4A 474?4; 4  ( 5   ( 6   ( 7  ( 8  (  *8D;4F<>4A:4@54D58D<>GF=<>45854A74A 54?B>F8C4F4>4A58D:8D4> 2 kg A B  1 kg $<>4C8D68C4F4A:D4HB89EF4F74A@8=4474?4; 4  7  5  8  6  *8D;4F<>4AEGEGA4A58A7458A74C474:4@54D58D<>GF 4 kg A B  1 kg %B89>4AF4D454?B>74A@8=4474?4;   $<>45854A74AC8D68C4F4A58A74 474?4;  @ E  4  @ E 7 @ E 5  @ E 8  @ E 6  @ E *8D;4F<>4A:4@54D58D<>GF>4AF4D458A7478A:4A5<74A: @4A GAFG> @8A7BDBA: 58A7478A:4A@4EE4#EGC4J474C4F58D:8D4>>84F4E 78A:4A>868C4F4AF8F4C474?4; 4 # 5 # 6 # 7 # 8  # 111  +85G4;58A7478A:4A@4EE4#7<58D<:4J4 ; $<>4:4J4:8E8>4AF4D458A7474A?4AF4<E4@4 78A:4A!C8D68C4F4A:8D4>58A74474?4;  ! 4  #  ! 5  # # 6   ! 7  #  ! #  ! +8BD4A:A8?4J4A@8AJ858D4A:<EGA:4<@8A::GA4>4A C8D4;G74JGA: *8D4;G74JGA:F8DE85GFE8?4?G7<4D4; >4AF8:4>?GDGEF8D;474C4D4;4DGE4868C4F 4A@ EE874A:>4A>868C4F4A4?>4A 78A:4A EG7GF 8?8H4E< L 74A >868C4F4A4I4? @ E $<>4C8D68C4F4A:D4H87G7G>4AC8?GDGE44F)E8>BA 474?4; 4 - @. @ 5 - @. 6 7 8 - @. @ - @.  @ - @. @ +85G4;C8?GDG7>4A78A:4A>868C4F4A4I4? @ E74AEG7GF8?8H4EE<@G@74AF=4G;@4>E<@G@J4A:7<64C4<B?8; C8?GDGF8DE85GF474?4; 4  7  5  8  6   *474C8D@45B?45B?4J4A:7 78A:4A EG7GF 8?8H4E< L $<>4:8E8>4A78A:4AG74D47<454<>4A 74A @ E 5B?4@8A64C4<=4D4>E8=4G; 4 @ 5 @ 6 @ 7  @ 8  @ 112 Mudah dan Aktif Belajar Fisika untuk Kelas XI  +85G4; E8C874 @BFBD @8@58?B> C474 F<>GA:4A 58D58AFG>5GEGD?4D4A78A:4A=4D<=4D< @ $<>4 >B894A4AF4D4DB7474A=4?4A  74A  @ E >868C4F4A@BFBDF8D58E4D4:4DE8C874@B FBDF<74>E?4A=4?4AJ4A: 74F4D78A:4A>8?4=G4A >@ =4@ $<>4>B894AF4D454A@B54A@B5@ 5 >@ 8 >@ 6 @  +85G4; 54?B> 58D@4EE4  >: F8D?8F4> C474 5<74A: @8A74F4D J4A: @8@CGAJ4< >B89 >  4?B>7<58D<:4J4 (74A58DEG7GF LF8D;474C  5<74A:@8A74F4D *8D68C4F4A54?B>F8DE85GF474?4;   @ E 4   @ E 5   @ E 6    @ E 7    @ E 8   $<>4@4EE4G?4A >4?<@4EE4G@<74A=4D<=4D<G?4A  >4?<=4D<=4D<G@<C8D54A7G@<  F8D;474CG?4A474?4; 4  7   5  8   6   $<>4C8D54A7;4FG?GFG5C8D54A7;4FG?GFG5474?4; 4  7   5  8  6   *8D54A74A@4EE4C?4A8FC 74A@4EE4G@<C58D54A74?<@4EE4G@< 74A58D=4D<=4D<>4?<=4D<=4D<G@< 8D4F58A747< C?4A8F 0 7<54A74A 78A:4A 58D4FAJ4 7< G@< @8A=47< 4 >4?< 5 >4?< a >4?< 6 b  >4?< 7  >4?< 8  +85G4; E4F8?8F44AG@< $<>47<>8F4;G<=4D<=4D<G@<474?4; C8D4D4A 4 5 6 7  +8BD4A:A8?4J4A@8A4D<>C8D4;GAJ478A:4AEG7GFL F8D;474C4D4;;BD4A8?4J4AF8DE85GF@8A4D<>C8D4;G78A:4A :4J4   ( 58E4D GE4;4 J4A: 7G>4A A8?4J4A F8DE85GF474?4; 4  $ 7  $ 5                    8        +85G4;58A74J4A:58D4747<G?4A58D:8D4>78A:4A C8D68C4F4A>4D8A4@8A74C4F:4J4  $<>458A74 F8DE85GF7<54I4>8G@<J4A::4J4:D4H4?<@4EE4G?4A74A58A74F8DE85GF7<58D<:4J4 =G:4 C8D68C4F4A474?4; 4       7   8   '8AGDGF "G>G@ ### %8C?8D >G47D4F C8DC?4A8F>8'4F4;4D< 6 C4A:>4FF<:4@4EE4C?4A8F 7 C4A:>4FF<:4=4D4>C?4A8F>8'4F4;4D< 8 >G47D4F=4D4>'4F4;4D<>8C?4A8F  $<>4C8D4?>84F4E;8F8F<>45B?458D474C474>8F48A8D:<CBF8AE<4?AJ4@G?4@G?4E858E4D $ 74A @ E >868C4F4A58A74F8C4FE858?G@E4@C4< 7<F4A4;474?4; 4 @ E 7  @ E 5 @ E 8  @ E 6 @ E +85G4; @8E8A74D44A 58D@BFBD @8@< 74J4 E858E4D ;C /4>FGJ4A:74A@8E@8A:;4E4A:4J4  (74A@8A::8D4>>4A >8A74D44AE8=4G; @474?4; 4 E8>BA 7 E8>BA 5 E8>BA 8 E8>BA 6 E8>BA +85G4;:D4A4F58D@4EE4 >:F<54F<54@8?874>74A C864;@8A=47<7G454:<4A78A:4AC8D54A7 58D?4I4A4A 4D4;  $<>4 C864;4A J4A: >86< >868C4F4A   @ E C8D54A7 C864;4A C8DF4@4 74A C864;4A>87G4E8E44FE8F8?4;:D4A4FF8DE85GF@8?874> 474?4; 4  7  5  8  6  !4EC4A4EJ4A:7<;4E4AB?8;E85G4;DB>8F@8@< >8?4=G4A @ E74AF8D=47<C8@54>4D4A:4EE854AJ4>  >:74?4@I4>FGE4FGE8>BA 8E4DAJ4:4J47BDBA: DB>8FF8DE85GF474?4; 4 ( 7  ( 5 ( 8  ( 6  ( Tes Kompetensi Fisika Semester 1 113  2($,"-/*3*"-%'0/%*%!"*#*/",/ *474EGEGA4A58A7458A74E8C8DF<C474:4@54D@4EE4 58A7474AE4@4J4: A B  $<>4>B894A>4AF4D458A7474A5<74A:  @4;C8D68C4F4A  E8F<4C58A74=<>4>87G458A74F8DE85GF74A *8D;4F<>4A:4@54D58D<>GF4>87G458A7474AF4?<@8@<F8:4A:4A  ( $<>4E4;>B894AF4D4  58A7474A5<74A: G458A7474AF8DEGEGAE8C8DF<:4@54D58D<>GF A B  114 '4EE4>:74A@4EE4>: @ E  ,8AFG>4A58E4DC8D68C4F4A58A7474AF8:4A:4A F4?4>B894AEF4F78A:4AC8D68C4F4AF8F4CJ4  @F8DAJ4F4 >868C4F4AAJ4@8A=47< @ E 4 8D4C4>4;>868C4F4A4I4?@B5FGF8@CG;@B5:74A@4EE4 '4F4;4D<  N  >: $<>4=4D4>4AF4D4'4F4;4D< 74AC?4A8F1GC:F8AFG>4A 4 :4J4:D4H4?4D4A  8D4FE8E8BD4A:7<G@<474?4; ( $<>4=4D<=4D< G@<N @@4EE4G@< N >: 74A>BAEF4AF4:D4H:  58D4C4>4;58D4FBD4A:F8DE85GFC474>8F44AG@<  <>8F4;G<@4EE4G@< N >:=4D<=4D<G@< N @74AN M ( @ >: $<>4 E85G4;E4F8?:58D874DC474 >8F@ 74D< C8D@G>44A G@< 78A:4A ??4D4A58D4C4>4;?4=G?4A >8 4F4E 78A:4A 8A8D:< > =BG?8 <>8F4;G<@4EE458A74 >: 74A @ E +8F8?4;@8A64C4<FCGA64>58A74 F8DE85GF>8@54?<>8F4A4; ,8AFG>4A?4;8A8D:<> 58A74C474E44F@8A64C4<>8F8F FBA 4?4@I4>FG E8>BADB>8FF8DE85GF@4@CG@8AJ8@5GD>4A:4E C4A4EE854AJ4> >: <>8F4;G<:4EC4A4EF8DE85GF 74A>8?G4D78A:4A>868C4F4A  @ E A::4CC8DG54;4AC8D54A74D 74A@4EE4DB>8FE4A:4F>864A?4;=4D4>=8?4=4;DB>8F74?4@ I4>FG @8A58D@4EE4 >:58D4747<4F4E?4AF4<74A 74?4@>84744A7<4@ %B8954?B>74A5<74A: ;BD>4A;BDF8DE85GF 74A7<4@7<74?4@54?B> $<>454?B>58D:8E8DE8=4G;  @8F8D 58D4C4>4; >868C4F4A C8?GDG >8F<>4 @8AG@5G>54?B> Bab 5 Sumber: Contemporary College Physics, 1993 Peloncat indah menekuk tubuhnya ketika mulai berputar dan merentangkan tubuhnya ketika hendak mendekati air. Gerak Rotasi dan Kesetimbangan Benda Tegar Hasil yang harus Anda capai: menerapkan konsep dan prinsip mekanika klasik sistem kontinu dalam menyelesaikan masalah. Setelah mempelajari bab ini, Anda harus mampu: memformulasikan hubungan antara konsep torsi, momentum sudut, dan momen inersia berdasarkan Hukum II Newton, serta penerapannya dalam masalah benda tegar. &3?3:=<1/A7<2/6 #3<5/>//A:3AA3?@30BA@3:/:B;3<39B9AB0B6BA/?!3A79/ 932B/:3<5/<2/<9/97/A 270/<27<59/<>/2/@//A27?33?=:36/970/A>3<5B?/<5/< ;=;3<7<3?@7/E/<527;7:797AB0B63?=:36 ;=;3< 7<3?@7/ E/<5 :3076 03@/? @367<55/ 9313>/A/< @B2BA/ A3?23<5/? 0B3?179/< /7? /:/; 0/0 7<7 <2/ /9/< ;3;>3:/8/?7 >?7<@7>>?7<@7> 47@79/ E/<5 ;3<8/27/1B/<2/?7>3?7@A7D/A3?@30BA/:/;93672B>/<@36/?76/?7<2/ /9/<0/:79/@7>3<3?/>/<9=<@3>27/E/<527;/9@B223<5/<;=;3<5/E/;=;3<  )30BA9/<83<7@83<7@93@3A7;0/<5/< 3:/@9/< 9=>3:2/<;=;3<7<3?@7/ 23<5/<0/6/@/<2/@3<27?7  >/6B0B<5/<//>3<53?A7/<2/?7A7A7903?/A03<2/ AB;)B2BA2/<B9B;!3>:3? A. Kinematika Gerak Rotasi Gambar 5.1 Baling-baling kipas berotasi pada porosnya. y P r s x O 79/<2/;3;>3?6/A79/<@30B/6>7?7<5/<67A/;E/<5@32/<503?>BA/? /A/B 0/:7<50/:7<5 97>/@ /<57< E/<5 @32/<5 03?>BA/? <2/ /9/< ;3:76/A 0/6D/ >7?7<5/< 67A/; 2/< 0/:7<50/:7<5 97>/@ /<57< A3?@30BA ;3:/9B9/< 53?/9 ?=A/@7 >/2/ @30B/6 @B;0B @A/@7=<3? A3A/> 2/:/; 93?/<59/ /1B/< 7<3?@7/A3?A332/ E/<5 @32/<5 03?>BA/? 2/< 9=;727 >BA/? 1. Posisi Sudut dalam Gerak Rotasi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y P,t2  2. Kecepatan Sudut Rata-Rata dalam Gerak Rotasi P,t1 x O 03<2/ A35/? 03?03 @B;0B-- >/2/ D/9AB )  !3;B27/< >/2/ @//A )  @B2BA E/<5 2703/A/< @B2BA ?/A/?/A/BA/?/< 9313>/A/< @B2BA ?/A/?/A/ 2/>/A  27BA/?/<@39=< Mudah dan Aktif Belajar Fisika untuk Kelas XI 3. Kecepatan Sudut Sesaat dalam Gerak Rotasi  ?/2  /5/7;//A/< @B2BA @3@//A 2/?7 @30B/6 03<2/A35/?E/<503?53?/9?=A/@7)/;/6/:/A/<@B2BA@3@//A 27A33?B0/6/< 9313>/A/</A/< @B2BA @3@//A >/2/ 53?/9 ?=A/@7 273?@/;//<   :7;  :7; )  )  ) /A/B   ) 0 I  3<5/< 23;797/< 9313>/A/< @B2BA @3@//A ;3?B>/9/< AB?B3?A/;/ 2/?7 >3?@/;//< >=@7@7 @B2BA @30/5/7 4B<5@7 D/9AB &3?6/A79/< 5?/479  A3?6/2/> ) >/2/ * .   Q P t1 t(s) t1 Gambar 5.4 Kecepatan sudut sesaat ( ) dapat ditentukan dari gradien grafik terhadap t pada sebuah titik. 79/ t  t2  t1 @/<5/A 9317: /A/B ;3<239/A7 <=: A7A79 ' /9/< @/<5/A 239/A 23<5/< & /A/B 0/69/< 03?7;>7A @367<55/ 93;7?7<5/< 5?/273< 5?/479 A3?6/2/> ) 27 A7A79 & ;3?B>/9/< 9313>/A/< @B2BA @3@//A %:36 9/?3/A/< @B2BA @3@//A 2/>/A >B:/ 273?@/;//< 03?79BA     A/< ) I  4. Percepatan Sudut dalam Gerak Rotasi )30B/6>/?A793:E/<503?53?/9?=A/@7/9/<;3;7:797>3?13>/A/<@B2BA 879/ >/?A793: A3?@30BA ;3<5/:/;7 >3?B0/6/< 9313>/A/< @B2BA 3<5/< 23;797/< >3?13>/A/< @B2BA /2/:/6 >3?B0/6/< 9313>/A/< @B2BA @3A7/> @/AB/< D/9AB @367<55/ @/AB/</A/< @B2BA ?/A/?/A/ 27/?A793: 03?53?/9 ;3:7<59/? 23<5/< 9313>/A/< @B2BA 1  >/2/ @//A )  93;B27/< 03?B0/6 ;3<8/27 2  >/2/ @//A )  >3?13>/A/< @B2BA ?/A/?/A/ >/?A793:A3?@30BA2/:/;@3:/<5D/9ABD)273?@/;//< 03?79BA    )  ) /A/B   ) I b. Percepatan Sudut Sesaat <2/A3:/6;3<53A/6B70/6D/9313>/A/<@B2BA@3@//A 27A33?B0/6/< 9313>/A/</A/< @B2BA @3@//A  >3?13>/A/<@B2BA@3@//A 8B5/;3?B>/9/<>3?13>/A/<@B2BA?/A/ ?/A/ E/<5 A3?8/27 2/:/; @3:/<5 D/9AB  )  E/<5 @/<5/A @7<59/A /A/B )    3<5/< 23;797/< >3?13>/A/< @B2BA @3@//A 273?@/;//< 03?79BA Gerak Rotasi dan Kesetimbangan Benda Tegar 117  :7; )   :7; )  1 B A t1  t (s) t1 I 3<5/< ;3<@B0@A7AB@79/< #./*+  4  93 2/:/; #./*+  4  27>3?=:36 >3?@/;//< >3?13>/A/< @B2BA @30/5/7 03?79BA 2 2 1  )  (rad/s1)  ) Gambar 5.5 Percepatan sudut sesaat berdasarkan gradien garis singgung = (t) di titik t.       ) )  )      ) I 3<5/< 23;797/< <2/ A3:/6 ;3<53A/6B7 0/6D/ >3?13>/A/< @B2BA @3@//A ;3?B>/9/< AB?B3?A/;/ 2/?7 9313>/A/< @B2BA @3@//A /A/B AB?B3?@/;//< >=@7@7 @B2BA @30/5/7 4B<5@7 D/9AB )3:/7< 7AB >3?13>/A/< @B2BA @3@//A 2/>/A >B:/ 27A3)27@B/ABA7A79&3?6/A79/<5?/479  ) >/2/ * .   &3?13>/A/< @B2BA @3@//A 27 A7A79  /2/:/6 A/< 1 , @32/<59/< >3?13>/A/< @B2BA @3@//A 27 A7A79  /2/:/6 A/< 2 . 5. Gerak Rotasi dengan Kecepatan Sudut Konstan 79/ @30B/6 03<2/ A35/? 03?53?/9 ?=A/@7 23<5/< 9313>/A/< @B2BA   9=<@A/< >3?@/;//< 53?/9 2/?7 03<2/ A35/? A3?@30BA 273?@/;//<   )   ) )     ) ) )     ) )    ) )    ) I 23<5/< 0 /2/:/6@B2BAE/<527A3;>B6>/2/@//A)  9/<A3A/>7879/>/?A793:A3?@30BA;3<5/:/;7>3?B0/6/<9313>/A/< @B2BA @367<55/ ;3<56/@7:9/< >3?13>/A/< @B2BA >3?@/;//< 53?/9 ?=A/@7 2/?7 03<2/ A35/? A3?@30BA 2/>/A 27AB?B<9/< 2/?7 #./*+  4 23<5/< <7:/7 A3A/>   )   ) )     ) ) Kata Kunci • posisi sudut • kecepatan sudut • percepatan sudut 118 Mudah dan Aktif Belajar Fisika untuk Kelas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inamika Gerak Rotasi r 1. Momen Gaya (Torsi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omen Inersia <2/A303<2/;3;7:7979313<23?B<5/< B3?A/6/<9/< 93/2//< 53?/9 03<2/E/<527/;/9/<A3A/>27/;2/>B<03<2/E/<5@32/<503?53?/9 :B?B@ 03?/AB?/< ;3;7:797 9313<23?B<5/< B 03?53?/9 :B?B@ 03?/AB?/<931B/:7/2/?3@B:A/<5/E/E/<5;3;3<5/?B673? A/6/<9/< 93/2//<B:/ 6/: ;3;>3?A/6/<9/< 53?/9 ?=A/@73<5/?B67=:36;/@@/2/<>=:/27@A?70B@7 ;/@@/ A3?6/2/> @B;0B >BA/? m r v Gambar 5.7 Partikel bermassa m berputar mengelilingi sebuah sumbu putar yang berjarak r dari partikel tersebut. a. Momen Inersia Benda Diskrit (Partikel) 79/ @30B/6 >/?A793: E/<5 03?;/@@/ # 03?>BA/? ;3<53:7:7<57 @B;0B >BA/? E/<5 03?8/?/9 ' 2/?7 >/?A793: A3?@30BA 2/>/A9/6 <2/ ;3<567AB<5 03@/?/?A793: A3?@30BA &3?6/A79/< * .  /:/; 53?/9 ;3:7<59/? 9313>/A/< :7<3/? 27/A/< @B2BA %:36 9/?3/?A793: 2/>/A 273?=:36 <7:/7 #'  E/<5 ;3/?A793:E/<503?53?/9;3:7<59/?#=;3<7<3?@7/27:/;0/<59/< 23<5/<  #' I  3<5/<23;797/<;=;3<7<3?@7/@30B/6>/?A793:@30/<27<523<5/<;/@@/ >/?A793: 2/< 9B/2?/A 8/?/9 //?A793: 2/< @B;0B >BA/?/9/< 03@/?/< @9/:/? E/<5 ;3;7:797 @/AB/< 95;  120 Mudah dan Aktif Belajar Fisika untuk Kelas XI b. Momen Inersia Benda Tegar )30B/603<2/A35/?A3?27?7/A/@@38B;:/6>/?A793:E/<5A3?>7@/6@/AB 23<5/<E/<5:/7<#=;3<7<3?@7//9/< 8B;:/6 2/?7 ;=;3< 7<3?@7/ @3;B/ >/?A793: 7AB E/9<7    #'  9/< A3A/>7B/A 27>7@/69/< @3>3?A7 * .  03?:/9B >3?@/;//<   ' # y dm r o sumbu rotasi x I  )30B/6 03<2/ 03?;/@@/ # E/<5 03?03/<8/<5  A/;>/9 @3>3?A7 * .  3<2/ A3?@30BA ;3;7:797 ;=;3< 7<3?@7/ A3?6/2/> >=?=@BA/?*7<8/B@30B/60/A/<5E/<5;3;7:797;/@@/# @3?0/ @/;/ 2/< >/<8/<5 0/A/<5  /?7 #./*+  4  2793A/6B7 0/6D/'-2/<#   @3?A/0/A/@0/A/@73?=:36 Gambar 5.8 -      -   -  Gambar 5.9 I  Momen inersia benda pejal dihitung dengan metode integral terhadap r2 dm. y L x 0 x1 x2 dm x Sebuah batang homogen memiliki massa m dengan panjang batang L. +BA/? E/<5 A3?:3A/9 >/2/ B8B<5 0/A/<5 @3>3?A7 * . 23<5/<-  2/<- ;/9/;=;3<7<3?@7/0/A/<5;3<8/27 y       - -    -                I  +BA/? E/<5 A3?:3A/9 >/2/ >3?A3<5/6/< 0/A/<5 @3>3?A7 A/;>/9>/2/* . /9/<27>3?=:36- I 2/<-   %:36 9/?3BA/?/2/>B@/A;/@@/ 27@30BA;=;3<7<3?@7/>B@/A;/@@/>; 79/@B;0B>BA/?/2/ >B@/A ;/@@/ B/A 275B3?@/;//< 03?79BA 7<7 E/<5 27@30BA @30/5/7 9/72/6 @B;0B @38/8/? >;# –1L 2 1L 2 Gambar 5.11 Momen inersia untuk sumbu putar yang terletak pada pertengahan 1 batang adalah I = ML2. 12 !3A3?/<5/< # ;/@@/03<2/  8/?/92/?7>B@/A;/@@/93@B;0B>BA/? #=;3< 7<3?@7/ 2/?7 0303?/>/ 03=@7@7 @B;0B A3?A3/A 27:76/A >/2/ A/03: 03?79BA 7<7 Gerak Rotasi dan Kesetimbangan Benda Tegar 121  #)  #=;3<<3?@7/3?0/5/73<2/ #+" * . ,.,/ 0/A/<5 @7:7<23? ,*#++#./& ;3:/:B7 >B@/A   ;3:/:B7 B8B<5   L Ingatlah 0/A/<5 @7:7<23? Momentum sudut merupakan besaran vektor. L 17<17< A7>7@    @7:7<23? >38/: ;3:/:B7 @B;0B @7:7<23? R ;3:/:B7 @B;0B @7:7<23? >38/: R @3>3?A7 A/;>/9 >/2/ 5/;0/? R       L R 0=:/ >38/: ;3:/:B7 27/;3A3? R 0=:/ 03?=<55/ 0=:/ >38/: ;3:/:B7 27/;3A3? R ;3:/:B7 @/:/6 @/AB 5/?7@ @7<55B<5/2/A3?6/2/>A7A79@B;0B<2/A3:/6;3<53A/6B70/6D/ >/2/ 03<2/ A35/?E/<503?=A/@75/E/E/<50393?8/>/2/03<2/;3:7>BA7@3:B?B60/57/< 03<2/A3A/>74=9B@>/2/5/;0/?A3?@30BA27D/97:7=:36A7A79E/<503?8/?/9 ' A3?6/2/> @B;0B ?=A/@7 /E/ A/<53<@7/:  0393?8/ 27 A7A79  @367<55/ 03<2/ 03?53?/9 ?=A/@7 23<5/< >3?13>/A/< A/<53<@7/: A 9=<@A/< #33?=:36 A'#A ' F r P x O Garis kerja F Lengan momen Gambar 5.12 Gaya F bekerja pada sebuah partikel P pada benda tegar menghasilkan torsi . B0B<5/</3?13>/A/<A/<53<@7/:A2/<>3?13>/A/<@B2BA  /2/:/6A '%:369/?33?=:36 A'# ' #' I  *3:/6 2793A/6B7 0/6D/  A ' %:36 9/?33?=:36 >3?@/;//< ;=;3< 5/E/ @303@/? #'  I  !3A3?/<5/< 03@/?;=;3<5/E/$;  03@/? >3?13>/A/< @B2BA ?/2@  ;=;3<7<3?@7/95;  Kata Kunci • • • • • • • benda diskrit benda tegar energi kinetik rotasi energi kinetik translasi momentum sudut sumbu putar torsi Contoh 5.1 )30B/60/A/<56=;=53<;3;7:797>/<8/<52/<;/@@/#/A/<5A3?@30BA2703?7 3<5@3:@367<55/2/>/A03?=A/@7@3>3?A7A/;>/9>/2/5/;0/?/A/<52/:/;93/2//< 27/;>/2/>=@7@76=?7F=3?13>/A/<@B2BA 2/<03@/? >3?13>/A/<A/<53<@7/:>/2/B8B<50/A/<5A93A79/0/A/<527:3>/@9/< 1 2  2 /E/03?/AE/<50393?8/>/2/0/A/<5/2/:/6 # 23<5/<8/?/9 "2/?7>B@/A?=A/@73<5@3: mg #=;3<<3?@7/0/A/<5E/<527>3?=:362/?7 #) /2/:/6  &3?@/;//< >3?13>/A/<@B2BA0/A/<5/2/:/6  #            #  /2703@/?>3?13>/A/<@B2BA0/A/<5/2/:/6    2/>B<03@/?>3?13>/A/<A/<53<@7/:>/2/B8B<50/A/<5/2/:/6 A  '      Tantangan untuk Anda Seorang pemain akrobat akan membutuhkan tongkat ketika melakukan aksi berjalan di atas tali. Jika ada dua buah tongkat yang sama panjang tetapi beratnya berbeda, tongkat manakah yang harus dipilih? Gerak Rotasi dan Kesetimbangan Benda Tegar 123 y 4. Momentum Sudut dan Hukum Kekekalan Momentum Sudut p sin r L O p d )3>3?A7 6/:/2/ 53?/9 A?/<@:/@7 >/2/ 53?/9 ?=A/@7 8B5/ A3?2/>/A 9=<@3> ;=;3/2/53?/9?=A/@7@/;/23<5/<>3/2/ 53?/9 A?/<@:/@7 &/2/* .  A3?:76/A@30B/6>/?A793:03?;/@@/#2/<;3;7:797 ;=;3/2/ >=@7@7 . A3?6/2/> A7A79 >B@/A  #=;3 A7A79 >B@/A  /2/:/6 x .J- Gambar 5.13 Diagram momen gaya atau torsi yang bekerja pada waktu membuka mur sebuah roda mobil. I  3@/?3?@/;//< '&@7< I  )B2BA /2/:/6@B2BAE/<52703072/<5E/<52703/A2703/:9/<8/?783;/?7A/<5/<9//9/<03@/?/<C39A=?E/<5/?/6/A 27AB:7@9/< @30/5/7 03?79BA @B2BA    G '&'#+'# '#' %:36 9/?33?=:36 dL  I d  I dt dt @367<55/ dL  dt I  #./*+  4  ;33?B0/6/< ;=;3/A2/?7>33?@/;//<A=?@72/<5/E/2/:/;03/A9/6 <2/ ;33?@/;//< A3?@30BA 79/ !()'$"   <7:/7  /9/< 9=<@A/< @367<55/ C39A=? ;=;3/?A793: A3A/> 9=<@A/< &3?/9/< B9B; !3939/:/< #=;33?B0/6/< 93:3;0/;/< ?=A/@7  /9/< 277;0/<57 =:36 9313>/A/< @B2BA 03<2/ /5/? @/:7<5;3<7/2/9/<%:369/?3/A 27AB:7@9/< @30/5/7 03?79BA   /A/B    Gambar 5.14 Momentum sudut ketika kedua tangan direntangkan adalah Ia a. 124 I  &/2/ * .   @3@3=?/<5 03?27?7 27 /A/@ >7?7<5/< E/<5 @32/<5 03?>BA/?>/2/932B/A/<5/<BA/? 27/;07: 03?7;>7A 23<5/< @B;0B AB0B6 =?/<5 7AB 2/< ;/@@/ 030/< E/<5 27>35/<5BA/? E/7AB @38/B6>/<8/<5?3BA/? Mudah dan Aktif Belajar Fisika untuk Kelas XI !3A79/>BA/?/<@32/<503?:/<5@B<52/<932B/A/<5/<E/<5;3;35/<5 030/< 27?/>/A9/< ;3<239/A7 AB0B6 @3>3?A7 >/2/ * .   ;/9/ ;=;3<7<3?@7/BA/?3?@/;//<#' 9313>/A/<@B2BAE/<527/:/;7 /9/< 03?A/;0/6 03@/? /: 7<7 27@30/09/< 9/?33/A/< @B2BA 93/2//<  ?/2@    03@/? ;=;3< 7<3?@7/ 93/2//<  95;  b  9313>/A/< @B2BA 93/2//<  ?/2@ >:79/@7:/7<2/?7B9B;!3939/:/<#=;3:/<3A 2/:/; ;3<53:7:7<57 #/A/6/?7 =6/<<3@ !3>:3? ;3:/<3A/9/<;3B:B/@2/3?/6 E/<5 @/;/ &3?6/A79/< * .   )30B/6 >:/<3A 03?53?/9 2/?7 >=@7@7 93>=@7@7@367<55/:B/@2/3?/6E/<527:/:B7:3?:B/@072/<5  @/;/23<5/<:B/@072/<5  79/ 6/: 7<7 279/7A9/< 23<5/< B9B; !3939/:/< #=;3:/<3A2/:/;93/2//< :7/2/93/2//< :7:/<3A2/:/;;3<53:7:7<57#/A/6/?7A72/99=<@A/<&/2/A7A79>3?763:7=<A7A79 >/:7<5 239/A 23<5/< #/A/6/?7 93:/8B/</:7<5 03@/? 2/< >/2/ A7A79 />63:7=< A7A79 >/:7<5 8/B6 23<5/< #/A/6/?7 93:/8B/</:7<5 9317: Contoh 5.2 )3=?/<5>3?3/>/<AB;>B2/:/; 9=<475B?/@7:B?B@23<5/<9313>/A/<@B2BA  >BA/?/<>3?@39=<A3?6/2/>>B@/A ;/@@/3?3>3?3/<8/<5 ;@3@//A@3A3:/6;3:=<1/A2/<;7?7>@30B/60=:/ 6=;=53<@//A03?5B:B<5>3?97?/9/<9313>/A/<@B2BABA/?/<@ 1; ; &/2/@//A/D/:>3?3=?=@27A7A79A3<5/6@367<55/ ;=;3<7<3?@7/3?3/A/<@B2BA@//A;3<55B:B<52767AB<523<5/<>3?@/;//<   /A/B    @367<55/   95 ; J  >BA/?/<@  >BA/?/<@  95 ; 5. Gerak Menggelinding / R F v 0 =0 0 F R 0 N 1 R O F fg mg Gambar 5.17 (a) Benda bergerak translasi. (b) Benda bergerak rotasi. (c) Benda menggelinding pada bidang yang permukaannya kasar. <2/ >/@A7 @3?7<5 ;3<8B;>/7 03<2/ E/<5 03?53?/9 ;3<553:7<27<5 ;7@/:/?9/< 27 /A/@ :/3?7@A7D/ 03?53?/9/07:/ A72/9 A3?8/27 @3:7> ;/9/ 932B/ 53?/9 03?:/<5@B<5 @31/?/ 03?@/;//< 2/< 8/?/9 E/<5 27A3;>B6 2/:/; @/AB >BA/?/< @/;/ 23<5/< 93:7:7<5 03<2/ a. Menggelinding pada Bidang Datar )30B/603<2/@7:7<23?A3?:3A/927/A/@072/<52/A/?2/<2703?75/E/ @3>3?A7>/2/* . !5/?@7:7<23?2/>/A;3<553:7<27<5;/9/ 072/<52/A/?/A/B:/ /27 >/2/ 072/<5 2/A/? 9/@/? 03<2/ ;3<5/:/;7 A?/<@:/@7 2/< 53?/9 ?=A/@7 3@/?/2/03<2/6/ >=?=@/A27AB:7@9/<  2/<  /?7 >3?@/;//< A3?@30BA /9/< 27>3?=:36    79/ 5/E/ 53@39  E/<5 0393?8/ >/2/ @7:7<23? 03?<7:/7 9=<@A/< 2/< 27@B0@A7AB@79/< 93 2/:/; >3?@/;//< 53?/9 A?/<@:/@7   0   # ;/9/ /9/< 27>3?=:36   # I   +38/: E/<5 ;3;7:797 ;=;3< 7<3?@7/   #  2/?7  #)  >3?@/;//< >3?13>/A/< 53?/9 A?/<@:/@7 /9/< ;3<8/27  # !3A3?/<5/<  03@/? 5/E/ E/<5 0393?8/ $   03@/? >3?13>/A/< A?/<@:/@7 ;@  #  ;/@@/ 03<2/ 95 126 Mudah dan Aktif Belajar Fisika untuk Kelas XI I  Contoh 5.3 )30B/6@7:7<23?>38/:03?;/@@/ 95;3;7:7978/?78/?7 1;)7:7<23?A3?@30BA272=?=<5 =:365/E/@303@/? $@3>3?A7>/2/5/;0/?*33?13>/A/<E/<527/:/;7 N @7:7<23?A3?@30BA879/ / A72/9/2/5/E/53@39/ F 0 A3?2/>/A53@39/<@367<55/@7:7<23?;3<553:7<27<5 2  793A/6B7# 95  $ 1;  ; fg $ mg  ;@  / )7:7<23?;3:B<1B?@3:7>    # 95 0 )//A@7:7<23?;3<553:7<27<55B3?13>/A/<@B2BA/A 5/E/ 53@39 //2/072/<5;7?7<5/5/?@7:7<23?2/>/A;3<53:7<27<5;/9/6/?B@/2/5/E/ 53@39 /3?@/;//<#@7< I5 #2/<   # 1=@  )7:7<23? /9/< 03?53?/9 ?=A/@7 879/ @7:7<23? 7<7 ;3;7:797 >3?13>/A/< @303@/?  ) @367<55/ /9/< 27>3?=:36 >3?13>/A/< @B2BA  &3?13>/A/< @B2BA 2/?7 53?/9 ?=A/@7 >/2/ @30B/6 @7:7<23? 27@30/09/< /2//2/ 072/<5 ;7?7<5 /2/:/6       /E/ :/7< E/<5 0393?8/ >/2/ @7:7<23? A3A/>7 A72/9 ;3<7;0B:9/< ;=;3<5/E/@3>3?A75/E/03?/AA72/927>3?67AB<59/</:7<7279/?3B@/A?=A/@73<5/<;3:/9B9/<3:7;73?@/;//< 27 /A/@ 27>3?=:36 >3?@/;//< # @7< #@7< 0  #     I   #    +38/: # >3?@/;//<>3?13>/A/<38/:6=;=53<03?;/@@/ 95;3;7:7978/?78/?7 1;!3;B27/< @7:7<23?A3?@30BA27A3;>/A9/<>/2/072/<5;7?7<523<5/<@B2BA93;7?7<5/< G *33?13>/A/<E/<527/:/;7@7:7<23?879/ / A72/9/2/53@39/<:/38/:03?53?/9@3>/<8/<5072/<523<5/<1/?/ ;3:B<1B?;3<553:7<17?   #   #@7< # @7<  ;@ @7< G ;@  ;@ 0 )//A@7:7<23?>38/:;3<553:7<27<55B3?=:36  # #  ;@  c. R M T T F mg Gambar 5.19 Beban dihubungkan dengan katrol. / T a mg 0 R R M F T Gambar 5.20 (a) Gaya-gaya pada benda m. (b) Gaya-gaya pada katrol. Beban Dihubungkan Melalui Katrol 7!3:/@,<2/A3:/6;3;>3:/8/?7A37 ;/@@/ 9/A?=: 27/0/79/< 9/?33:/8/?7 9=<@3> ;=;3< 7<3?@7/ )39/?/<5 <2/ A3:/6 ;3;>3:/8/?7 ;=;3< 7<3?@7/ 3<5/< 23;797/< <2/ 2/>/A ;3<55B ;=;3< 7<3?@7/ @367<55/ 2/>/A ;3;>3?67AB<59/< ;/@@/ 9/A?=: >/2/ @7@A3; 9/A?=: 7<7 &3?6/A79/< * .  )30B/6 030/< 03?;/@@/ # 276B0B<59/< 23<5/< @3BA/@ A/:7 A72/9 03?;/@@/ ;3:/:B7 @30B/6 9/A?=: E/<5 2/>/A 03?53?/9?=A/@7!/A?=:;3;7:797;/@@/2/<03?8/?78/?7@3?A/;3;7:797 ;=;3< 7<3?@7/  */:7 27A/?79 =:36 5/E/  @367<55/ 030/< 03?53?/9 93 /A/@ 2/< ;3<5/:/;7 >3?13>/A/< A?/<@:/@7 @303@/?  &3?@/;//< 53?/9 A?/<@:/@7 >/2/ 03<2/ /2/:/6   #  I##  ## &3?@/;//< 53?/9 ?=A/@7 >/2/ 9/A?=: /2/:/6          0           I  79/A35/<5/<A/:7>/2/#./*+ 4 27@B0@A7AB@79/<93#./*+  4  /9/< 27>3?=:36 >3?@/;//<   #  #      #   /A/B I  #  79/9/A?=:03?B>/@7:7<23?>38/:23<5/<;/@@/;=;3<7<3?@7/   #./*+  4  ;3<8/27  #   #  128 I  Mudah dan Aktif Belajar Fisika untuk Kelas XI   #    # I  !3A3?/<5/<   03@/? >3?13>/A/< :7<3/? ;@   03@/? 5/E/ A/?79$ #  ;/@@/ 03<2/ 95   ;/@@/ 9/A?=: 95 Tantangan untuk Anda Contoh 5.5 &3?6/A79/< 5/;0/? 27 @/;>7<5 B/ 0B/6 03<2/ E/<5 ;/@@/3?13>/A/<:7<3/?@7@A3; T2 0 A35/<5/<A/:7 2/<  m2 2  m1 / )7@A3;;B:/;B:/2/:/;93/2//<27/; !3A79/27:3>/@@7@A3;;B:/703?53?/993/?/6# @367<55/03<2/# 6=;=53< *7<8/B9/A?=:    #9   I     I   #9 I    #9 I  )B0@A7AB@79/<6/?5/ 2/< 2/?753?/9A?/<@:/@7932/:/;>3?@/;//<53?/9 ?=A/@7;/9/27>3?=:36 # -# I# I# # . R 9  #  #  #  # I#  T1  !  T2   a  #  #   #  #  # m1. g ! m2. g 95 ;@  95  95 ;@     ;@ 95  95   95  95   /27>3?13>/A/<:7<3/?@7@A3;/2/:/6  ;@  0 *35/<5/<A/:7 2/<   # #  95 ;@  95  ;@  $  # I#  95 ;@ I 95  ;@   $ /27A35/<5/<A/:7 2/< 03?AB?BAAB?BA/2/:/6 $2/<  $ Dengan kecepatan yang sama, mobil manakah di antara mobil yang bergerak di atas jalan kasar dan mobil yang bergerak di atas jalan licin, yang terlebih dahulu sampai? Mengapa demikian? 6. Energi dalam Gerak Rotasi v a. Energi Kinetik Rotasi )3A7/> 03<2/ E/<5 03?53?/9 ;3;7:797 3<3?57 97<3A79 )/;/ 6/:/A/<:7<3/?+@32/<59/<53?/9?=A/@7/A/<@B2BA  3<2/ E/<5 ;3<553:7<27<5 ;3;7:797 3<3?57 97<3A79 A?/<@:/@7 2/< 3<3?57 97<3A79 ?=A/@7 )31/?/ ;/A3;/A7@ ;3;33?@/;//< !A=A/: #+   !A=A/: ! !?=A/@7 !3A3?/<5/< !A=A/:  3<3?57 97<3A79 A=A/: A v h B Gambar 5.22 Silinder yang mula-mula diam bergerak menggelinding. I  c. Hukum Kekekalan Energi Mekanik pada Gerak Rotasi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h #    #+ #    #+   #       #+   B # 2/<+ @367<55/    +  #   #    #+        +  +      +  +   !3:/8B/<0=:/93A79/03?53?/9;3:B<1B?23<5/<072/<527/<55/>:717< & ! &  ! #   #+   +     /<27<59/< =:36 <2/ !3:/8B/< 93A79/ 0=:/ 03?53?/9 ;3<553:7<27<5 /2/:/6 +   2/<93:/8B/<93A79/0=:/03?53?/9;3:B<1B?/2/:/6 +    />/A  27@7;>B:9/<0/6D/0=:/E/<503?53?/9;3<553:7<27<5:3076:/;0/A2/?7>/2/0=:/ E/<503?53?/9;3:B<1B?/:A3?@30BA27@30/09/<53?/9?=A/@7>/2/0=:/;3<8/27 >3<56/;0/AA3?6/2/>:/8B0=:/ +38/:   Tes Kompetensi Subbab B #.'(+)%")* 1(1)0&%+  &3?6/A79/<5/;0/?03?79BA7<7 10 N a 30° O  12 N b  9N *3/2/?=2/ A3?6/2/>>=?=@879/ 1;2/< 1; )30B/6@7:7<23?>38/:23<5/<8/?78/?72/<03?;/@@/ 275B:717<*33?13>/A/<3;03? @//A8/AB693@B;B? ;>/A0B/6>/?A793:;/@7<5;/@7<5;/@@/3?A7 A/;>/9>/2/5/;0/?*3BA/?38/:03?;/@@/ 9527:3A/99/<>/2/ @30B/6072/<5;7?7<523<5/<@B2BA93;7?7<5/< G *33?13>/A/<E/<527/:/;73?A75/;0/?#=;3<7<3?@7/@7@A3; 9/A?=:/2/:/6 95# 23<5/<'  1;2/<'  1;  r1 r2 T2 T1 m1 m2 *33?13>/A/<@B2BA9/A?=: 0 A35/<5/<A/:7 2/<  C. Kesetimbangan Benda Tegar <2/ A3:/6 ;3<53A/6B7 0/6D/ @30B/6 >/?A793: 279/A/9/< 2/:/; 93/2//< @3A7;0/<5 879/ >/?A793: A3?@30BA A72/9 ;3<5/:/;7 >3?13>/A/< /?A7/2/>/?A793:A3?@30BA /2/:/6<=:  F   /:E/<5@/;/03?:/9B>B:/B/?A793: E/7AB >B@/A ;/@@/ B3?13>/A/< <=: 879/ ?3@B:A/< C39A=? 2/?7 @3:B?B6 5/E/ :B/? E/<5 0393?8/ >/2/ 03<2/ /2/:/6 <=: /: A3?@30BA 27933?A/;/ B=<3<9=;>=<3<3?@/;//<  -   NB  NA w fA I    I  3<5/< 23;797/< @B/AB 03<2/ A35/? 279/A/9/< @3A7;0/<5 879/ A Gambar 5.23 Sebuah tangga bersandar pada dinding yang kasar dengan lantai yang kasar pula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ngatlah  =4m  .   I, ,  NA w   >B@/A27  1=@ I,  1=@    1=@  ,1=@  1=@     ,     ,   )B0@A7AB@79/<&3?@/;//< 2/< 93>3?@/;//< 27>3?=:36 ,  (,   (  /279=347@73<53@39/<8/<5; 2703?7 3<5@3: >/2/ @30B/6 27<27<5 +8B<5 E/<5 @/AB/<523<5/<@3BA/@9/D/A2/<;3;036=?7F=/07:/@3@3=?/<5E/<5 03?/A/2/8/?/9 ;2/?727<27<5A3/2/0/A/<5 Kata Kunci T 53° • momen gaya • lengan torsi 5m 0 Gerak Rotasi dan Kesetimbangan Benda Tegar 133 2  /E/5/E/A?/<@:/@7 Ingatlah T R Batang homogen adalah batang yang letak titik beratnya tepat di tengah-tengah. Ty Ry Rx  -  -I-  1=@ I*1=@   1=@ I*1=@   1=@  *  .  ..I, I,   @7< @7<    @7<     Tx w2   w1 /E/5/E/?=A/@7 + 2m T 53@393<5@3:  :3<5/<;=;3<  @7<    :3<5/<;=;3<,   @7<    :3<5/<;=;3<,   @7<       @7< I  @7< , I  @7< ,    I   I     *  * $  w1 Pembahasan Soal w2 Jarak sumbu roda depan dan sumbu roda belakang sebuah truk yang bermassa 1.500 kg adalah 2 m. Pusat massa truk 1,5 m di belakang roda depan. Jika g = 10 m/s2. Beban yang diterima roda depan adalah .... a. 1.250 N b. 2.500 N c. 3.750 N d. 5.000 N e. 6.250 N  =5m )B0@A7AB@79/< 93 2/< 27>3?=:36 1=@      $ @7<    @7<   $  @7< A/<   1=@  $      $  /275/E/?3/9@73<5@3:/2/:/6  $   @7< Soal UMPTN Tahun 1995 Pembahasan:  =0 mg  AP  – NB  AB  = 0 NB 1 2 mg  AP  AB 1.500 10  0,5 = 2m = 3.750 N =  $   $  Jawaban: c Tes Kompetensi Subbab C #.'(+)%")* 1(1)0&%+  134 )30B/6 0/A/<5  >/<8/<53?A7 5/;0/?27@/;>7<53?/>/9/68/?/9;/9@7;B;2/?7 A7A79@303:B;9/D/A>BAB@ Mudah dan Aktif Belajar Fisika untuk Kelas XI T A x tumpuan B w 2m  )30/A/<50/:=9E/<5>/<8/<53?A7>/2/5/;0/? 79/8/?/9  ; ;2/< ;A33?0/<27<5/<A35/<5/<A/:7 2/<  T1 T2 1m A   7AB<5:/65/E/;7<7;B;E/<56/?B@2703?79/</5/? ?=2/2/>/A3?13>/A/< 5?/C7A/@7 ;@  )30B/6 0/A/<5  >/<8/<53?A7 >/2/5/;0/? 4m T1 3m C B D T2 A B 0,5 m )30B/6>/>/<79:/<03?;/@@/ 95;3<3;>3:>/2/ @30/A/<5>7>/E/<503?/A/<8/<5 3:>/2/27<27<5 @3>3?A7A/;>/9>/2/5/;0/? 30° 2,5m w = 60 N &/2/8/?/9 ;3A3?2/?7275//A9/< 27 A7A79  2/< 27 A7A79  2779/A >/2/ A3;0=923<5/<@3BA/@A/:7A/903?;/@@/ 79/@7@A3; @37;0/<567AB<5:/6 / A35/<5/<A/:7 0 03@/?5/E/3<5@3:@7< G   F R h 40 cm Rangkuman  &=@7@7 @B2BA 03<2/ A35/? E/<5 03?53?/9 ?=A/@7 273?@/;//<    ( ' )     ) ) #=;3<5/E//A/BA=?@7;3?B>/9/<03@/?/<E/<5 ;3>=?=@/A/<@B2BA?/A/?/A/03<2/A35/?E/<503?53?/9 ?=A/@7273?@/;//<   ) 2/>B<9313>/A/<@B2BA@3@//A/A/<@B2BA@3@//A03<2/A35/?E/<503?=A/@7 273?@/;//<    ) )  Gerak Rotasi dan Kesetimbangan Benda Tegar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eta Konsep #.(,0/& ;3;0/6/@ !3@3A7;0/<5/< 3<2/*35/? #=;3< /E/ #=;3< <3?@7/ #=;338/:03?8/?7 8/?7  2/< 03?;/@@/ # !3;B27/< 03<2/ A3?@30BA 27>BA/?>/2/@B;0B3?7=233@/?3<3?57 97<3A79?=A/@73?;B9//< 072/<5 ;7?7<5E/<5;3;03072/<5 6=?7F=/@9/<2/?793/2//< 27/;>/2/93A7<557/<;@31/?/A35/9:B?B@2/?7 072/<56=?7F=/A/<:7<3/?17<17<A3?@30BA @3D/9AB;3<1/>/79/97072/<5;7?7<5/2/:/6 / ;@ 2 ;@ 0     ;@ 3 ;@ 1  ;@ )30B/6 0=:/ >38/: 03?A?/<@:/@7 2/< 03?=A/@7 23<5/< 9313>/A/<:7<3/?2/<9313>/A/<@B2BA;/@7<5;/@7<5+ 2/< <3?5797<3A79A=A/:0=:/>38/:A3?@30BA/2/:/6 #+  / 2 #+ 0 #+ 3  #+   #+ 1 )30B/60/A/<5E/<5>/<8/<5/A 03?>BA/?030/@>/2/@/:/6@/ABB8B<5/@ 2/?7 93/2//< 27/; 23<5/< >=@7@7 ;3<2/A/?03@/?>3?13>/A/<@B2BA0/A/<5/2/:/6   2 / " "  0 3  "  1 " )30B/6@7:7<23?>38/:E/<5;/@@//@A/<>/9313>/A/</D/:2/?7>B<1/9072/<5 ;7?7<5 E/<5 9/@/? 23<5/< @B2BA 93;7?7<5/< A3?6/2/>072/<56=?7F=3?13>/A/<5?/C7A/@7 0B;7/2/:/6@7:7<23?A3?@30BA/9/< / ;3:B<1B?23<5/<>3?13>/A/<@7< 0 ;3:B<1B?23<5/<>3?13>/A/< @7< 1 ;3<553:7<27<523<5/<>3?13>/A/<@7< 2 ;3<553:7<27<523<5/<>3?13>/A/< @7< 3 ;3<553:7<27<523<5/<>3?13>/A/< @7<  B/03<2/2/<;/@7<5;/@7<5;/@@//<8/<5B@/A 0/A/<5 275BBA/?;=;3<7<3?@7/>/2/>B@/A0/A/<5 A3?@30BA/2/:/6 / 95; 2  95; 0  95; 3  95; 1 95;  )30B/6?=2/2/>/A;3<5 53:7<27<5A/<>/@3:7>>/2/ @30B/6072/<52/A/?E/<5 F=2N 9/@/?#/@@/?=2/ 952/< 8/?78/?73?13>/A/<@B2BA9=<@A/<@3>3?A7A/;>/9>/2/5/;0/? 3@/?;=;3<5/E/E/<50393?8/>/2/?=2//2/:/6 / <=: 2 $; 0  $; 3 $; 1  $;  )30B/6?=2/03?033?13>/A/< @B2BA ?=2/ A3?@30BA/2/:/6 / ?/2@ 2 ?/2@ 0 ?/2@ 3  ?/2@ 1 ?/2@  &3?6/A79/<5/;0/?03?79BA y 2m a 3m a O 2a m x *75/0B/6>/?A793:23<5/<;/@@/# #2/< #27 >/@/<5>/2/B8B<593?/<59/E/<5;/@@//2/072/<5-. 79/@7@A3;27>BA/? A3?6/2/>@B;0B-.;=;3<7<3?@7/@7@A3;27A7A79 /2/:/6 / # 2 # 0 # 3 # 1 #  &3?6/A79/<5/;0/?03?79BA m1 m2 Gerak Rotasi dan Kesetimbangan Benda Tegar 137 B/0B/603<2/E/<5;/@7<5;/@7<5;3;7:797;/@@/ #  952/<#  95276B0B<59/<23<5/<9/A?=: >38/:03?;/@@/ 95 79/>3?13>/A/<5?/C7A/@7 ;@  >3?13>/A/<E/<527/:/;7# 2/<# /2/:/6 / ;@ 2 ;@ 0 ;@ 3 ;@ 1  ;@  B/ 03<2/ ;/@7<5 B ;/@7<503?;/@@/#  95 2/<#  95276B0B<5 m1 9/< 23<5/< 9/A?=: >38/: A m2 30°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udah dan Aktif Belajar Fisika untuk Kelas XI T1  &/2/ 5/;0/? 27 @/;>7<5 C ;/@@/0/:=9;/@@/030/< A licin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ab 6 Sumber: www.chez.com Pesawat dapat terbang karena mengalami gaya angkat yang bebas pada sayapnya. Fluida Hasil yang harus Anda capai: menerapkan konsep dan prinsip mekanika klasik sistem kontinu dalam menyelesaikan masalah. Setelah mempelajari bab ini, Anda harus mampu: menganalisis hukum-hukum yang berhubungan dengan fluida statis dan dinamis serta penerapannya dalam kehidupan sehari-hari. +:FC6=@6=C967:FH6CL6B:C<6E6E:G6K6H96E6HH:F76C<+:G6K6H 96E6H H:F76C< @6F:C6 B:C<6A6B> <6L6 6C<@6H L6C< 7:G6F  "6L6 6C<@6H E696E:G6K6H9>G:767@6CDA:=@DCGHFI@G>G6L6EE:G6K6HL6C<B:CL:767@6C 696CL6 E:F7:966C @:8:E6H6C 6A>F 96F> ;AI>96 I96F6 9> 6H6G G6L6E 9:C<6C 9> 76K6= G6L6E  +F>CG>E H:FG:7IH B:FIE6@6C 6EA>@6G> 96F> E:FG6B66C :FCDIAA> 6A6B 767 >C> C96 6@6C 7:A6?6F H:CH6C< ;AI>96 GH6H>G 96C ;AI>96 9>C6B>G  &DCG:E H:CH6C< ;AI>96 76CL6@ 9>6EA>@6G>@6C 96A6B @:=>9IE6C G:=6F> =6F> A. Fluida Statis B. Viskositas Fluida C. Fluida Dinamis 139 Tes Kompetensi Awal ""(0))"),"(&-%'+*.",(0%!'"-&'*($.+(.+("-%'0/!()0'0(/%$* +:FC6=@6= C96 96H6C< @: H:BE6H 8I8> BD7>A AD<6BBIA>6:B6G=6CL69:C<6CB:C8:AIE@6CCL6@: #I@IB 6E6@6= L6C< 9>H:F6E@6C 96A6B 6A6H E:C< 96A6B6>F 6C<@6HBD7>A9>G6C66<6>B6C686F6@:F?66A6HE:C<  (:C<6E6CL6BI@96E6H7:F?6A6C9>6H6GE:FBI@66C 6C<@6HBD7>AH:FG:7IH 6>F  +:F86L6@6= C96 ?>@6 696 H:B6C C96 L6C<  %:A6G@6C9:C<6C76=6G6BC96G:C9>F>86F6@:F?696F> B:CL6H6@6C 76=K6 9>6 7>G6 B:C:CHI@6C @:6GA>6C J:CHIF>B:H:F96CE>E6E>HDH A. Fluida Statis !AI>96B:FIE6@6CM6HL6C<96E6HB:C<6A>F DCHD=;AI>969>6CH6F6CL6 6>FB>CL6@GIGI7:CG>CGDA6FI6E<6G96C6G6E !AI>96H:F9>F>6H6G9I6 B686B L6>HI ;AI>96 L6C< 96E6H 9>B6BE6H@6C 6H6I $"%&'! 96C L6C< H>96@ 96E6H 9>B6BE6H@6C 6H6I # $"%&'! 1. Tekanan Gambar 6.1 Tekanan yang dilakukan seorang anak terhadap meja. D76C96H:@6CG:7I6=EIAE:C@:96A6BH6C6=@:BI9>6C76C9>C< @6C H>C<@6H @:GI@6F6CCL6 9:C<6C ?6FIB L6C< 9>H:@6C @: 96A6B H6C6= +IAE:C 6@6C A:7>= GI@6F B6GI@ @: 96A6B H6C6= 96F>E696 ?6FIB L6C< 9>B6GI@@6C @: 96A6B H6C6=  (:C<6E6 9:B>@>6C />C<@6H@:GIA>H6CG:G:DF6C<96A6BB:C:@6CGI6HI7:C967:F=I7IC<6C 9:C<6C AI6G 96:F6= L6C< 9>H:@6C  .:B6@>C AI6G 96:F6= L6C< 9>H:@6C G:B6@>C @:8>A H:@6C6C L6C< 9>=6G>A@6C   ## "&)% # '& - -#  & % ')() %&") #  ## !)' %&") # (&')( %>@6<6L6 7:@:F?6H:<6@AIFIGE696E:FBI@66C7:C96G:AI6G 7:G6FCL6 H:@6C6C G:86F6 B6H:B6H>G 9>HIA>G@6C G:76<6> 7:F>@IH % P  &:H:F6C<6C % H:@6C6C) B E6G86A <6L6)  AI6G 7>96C< H:@6C B 2. Tekanan Hidrostatik A h +:F=6H>@6C )-   +696 <6B76F H:FG:7IH H:FA>=6H G:7I6= H67IC< 7:F>G> M6H 86>F 7:FB6GG6 ?:C>G  @:96A6B6C  96C AI6G E:C6BE6C<  36H 86>FL6C<7:F6969>96A6B7:?6C6B:B>A>@><6L67:F6H1L6C<B:C:@6C96G6F H67IC<  .:B6@>C H>C<<> E:FBI@66C M6H 86>F G:B6@>C 7:G6F H:@6C6C L6C< 9>=6G>A@6C E696 96G6F H67IC<  .:86F6 B6H:B6H>G =I7IC<6C 6CH6F6 7:G6F H:@6C6C L6C< 9>=6G>A@6C 96C @:H>C<<>6C M6H 86>F 9>HIA>G@6C G:76<6> 7:F>@IH  "         % +  w Gambar 6.2 Tekanan hidrostatik pada dasar tabung. :F96G6F@6C"-.)*4 96E6H9>G>BEIA@6C76=K6E:FG6B66C H:@6C6C =>9FDGH6H>@ 696A6= %   &:H:F6C<6C %  H:@6C6C =>9FDGH6H>@ ) B 6H6I +6 B6GG6?:C>GM6H86>F@< B 140 P Mudah dan Aktif Belajar Fisika untuk Kelas XI P   @:96A6B6C M6H 86>F B   E:F8:E6H6C H6G> B G 6F>E:FG6B66CH:FG:7IH96E6H9>E:A6?6F>76=K6H:@6C6C=>9FDGH6H>@ G6C<6H 9>E:C<6FI=> DA:= <6L6 H6G> 96C @:96A6B6C M6H 86>F +:F=6H>@6C)-   +696 @6GIG G:E:FH> >C> ICHI@ M6H 86>F L6C< G:?:C>G H:@6C6C M6H 86>F H>96@ 7:F<6CHIC< E696 AI6G E:C6BE6C< 96C 7:CHI@7:?6C6H:H6E>7:F<6CHIC<E696@:96A6B6CM6H86>F %69>H:@6C6C =>9FDGH6H>@ E696 H>H>@   96C  696A6= G6B6 7:G6F  *A:= @6F:C6 >HI 7:F96G6F@6C "-.)* 4  6@6C 9>96E6H %%%  A B C Gambar 6.3 Tekanan hidrostatik pada titik A, B, dan C adalah sama. P +:F=6H>@6C )-   (IA6 BIA6 7:?6C6 E696 <6B76F H:FG:7IH 9>>G>M6H86>FE:FH6B6L6C<7:FB6GG6?:C>G 1 &:BI9>6C@:96A6BBIAIH 7:?6C6G:7:A6=@6C6C9>B6GI@@6CM6H86>F@:9I6L6C<7:FB6GG6?:C>G 2 />H>@7:F696E696E:F76H6G6C@:9I6M6H86>FH:FG:7IH96C9>H:@6CDA:= M6H86>F@:9I6G:H>C<<> />H>@7:F696E696M6H86>FE:FH6B696C9>H:@6C DA:= M6H 86>F E:FH6B6 G:H>C<<>   />H>@  96C  7:F696 E696 G6HI <6F>G .:GI6> 9:C<6C #I@IB #>9FDGH6H>@6 @:9I6 H>H>@ H:FG:7IH B:B>A>@> H:@6C6CL6C<G6B6 @6CH:H6E>H:@6C6CE696H>H>@96CH>96@G6B6 @6F:C6 ?:C>G M6H 86>F 9> @:9I6 H>H>@ H:FG:7IH 7:F7:96 %%  #  # h h1 C D A B air P 0CHI@ A:7>= B:B6=6B> H:CH6C< H:@6C6C =>9FDGH6H>@6 A6@I@6CA6= @H>J>H6G !>G>@6 7:F>@IH >C> h2 Gambar 6.4 Pipa U diisi dua zat cair berbeda, tekanan di A sama dengan tekanan di B. Aktivitas Fisika 6.1 Tekanan Hidrostatik Tujuan Percobaan Memahami tekanan hidrostatika Alat-Alat Percobaan 1. Sebuah ember 2. dua buah gelas plastik bening Langkah-Langkah Percobaan 1. Isilah ember dengan air. 2. Jawablah pertanyaan berikut sebelum melakukan percobaan. a. Apa yang akan terjadi jika sebuah gelas plastik dicelupkan perlahan ke dalam air dalam keadaan terbalik? Jelaskan apa yang akan terjadi, berikut alasannya. b. Lakukan hal yang sama, namun dengan gelas yang diberi lubang pada dasar gelasnya. Jelaskan apa yang akan terjadi, berikut alasannya. 3. Buktikanlah jawaban Anda dengan melakukan percobaan. 4. Buatlah hukum tentang tekanan menurut versi Anda, berdasarkan jawaban dan hasil percobaan yang Anda peroleh. 5. Bandingkanlah dengan hukum hidrostatika yang telah Anda pelajari. 6. Buatlah kesimpulan dari percobaan tersebut. Contoh 6.1 .:7I6=H:BE6H6>F7:F7:CHI@@I7IGB:B>A>@>E6C?6C<FIGI@ 8B9>>G>  A>H:F6>F B6GG6?:C>G6>F @< B %>@6 B GH:CHI@6CA6= 6 H:@6C6C=>9FDGH6H>@E69696G6F@I7IG 7 <6L6=>9FDGH6H>@E69696G6F@I7IG96C 8 <6L6=>9FDGH6H>@E696H>H>@L6C<7:F?6F6@ B96F>E:FBI@66C6>F Fluida 141 1 >@:H6=I> hA    A>H:F  B  @< B hB   B G  B '  8B B s = 60 cm   B     B  B 6 %    @< BQ B GQ B +6 7  %  +6Q B  ) 8 %     @< BQ B GQ B  +6  %   +6Q B ) %69>7:G6FH:@6C6C=>9FDGH6H>@E69696G6F@I7IG696A6=% +6<6L6=>9FDGH6H>@E696 96G6F@I7IG696A6=   )96C<6L6=>9FDGH6H>GE696H>H>@696A6=  ) Contoh 6.2 P piston zat cair Gambar 6.5 3. Hukum Pascal Tabung Pascal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p1 A2 A1 F2 p2 Gambar 6.6 Prinsip kerja dongkrak hidrolik. 142 +696<6B76F7:F>@IHG:7I6=E>E67:F7:CHI@=IFI;09>>G>9:C<6C6>F 6>F  < 8B &6@>E>E6G:7:A6=@>F>9>>G>7:CG>C9:C<6C 7:CG>C  < 8BG:H>C<<>8B .:7:A6= @6C6C 9>>G> B>CL6@ H6C6= 9:C<6C B>CL6@   < 8B G:H>C<<>  8B  #>HICC<<>6>F6CH6F6E>E6@6C6C96CE>E6@>F> 1 minyak tanah >@:H6=I> bensin 6>F  < 8B 7:CG>C  < 8B h2 h3 B>CL6@  < 8B h1{  8B A B  8B /:@6C6C=>9FDGH6H>@9>H:@6C6C=>9FDGH6H>@9>  6>F   7:CG>C  B>CL6@  air  Q  Q Q        8B %69>E:F7:966CH>C<<>6>FE696@:9I6E>E6696A6= 8B Mudah dan Aktif Belajar Fisika untuk Kelas XI %>@6 E:C<>G6E  9>H:@6C 9:C<6C <6L6  M6H 86>F 6@6C B:C:FIG@6C H:@6C6C H:FG:7IH @: G:<6A6 6F6=  :G6FCL6 H:@6C6C E696 E:C<>G6E 9>CL6H6@6C 9:C<6C E:FG6B66C %  P %>@6 9> 6H6G E:C<>G6E  9>A:H6@@6C 7:76C <6L6 6C<@6H @: 6H6G E696 E:C<>G6E  696A6=  L6C< 9>CL6H6@6C 9:C<6C E:FG6B66C %  P  (:CIFIH #I@IB +6G86A H:@6C6C L6C< 9>H:FIG@6C @: G:<6A6 6F6= 696A6= G6B6 7:G6F G:=>C<<6 % %    P %>@6 7:CHI@ E:C6BE6C< H67IC< 7:FIE6 A>C<@6F6C 9:C<6C ?6F> ?6F> & 96C & 6@6C 9>E:FDA:= E:FG6B66C   6H6I     & &   F2 Gambar 6.7 Pengangkat hidrolik menerapkan Konsep Hukum Pascal. Tokoh Douglas Dean Osheroff (1945 – sekarang) P >6B:H:FE:C6BE6C<E696"-.)*4696A6=96C %69> 9:C<6C<6L6L6C<@:8>AC9696E6HB:C<6C<@6H7:76CL6C<7:G6F +F>CG>E +6G86A H:FG:7IH G:F>C< 9>?IBE6> 96A6B @:=>9IE6C G:=6F> =6F> G:E:FH> 9DC<@F6@ BD7>A 96C EDBE6 =>9FDA>@ Contoh 6.3 .:7I6=EDBE6=>9FDA>@B:B>A>@>E>E6@:8>A7:F?6F> ?6F>8BG:96C<@6CE>E67:G6F 7:F?6F> ?6F> 8B <6F7:76CL6C<7:F6HCL6 )C6>@G:H>C<<>8BH:CHI@6CA6= 6 <6L6L6C<9>@:F?6@6CE696E>E6@:8>A 7 ?6F6@L6C<9>H:BEI=E:C<>G6EE>E6@:8>A 1 >@:H6=I> & 8B & 8B  ) 8B        &     &      ) 7    Q  Q  Q  Q   8B %69>9>7IHI=@6C<6L6G:7:G6F )96C?6F6@E:C<>G6E 8BE696E>E6@:8>A 6 F1 Sumber: Republika, 19 November 2005 Douglas Dean Osheroff dilahirkan pada tahun 1945. Setelah menyelesaikan pendidikan sarjananya di California Institute Of Technology, ia pindah ke Cornell University untuk mengambil gelar doktor. Di sana, ia bertemu dengan David M. Lee dan Robert C. Richardson. Bersama dua koleganya tersebut, ia melakukan penelitian selama bertahun-tahun sampai menemukan satu fenomena yang menghebohkan dunia ilmiah, yaitu superfluiditas. Superfluiditas tersebut terjadi ketika helium-3 didinginkan mendekati suhu nol mutlak (–273,15°C). Pada suhu tersebut, helium-3 tidak lagi memiliki viskositas dan friksi sehingga dapat meluap dari sebuah cangkir datar melalui pori-pori yang teramat kecil. Fenomena lainnya adalah helium-3 ini dapat melawan gaya gravitasi Bumi. Atas penemuannya ini, Osherhof bersama kedua rekannya mendapat hadiah Nobel pada tahun 1996. Fluida 143 4. Hukum Archimedes 6 7 35 N 50 N w air Gambar 6.8 Berkurangnya berat benda di dalam zat cair disebabkan oleh gaya ke atas yang dikerjakan oleh zat cair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ontoh 6.4 .:7I6=76HIL6C<JDAIB:CL6 8B7:F6969>96A6B6>F %>@6B6GG6?:C>G6>F < 8B H:CHI@6C<6L6H:@6C@:6H6GE69676HI 1 >@:H6=I> 6>F  < 8B @< B 1DAIB:76HIJDAIB:M6H86>FL6C<9>E>C96=@6C  8BQ PB  B G "6L6@:6H6G<6L6F8=>B:9:G   6>F   @< B B GQ PB ) 96CL6 <6L6 @: 6H6G <6L6 F8=>B:9:G E696 G:7I6= 7:C96 L6C< B6GI@@:96A6BM6H86>FB:CL:767@6C7:C9696E6HB:C<6EIC<B:A6L6C< 6H6I H:C<<:A6B a. Benda Mengapung %>@6 =6CL6 G:76<>6C 7:C96 L6C< H:F8:AIE @: 96A6B M6H 86>F 7:C96 9>G:7IHB:C<6EIC< 6A6B@:6966C>C>7:F6H7:C96<6L6@:6H6G96F> M6H 86>F  .:86F6 B6H:B6H>G 9>HIA>G@6C G:76<6> 7:F>@IH 1  "    #   #  #      Gambar 6.9 Perahu dapat terapung di atas air karena massa jenisnya lebih kecil dari massa jenis air. 144 P  &:H:F6C<6C  JDAIB:7:C96L6C<H:F8:AIEB  JDAIB:7:C96G:AIFI=CL6B "-.)* 4  B:CIC?I@@6C 76=K6 GIE6L6 7:C96 B:C<6EIC< B6GG6?:C>G7:C96=6FIGA:7>=@:8>A96F>E696B6GG6?:C>GM6H86>F   C Mudah dan Aktif Belajar Fisika untuk Kelas XI b. Benda Melayang %>@6 G:AIFI= 76<>6C 7:C96 7:F696 9> 96A6B M6H 86>F C6BIC 7:C96 H:FG:7IH H>96@ G6BE6> B:CL:CHI= 96G6F H67IC< B6@6 7:C96 9>@6H6@6C B:A6L6C< 6A6B@:6966CG:>B76C<7:F6H7:C96G6B69:C<6C<6L6H:@6C @: 6H6G DA:= M6H 86>F  .:86F6 B6H:B6H>G 96E6H 9>HIA>G@6C G:76<6> 7:F>@IH 1  " #   #  #   #       P  .:E:FH> E696 )-   G:AIFI= 7:C96 B6GI@ @: 96A6B M6H 86>F G:=>C<<6 JDAIB: 7:C96 G6B6 9:C<6C JDAIB: M6H 86>F L6C< 9>E>C96=@6C *A:= @6F:C6 >HI ICHI@ @6GIG B:A6L6C< B6GG6 ?:C>G 7:C96 96C B6GG6 ?:C>G M6H 86>F 696A6= G6B6 c. Benda Tenggelam :C96 H:C<<:A6B H:F?69> @6F:C6 <6L6 7:F6H 7:C96 L6C< A:7>= 7:G6F 96F>E696 <6L6 H:@6C @: 6H6G  :C96 L6C< H:C<<:A6B 6@6C B:CL:CHI= 96G6FH67IC<G:E:FH>L6C<H:FA>=6HE696)- .:86F6B6H:B6H>G 96E6H 9>HIA>G@6C G:76<6> 7:F>@IH 1  " #   #   # *A:=@6F:C6JDAIB:7:C96L6C<H:C<<:A6BG6B69:C<6CJDAIB:M6H 86>F L6C< 9>E>C96=@6C L6>HI    96E6H 9>HIA>G@6C 76=K6    P  Gambar 6.10 Penyelam dan ikan-ikan dapat melayang di air. Tahukah Anda, mengapa ikan dan penyelam dapat melayang dalam air? Gambar 6.11 Batu tenggelam dalam air karena massa jenis batu lebih besar daripada massa jenis air. %69>?>@6B6GG6?:C>G7:C96A:7>=7:G6F96F>E696B6GG6?:C>GM6H86>F 7:C96 6@6C H:C<<:A6B Contoh 6.5 .:7I6=7:C96?>@67:F6969>I96F67:F6HCL6 ) %>@69>H>B76C<9>96A6B6>F7:F6H 7:C96H:FG:7IHG:DA6= DA6=B:C?69>) %>@6B6GG6?:C>G6>F < 8BH:CHI@6CA6= B6GG6?:C>G7:C96H:FG:7IH B G 1 :F6H7:C969>I96F6+I96F6 ):F6H7:C969>6>F+6>F) 6>F  @< B "6L6H:@6C@:6H6GL6C<7:@:F?6E6967:C96696A6=  +I96F6P+6>F )P)) "6L6F8=>B:9:G ) Q PB  8B           @< B  B G  (6GG67:C96 + "  I96F6   )  @< <  B G G:=>C<<6B6GG6?:C>G7:C96696A6= "  < < 8B        8B  %69>B6GG6?:C>G7:C96H:FG:7IH696A6=< 8B Ingatlah benda  fluida mengapung benda  fluida melayang benda  fluida tenggelam Fluida 145 5. Penerapan Hukum Archimedes Gambar 6.12 Balon udara merupakan salah satu penerapan Hukum Archimedes. 6 7 Gambar 6.13 (a) Hidrometer di dalam raksa. (b) Hidrometer di dalam air. +:C:F6E6C #I@IB F8=>B:9:G 96E6H C96 ?IBE6> 96A6B @:=>9IE6C G:=6F> =6F> DCHD=CL6F6@>HE:F6=I@6E6AA6IH96C76ADCI96F6 +69696G6F CL6G:BI6?:C>G@:C96F66CA6IHB:C<CG>E=I@IBF8=>B:9:G 696C@6E6A9>7I6H7:FDC<<66<6F96E6HB:B>C96=@6CJDAIB:6>FA6IHA:7>= 7:G6F G:=>C<<6 B6GG6 ?:C>G @6E6A B:C?69> A:7>= @:8>A 96C <6L6 6C<@6H DA:= 6>FA6IHG:B6@>C7:G6F 6F>@:H:F6C<6C>C>96E6H9>@:H6=I>E:CL:767@6E6A A6IHL6C<B:B>A>@>B6GG6G6C<6H7:G6F96E6HH:F6EIC<E696E:FBI@66C6>F +F>CG>E #I@IB F8=>B:9:G ?I<6 9>@6B6GG6?:C>G96F>@:G:AIFI=6C76ADC I96F6 H:FG:7IH A:7>= @:8>A 96F>E696 B6GG6 ?:C>G I96F6  1DAIB: <6G 96A6B 76ADC I96F6 =6FIG 9>E:F7:G6F 6H6I B:C<GCL6 A:7>=@:8>A96F>E696B6GG6?:C>GI96F6AI6F6<6F76ADCH:FG:7IH96E6HH:F6C<@6H &:H>C<<>6C76ADC@:H>@6H:F76C<96E6H9>6HIF9:C<6CB:C6B76=@6C <6G @: 96A6B 76ADC I96F6  (6GG6 7:76C L6C< 96E6H 9>6C<@6H DA:= 76ADC I96F6 696A6= "    I  <  P  &:H:F6C<6C "  B6GG6 7:C96 @<  JDAIB:7:C96B I  B6GG6 ?:C>G I96F6 @< B < B6GG6?:C>G<6G@< B #I@IB F8=>B:9:G ?I<6 9>B6C;66H@6C E696 =>9FDB:H:F L6>HI 6A6H ICHI@B:CGM6H86>F )- B:CIC?I@@6CG:7I6= =>9FDB:H:FL6C<H:F6EIC<96A6BM6H86>F 1DAIB:=>9FDB:H:FG6B69:C<6C JDAIB:M6H86>FL6C<9>E>C96=@6CDA:=76<>6C=>9FDB:H:FL6C<H:F8:AIE (:A6AI>E:FG6B66C=I@IBF8=>B:9:G96E6H9>I@IFB6GG6?:C>GM6H86>F H:FG:7IH 9:C<6C A6C=6H G@6A6 E696 =>9FDB:H:F 6. Tegangan Permukaan Gambar 6.14 Serangga dapat berjalan di atas air karena adanya tegangan permukaan. B A Gambar 6.15 Dua molekul zat cair yang berbeda posisi memiliki gaya kohesi yang berbeda. 146 /6=I@6=C96L6C<9>B6@GI99:C<6CH:<6C<6CE:FBI@66CM6H86>F +:FC6=@6= C96 B:A>=6H G:F6C<<6 L6C< 96E6H 7:F?6A6C 9> 6H6G 6>F (:C<6E6 G:F6C<<6 H:FG:7IH 96E6H B:A6@I@6CCL6 /:<6C<6C E:FBI@66C M6H86>FH:F?69>@6F:C6696CL6@D=:G>L6>HI<6L6H6F>@ B:C6F>@6CH6FE6FH>@:A G:?:C>G DCHD=L6C<B:C<<6B76F@6C696CL6H:<6C<6CE:FBI@66C696A6= 76ADC L6C< H:F7I6H 96F> 6>F G67IC  C96 7>G6 B:B7I@H>@6CCL6 9:C<6C 86F6B:C8:AIE@6CH6C<6CC96@:96A6B6>FG67ICH:FG:7IHA6AI7I6HA6= A>C<@6F6C 9:C<6C ?6F> ?:BEDA 96C H:AIC?I@ C96 B6@6 6@6C H:FA>=6H 6>F G67IC L6C< B:B7:CHI@ 7>96C< 96H6F +:F=6H>@6C)- "6B76FH:FG:7IHB:CIC?I@@6C<6L6@D=:G> L6C<7:@:F?6E696BDA:@IA96CBDA:@IA (DA:@IAB:C<6A6B><6L6 @D=:G>96F>G:<6A66F6=L6C<G6B67:G6FG:=>C<<696E6H9>CL6H6@6C76=K6 BDA:@IA H:FG:7IH 7:F696 96A6B @:G:>B76C<6C  :F7:96 9:C<6C BDA:@IA  L6C< H:FA:H6@ E696 E:FBI@66C M6H 86>F  (DA:@IA >C> =6CL6 B:C<6A6B> <6L6@D=:G>DA:=E6FH>@:A E6FH>@:AL6C<7:F6969>76K6=96C9>G6BE>C76HCL6 E696 E:FBI@66C 6>F H:F?69> H6F>@6C @: 76K6= G:=>C<<6 E:FBI@66C M6H 86>F G:E:FH> G:A6EIH H>E>G  B6H>A6= ?>@6 E>G6I G>A:H 9>H:BE6H@6C G:86F6 B:A>CH6C< E696 E:FBI@66C 6>F  26A6IEIC B6GG6 ?:C>GCL6 A:7>= 7:G6F 9>76C9>C<@6C B6GG6 ?:C>G 6>F G>A:H H:FG:7IH 96E6H H:F6EIC< @6F:C6 696CL6 H:<6C<6C E696 E:FBI@66C 6>F Mudah dan Aktif Belajar Fisika untuk Kelas XI +:F=6H>@6C G:?IBA6= H:H:G6C :B7IC E6<> L6C< ?6HI= 9> 6H6G FIBEIH /:H:G6CH:FG:7IH6@6C7:F7:CHI@G:E:FH>7DA6 7DA6@:8>A "6L6@D=:G>BDA:@IA BDA:@IA L6C< H:FA:H6@ E696 E:FBI@66C 6>F @: 6F6= 96A6B 6@6C G6B6 7:G6F G:=>C<<6 H:H:G6C 6>F H:FG:7IH 6@6C 7:F7:CHI@ 7DA6  /:A6= 9>@:H6=I> 76=K6 7DA6 B:FIE6@6C 76CA>@> AI6G E:FBI@66C H:F@:8>A  +:F BI@66C 6>F >C> B:CL:FIE6> G:A6EIH H:<6C< L6C< :A6GH>G 0CHI@ B:C<:H6=I> 7:G6F H:<6C<6C E:FBI@66C H:FG:7IH E:F=6H>@6CA6= 8DCHD=7:F>@IH B7>AA6=G:EDHDC<@6K6H@:BI9>6C7:CHI@A6=B:CL:FIE6> 7:CHI@ 0 G:E:FH> E696 )-    &:9I6 @6@> @6K6H 0 9>=I7IC<@6C 9:C<6C@6K6H9:C<6CE6C?6C<  96C7:F6H1 %>@6@6K6H09>8:AIE@6C @: 96A6B 7:?6C6 L6C< 7:F>G> 6>F G67IC @:BI9>6C E696 76H6C<  9>7:F> G:7I6=7:76CG:7:F6H+ 6@6C9>E:FDA:=<6L6H:<6C<6CE:FBI@66C L6>HI ++ P  *A:= @6F:C6 G>G> @6K6H L6C< @DCH6@ 9:C<6C E:FBI@66C 6>F 696 9I6 G>G> G>G> AI6F   96C G>G> 96A6B    9:C<6C E6C?6C< 9>6C<<6E G6B6  %69> E6C?6C< G>G> @6K6H HDH6A L6C< @DCH6@ 9:C<6C 6>F G:E6C?6C<   G:=>C<<6 H:<6C<6C E:FBI@66C E696 A6FIH6C G67IC 696A6=   P  &:H:F6C<6C   H:<6C<6C E:FBI@66C ) B 96E6H 9>6C<<6E G:76<6> <6L6 G:H>6E G6HI6C E6C?6C<   E6C?6C< @6K6H B %>@6 ' 696A6= E:FE>C96=6C @6K6H "-.)* 4  96E6H 9>HIA>G G:76<6> 7:F>@IH ' IG6=6   P  ' AI6G %69> H:<6C<6C E:FBI@66C 96E6H EIA6 9>6FH>@6C G:76<6> IG6=6 G:H>6E G6HI6CAI6G96CG6HI6CCL6696A6=?DIA: B:H:F% B 0CHI@A:7>=B:B6 =6B>;:CDB:C6H:CH6C<H:<6C<6CE:FBI@66CA6@I@6CA6=@H>J>H6G!>G>@6 7:F>@IH >C> Gambar 6.16 Tetesan air yang jatuh ke atas rumput. B A F A B w1 2 1 s w2 Gambar 6.17 Tegangan permukaan air sabun pada kawat. Pembahasan Soal Sebuah benda terapung di atas permukaan air yang berlapiskan minyak. Sebanyak 50 % volume benda berada di dalam air dan 30 % di dalam minyak. Jika massa jenis minyak = 0,8 g/cm3 maka massa jenis benda tersebut adalah .... a. 0,62 g/cm3 b. 0,68 g/cm3 c. 0,74 g/cm3 d. 0,78 g/cm3 e. 0,82 g/cm3 Soal UMPTN Tahun 1993 Aktivitas Fisika 6.2 Pembahasan: Tegangan Permukaan Tujuan Percobaan Memahami fenomena tegangan permukaan Alat-Alat Percobaan 1. Panci berisi air 2. Jarum 3. Kertas tisu 4. Minyak pelumas 5. Detergen Langkah-Langkah Percobaan 1. Ambil jarum yang sudah diolesi minyak pelumas, kemudian simpan jarum tersebut di atas kertas tisu. 2. Letakkan jarum dan kertas tisu secara perlahan-lahan di atas permukaan air. 3. Amati yang terjadi pada jarum dan kertas tisu tersebut. 4. Taburkan detergen secara perlahan-lahan di sekitar jarum yang terapung, kemudian amati yang terjadi pada jarum tersebut. 5. Dari hasil Aktivitas Fisika 6.2, lakukanlah diskusi tentang hasil kegiatan tersebut bersama teman dan guru Fisika Anda. Kemudian, presentasikan hasil diskusi tersebut. 30 % minyak 50 % air Benda dalam keadaan setimbang, maka gaya berat benda sama dengan gaya angkat Archimedes oleh air dan minyak. mbg = FA (air) + FA (minyak) bVb g = aVa g + mVm g b = a Va V + m m Vb Vb = (1 g/cm3)(50 %) + (0,8 g/cm3)(30 %) = 0,74 g/cm 3 Jawaban: c Fluida 147 Tugas Anda 6.1 Tegangan permukaan dapat dikatakan sebagai kecenderungan permukaan zat cair untuk berkontraksi (mengerut). Menurut Anda, bagaimanakah sifat tegangan permukaan zat cair ketika zat cair tersebut dipanaskan? &:H>@6 ?6FIB L6C< 7:F696 9> 6H6G @:FH6G H>GI 9> A:H6@@6C G:86F6 E:FA6=6C A6=6C 9> 6H6G E:FBI@66C 6>F ?6FIB 96C H>GI 6K6ACL6 6@6C H:F6EIC< 9> 6H6G E:FBI@66C 6>F  .:G66H @:BI9>6C @:FH6G H>GI 6@6C B:CL:F6E 6>F G:=>C<<6 B:C?69> 76G6= 96C H:C<<:A6B G:96C<@6C ?6FIB H:H6E H:F6EIC< 6@>76H 696CL6 H:<6C<6C E:FBI@66C %6FIB 6@6C H:C<<:A6B @:H>@6 7I7I@ 9:H:F<:C 9>H67IF@6C 9> G:@>H6F ?6FIB L6C< H:F6EIC<  #6A H:FG:7IH 9>G:767@6C B:C<:8>ACL6 H:<6C<6C E:FBI@66C 6>F @6F:C6 9:H:F<:C 7:F:6@G> 9:C<6C B>CL6@ E:AIB6G E696 ?6FIB  @>76HCL6 ?6FIB B:C?69> 76G6= 96C H:C<<:A6B Contoh 6.6 .:76H6C<@6K6H9>7:C<@D@@6CG:E:FH>=IFI;0 &:BI9>6C @6K6H@:8>A+,L6C<7:FB6GG6 <9>E6G6C<E696@6K6H H:FG:7IHG:E:FH>E696<6B76F .:A6C?IHCL6@6K6H @6K6H >C>9>8:AIE@6C96A6BA6E>G6CG67IC96C9>6C<@6HJ:FH>@6A G:=>C<<6H:F7:CH6C<G6HIA6E>G6CG67IC /6BE6@@6K6H @:8>A +, B:C<6A6B> <6L6 H6F>@ @: 6H6G  <6F H:F?69> Q @:G:H>B76C<6CB6@6E696@6K6H@:8>A+,9><6CHIC<@6C P B6GG6G:7:F6H @6E6C?6C<@6K6H+, 8B=>HICG6CG67ICH:FG:7IH $C<6HA6E>G6CG67ICB:B>A>@>E:FBI@66CL6>HI9:E6C96C7:A6@6C< 1 +696@:6966CG:H>B76C<<6L6 <6L6L6C<7:@:F?6G6B67:G6F "6L6@:76K6=696A6= 7:F6H@6K6H96C7:F6H7:76C 96EIC<6L6@:6H6G696A6=<6L6H:<6C<E:FBI@66C +@+ "  "7    "@"7    @  >@:H6=I> "@ < Q P@<" < Q P@<  B G   8B  B (6@69>E:FDA:= Kata Kunci • • • • • • • • • gaya Archimedes kapilaritas melayang mengapung meniskus cekung meniskus cembung tegangan permukaan tekanan hidrostatik tenggelam   "@  " 7    air FA F Fk 6 raksa FA Fk F 7 Gambar 6.18 (a) Meniskus cekung (b) Meniskus cembung 148     @<     @<  B G   B   ) B a. Meniskus Cembung dan Meniskus Cekung "6L6H6F>@B:C6F>@6CH6F6E6FH>@:A E6FH>@:AL6C<G:?:C>G96A6BGI6HI M6H9>G:7IH<6L6 $'G:96C<@6C<6L6'696A6=<6L6H6F>@B:C6F>@ 6CH6F6 E6FH>@:A E6FH>@:A L6C< H>96@ G:?:C>G  DCHD= <6L6 ' 696A6= H:H:G6C 6>F E696 E:FBI@66C @686 L6C< A6B6 A6B6 6@6C B:AI6G  #6A H:FG:7IH H:F?69> @6F:C6 <6L6 69=:G> E6FH>@:A @686 96C 6>F A:7>= 7:G6F 96F>E696 <6L6 @D=:G>  :F7:96 9:C<6C 6>F ?>@6 F6@G6 9>H:H:G@6C E696 E:FBI@66C @686 B6@6 F6@G6 H:FG:7IH 6@6C B:C< @6F:C6 <6L6 @D=:G> A:7>= 7:G6F 96F>E696 <6L6 69=:G>CL6 @>76H ;:CDB:C6 H:FG:7IH ?>@6 @:9I6 86>F6C H:FG:7IH 9>B6GI@@6C @:96A6BH67IC<@6866@6CH:FA>=6HG:E:FH>E696)-  >@:H6=I>  696A6= <6L6 @D=:G> 96C  696A6= <6L6 69=:G>  )-   B:CIC?I@@6C"#' )' )#L6C<H:F?69>@6F:C6<6L669=:G>A:7>=7:G6F 96F>E696 <6L6 @D=:G>  96EIC )-   B:FIE6@6C "#' )' Mudah dan Aktif Belajar Fisika untuk Kelas XI ")# L6C< H:F?69> @6F:C6 <6L6 @D=:G> L6C< A:7>= 7:G6F 96F>E696 <6L6 69=:G>  .I9IH @DCH6@  E696 B:C>G@IG 8:@IC< 696A6= GI9IH A6C8>E  N .:76A>@CL6 GI9IH@DCH6@E696B:C>G@IG8:B7IC<696A6=GI9IH HIBEIA  N b. Kapilaritas ! %!&(' 696A6= E:F>GH>K6 C6>@ 6H6I HIFICCL6 E:FBI@66C M6H 86>F B:A6AI> AI76C< AI76C< @:8>A 6H6I @6E>A:F  A6H L6C< 96E6H 9> <:?6A6 @6E>A6F>H6G 696A6= E>E6 @6E>A:F  %>@6 E>E6 @6E>A:F 9>B6GI@@6C@:96A6BH67IC<L6C<7:F>G>6>FE:FBI@66C6>F9>96A6BE>E6 @6E>A:F 6@6C C6>@ G:E:FH> H:FA>=6H E696 )-    @6C H:H6E> ?>@6 E>E6@6E>A:F9>B6GI@@6C@:96A6BH67IC<F6@G6E:FBI@66CF6@G69>96A6B H67IC<H:FG:7IH6@6CHIFIC /6=I@6=C96B:C<6E6=6AH:FG:7IHH:F?69> +:F=6H>@6C )-    :CHI@ E>E6 @6E>A:F L6C< B:CL:FIE6> H67IC< 6@6C B:CL:767@6C M6H 86>F B:CL:CHI= 9>C9>C< G:7:A6= 96A6B G:=>C<<6 E:FBI@66C M6H 86>F B:C6F>@ E>E6 9:C<6C <6L6 G:7:G6F L   &  96EIC @:A>A>C< 9>C9>C< E>E6 @6E>A:F    & >C9>C< E>E6 @6E>A:F B:B7:F>@6C <6L6 F:6@G> H:F=696E M6H 86>F G:7:G6F L  &  8DG "6L6>C>9>>B76C<>DA:=7:F6HM6H86>FG:H>C<<>-96A6BE>E6L6>HIG:7:G6F 1 "#  #   &  8DG   &-# G:=>C<<6 9>E:FDA:= H>C<<> M6H 86>F 9> 96A6B E>E6 @6E>A:F L6>HI  8DG - P  #& &:H:F6C<6C - H>C<<> M6H 86>F B   H:<6C<6C E:FBI@66C 96A6B E>E6 @6E>A:F ) B  GI9IH @DCH6@ B6GG6?:C>GM6H86>F@< B   E:F8:E6H6C H6G> B G &  ?6F> ?6F> E>E6 @6E>A:F B Tes Kompetensi Subbab pipa kapiler air raksa Gambar 6.19 Gejala kapilaritas pada pipa kapiler.  cos  A B y Gambar 6.20 Pada keadaan setimbang, gaya tegangan permukaan di titik A sama dengan di titik B. A "-&'*($!()0'0(/%$*   .:7I6=9FIB7:F>G>B>CL6@L6C<B:B>A>@>B6GG6?:C>G  @< B96CH>C<<>CL6 8B :F6E6@6= 6 H:@6C6C=>9FDGH6H>@E69696G6F9FIB 7 H:@6C6C=>9FDGH6H>@9>H>H>@L6C<7:F696 8B 9>6H6G96G6F9FIB .:7I6= E>E6 7:F7:CHI@ =IFI; 0 9>>G> 9:C<6C 6>F &:BI9>6C@6@>G:7:A6=@>F>9>>G>B>CL6@=>C<<66>F H:F9:G6@G:?6I=8B96F>@:9I9I@6CG:H>B76C@6 6>F  < 8B B>CL6@  < 8B96CAI6G E:C6BE6C<E>E68B=>HICCL6@ L6C<9>B6GI@@6C@:96A6BE>E6 I67:?6C6L6C<7:F=I7IC<6C7:F>G>6>F96CF6@G6   < 8B air b 2,5 cm B A air raksa 6 7 :F6E6@6=E6C?6C<A6?IF6>FGIE6L6?6F6@6CH6F6 @:9I6E:FBI@66CF6@G696A6B7:?6C6H:FG:7IH 8B :F6E6 8B 6A@D=DA     < 8B  =6FIG 9>HI6C<@6C9>6H6GF6@G66<6FE:FBI@66C6>FC6>@ 8BAI6GE:C6BE6C<7:?6C68B Fluida 149  "6B76F7:F>@IHB:AI@>G@6CG:7I6=EDBE6=>9FDA>@ F  .:7I6=76AD@L6C<JDAIB:CL6B96CB6GG6?:C>GCL6    @< B 9>B6GI@@6C @: 96A6B B>CL6@ L6C< B6GG6?:C>GCL6 @< B 6 6<6>B6C6@6=EDG>G>7:C96 7 #>HIC<JDAIB:7:C96E696E:FBI@66CB>CL6@ 8 #>HIC< <6L6 F8=>B:9:G L6C< 7:@:F?6 E696 7:C96H:FG:7IH +:C6BE6C<@:8>AAI6GCL6 8B96CAI6GE:C6BE6C< 7:G6F 8B %>@6E696E:C6BE6C<L6C<@:8>A9>7:F> <6L6  ) 7:F6E6@6= <6L6 L6C< 7:@:F?6 E696 E:C6BE6C<7:G6F B. Viskositas Fluida "( &D:;>G>:C1>G@DG>H6GICHI@:F76<6> (686B!AI>96 (0%! >F 6F6= +A6GB696F6= H=>A6A@D=DA *A>.   "A>G:F>C 096F6 #>9FD<:C 06E6>F "),"-/03         . Q P  Q P Q P  Q P P  Q Q P  Q P  Q P  Q P  Q P  Q P Sumber: Physics, 1993 ' $'('6H6I@:@:CH6A6CB:FIE6@6C<:G:@6CL6C<9>B>A>@>DA:=;AI>96 ":G:@6C 96E6H H:F?69> 6CH6FE6FH>@:A M6H 86>F 6H6I <:G:@6C 6CH6F6 M6H 86>F 96C 9>C9>C< E:FBI@66C H:BE6H M6H 86>F H:FG:7IH 7:F696 .:H>6EM6H86>FB:B>A>@>J>G@DG>H6GL6C<7:F7:96 +696"( 96E6H 9>A>=6H @D:;>G>:C J>G@DG>H6G 7:7:F6E6 ;AI>96 E696 7:F76<6> GI=I  &:6966C GI=I9>86CHIB@6C96A6BH67:AH:FG:7IH@6F:C6J>G@DG>H6G7:F<6CHIC<E696 GI=I  .:B6@>C 7:G6F GI=I B6@6 G:B6@>C @:8>A J>G@DG>H6GCL6 7:<>HI EIA6 G:76A>@CL6  .6HI6C J>G@DG>H6G 96A6B G>GH:B .$ 696A6= )G B G:96C<@6C 96A6B G>GH:B 896>9:6A696A6=;AI>96L6C<H>96@B:B>A>@>J>G@DG>H6G@:@:CH6A6C %>@6 G:7I6= 7:C96 7:F<:F6@ 9> 96A6B ;AI>96 >9:6A 7:C96 H:FG:7IH H>96@ 6@6C B:C<6A6B> <6L6 <:G:@6C  %69> H:@6C6C ;AI>96 G:7:AIB 96C G:GI96= B:A:K6H> GI6HI E:C<=6A6C< H>96@ 6@6C 7:FI76= 6H6I 7:G6FCL6 H:H6E -:GIAH6C <6L6 L6C< 7:@:F?6 E696 G:H>6E H>H>@ 6A>F6C ;AI>96 696A6= CDA %>@6 7:C96 7:F<:F6@ 96A6B ;AI>96 L6C< B:B>A>@> J>G@DG>H6G 6@6C H:F?69><6L6<:G:@6CH6F67:C9696C;AI>96 "6L6H:FG:7IH9>C6B6@6C- ($ '  %>@6 7:C96 L6C< 7:F<:F6@ 96A6B ;AI>96 H:FG:7IH 7:F7:CHI@ 7DA6 7:G6FCL6 <6L6 .HD@:G 9>FIBIG@6C G:76<6> 7:F>@IH .   &* 6 7 Gambar 6.21 (a) Sebuah kelereng dijatuhkan ke dalam fluida ideal. (b) Sebuah kelereng dijatuhkan ke dalam fluida tak ideal. 150 P  &:H:F6C<6C  <6L6.HD@:G)   @D:;>G>:C J>G@DG>H6G )G B &  ?6F> ?6F>7DA6 B *  @:8:E6H6C F:A6H>; 7DA6 H:F=696E ;AI>96 B G +:F=6H>@6C )-   .:7I6= @:A:F:C< 9>?6HI=@6C 9> 96A6B H67IC< L6C< 7:F>G> GI6HI ;AI>96  %>@6 @:A:F:C< H:FG:7IH 9>?6HI=@6C @: 96A6BH67IC<L6C<7:F>G>;AI>96>9:6A)- H>96@6@6CH:F?69> E:FI76=6CF:GIAH6C<6L66@>76H<:G:@6C;AI>96 @6CH:H6E>?>@6@:A:F:C< 9>?6HI=@6C @: 96A6B H67IC< L6C< 7:F>G> ;AI>96 H>96@ >9:6A ) 6@6CH:F?69>E:FI76=6CF:GIAH6C<6L6L6C<7:@:F?6 #6AH:FG:7IH 9>@6F:C6@6C 696CL6 E:C<6FI= <6L6 <:G:@6C Mudah dan Aktif Belajar Fisika untuk Kelas XI +696 )-   <6L6 <6L6 L6C< 7:@:F?6 E696 @:A:F:C< 696A6= <6L67:F6H@:A:F:C<L6C<9>>B76C<>DA:=<6L6.HD@:G96C<6L6F8=>B:9:G +:C<>B76C<6C<6L6H:FG:7IHH:FIG7:FA6C?IHG:>F>C<9:C<6C<:F6@@:A:F:C< +696G66HH:FH:CHI<6L6L6C<7:@:F?6G:>B76C<G:=>C<<6F:GIAH6CG:AIFI=<6L6 H:FG:7IH 6@6C G6B6 9:C<6C CDA  %>@6 7:C96 7:F<:F6@ 9:C<6C @:8:E6H6C B6@G>BIB L6C< H:H6E @:8:E6H6CCL6 >C> 9>G:7IH %(# (&"#!  .:86F6 B6H:B6H>G@:8:E6H6CH:FB>C6A96E6H9>HIFIC@6C96F>FIBIG FIBIG7:F>@IH    "#PPG  G "#P P  FA Fs w = mg Gambar 6.22 Gaya-gaya yang bekerja pada kelereng di dalam fluida. 0CHI@ <6L6 @: 6H6G F8=>B:9:G   f # 0CHI@ <6L6 .HD@:G G   &*H :F6H7:C961"#   # 96EIC@:8:E6H6CH:FB>C6A7:C96G:H:A6=<6L6 <6L6L6C<7:@:F?6G:>B76C< 696A6= *(  *       & P  0CHI@ 7:C96 7:F7:CHI@ 7DA6 9:C<6C ?6F> ?6F> & B6@6 JDAIB: 7:C96  7  &   %69> &        *(    P G:96C<@6C J>G@DG>H6GCL6 696A6= &         *( P &:H:F6C<6C b  B6GG6 ?:C>G 7:C96 7DA6 @< B f  B6GG6 ?:C>G ;AI>96 @< B  JDAIB:7:C96B v t  @:8:E6H6C H:FB>C6A 7:C96 B G   @D:;>G>:C J>G@DG>H6G )G B Contoh 6.7 .:7I6=@:A:F:C<L6C<7:F?6F> ?6F> 8B9>?6HI=@6C@:96A6BB>CL6@E:AIB6GL6C< 7:F69696A6BH67IC< /:CHI@6CA6=@:8:E6H6CH:FB>C6AL6C<9>86E6>@:A:F:C<?>@6 B6GG6?:C>GB>CL6@ @< B@D:;>G>:CJ>G@DG>H6GB>CL6@ Q P+6GB6GG6?:C>G @:A:F:C<Q @< B96CE:F8:E6H6CH6G> B G 1 bQ @< B &  8BQ PB  f  @< B   B G P   Q +6G Kata Kunci • gaya stokes • kecepatan terminal • viskositas Fluida 151    &           B * H    Q B GQ  @< BP @< B     +6 G   B G %69>@:8:E6H6CH:FB>C6A@:A:F:C<696A6=B G  Tes Kompetensi Subbab  B "-&'*($!()0'0(/%$* &:8:E6H6CH:FB>C6AL6C<9>86E6>DA:=G:H:H:GB>CL6@  "  @< BL6C<?6HI=9>I96F6 I96F6   @< B 696A6=   BB G  #>HIC ?6F> H:H:G6CB>CL6@H:FG:7IH?>@6  Q P@< BG  #>HICBIB@:8:E6H6CH:FB>C6A 96F> G:7I6= 7DA6 76?6 7:F9>6B:H:F  BB L6C< 9>?6HI=@6C96A6BG:?:C>GB>CL6@ @< B L6C<B:B>A>@>@D:;>G>:CJ>G@DG>H6G @< BRG (6GG6 ?:C>G76?6  @< B C. Fluida Dinamis turbulen laminer Sumber: Dokumentasi Penerbit Gambar 6.23 Aliran laminer dan aliran turbulen pada asap rokok. A B D E P Q X Y C F R Z Gambar 6.24 Garis aliran A–B–C, D–E–F, P–Q–R, dan X–Y–Z merupakan garis aliran laminer. 6A6B ;AI>96 L6C< 7:F<:F6@ ;AI>96 9>C6B>G G:H>6E E6FH>@:A E696 ;AI>96 H:FG:7IH B:B>A>@> @:8:E6H6C ICHI@ G:H>6E EDG>G>CL6  *A:= @6F:C6 >HI ;AI>96 9>C6B>G 96E6H 9><6B76F@6C G:76<6> B:96C @:8:E6H6C *& %>@6 A>CH6G6C E6FH>@:A H>H>@ E696 ;AI>96 9><6B76F@6C 6@6C 9>E:FDA:= GI6HIA>CH6G6CL6C<9>C6B6@6C<6F>G6A>F6C 6A6B;AI>969>C6B>G6969I6 <6F>G 6A>F6C L6>HI !&# !"#& 96C !&# ()&)!#  A>F6C A6B>C:F 696A6= 6A>F6C ;AI>96 L6C< @:8:E6H6C 6A>F6C E696 G:H>6E H>H>@ E696 ;AI>96 H:FG:7IH H>96@7:FI76=H:F=696EK6@HI 96EIC6A>F6CHIF7IA:C696A6=6A>F6C;AI>96 L6C< @:8:E6H6C 6A>F6C G:H>6E H>H>@ E696 ;AI>96 H:FG:7IH 96E6H 7:FI76= )- B:C<<6B76F@6C6A>F6C6G6EFD@D@ A>F6C6G6EFD@D@ 76<>6C 76K6= 7:F7:CHI@ 6A>F6C G:?6?6F  A>F6C G:E:FH> >C> 9>G:7IH !&# !"#& 6H6I 6A>F6C L6C< B:C<>@IH> <6F>G 6FIG  96EIC 6G6E E696 76<>6C 6H6G 7:FEIH6F EIH6F 96C G:H:FIGCL6 B:CL:76F @: G:<6A6 6F6=  A>F6C H:FG:7IH 9>C6B6@6C !&# ()&)!# +:F=6H>@6C )-   +696 <6B76F H:FG:7IH 9>AI@>G@6C :BE6H <6F>G 6A>F6C E6FH>@:A E6FH>@:A ;AI>96  +6FH>@:A E6FH>@:A ;AI>96 E696 G:H>6E <6F>G6A>F6C=6CL6B:C<>@IH><6F>G6A>F6CH:FG:7IH96CH>96@7:FE>C96=@: <6F>G6A>F6CL6C<A6>C #6AH:FG:7IHB:FIE6@6CGI6HI<6B76F6C96F>6A>F6C ;AI>96 >9:6A L6C< 9>C6B6@6C 6A>F6C GH6G>DC:F 6A6B ;AI>96 >9:6A G:H>6E 6A>F6C ;AI>96 B:B>A>@> @:8:E6H6C 6A>F6C L6C< G6B6 ?I<6 H>96@ 696 <6L6 <:G:@ 6CH6F6 A6E>G6C 6A>F6C ;AI>96 L6C< H:F9:@6H 9:C<6C 9>C9>C< H67IC< 6H6I H:BE6H ;AI>96 B:C<6A>F  :C<6C 9:B>@>6C !) ! 696A6= ;AI>96 L6C< H>96@ H:FE:C<6FI= DA:= <6L6 H:@6CL6C<9>H:F>B6CL6 FH>CL6JDAIB:96CB6GG6?:C>GCL6H>96@7:FI76= B:G@>EIC 696 H:@6C6C 1. Persamaan Kontinuitas v1 A1  s1 v2  s2 A2 Gambar 6.25 Fluida mengalir pada penampang yang berbeda. 152 +:F=6H>@6C)- +696<6B76FH:FG:7IHM6H86>FB:A6AI>G:7I6= E>E6E696E:C6BE6C< 9:C<6C@:8:E6H6C6A>F6C* B:CI?I@:E:C6BE6C< L6C< A:7>= G:BE>H  9:C<6C @:8:E6H6C 6A>F6C *  :C<6C 6GIBG> 76=K6 ;AI>96L6C<B:C<6A>FH>96@@DBEF:G>7:AB6@696A6BG:A6C<K6@HIL6C<G6B6 ?IBA6= M6H 86>F L6C< B:C<6A>F B:A6AI> E:C6BE6C<  6@6C G6B6 9:C<6C ?IBA6=M6H86>FL6C<B:C<6A>FB:A6AI>E:C6BE6C<  1DAIB:M6H86>FE696 E:C6BE6C< G6B69:C<6CJDAIB:M6H86>FE696E:C6BE6C<  Mudah dan Aktif Belajar Fisika untuk Kelas XI      '    '  *  (  *  ( 0CHI@ G:A6C< K6@HI L6C< G6B6 6@6C 9>E:FDA:= *  * Ingatlah P Prinsip utama dari persamaan kontinuitas adalah pada selang waktu yang sama, debit fluida akan sama. 6H6I   P &:H:F6C<6C AI6GE:C6BE6C< B AI6GE:C6BE6C<B * @:8:E6H6CM6H86>FE696E:C6BE6C< B G * @:8:E6H6CM6H86>FE696E:C6BE6C<B G   * 9:7>HM6H86>F9>E:C6BE6C< B G   *9:7>HM6H86>F9>E:C6BE6C<B G "-.)* 4  96C "-.)* 4  9>C6B6@6C %&'"# $#(#)(' Contoh 6.8   .:7I6=E>E6L6C<AI6GE:C6BE6C6A>F>6>F +696E:C6BE6C<L6C< 7:G6FA6?I6A>F6C6>FCL6696A6=B G :F6E6@6=A6?I6A>F6C6>FE696E:C6BE6C<L6C<@:8>A 1 >@:H6=I>  8B Q PB  8B Q PB * B G :C<6CB:C<H6>F9>E:FDA:=    QB GB G *  *      Aktivitas Fisika 6.3 Persamaan Kontinuitas Tujuan Percobaan Mengamati dan memahami persamaan kontinuitas Alat-Alat Percobaan 1. Dua buah selang yang berdiameter 1 cm atau lebih dengan panjang masingmasing 2 meter 2. Dua buah ember 3. Plastik tebal. Langkah-Langkah Percobaan 1. Tutuplah salah satu ujung selang dengan plastik tebal yang telah dilubangi. Diameter lubang plastik ±0,5 cm. 2. Sambungkan kedua selang pada kran yang aliran airnya sama besar. 3. Jawablah pertanyaan berikut. a. Untuk posisi kedua selang sama, semburan air pada selang manakah yang paling jauh? b. Apa yang akan terjadi jika dalam selang waktu yang sama, setiap air selang dialirkan pada ember yang berukuran sama? 4. Tulislah kesimpulan dari percobaan tersebut. 5. Buatlah Hukum Kontinuitas menurut versi Anda berdasarkan percobaan yang telah Anda lakukan. 6. Bandingkan dengan Hukum Kontinuitas yang sudah Anda pelajari. Informasi untuk Anda Seorang penyelam pemula sedang menarik napas pada kedalaman L untuk berenang ke atas. Dia mengabaikan instruksi untuk mengeluarkan napas secara perlahanlahan selama menuju ke permukaan. Selama perjalanan ke atas, tekanan udara luar pada tubuhnya berkurang hingga mencapai tekanan atmosfer. Tekanan darahnya juga berkurang sampai normal kembali. Oleh karena ia tidak membuang napas, ketika sampai ke permukaan terdapat perbedaan antara tekanan udara di dadanya dengan di dalam paru-parunya. Perbedaan tekanan ini dapat mengakibatkan paru-parunya pecah. Selain itu, tekanan darahnya turun drastis sehingga udara pun masuk ke dalam jantungnya. Hal ini dapat mengakibatkan kematian bagi penyelam tersebut. Information for You A novice scuba diver takes enough air from his tank to fully expand his lung at depth L and swimming to the surface. He ignores instructions and fails to exhale during his ascent. As he ascends, the external pressure on him decreases, until it reaches the atmosphere pressure at the surface. His blood pressure also decreases, until it become normal again. However, because he does not exhale the air pressure in his lungs remain at the value it had at depth L. This pressure difference can explode his lungs. Besides that, his blood pressure decrease drastically which then carries the air to the heart. This two things can kill that novice diver. Sumber: Fundamentals of Physics, 2001 Fluida 153 2. Hukum Bernoulli A B C v Gambar 6.26 Fluida mengalir. v1  t p1 A1 v2  t h1 +696 7:?6C6 7:F=I7IC<6C E:FBI@66C M6H 86>F E696 G:H>6E H:BE6H 6@6C G6B6 H>C<<>  #6A H:FG:7IH 7:FA6@I E696 M6H 86>F L6C< 9>6B  %69> ?>@6 M6H 86>F H:FG:7IH 7:F<:F6@ @:6966C H:FG:7IH H>96@ 6@6C H:F?69> +:F=6H>@6C)-    %>@6 M6H 86>F 96A6B H67IC< H>96@ 7:F<:F6@ B6@6 H>C<<> E:FBI@66C M6H 86>F E696 E>E6  E>E6  96C E>E6  6@6C G6B6  )6BIC H>C<<> E:FBI@66C M6H 86>F E696 G:H>6E E>E6 6@6C 7:F7:96 ?>@6 M6H 86>F H:FG:7IH B:C<6A>F @: @6C6C C96 H:A6= B:C<:H6=I> 76=K6 @:A6?I6C M6H 86>F E6A>C< 7:G6F H:F96E6H E696E>E6L6C<G:BE>HC6BIC6E6@6==6AH:FG:7IH7:FA6@IEIA6E696H:@6C6C CL6 0CHI@ B:C<:H6=I> ?6K676C H:FG:7IH E:F=6H>@6C )-   .:86F6B6H:B6H>GE:FG6B66CL6C<B:C<<6B76F@6C6A>F6C;AI>96E696 <6B76F H:FG:7IH 696A6= p2 )' -/&   ' % *( h2 Gambar 6.27 Perbedaan ketinggian fluida mengalir. Tokoh Daniel Bernoulli (1700–1782) P 0G6=6 HDH6A L6C< 9>F@6C ;AI>96 96F> @:6966C  @: @:6966C  G6B6 9:C<6C E:FI76=6C :C:F<> B:@6C>@ ;AI>96  .:86F6 B6H:B6H>G 96E6H 9>HIA>G G:76<6> 7:F>@IH HDH6A "   P    %   % * (P%* (   "*   "*  "P"     % * ( "*  " %* ( "* "    +:F=6H>@6C"-.)* 7:FH6C96C:<6H>;@6F:C66F6=<6L6  7:FA6K6C6C 6F6= 9:C<6C 6F6= <:F6@ ;AI>96 (:CIFIH=I@IB@DCH>CI>H6G?IBA6=;AI>96L6C<B:C<6A>FE696E>E6 G6B69:C<6C?IBA6=;AI>96L6C<B:C<6A>FE696E>E6G:=>C<<69>E:FDA:= E:FG6B66C 7:F>@IH * ( *(  :C<6CB:CGI7GH>HIG>@6C"-.)*@:"-.)*6@6C 9>=6G>A@6C E:FG6B66C Sumber: World Book Encyclopedia Daniel Bernoulli adalah putra dari Johan Bernoulli, lahir di kota Basel dan bekerja sebagai dosen Matematika di Universitas Basel. Pamannya seorang matematikawan di Universitas tersebut yang pernah menciptakan materi baru dalam teori probabilitas, analisis geometri, dan kalkulus variasi. Bernoulli berhasil menciptakan prinsip hidrodinamika dan perhitungan aliran fluida. Selain itu, Bernoulli sangat berperan dalam mengembangkan teori probabilitas, kalkulus, dan persamaan diferensial. 154 %  "*  " % "* " P   %>@6C96 B:CGI7GH>HIG>@6C   " @:"-.)* 4  6@6C 9>E:FDA:= % "  "*  " % "  "* "   P &:BI9>6C ?>@6 C96 B:C<6A>@6C "-.)* 4  9:C<6C  6@6C 9>E:FDA:= %  *   gh % *      P "-.)* 4  9>G:7IH ?I<6 &'"# &#$)!! L6C< G:86F6 IBIB 96E6H 9>CL6H6@6C 9:C<6C E:FG6B66C 7:F>@IH >C> Mudah dan Aktif Belajar Fisika untuk Kelas XI %  *   @DCGH6C P  :F96G6F@6CE:FG6B66C:FCDIAA>9>@:H6=I>76=K6H:@6C6C9>96A6B ;AI>96 L6C< 7:F<:F6@ 9>E:C<6FI=> DA:= @:8:E6H6C 6A>F6C ;AI>96 H:FG:7IH 3. Penerapan Hukum Bernoulli a. Alat Penyemprot Nyamuk +:F=6H>@6CA6= )-   L6C< B:BE:FA>=6H@6C G:7I6= 6A6H E:CL:BEFDH CL6BI@  A6H H:FG:7IH B:C<CG>E #I@IB :FCDIAA>  %>@6 E:C<>G6E EDBE6 9>H:@6C I96F6 6@6C B:C<6A>F 9:C<6C @:8:E6H6C H>C<<> 96C @:AI6F B:A6AI> AI76C< G:BE>H E696 H67IC< I96F6 &:8:E6H6CI96F6L6C<H>C<<>B:CL:767@6CH:@6C6CE696E:FBI@66CE>E6 J:CHIF>B:C?69>F:C96= #6AH:FG:7IHB:CL:767@6C86>F6CD76HCL6BI@96E6H C6>@@:6H6GB:A6AI>E>E6J:CHIF>96CB:CL:B7IF@:AI6F7:F86BEIFI96F6 b. Daya Angkat pada Sayap Pesawat Terbang /6=I@6= C96 L6C< B:CL:767@6C E:G6K6H 96E6H H:F76C< +:G6K6H 96E6H H:F76C< @6F:C6 696CL6 96L6 6C<@6H E696 G6L6E  6L66C<@6HE696 E:G6K6HH:F76C<?I<6B:C<CG>E#I@IB:FCDIAA> :CHI@76<>6C 6H6GG6L6EE:G6K6HL6C<8:B7IC<B:CL:767@6C696CL6E:F7:966CA6?II96F6 E696 76<>6C 6H6G 96C 76<>6C 76K6=CL6 G:E:FH> 9><6B76F@6C DA:= <6F>G <6F>G <6L6E696)-  A>F6CI96F6E69676<>6C6H6GG6L6E7:F<:F6@A:7>= 8:E6H 96F>E696 76<>6C 76K6=CL6  (:CIFIH #I@IB :FCDIAA> H:@6C6C E696 76<>6C6H6GE:G6K6HB:C?69>A:7>=@:8>A96F>E696H:@6C6CE69676<>6C76K6= G6L6E +:F7:966CH:@6C6C>C>A6=L6C<B:B7I6H696CL6<6L66C<@6H@:6H6G L6C<7:G6FCL696E6H9>HIA>G@6CG:76<6>7:F>@IH P   % P% P    * P *  P  P    *P*  F pipa venturi Gambar 6.28 Alat penyemprot nyamuk. gaya angkat (F1) gaya berat (F2) Gambar 6.29 Garis arus fluida ideal pada sayap pesawat terbang. :F96G6F@6C"-.)*4 96E6H9>6C6A>G>G76=K6?>@6E:G6K6H 7:F<:F6@ A:7>= 8:E6H B6@6 6@6C B:C<=6G>A@6C <6L6 6C<@6H L6C< A:7>= 7:G6F EIA6  :C<6C 9:B>@>6C G:B6@>C AI6G E:C6BE6C< G6L6E G:B6@>C 7:G6F EIA6 <6L6 6C<@6HCL6 Contoh 6.9 .:7I6=E:G6K6HH:F76C<9:C<6CAI6GE:C6BE6C<G6L6E B7:F<:F6@G:=>C<<6 B:C<=6G>A@6CE:F7:966C@:8:E6H6C6A>F6CI96F6E69676<>6C6H6GG6L6EE:G6K6H96C 76<>6C76K6=CL6L6C<B6G>C< B6G>C<7:G6FCL6 B G96C B G :F6E6@6= 7:G6F<6L66C<@6HE696G6L6E?>@6B6GG6?:C>GI96F6 @< B 1 >@:H6=I>  B* B G *  B G  @< B   P    *  *    Q @< BQ BQ4 B GP B G5  )  %69><6L66C<@6HE696G6L6EE:G6K6HH:FG:7IH696A6=  ) Fluida 155 c. karburator Sumber: www.firetrucks.uw.hu Gambar 6.30 Karburator pada motor. h p1 v1 h1 p2 v2 h2 Karburator &6F7IF6HDF B:FIE6@6C 6A6H E:C86BEIF 76=6C 76@6F 96C I96F6 +:C86BEIF6C H:FG:7IH 7:FHI?I6C ICHI@ B:BE:FBI96= E:B76@6F6C &6F7IF6HDF H:F9>F> 6H6G H6C<@> @6F7IF6HDF E:A6BEIC< E>E6 J:CHIF> 96C E:CL:BEFDH I96F6 #$.!  096F6 L6C< B6GI@ @: 96A6B @6F7IF6HDF B:B>A>@> @:8:E6H6C L6C< H>C<<> G:=>C<<6 B:CL:767@6C H:@6C6C E696 I?IC< E>E6 J:CHIF> B:C?69> F:C96=  /:@6C6C L6C< F:C96= E696 I?IC< E>E6 J:CHIF> B:CL:767@6C 76=6C 76@6F 86>F @:AI6F 96F> H67IC< 76=6C 76@6F B:A6AI> E>E6 J:CHIF> B:CI?I #$.!  .:B7IF6C 76=6C 76@6F 86>F L6C<7:F86BEIF9:C<6CI96F696E6HB:C<=6G>A@6C<6GL6C<9>G:7IH"#.! L6C< 7:FG>;6H BI96= H:F76@6F  "6G "#.! >C>A6= L6C< 9>76@6F G:=>C<<6 B:B>A>@> H:@6C6C L6C< H>C<<> 96C B:C:@6C E>GHDC  :B>@>6C G:H:FIGCL6 G:=>C<<6 FD96 6@6C 7:F<:F6@ G:>F>C< 9:C<6C <:F6@6C C6>@ HIFIC E>GHDC H:FG:7IH d. Pipa Venturi .:A6>C 9>B6C;66H@6C 96A6B @6F7IF6HDF E>E6 J:CHIF> ?I<6 9>B6C;66H @6C ICHI@ B:C:CHI@6C @:A6?I6C M6H 86>F 96A6B G:7I6= E>E6  +:F=6H>@6C )-   "6B76F H:FG:7IH B:BE:FA>=6H@6C 6A>F6C ;AI>96 96F> EDG>G> @:EDG>G> 0CHI@B:C:CHI@6C@:A6?I6C6A>F6C;AI>96H:FG:7IHJ:CHIF>B:H:F =6FIG 9>A:H6@@6C B:C96H6F G:=>C<<6      :C<6C B:C< 9>E:FDA:= %  %   *  *    Gambar 6.31 Pipa venturi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udah dan Aktif Belajar Fisika untuk Kelas XI P e. Venturimeter dengan Manometer )- B:CIC?I@@6CJ:CHIF>B:H:FL6C<9>A:C<@6E>B6CDB:H:F 96C9>>G>9:C<6CM6H86>FL6C<B:B>A>@>B6GG6?:C>G  :C<6CB:C<@:8:E6H6C;AI>96L6C<B:C<6A>FB:A6AI>E:C6BE6C< 7:G6F J:CHIF> B:H:F 96E6H 9>I@IF G:76<6> 7:F>@IH %  *     %  *     *A:= @6F:C6 @:H>C<<>6C E>E6 @:8>A 9:C<6C E>E6 7:G6F G6B6     9>E:FDA:= %  *   %  *   %  %   *  *    tekanan tinggi tekanan rendah v1 .1 .2 v2 h A B Gambar 6.32 P Venturimeter yang dilengkapi manometer. /:@6C6C =>9FDGH6H>@ 9>   H:@6C6C =>9FDGH6H>@ 9>  G:=>C<<6   %     % % P%  P  P *  * P +:FG6B66C @DCH>CI>H6G :C<6C B:A6@I@6C GI7GH>HIG>@6C 96F> "-.)* 4  96C "-.)* 4  @: 96A6B "-.)* 4  9>96E6H@6C E:FG6B66C     *      P &:H:F6C<6C *  @:8:E6H6C M6H 86>F L6C< 9>I@IF B G   B6GG6 ?:C>G F6@G6 @< B  B6GG6 ?:C>G M6H 86>F L6C< 9>I@IF @< B AI6GE:C6BE6C<E>E67:G6FB  AI6GE:C6BE6C<E>E6@:8>AB   E:F7:966C H>C<<> F6@G6 B   E:F8:E6H6C H6G> B G f. Pipa Pitot +>E6 E>HDH 696A6= 6A6H ICHI@ B:C@6C)- +>E6E>HDHH:F9>F>6H6GE>E6J:CHIF>L6C<7:F>G>@6C F6@G6 0?IC<H:F7I@6@:6H6GG:96C<@6CI?IC<H:F7I@6B:B6C?6C< G:6F6= 9:C<6C 96H6CC<<> F6@G6 96A6B E>E6 9>G:767@6C DA:= E:F7:966C H:@6C6C 9>  96C  A>F6CI96F6L6C<B6GI@@:96A6BH67IC<9>H:FIG@6C@:96A6BE>E6 B:A6AI>I?IC<9:C<6C@:8:E6H6C7:F@IF6C<=>C<<6B:C86E6>CDA +696 @:6966CH:FG:7IHH:@6C6C9>G6B69:C<6CH:@6C6C9>H>H>@96C<6G 96A6B @:6966C 9>6B :C<6C B:C<  9:C<6C      96C @:8:E6H6C <6G 9>  G6B6 9:C<6C CDA 6@6C 9>96E6H aliran gas A v1 v2 B 2 1 p1 h D C Gambar 6.33 Pipa pitot Fluida 157 %  *   %  %  %  *   P  :96H:@6C6C6CH6F6H>H>@ 96CH>H>@%P% G6B69:C<6CH:@6C6C =>9FDGH6H>@ M6H 86>F 9> 96A6B B6CDB:H:F L6>HI %  %    :C<6CB:A6@I@6CGI7GH>HIG>"-.)*4 @:"-.)*4  9>E:FDA:= *           *  Kata Kunci • • • • • • aliran turbulen aliran laminer hukum Bernoulli manometer persamaan kontinuitas venturimeter Tes Kompetensi Subbab P  *        * 6H6I P &:H:F6C<6C *  @:8:E6H6C 6A>F <6G I96F6 B G   B6GG6 ?:C>G 6>F F6@G6 @< B  B6GG6 ?:C>G <6G I96F6 @< B   E:F7:966C H>C<<> 6>F F6@G6 B C "-&'*($!()0'0(/%$*   158 :F6HG:7I6=E:G6K6HL6C<B:B>A>@>AI6GHDH6AG6L6E  B696A6=  ) &:8:E6H6C6A>F6CI96F6E696 76<>6C 76K6= G6L6E   B G  :F6E6@6= @:8:E6H6C 6A>F6CI96F6E69676<>6C6H6GG6L6E?>@6<6L66C<@6H 9>C6B>@CL6 G6B6 9:C<6C 7:F6H E:G6K6H H:FG:7IH E:G6K6H96A6B@:6966CG:>B76C< (6GG6?:C>GI96F6 G66H>HI @< B .:7I6=76@H:F7I@67:F>G>6>FG:H>C<<>B :F6E6@6= @:8:E6H6C @:AI6FCL6 6>F E696 G:7I6= AI76C< L6C< H:FA:H6@ 9> 96G6F 76@ ?>@6 AI6G E:FBI@66C AI76C< H:FG:7IH 8B#>HIC<76CL6@CL66>FL6C<96E6H 9>H6BEIC<96A6BK6@HI ?6B :F6E6@6=<6L6@:6H6GL6C<9>6A6B>DA:=G:7I6= E:G6K6HL6C<B:B>A>@>A:76FG6L6EHDH6A B?>@6 @:8:E6H6C6A>F6CI96F69>6H6G96C9>76K6=G6L6E  B G96C B G(6GG6?:C>GI96F6E696@:H>C<<>6C >HI  @< B Mudah dan Aktif Belajar Fisika untuk Kelas XI    .:7I6=E:G6K6HB:C96E6HH:@6C6C@:6H6GG:7:G6F ) B %>@6@:8:E6H6C6A>F6CI96F6E69676<>6C 6H6GG6L6EE:G6K6H B G7:F6E6@6=@:8:E6H6C6A>F6C I96F6E69676<>6C76K6=G6L6EE:G6K6HH:FG:7IH?>@6 B6GG6?:C>GI96F6 @< B +:F7:966CH>C<<>F6@G696A6BG:7I6=B6CDB:H:FGI6HI J:CHIF>B:H:F>6A6=8B :F6E6@6=@:8:E6H6C6>FE696 E:C6BE6C<L6C<A:7>=7:G6F?>@6AI6GE:C6BE6C<L6C< 7:G6F 96C @:8>A B6G>C< B6G>C<   8B 96C   8B >@:H6=I>B6GG6?:C>GF6@G6 F6CE69676<>6CE>E6L6C<7:G6F96F> GI6HIJ:CHIF>B:H:F 8B G :F6E6@6=E:F7:966C H>C<<>F6@G6B6GG6?:C>G < 8BE696B6CDB:H:F ?>@6E:F76C9>C<6C6CH6F6AI6GE:C6BE6C<7:G6F96C @:8>A696A6=  Rangkuman  /:@6C6CB:FIE6@6C7:G6F<6L6L6C<7:@:F?6E696 GI6HIE:FBI@66C9>76<>9:C<6CAI6G<6L6 ,  /:@6C6C =>9FDGH6H>@6 B:FIE6@6C H:@6C6C L6C< 9>6A6B>M6H86>FE696@:96A6B6CH:FH:CHI /:@6C6C =>9FDGH6H>@6G6C<6H9>E:C<6FI=>DA:=<6L6H6G> 96C@:96A6B6C6>F , # #I@IB+6G86AB:CL6H6@6C76=K6H:@6C6CL6C< 9>7:F>@6CE696GI6HIM6H86>F96A6BFI6C<H:FHIHIE 9>H:FIG@6CG6B67:G6F@:G:<6A66F6= +F>CG>E@:F?6 9DC<@F6@=>9FDA>@96CE:C<6C<@6H=>9FDA>@7:@:F?6 7:F96G6F@6C#I@IB+6G86A    ":?6A6@6E>A6F>H6G696A6=E:F>GH>K6C6>@6H6IHIFICCL6 E:FBI@66CM6H86>FB:A6AI>AI76C< AI76C<@:8>A6H6I @6E>A:F />C<<>M6H86>F9>96A6BE>E6@6E>A:F696A6= -        #I@IBF8=>B:9:G7:F7ICL>7:C96L6C<H:F8:AIE @: 96A6B ;AI>96 M6H 86>F 76>@ G:76<>6C 6H6IEIC G:AIFI=CL66@6CB:C<6A6B><6L6@:6H6GG:7:G6F 7:F6HM6H86>FL6C<9>E>C96=@6CDA:=7:C96H:FG:7IH "6L6 @: 6H6G >C> 9>G:7IH <6L6 F8=>B:9:G L6C< 7:G6FCL69>CL6H6@6CG:76<6>7:F>@IH  " #   @>76H696CL6<6L6F8=>B:9:GE6967:C96L6C< B6GI@@:96A6BM6H86>F696H><6@:BIC<@>C6CL6C< 6@6CH:F?69>E6967:C96L6>HI 6 7:C96B:C<6EIC<?>@61  7 7:C96B:A6L6C<?>@61  8 7:C96H:C<<:A6B?>@61  #I@IBF8=>B:9:G9>H:F6E@6CE696@:C96F66C A6IH96CI96F6G:E:FH>E:F6=I96C76ADCI96F6 /:<6C<6CE:FBI@66CM6H86>FH:F?69>@6F:C6696CL6 @D=:G> <6L6H6F>@ B:C6F>@6CH6FE6FH>@:AG:?:C>G   8DG & 1>G@DG>H6G 6H6I @:@:CH6A6C 696A6= <:G:@6C L6C< 9>B>A>@>DA:=;AI>96 #I@IB .HD@:G B:CL6H6@6C 76=K6 ;AI>96 >9:6A 696A6=;AI>96L6C<H>96@B:B>A>@>J>G@DG>H6GG:=>C<<6 7:C96L6C<7:F<:F6@9>96A6BCL6H>96@B:C<6A6B> <6L6<:G:@ .:76A>@CL6E696;AI>96L6C<B:B>A>@> J>G@DG>H6G6@6CH:F?69><6L6<:G:@L6C<9>C6B6@6C <6L6GHD@:G G   &* &:8:E6H6C H:FB>C6A L6C< 9>6A6B> 7:C96 @:H>@6 7:F<:F6@96A6B;AI>96L6C<B:B>A>@>J>G@DG>H6G696A6= *      *(   & +696;AI>96L6C<7:F<:F6@7:FA6@I 6 +:FG6B66C&DCH>CI>H6G   7 #I@IB:FCDIAA>    @DCGH6C  * #I@IB:FCDIAA>9>B6C;66H@6CE696 6 6A6HE:CL:BEFDHD76HCL6BI@ 7 96L66C<@6HE696G6L6EE:G6K6HH:F76C< 8 @6F7IF6HDF 9 E>E6J:CHIF> : J:CHIF>B:H:F9:C<6CB6CDB:H:F96C ; E>E6E>HDH %  Fluida 159 Peta Konsep (0%! B:B76=6G !AI>96.H6H>G !AI>96>C6B>G B:B76=6G 9>6C<<6E /:@6C6C#>9FDGH6H>G !AI>96$9:6A #I@IBF8=>B:9:G /:<6C<6C+:FBI@66C #I@IB+6G86A B:C<=6G>A@6C +:FG6B66C&DCH>CI>H6G +:FG6B66C:FCDIAA> 9>6EA>@6G>@6C E696 &6E>A6F>H6G O "6L6C<@6H+:G6K6H O /67IC<1:CHIF> O +>E6+>HDH +:FG6B66C1>G@DG>H6G Refleksi Setelah mempelajari bab ini, Anda tentu dapat mengetahui konsep tekanan pada zat cair,hukum-hukum yang berlaku baik pada zat cair yang diam maupun pada zat cair yang bergerak. Dari materi-materi yang ada pada bab ini, bagian manakah yang menurut Anda paling sulit 160 Mudah dan Aktif Belajar Fisika untuk Kelas XI dipahami? Coba Anda diskusikan dengan teman atau guru Fisika Anda. Dalam bab ini, dijelaskan pula beberapa manfaat dari konsep yang dibahas. Coba sebutkan manfaat yang Anda peroleh setelah mempelajari materi pada bab ini. Tes Kompetensi Bab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@DA6B   162 Mudah dan Aktif Belajar Fisika untuk Kelas XI  .:7I6=E:G6K6HH:F76C<9:C<6CAI6GE:C6BE6C<G6L6E   B 7:F<:F6@ G:=>C<<6 B:C<=6G>A@6C E:F7:966C @:8:E6H6C6A>F6CI96F6E69676<>6C6H6GG6L6EE:G6K6H 96C76<>6C76K6=CL6B6G>C< B6G>C<7:G6FCL6 B G 96C B G :G6FCL6<6L66C<@6HE:G6K6H?>@6B6GG6 ?:C>GI96F6 @< B696A6= 6 ) 9   ) 7  ) :   ) 8   )  'I6GE:C6BE6C<@:F6CE696G:7I6=76@696A6=8B 6A6B 9:H>@6>FL6C<H:FH6BEIC<9>76@H:FG:7IH 696A6= A>H:F &:8:E6H6CF6H6 F6H66>FL6C<@:AI6F96F> @:F6CH:FG:7IH696A6= 6 B G 9  B G 7 B G : B G 8 B G  +:F=6H>@6C<6B76F7:F>@IH h1 h2 A C %>@6  B B96C6>F?6HI=9>?6F6@ 6CH6F6H>H>@96C B 6  9  7  :  8   .:7I6=E>E6L6C<AI6GE:C6BE6CC< B6G>C< 8B 96C  8B 9>6A>F> 6>F  '6?I 6A>F6C 6>F E696 E:C6BE6C<L6C<7:G6F696A6=B GA6?I6A>F6CE696 E:C6BE6C<L6C<@:8>A696A6= 6  B G 9  B G 7  B G :  B G 8  B G   +:F7:966CH>C<<>6>FF6@G696A6BB6CDB:H:FG:7I6= J:CHIF>B:H:F696A6=8B %>@6AI6GE:C6BE6C<E>E6 7:G6F 8B96CE>E6@:8>A 8B 6>F @< B 96CB6GG6?:C>G6>FF6@G6 Q @< B B G =>HICF6C6>FG66H>HI .:7I6=@DA6B9:C<6CJDAIB:B96A6B@:6966C @DGDC<9>6A>F>6>FA:K6HG:A6C<EA6GH>@L6C<7:FE:C6BE6C< 8B %>@66>FB:C<6A>F9:C<6C@:8:E6H6C B GG:H:A6= 7:F6E69:H>@@6=@DA6BH:FG:7IHE:CI= Bab 7 Sumber: www.dailytimes.com.pk Balon udara dapat terbang karena di dalamnya berisi udara panas yang lebih ringan daripada udara di sekitarnya. Teori Kinetik Gas Hasil yang harus Anda capai: menerapkan konsep termodinamika dalam mesin kalor. Setelah mempelajari bab ini, Anda harus mampu: mendeskripsikan sifat-sifat gas ideal monoatomik. #1.54 0-=5 >1-.-0 C-:3 8-8@ .-8;: @0-=- 05.@-? >1.-3-5 >-=-:?=-:><;=?->5*-4@7-4:0-.-3-5-9-:-<=5:>5<71=6-.-8;:@0-=-'=5:>5< 71=6- .-8;: @0-=- -3-= 0-<-? ?1=.-:3 >-:3-? >101=4-:- C-5?@ 01:3-: 919-:2--?7-: 9->>- 61:5> 3-> 0-: 1:1=35 75:1?57 C-:3 05958575 3-> '-0- .-. 5:5 :0- -7-: 919<18-6-=5 ?1;=5 75:1?57 3-> C-:3 91:1=-:37-: ?1:?-:3 >52-?>52-? 3-> .1=0->-=7-: 31=-7 -/-7 <-=?5718 <-=?5718:C- C-:3 .1=8-:3>@:3 ?1=@> 91:1=@> 0-<@: 3-> C-:3 -7-: 05.-4-> -0-8-4 3-> 501-8 C-5?@ 3-> C-:3 >1/-=- ?1<-? 9191:@45 4@7@9 4@7@93->)18-5:5?@:0--7-:919<18-6-=5<=5:>5<17@5<-=?5>51:1=35 0-: 71/1<-?-: 1217?52 0-=5 <-=?5718 3-> A. Gas Ideal B. Prinsip Ekuipartisi Energi C. Kecepatan Efektif Partikel Gas 163 Tes Kompetensi Awal '$'-5..'.1'-#+#2*,0/3'1!'02**/'4*,#3,'2+#,#/-#)30#-30#-$'2*,54&#-#.$5,5-#4*)#/  )1.@?7-:/;:?;43->C-:3?1=0-<-?05-?9;>21=<-  $1:3-<-.-8;:@0-=-0-<-??1=.-:3-3-59-:-/-=7-43->?1=>1.@??1=9->@73->501-8 91:31:0-857-:.-8;:@0-=--3-=0-<-?.1=31=-7:-57  <-7-4C-:3059-7>@001:3-:9;8-=5?->3-> ?@=@:0-:.1=.18;7  <-<1:31=?5-:0-=51:1=350-8-93-> A. Gas Ideal *-4@7-4 :0- C-:3 059-7>@0 01:3-: 3-> 501-8 -3-59-:-7-4 .1:?@70-=5<1=>-9--:3->501-8+:?@791:31?-4@5:C-<18-6-=58-4@=-5-: .1=57@? >1/-=- >-7>-9- 1. Pengertian Gas Ideal -8-9 .-. 5:5 :0- -7-: 919<18-6-=5 ?1;=5 75:1?57 3-> <-0- 3-> 501-8 '-0- 71:C-?--::C- >52-?>52-? 3-> 501-8 ?50-7 ?1=0-<-? 05 -8-9 7-:?1?-<5<-0->@4@7-9-=0-:?17-:-:?1=?1:?@3->0-<-?91958575 >52-? C-:3 91:017-?5 3-> 501-8 )1/-=- 957=;>7;<5> 3-> 501-8 91958575 >52-?>52-? >1.-3-5 .1=57@? - -> ?1=05=5 -?-> <-=?5718<-=?5718 0-8-9 6@98-4 C-:3 .1>-= 0-: ?50-7 ?1=6-05 5:?1=-7>5 -:?-=<-=?5718 3-> ?1=>1.@? . )1?5-< <-=?5718 >18-8@ .1=31=-7 71 >19.-=-:3 -=-4 / '-=?5718<-=?5718 3-> ?1=>1.-= 91=-?- 0-8-9 =@-:3 C-:3 >19<5? 0 !-=-7 -:?-=<-=?5718 6-@4 81.54 .1>-= 0-=5<-0- @7@=-: <-=?5718 1 +7@=-: <-=?5718 3-> 0-<-? 05-.-57-: 2 *50-7 ?1=0-<-? 3-C- -:?-=<-=?5718 71/@-85 657- ?1=6-05 ?@9.@7-: 3 @7@9 %1B?;: ?1:?-:3 31=-7 .1=8-7@ <-0- >5>?19 3-> ?1=>1.@? y l A x z Gambar 7.1 Gerak arah partikel-partikel gas dalam ruang tertutup. tekanan (p) 2. Persamaan Gas Ideal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p2 100 K isotermal p1 V1 V2 volume (V) Gambar 7.2 Grafik hubungan tekanan (p) terhadap volume (V) pada suhu konstan. 164 F  "1?1=-:3-:  ?17-:-:% 9 -?-@'-  A;8@919  '23#.##/ 9  0571:-8 >1.-3-5 @7@9 ;C81 0-: .1=8-7@ @:?@7 4-9<5=>19@-3->01:3-:71=-<-?-:=1:0-4=-2574@.@:3-:-:?-=-?17-:-: 0-: A;8@91 3-> ?-9<-7 <-0- #.$#2   !57- ?17-:-: 05?@=@:7-: A;8@91 3-> -7-: :-57 )1.-857:C- 657- ?17-:-: 3-> 05:-577-: A;8@91 3-> -7-: 91:31/58 01:3-: >C-=-? >@4@ 3-> ?1?-< Mudah dan Aktif Belajar Fisika untuk Kelas XI )#2-'3 F  0-:03'1)#8533#% F  918-7@7-: <1:3-9-?-:01:3-:<1=/;.--:?1:?-:34@.@:3-:-:?-=->@4@0-:A;8@91 <-0- ?17-:-: ?1?-< $1=17- 91:3-?-7-: 657- ?17-:-: 3-> 0-8-9 =@-:3 ?1=?@?@< 056-3- 7;:>?-: A;8@91 3-> >1.-:05:3 01:3-: >@4@ 9@?8-7:C- )1/-=- 9-?19-?5> 05:C-?-7-: 01:3-: <1=>-9--:    7;:>?-:-?-@     F  "1?1=-:3-: A;8@919  >@4@9@?8-7  Tokoh Joseph Louis Gay Lussac (1778–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umber: Jendela Iptek 3, 1997 Ia dilahirkan di Prancis tahun 1778. Setahun setelah lulus dari politeknik Paris, ia ditawari pekerjaan oleh Claude-Louis Berthollet, kimiawan Prancis yang terkemuka. Berthollet memiliki laboratorium sendiri dan memimpin sekelompok ilmuwan muda di daerahnya. Gay Lussac mengadakan banyak riset bersama Berthollet dan Pierre Simon Laplace, dua ilmuwan yang dibiayai dan dilindungi oleh Napoleon Bonaparte. Gay-Lussac selamat dari arus revolusi Prancis, tetapi ayahnya tertangkap dan dipenjarakan. Pada 1802, ia mengulangi percobaan Alexander Cesar Charles. Ia menemukan fakta bahwa jika gas dipanaskan pada suhu tetap, volumenya akan bertambah sebanding dengan suhu mutlak. Jika suhunya dinaikkan dua kali lipat, volumenya akan meningkat dua kali. Hukum ini kali pertama ditemukan oleh Charles. Akan tetapi, karena Charles tidak mempublikasikannya, hukum tersebut kadang-kadang disebut hukum Charles, kadangkadang disebut Hukum Gay-Lussac. "1?1=-:3-: 6@98-49;83->  ! 9;8"?1?-<-:@9@93-> !@98-49;83->91=@<-7-:<1=.-:05:3-:-:?-=-9->>-3->01:3-: 9->>-9;817@8=18-?52:C- )1/-=-9-?19-?5>6@98-49;83->0-<-? 05:C-?-7-: 01:3-: <1=>-9--:   -?-@ F Teori Kinetik Gas 165 !57- '23#.##/ 9 05>@.>?5?@>57-: 71 0-8-9 '23#.##/ 9 -7-: 05<1=;814 <1=>-9--: .1=57@?  V (m3) F -=5'23#.##/90-<-?05?1:?@7-:9->>-61:5>  >@-?@3-> C-5?@     F    p1 p2 p3 T (K) )18-5: 0-<-? 05:C-?-7-: 0-8-9 6@98-4 9;8 <1=>-9--: @9@9 3-> 501-8 6@3- 0-<-? 05:C-?-7-: 0-8-9 6@98-4 <-=?5718 3-> ?1=>1.@?   !@98-4<-=?57183->91=@<-7-:4->587-856@98-49;83->?1=>1.@?01:3-: .58-:3-: A;3=-0;   Gambar 7.3 Grafik hubungan volume (V) terhadap suhu mutlak (T) secara isobarik dengan p1 > p2 > p3. p (Pa)   V1 V2 V3 T (K)   F  !57-'23#.##/ 9  05>@.>?5?@>57-: 71 0-8-9 '23#.##/ 9 -7-: 05<1=;814 <1=>-9--: .1=57@?    !57-    <1=>-9--: ?1=>1.@? 91:6-05    F  "1?1=-:3-:  6@98-4 <-=?5718 3->  .58-:3-:A;3-0=; G 9;817@8 9;8  ?1?-<-:;8?D9-:  G F ! " Gambar 7.4 Grafik hubungan tekanan (p) terhadap suhu mutlak secara isokhorik dengan V 1 > V2 > V 3. Ingatlah Pada suhu kamar dan tekanan tertentu, gas dapat memiliki sifat yang mendekati gas ideal. Contoh 7.1 )-?@9;83->91:19<-?5A;8@91 9 0-:>@4@3-><-0->--??1=>1.@?-0-8-4 E *1:?@7-:8-4?17-:-:3->?1=>1.@? #7#$ 571?-4@5  9;8  ! 9;8"  9  E    " 1:3-:91:33@:-7-:<1=>-9--:05<1=;814  9  9;8 ! 79;8" "   G % 9 !-05?17-:-:3->?1=>1.@?-0-8-4  G % 9  Contoh 7.2 )-?@85?1=3->91958575?17-:-: -?9<-0-?19<1=-?@=F E1=-<-7-4?17-:-: 3->?1=>1.@?657-A;8@91:C-91:6-05 85?1=0-:?19<1=-?@=:C-91:6-05E #7#$ 571?-4@5  F     "  85?1=      "  -?9   85?1= 166 Mudah dan Aktif Belajar Fisika untuk Kelas XI 1:3-:91:33@:-7-:'23#.##/905<1=;814    #   -?9  #          "  "     -?9 !-05?17-:-:3->?1=>1.@?-0-8-4 -?9 Contoh 7.3 Kata Kunci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• gas ideal • jumlah mol      Tes Kompetensi Subbab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rinsip Ekuipartisi Energi '-0-.-4->-:>1.18@9:C-?18-405618->7-:.-4B->1?5-<<-=?57183-> 501-8>18-8@ .1=31=-7 >145:33- 91:34->587-: 1:1=35 75:1?57 &8147-=1:>52-? 3-> 501-8 05?5:6-@ >1/-=- 71>18@=@4-: 1:1=35 75:1?57 >1?5-< <-=?5718 :C- 91=@<-7-: 1:1=35 75:1?57 =-?-=-?- -8 ?1=>1.@? 91:C1.-.7-: ?59.@8:C- <=5:>5< 17@5<-=?5>5 1:1=35 Teori Kinetik Gas 167 y 1. Tekanan Gas dalam Ruang Tertutup  dinding A m0 vx  dinding B x Gambar 7.5 z Tanda panah menyatakan momentum sebuah molekul setelah menumbuk dinding. '1=4-?57-: #.$#2   )@-?@ 3-> 501-8 ?1=7@=@:3 0-8-9 >1.@-4 7@.@> C-:3 91958575 <-:6-:3 =@>@7   )1.@-4 <-=?5718 0-=5 3-> 501-8 ?1=>1.@? .1=31=-7 0-8-9 -=-4 >@9.@-# 01:3-: 71/1<-?-: " #  0-: 918-7@7-: 31=-7 .;8-7.-857 0-=5 05:05:3  71 05:05:3  719@05-: 719.-858-357105:05:3!-=-7C-:305?19<@4<-=?5718?1=>1.@?-0-8-4  "1/1<-?-:>18-9-.1=31=-7>18-8@>-9-7-=1:-?@9.@7-:C-:3?1=6-05 -:?-=<-=?5718 0-: 05:05:3 05->@9>57-: >1.-3-5 ?@9.@7-: 81:?5:3 >19  <@=:- ,-7?@ ?19<@4 <-0- 31=-7 .;8-7.-857 ?1=>1.@? -0-8-4   "  # >10-:37-: .-:C-7:C- ?@9.@7-: <1= >-?@-: B-7?@ C-:3 05.@-? ;814 " <-=?5718 0-: 05:05:3  -0-8-4 #  0-<@: <1=@.-4-: 9;91:?@9 C-:3  05-8-95 9;817@8 0-<-? 05?@85>7-: >1.-3-5 .1=57@? <1=@.-4-:9;91:?@99;91:?@9-745=F9;91:?@9-B-8 1 F<6#F<6# 1 F <6# Tantangan untuk Anda F  *-:0- :13-?52 <-0- 9;91:?@9 -745= <-=?5718 91:@:6@77-: -=-4 31=-7<-=?5718>1?18-4?@9.@7-:C-:3.1=8-B-:-:-=-401:3-:-=-431=-7 -B-8:C- -=5 <1=>-9--: <1=@.-4-: 9;91:?@9 ?1=>1.@? 0-<-? 05/-=5 3-C- C-:3 .171=6- <-0- <-=?5718 C-5?@ <1=@.-4-: 9;91:?@9 C-:3 05<5:0-47-: ;814 <-=?5718 71 05:05:3 <1= >-?@-: B-7?@ 1      < 6 #    "# < 6 #   F   '-0- 71:C-?--::C- <-=?5718 C-:3 91:@9.@7 05:05:3 ?50-7 4-:C>-?@ <-=?5718 ?1?-<5 >16@98-4  <-=?5718 &814 7-=1:- 5?@ 3-C- C-:3 05?1=59- 05:05:3 -75.-? ?@9.@7-:  <-=?5718 -0-8-4  < 6 # #  Sumber: Fundamentals of Physics, 2001 Pernahkah Anda minum minuman bersoda? Ketika Anda membuka tutup botolnya, akan terbentuk kabut tipis di sekitar tutup botol tersebut. Mengapa hal ini terjadi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udah dan Aktif Belajar Fisika untuk Kelas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v < v   !-05    F  "1?1=-:3-:   1:1=35 75:1?57 =-?-=-?- >-?@ <-=?5718 3-> 6;@81 Contoh 7.4 !57-71/1<-?-:<-=?57183->91:6-050@-7-8571/1<-?-:>19@8-?1:?@7-:8-4.1>-=:C?17-:-:C-:3054->587-: #7#$   " @.@:3-:?17-:-:?1=4-0-<718-6@-:"-0-8-4  &8147-=1:-:58-5  7;:>?-::58-5>1.-:05:301:3-: " >145:33   "  "      " " !-05?17-:-:3->91:6-0519<-?7-85?17-:-:>19@8- Contoh 7.5 )1.@-4?-.@:301:3-:A;8@91  9 91:3-:0@:3 9;8185@9<-0->@4@ E 1:3-:91:3-:33-<185@9>1.-3-53->501-8?1:?@7-: - 1:1=3575:1?573->185@9 . 1:1=3575:1?57=-?-=-?->1?5-<9;83->185@9?1=>1.@? #7#$ - 571?-4@5 A;8@91?-.@:3  9  9;8    " Teori Kinetik Gas 169 Pembahasan Soal Sebuah ban sepeda memiliki volume 100 cm3. Tekanan awal dalam ban sepeda adalah 0,5 atm. Ban tersebut dipompa dengan suatu pompa yang volumenya 50 cm3. Jika diasumsikan temperatur tidak berubah, tekanan dalam ban sepeda setelah dipompa 4 kali adalah .... a. 0,1 atm d. 4,5 atm b. 2,5 atm e. 5,0 atm c. 4,0 atm Soal Tes ITB Tahun 1975 Pembahasan: Volume ban = V1 = 100 cm2 p1 = 0,5 atm V2 = 4 × 50 cm3 = 200 cm3 p2 = 76 cmHg = 1 atm Setelah pemompaan ban selesai maka akan berlaku: pban Vban = p1V1 + p2V2 pban = = p1V1 + p2V2 Vban 0,5 atm100 cm3  + 1atm200 cm3  100 cm3 = 2,5 atm. Jadi, tekanan ban setelah dipompa sebesar 2,5 atm. Jawaban: b . 1:3-:91:33@:-7-:'23#.##/9 05<1=;814  -?-@              9;8 ! 9;8" " ! !-051:1=3575:1?57?;?-83->-0-8-4 6;@81 !@98-49;817@83->-0-8-4    9;8 G 9;817@8 9;8  G :1=3575:1?57=-?-=-?->1?5-<9;817@8-0-8-4  !     6;@81         +:?@77->@>A;8@913->?50-705<1=45?@:37-: 2. Energi Kinetik dan Energi Dalam Gas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udah dan Aktif Belajar Fisika untuk Kelas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y x z . x y / z F  1:3-: 019575-: .1>-=:C- 1:1=35 75:1?57 <-=?5718 .1=3-:?@:3 <-0>@4@0-:?17-:-:C-:3-7-:9191:3-=@4531=-7-:0-=5<-=?5718?1=>1.@? '-0->1?5-<31=-7-:?=-:>8->5=;?->50-:A5.=->5>1?5-<<-=?571891958575 /-=- @:?@7 91:C59<-: 1:1=35:C- '1:5:6-@-: 1:1=35 75:1?57 >1<1=?5 5:5 05:-9-7-:  !  '=5:>5<5:591:C-?-7-:.-4B-@:?@7>@-?@>5>?19<-=?57183-><-0>@4@ 9@?8-7  01:3-: >1?5-< <-=?5718:C- 91958575  01=-6-? 71.1.->-:    1:1=35 75:1?57 =-?-=-?- >1?5-< <-=?5718 7 -0-8-4   7     z - x y Gambar 7.6 Gerak molekul diatomik: (a) gerak translasi dari pusat massa; (b) gerak rotasi terhadap sumbu kartesius; dan (c) gerak vibrasi sepanjang sumbu molekul. F  &8147-=1:-3->?1=05=5-?-> <-=?57186@98-4>18@=@41:1=3575:1?57 <-=?5718 3-> 0-8-9 >@-?@ =@-:3 ?1=?@?@< 05>1.@? 6@3- 1:1=35 0-8-9 3-> 05:C-?-7-: 01:3-: <1=>-9--:          F  +:?@73->05-?;957>1<1=?53-> & 0-:% 919585751:1=350-8-9  >1.-3-5 .1=57@?  '-0->@4@=1:0-4  " ?53-01=-6-?71.1.->-:  7   F  '-0->@4@>10-:3 "859-01=-6-?71.1.->-:   7  Ingatlah F  • Untuk gas monoatomik, f = 3. • Untuk gas diatomik suhu sedang, f = 5. • Untuk gas diatomik suhu tinggi, f = 7. Teori Kinetik Gas 171 Kata Kunci • • • • ekuipartisi energi energi dalam gas energi kinetik gas tekanan gas  '-0->@4@ ?5:335    " ?@6@4 01=-6-? 71.1.->-:   7  F  !57->@-?@3->0-8-9>1.@-4?-.@:391:3-8-95<1=@.-4-:>@4@0-=5  91:6-05 1:1=350-8-93->6@3--7-:91:3-8-95<1=@.-4-:+:?@7 3-> 9;:;-?;957 .1=8-7@       F  F  )1/-=- @9@9 05?@85>      F  Contoh 7.6 )1.@-4?-:375.1=5>5 9;83->4185@9.1=>@4@ E!57-4185@905-:33-<>1.-3-53-> 501-845?@:38-41:1=35?;?-8>5>?190-:6@3-1:1=3575:1?57=-?-=-?->1?5-<9;817@8 #7#$ :1=35?;?-89;817@80-<-?0545?@:301:3-:=@9@> 7-=1:-4185@9-0-8-4 3->9;:;-?;9570-<@:1:1=35=-?-=-?-<1=9;817@80-<-?0545?@:301:3-: =@9@>  571?-4@5  9;8  ! 9;8"      "      9;8 ! 9;8"  " !        G F ! "  " G F ! Contoh 7.7 *1:?@7-:1:1=350-8-90-=5>-?@9;83->9;:;-?;957<-0->@4@ E #7#$ 571?-4@5   9;8 *     "   G 9;8   ! 9;8"   &8147-=1:-3->9;:;-?;9579-7    9;8 ! 9;8" " ! 172 Mudah dan Aktif Belajar Fisika untuk Kelas XI Tes Kompetensi Subbab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ecepatan Efektif Partikel Gas !57-0-8-9>@-?@=@-:3?1=?@?@<?1=0-<-?>1.-:C-7 9;817@8C-:3 .1=31=-7 01:3-: 71/1<-?-: "   9;817@8 C-:3 .1=31=-7 01:3-: 71/1 <-?-:" 0-:>1?1=@>:C-=-?-=-?-7@-0=-?71/1<-?-:<-=?57183->" 0-<-? 05?@85> >1.-3-5 .1=57@? "  "  "     "   "         F  "1/1<-?-:1217?52<-=?57183->"=9>=9> !050125:5 >57-: >1.-3-5 -7-= 0-=5 =-?-=-?- 7@-0=-? 71/1<-?-: "=9> " -?-@"=9>  " F  +:?@7 91:C-?-7-: 71/1<-?-: =-?-=-?- 0-=5 <-=?5718 3-> ?5:6-@8-4 4@.@:3-: -:?-=- 1:1=35 0-8-9  0-: 1:1=35 75:1?57 =-?-=-?- <-=?5718 3->  C-5?@  7 -?-@ <"=9>   >145:33- 05<1=;814 "=9>   -?-@"=9>  < < F  ;814 7-=1:-  < 0-:   1:3-: -0-8-49->>-9;817@8=18-?52 -0-8-4.58-:3-:A;3-0=; 0-:-0-8-47;:>?-:?-3->'23#.##/9 0-<-?05?@85>7-:>1.-3-5.1=57@? "=9>  F  !57- <1=>-9--:    05>@.>?5?@>57-: 71 '23#.##/ 9  -7-: 050-<-?7-: <1=>-9--: .1=57@? "=9>   F  Teori Kinetik Gas 173 1:3-: >1.-3-59->>-?;?-83->0-:9->>-61:5>3->     9-7- '23#.##/ 9  0-<-? 05?@85> "=9>   F  '1=:C-?--:71/1<-?-:1217?52<-0-'23#.##/9 91:@:6@77-: .-4B-<-0->@4@?1=?1:?@9;817@89;817@83->C-:381.54=5:3-:=-?-=-?.1=31=-781.54/1<-?->450=;31:01:3-:9->>-9;817@8 3 9;8-7-:.1= 31=-719<-?7-8581.54/1<-?0-=5<-0-3->;7>531:*-.18.1=57@?919<1= 854-?7-: 71/1<-?-: 1217?52 "=9> .1.1=-<- 61:5> 3-> <-0- >@4@ ?1=?1:?@ !#$'- "1/1<-?-:217?521.1=-<--><-0-)@4@ E Informasi untuk Anda Energi Matahari berasal dari reaksi fusi nuklir yang berasal dari penggabungan 2 buah proton. Sebenarnya, proton memiliki gaya tolak menolak dengan proton lainnya karena muatannya sejenis. Selain itu, proton tidak memiliki energi kinetik yang cukup besar untuk mengatasi gaya tolak-menolak tersebut. Akan tetapi, ada sebagian proton yang memiliki kecepatan tinggi sehingga memiliki energi kinetik yang cukup besar. Oleh karena itu, Matahari masih bersinar. Information for You The suns energy is supplied by nuclear fusion process that starts with the merging of two protons. However, protons have a motion to repel each other because of their electrical charges and protons of average speed do not have enough kinetic energy to overcome the repulsion. Very fast protons with speed can do so, however and for that reason the sun can shine. Sumber: Fundamentals of Physics, 2001 #3 #33# .0-(#3 9 ,(.0- 2.3.3  1  & %1 % -?-@& %& & )&                    Sumber: Fundamental of Physics, 2001 Contoh 7.8 5?@:38-471/1<-?-:1217?523->.1=9->>-61:5> 73 9 C-:3.1=-0-0-8-9?-.@:3 .1=?17-:-: G '- #7#$ 571?-4@5   73 9  G '"1/1<-?-:1217?52<-=?57183->0545?@:301:3-:91:33@:-7-:'23#.##/9   "=9>     '-     9 > 9 >  73 9 !-0571/1<-?-:1217?523->-0-8-4 9 > Contoh 7.9 *1:?@7-:<1=.-:05:3-:71/1<-?-:1217?52-:?-=-9;817@89;817@83->450=;31: $= 3 9;80-:3->;7>531: = 3 9;8<-0->@4@?1=?1:?@ #7#$  "1/1<-?-:1217?52>1.-:05:301:3-:-7-=0-=571.-857-:9->>-9;817@8=18-?52:C- )1/-=-9-?19-?5>05?@85>7-: "=9>     "=9>    "   3 9;8     =9>  3 9;8 "=9>   "=9>        174 Mudah dan Aktif Belajar Fisika untuk Kelas XI Tes Kompetensi Subbab C '2+#,#/-#)&#-#.$5,5-#4*)#/  )1.@-4?-:375.1=5>5@0-=-<-0-?17-:-:?1=?1:?@!57?17-:-: @0-=- 0-8-9 ?-:375 :-57 91:6-05  7-85 ?17-:-:>19@8-.1=-<-7-471/1<-?-:=9>9;817@8 @0-=-0-8-9?-:37505.-:05:37-:01:3-:71/1<-?-: =9>9@8-9@8-  )1.@-4?-.@:301:3-:A;8@91 9 91:3-:0@:3 9;83->:1;:<-0->@4@E - *1:?@7-:1:1=3575:1?57?;?-83->:1;:?1=>1.@? . 1=-<-7-41:1=3575:1?57=-?-=-?->1?5-<9;83->  ! 9;8"  )1.@-4?-:37501:3-:A;8@91 85?1=.1=5>5 9;83-> 9;:;-?;957!57->1?5-<9;817@83->919585751:1=35 75:1?57=-?-=-?- G F !?1:?@7-:?17-:-:3-> 0-8-9?-:375 -?9  G '-  1=-<-7-41:1=3575:1?57=-?-=-?-9;817@83-><-0>@4@  "     *1:?@7-:8-41:1=350-8-90-=5>-?@9;83-><-0->@4@ E 3-= 71/1<-?-: 1217?52 <-=?5718 >@-?@ 3-> .1=@.-4 91:6-05 7-85>19@8-.1=-<-01=-6-?>@4@3->?1=>1.@? 4-=@>05?5:37-?7-: 1=-<-7-4.-:C-7:C--?;94185@9C-:305<1=8@7-: @:?@791:35>5.-8;:.1=05-91?1= /9<-0->@4@ E-3-=?17-:-::C- -?95?@:38-41:1=3575:1?57 0-=5>1?5-<-?;9185@91=-<-7-471/1<-?-:=-?- =-?-0-=5>1?5-<-?;94185@90-:.1=-<-7-471/1<-?-: 1217?52:C- "1/1<-?-:1217?52"=9> >@-?@<-=?57183-> 9 > !57-3->?1=>1.@?.1=-0-0-8-9?-.@:3.1=?17-:-: -?9-?9G '-?1:?@7-:8-49->>-61:5> 3->?1=>1.@? Rangkuman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eori Kinetik Gas 175 Peta Konsep !'02**/'4*,#3 919.-4-> -> 01-8 '=5:>5<7@5<-=?5>5:1=35 .1=8-7@ "1/1<-?-:217?52 '-=?5718-> 919.-4-> @7@9;C81 @7@9 ;C81-C#@>>-/ *17-:-:->0-8-9 (@-:3*1=?@?@< 0-<-? 91:/-=5 ?1?-< :1=35"5:1?570-: :1=35-8-9-> 0-:  ?1?-<   7;:>?-:?- 0-:  ?50-7 ?1?-<    <-0- -> $;:;-?;957 -> 5-?;957 Refleksi Setelah mempelajari bab ini, Anda tentu akan mengetahui bahwa gas ideal di alam tidak ada. Anda juga tentu menjadi paham tentang prinsip ekuipartisi energi, energi kinetik, dan energi dalam gas, serta kecepatan efektif dari gerak partikel gas. Dari materi yang dipelajari pada bab ini, bagian manakah yang 176 Mudah dan Aktif Belajar Fisika untuk Kelas XI menurut Anda sulit dipahami? Coba diskusikan bersama teman atau guru Fisika Anda. Anda menjadi tahu alasan mengapa balon gas dapat mengapung merupakan manfaat mempelajari bab ini. Coba Anda cari manfaat lain mempelajari bab ini. Tes Kompetensi Bab 7  *-*)-#)3#-#)3#45+#7#$#/8#/(1#-*/(4'1#4&#/,'2+#,#/-#)1#&#$5,5-#4*)#/   '-0-@7@9;C8101:3-:-0-8-4 - 0-C0 >@4@ . @>-41 7;:>?-:?-3-> / 9;91:?@985:1-= '-0-3-9.-=.1=57@?A;8@91?-.@:3>-9-01:3-: 7-85A;8@91?-.@:3 - . V p V 1 V p V p V    T p T 3N )5>?19?1=>1.@?055>501:3-:3->501-8!@98-49;817@8 0-8-9?-.@:3>-9-01:3-:%0-:0-8-9?-.@:3 -0-8-4 %!57-3->0-8-9?-.@:3.1=>@4@ " >@4@3->0-8-9?-.@:3-0-8-4 - " 0  " .  " 1  " / " ;C81919.@-?>@-?@4@.@:3-:-:?-=-?17-:-:0-: A;8@910-=5>@-?@3->!57-05:C-?-7-:0-8-93=-257 -7-:.1=.1:?@7>1<1=?53=-257 p p - 0 / p B N . T 1 p T / A p T kapiler  0 p -8-9>-?@-:>5>?19 :?1=:->5;:-8>-?@-:?17-:-:3-> 05:C-?-7-:01:3-: - -?9 0 /93 . % 9 1 6;@81 / % 9 ->0-8-9=@-:3?1=?@?@<.1=>@4@ E0-:.1=?17- :-:-?9>1=?-A;8@91:C-85?1=!57-3->05<-:->7-: >-9<-5E?17-:-::-57>1.1>-= -?90-:A;8@91 3->-7-: - .1=7@=-:3  0 .1=?-9.-4  . ?1?-< 1 .1=?-9.-4  / .1=7@=-:3  =-257-:?-=-?17-:-:3->C-:39->>-:C-?1=?1:?@ <-0-A;8@91?1?-<>1.-3-52@:3>50-=5>@4@9@?8-7 -0-8-4  )@-?@ 3-> 501-8 <-0- ?17-:-:  0-: >@4@ E 059-9<-?7-:45:33-A;8@91:C-91:6-05>1?1:3-4 7-85 >19@8- !57- >@4@:C- 05:-577-: 0@- 7-85 85<-? 91:6-05E?17-:-:3->?1=>1.@?91:6-05 -   0  .  1   /   )@-?@3->501-8059-9<-?7-:>1/-=-5>;?1=95745:33A;8@91:C- 91:6-05 >1?1:3-4 7-85 A;8@91 >19@8- 75.-?:C- - ?17-:-:0-:>@4@3->?1?-< . ?17-:-:3->91:6-050@-7-850-:>@4@3->?1?-< / ?17-:-:3->?1?-<0-:>@4@3->91:6-050@-7-85 >19@80 ?17-:-:3->0-:>@4@3->91:6-050@-7-85>@4@ >19@81 ?17-:-:3->91:6-050@-7-85:C-0-:>@4@3-> 91:6-050@-7-85>@4@>19@8 $->>-61:5>>@-?@3->501-8<-0->@4@9@?8-70-: ?17-:-:  -0-8-4   !57- ?17-:-: 3-> ?1=>1.@? 056-057-: 0-:>@4@:C-05?@=@:7-:91:6-05  9->>-61:5>3->91:6-05 -   0    .   1    /     )1.@-4>585:01=3->91958575A;8@91   9 0-:.1=5>5 @0-=-<-0-?17-:-: G '-"19@05-:>585:01= 05.@7->145:33-.1=4@.@:3-:8-:3>@:301:3-:@0-=8@-=!57->@4@05-:33-<?50-7.1=@.-4A;8@91@0-=C-:3718@-=0-=5>585:01=-0-8-4?17-:-:@0-=-8@-= -0-8-4 -?9 -?9 '- -  9 0  9 .  9 1  9 /  9  !57-";:>?-:?-;8?D9-:  G F !1:1=35 75:1?57>1.@-4-?;94185@9<-0->@4@ E-0-8-4 -  G F ! 0  G F ! F .  G ! 1  G F ! F / G ! Teori Kinetik Gas 177  !57->16@98-43->501-891:3-8-95<=;>1>-05-.-?57 9-7- - ?1=6-05<1=@.-4-:A;8@91<-0->5>?19?1=>1.@? . ?1=6-05<1=@.-4-:>@4@<-0->5>?19?1=>1.@? / ?1=6-05<1=@.-4-:?17-:-:<-0->5>?19?1=>1.@? 0 ?50-7?1=6-05<1=?@7-=-:7-8;=-:?-=->5>?19?1= >1.@?01:3-:8@-=>5>?19 1 ?1=6-05<1=@.-4-:6@98-49;817@8  $;817@8;7>531: = 05-?9;>21=@9591958575 71/1<-?-:1217?52>175?-= 9 >"1/1<-?-:1217?52 9;817@8185@9 =05-?9;>21=@95-0-8-4 -  9 > 0  9 > .  9 > 1  9 > /  9 >  $->>->1.@-49;817@8:5?=;31:-0-8-4 7-859->>>1.@-49;817@8450=;31:1:3-:019575-:9;817@8 9;817@8:5?=;31:<-0->@4@ "919585758-6@=-?- =-?-C-:3>-9-01:3-:9;817@8450=;31:<-0->@4@ - " 0  " .  " 1  " / "  -8-9 >@-?@ =@-:3-: ?1=0-<-?   95853=-9 3-> 01:3-:?17-:-: -?9"18-6@-:=-?-=-?-<-=?57183-> ?1=>1.@?-0-8-4 9 >!57- -?9 % 9 A;8@91 =@-:3-:?1=>1.@?-0-8-4 - G F 9 0 G F 9 F .  G 9 1 G F 9 F / G 9  !57->16@98-43->C-:39->>-:C-?1?-<05?17-:<-0>@4@?1?-<9;817@89;817@8:C--7-: - 919585751:1=3575:1?5781.54.1>-= . 919585759;91:?@981.54.1>-= / 81.54>1=5:391:@9.@705:05:3?19<-?3-> #7#$-#)1'24#/8##/$'2*,54*/*&'/(#/4'1#4  -8-9>@-?@?-.@:3?1=?@?@<+ gas ?1=0-<-? >161:5> 3-> 501-8 !57?17-:-:@0-=-8@-= 993 A;8@913-> /9 0-:>@4@:C E?1:?@7-:A;8@913->?1= raksa >1.@?<-0-71-0--::;=9-8 E  993 )@-?@61:5>3->91:19<-?5A;8@91 /9 <-0->@4@ E0-:?17-:-: -?9!57->@4@:C-91:6-05 E 0-:?17-:-:91:6-05 -?9?1:?@7-:A;8@91-745= 3->?1=>1.@? $->>-61:5>>@-?@3->501-8<-0->@4@9@?8-70-: ?17-:-:-0-8-4 3 /9 !57-?17-:-:3->?1=>1.@? 056-057-:  0-: >@4@:C- ?@=@: 91:6-05   ?1:?@7-:9->>-61:5>3->?1=>1.@?    /  10 cm     178 Mudah dan Aktif Belajar Fisika untuk Kelas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ab 8 Sumber: Physics for Scientists and Engineers, 2000 Kereta uap dapat berjalan dengan memanfaatkan energi uap yang diubah menjadi energi kinetik. Termodinamika Hasil yang harus Anda capai: menerapkan konsep termodinamika dalam mesin kalor. Setelah mempelajari bab ini, Anda harus mampu: menganalisis perubahan keadaan gas ideal dengan menerapkan hukum termodinamika. ,6;2=2? 56?82? A6B<6>32?82? I2>2? C2B2?2 DB2?CA@BD2C: H2?8 5:8E?2<2? >2?EC:2 D6BEC 36B<6>32?8 12>2? 529E=E 6?;25: AB:>25@?2 2?8@D@B >@3:= 52? <6B6D2 $6=63:92? 52B: C2B2?2 DB2?CA@BD2C: >@56B? :?: 252=29 D6?282 H2?8 5:92C:=<2??H2 =63:9 36C2B 52B:A252 D6?282 =29A6?E>A2?852?32B2?8H2?852A2D5:2?82<:?32?H2< )25252C2B?H2A6B<6>32?82?C2B2?2DB2?CA@BD2C:D6BC63EDD:52<=6A2C 52B: <6>2;E2? D6@5:?2>:<2 !2>A:B C6>E2 >6C:? H2?8 252 >6?88E?2<2? AB:?C:A D6B>@5:?2>:<2 H2:DE >6?8E329 6?6B8: <2=@B >6?;25: 6?6B8: 86B2< A. Usaha pada Berbagai Proses Termodinamika B. Hukum I Termodinamika C. Kapasitas Kalor Gas dan Siklus Termodinamika D. Hukum II Termodinamika 179 Tes Kompetensi Awal &#&-5..&.1&-"+"2*,0/3&1 &2.0%*/".*,",&2+","/-")30"-30"-#&2*,54%"-".#5,5-"4*)"/  &6?82A286=2CD:A:CH2?83:2C2?H25:8E?2<2?E?DE<  A2<29H2?85:>26C:? >:?E>6C3:C2A6429<6D:<25::C:2:BA2?2C  &6?EBED?522A2<29H2?85:>2@C C69:?8822:B3:C2D6D2AA2?2C A. Usaha pada Berbagai Proses Termodinamika 1. Usaha yang Dilakukan Gas ds F = pA -:?;2E=29 C63E29 C:CD6> H2?8 5:=6?8<2A: 56?82? C63E29 D23E?8 52? A6?8:C2A 82C H2?8 52A2D 36B86B2< 3632C C6A6BD: D2>A2< A252 ".#"2   .C292H2?85:=26 82C252=29C63282:36B:E5:2? A6?8:C2A 36B86C6B C6;2E9 . <6 2D2C 56?82? =E2C A6?2>A2?8 A6?8:C2A   EC292  H2?8 5:=2 82C D6B9252A =:?84>!8  )2 .?DE<AB@C6C52B: <6 EC292<6B;2H2?85:=2 0 luas = W 2 V1 2 V2 V pemampatan W < 0 luas = W p 1 2 V1 3 V2 V Gambar 8.2 (a) Usaha yang dilakukan oleh sistem adalah positif (W = p  V ). (b) Usaha yang dilakukan oleh sistem adalah negatif (W = –p  V ). 180 $6D6B2?82?   EC292 H2?8 5:=2 82C ,  D6<2?2? 82C <@?CD2?  F@=E>62G2=  F@=E>62<9:B &23".""/ 9  36B=22 A6BE3292?F@=E>6D6BC63EDEC29252A2D36B?:=2:A@C:D:72D2E?682D:7 56?82? <6D6?DE2? C63282: 36B:6=232?82? EC292  36B?:=2: A@C:D:7 ,:CD6> >6=26?H6323<2? F@=E>6?H2 36BD2>329    #:<2 82C 5:>2>A2D<2?  36B?:=2: ?682D:7 )252 C:CD6> D6BC63ED 5:=26?H6323<2? F@=E>6?H2 36B 5:C63ED 0.$ (0- %E2C 2B62 5: 32G29  )6B92D:<2? ".#"2   Contoh 8.1 ,E2DE82C52=2>C:=:?56BD6BDEDEA>6?82=2>:AB@C6CC6A6BD: D2>A2<A25282>32B-6?DE<2?EC292H2?85:=2256?82?=E2C 52?36B?:=2:A@C:D:7<2B6?22B29 AB@C6C<6<2?2? =E2C  P %O %  <)2  %  P )2 <# 3 .C29252B: <6 C2>256?82?=E2C 52?36BD2?52?682D:7<2B6?22B29 AB@C6C<6<:B:  =E2C O    O  <)2  <)2%O %O<# 4 .C29252B: C2>256?82??@=<2B6?2 D:52<>6>36?DE<3:52?856?82? CE>3E=E2C?H2  5 .C292<6C6=EBE92?AB@C6C252=29   O  #<# .C292D@D2=52A2D;E825:9:DE?8C642B2=2?8CE?8  D@D2= =E2C       <)2O <)2%O %<# p 2. Usaha pada Proses yang Dialami Gas 2C H2?8 36B252 52=2> BE2?8 D6BDEDEA 52A2D 5:E329 <62522??H2 >6=2=E: 3636B2A2 AB@C6C H2:DE AB@C6C :C@D6B>2= AB@C6C :C@<9@B:< AB@C6C :C@32B:< 52? AB@C6C 25:232D:< a. Proses Isotermal )B@C6C :C@D6B>2= 252=29 AB@C6C A6BE3292? <62522? C:CD6> A252 CE9E D6D2A".#"2  )B@C6CD6BC63EDC6CE2:56?82?!E@H=6H2:DE, <@?CD2?-:?;2E=29A6BC2>22?82C:562=,*(=69<2B6?2CE9E *52?D6D2A>2<2 ,  ,  O  p1 p2 V1 V V2 Gambar 8.3 Kurva p–V dengan T konstan pada proses isotermal. .C292H2?85:=252A2D5:D6?DE<2?>6?88E?2<2?A6BC2>22? 36B:22?:?D68B2=  1  *  * =? 1  *=?O=? #25: EC292 H2?8 5:=2 A252 AB@C6C :C@D6B>2= 252=29  *=?  O Contoh 8.2 E2>@=82C2B8@?>6>E2:C642B2:C@D6B>2=A252CE9E L52B:F@=E>62G2=  > >6?;25:  > -6?DE<2?EC292H2?85:=2@=$ "7"# :<6D29E: * >@= /@=E>62G2=   > /@=E>62<9:B   > Termodinamika 181 Tantangan untuk Anda Menurut Anda, benarkah angin itu tidak mendinginkan suhu, melainkan menaikkan suhu di sekitarnya?  # >@=$    < $ .C292H2?85:=22=52A2D5:9:DE?856?82?&23".""/ 9    * =?     >  =?   ;@E=6  >@= # >@=$ $=?     >  b. Proses Isokhorik )B@C6C :C@<9@B:< 252=29 AB@C6C A6BE3292? <62522? C:CD6> A252 F@=E>6 D6D2A ".#"2   -:?;2E=29 <6>32=: A6BC2>22? <62522? 82C :562= p p1 ,  ,*F@=E>6D6D2A  p2 V V1 = V2 ,  * E?DE<82C:562=56?82?*52?  C6=2=E D6D2A <:32D?H2   <@?CD2? 2D2E , ,    Gambar 8.4 Proses isokhorik pada grafik p–V. O )252 AB@C6C :C@<9@B:< C:CD6> D:52< >6?82=2>: A6BE3292? F@=E>6      C69:?882 EC292 H2?8 5:=22 56?82? ?@= H2:DE,   )6BE3292?D6<2?2?A25282C2<2?>6?H6323<2? A6BE3292? CE9E 82C #:<2 CE9E 82C 5:?2:<<2? D6<2?2? 52=2> 82C 2<2? 36BD2>329 C6A6BD: 5:DE?;E<<2? A252 ".#"2   /@=E>6 D:52< D6B A6?82BE9 A6BE3292? D6<2?2? 82C p Contoh 8.3 T Gambar 8.5 Grafik p–T pada V konstan. p(Pa) ,63E29D23E?836B:C: =:D6B82C:562=A252CE9E L52?D6<2?2? P )2 -23E?8D6BC63ED5:A2?2C<2?9:?882>6?42A2:CE9E L#:<2F@=E>6D23E?85:3E2D D6D2AD6?DE<2?D6<2?2?82C5:52=2>D23E?8 "7"# :<6D29E:     $ $,  P )2     $ $ )6BC2>22?<62522?82CA252AB@C6C:C@<9@B:<  , , , ,  P )2     )2   $ 600 K   c. V1 V2 V(L) Gambar 8.6 Grafik p–V pada tekanan (p) konstan. V (volume) T (suhu) Gambar 8.7 Grafik V–T pada tekanan (p) konstan. 182 Proses Isobarik )B@C6C:C@32B:<252=29AB@C6CA6BE3292?<62522?C:CD6>A252D6<2?2? D6D2A )252 ".#"2  D2>A2< 329G2 A6BE3292? F@=E>6 D:52< >6?8 92C:=<2?A6BE3292?D6<2?2?,6CE2:56?82?A6BC2>22?82C:562=,* *  D6<2?2?,D6D2A52?   , (=69<2B6?2*52?C6=2=ED6D2A>2<2    <@?CD2?2D2E    O  B27:<9E3E?82?2?D2B252?E?DE<AB@C6C:C@32B:<D2>A2<A252 ".#"2)252AB@C6C:C@32B:<D6<2?2?82C5:EC292<2?D6D2AC69:?882 A6BE3292?CE9EA25282C2<2?>6?:>3E=<2?A6BE3292?F@=E>682CE?DE< >6>A6BD292?<2? 282B D6<2?2? 82C D6D2A .C292H2?85:=222? 36B:=2982C52=2>BE2?8D6BDEDEAF@=E>6?H2 =:D6BD6<2?2? 2D>52?CE9E?H2 L 2CD6BC63ED5:A2?2C<2?56?82?D6<2?2?D6D2AC69:?882>6?42A2:CE9E L -6?DE<2?F@=E>682C52?EC292H2?85:=2    $ $   =:D6B    $ $   2 )6BC2>22?82CA252D6<2?2?D6D2A252=29     =:D6B    =:D6B $  $ C69:?882F@=E>682C>6?;25:=:D6B 3 , O  O  ;@E=6 d. Proses Adiabatik )B@C6C 25:232D:< 252=29 AB@C6C A6BE3292? <62522? C:CD6> D2?A2 252?H2 A6BDE<2B2? <2=@B 56?82? =:?82EAE? H2?8 5:D6B:>2 @=69 82C D6BC63ED C69:?882    B27:<A252".#"2>6?E?;E<<2?329G2A252AB@C6C25:232D:< D6B;25:A6BE3292?CE9ED6<2?2?52?F@=E>6)B@C6C:?:36B52C2B<2?-0)0. +%..+* H2?8 5:DE=:C<2? ,    <@?CD2? 2D2E ,   ,   O 52?       D6D2A 2D2E           A F proses adiabatik proses isotermik p1 p2 V1 V2 O 6?82?     252=29 '+*./*/ ,(! H2?8 >6BEA2<2? A6B32? 5:?82?<2A2C:D2C<2=@B82CA252D6<2?2?D6D2AA52?<2A2C:D2C<2=@B82C A252 F@=E>6 D6D2A F ,642B2 >2D6>2D:C 36C2B2? D6BC63ED 5:DE=:C   p V Gambar 8.8 Grafik p–V pada proses adiabatik lebih curam daripada proses isotermal.   <:32D D:52< 252?H2 A6BDE<2B2? <2=@B 56?82? =:?86?8E329 6?6B8: 52=2> 6C2B?H2 EC292 D6BC63ED 52A2D 5:D6?DE<2? 56?82? >6BE;E< &23".""/ 9  C69:?882 5:A6B@=69 A6BC2>22?    ,  O,   O  2D2E  *  O  O  .C292 H2?8 5:=26?88E?2<2? &23".""/ 9  52? &23".""/ 9  ;:<2 <62522?2G2=52?<62522?2<9:B5:<6D29E:@?D@9AB@C6C25:232D:<52=2> <69:5EA2? C692B:92B: 252=29 A6>E2:2? 82C A2?2C A252 >6C:? 5:6C6= 52? >6C:? A6?5:?8:? Contoh 8.5 2C:562=>6?82=2>:6E=236C2BD6<2?2?82C252=29 P )2,6D6=2966?;25: )2-6?DE<2?F@=E>682C2<9:B ;:<2F@=E>682C>E=2>E=2  > C6BD2<@?CD2?D2%2A=246   Termodinamika 183 "7"# :<6D29E:,  P )2,  P )2   >   )6BC2>22?82CA252AB@C6C25:232D:<252=29 ,   ,           >                  $65E2BE2C5:A2?8<2D<2? C69:?8825:A6B@=69                 >      >      > #25:F@=E>682CC6D6=296     Tes Kompetensi Subbab  A &2+","/-")%"-".#5,5-"4*)"/   ,6;6?:C82C36BD6<2?2?2D>36B25252=2>G2529 H2?8>6>:=:<:F@=E>6 =:D6B!:DE?8=29EC292H2?8 5:=26>E2: A252 D6<2?2? D6D2A C69:?882 F@=E>6?H2 <2=:F@=E>6C6>E=252? 3 82C5:>2>A2D<2?A252D6<2?2?D6D2AC69:?882 F@=E>6?H2 >6?;25: 5E2 A6B D:82 <2=: F@=E>6 C6>E=2 2D> )2 -6?DE<2?=29EC292H2?85:=2,636B:6%36B:C:82C:562= 56?82?CE9E L52?D6<2?2?  P )2-23E?8 D6BC63ED5:A2?2C<2?9:?882>6?42A2:CE9E  L #:<2F@=E>6D23E?85:2?882AD6D2A36B2A2D6<2?2? 82C52=2>D23E?8 ,E2DE 82C :562= H2?8 F@=E>6 2G2=?H2   > 5:66 2<9:B?H2 >6?;25:  > A252D6<2?2?D6D2A <)2 2 -6?DE<2?=29 EC292 H2?8 5:=26>A6B<64:= F@=E>6 C63E29 82C >6?;25: C6D6?829?H2C642B2:C@D6B>2=5:A6B=E<2?EC292 # 6B2A2<29EC292H2?85:A6B=E<2?E?DE<>6>A6B<64:= F@=E>682CD6BC63ED>6?;25:C6A6BC6AE=E952B:F@=E>6 2G2= ,63E29>6C:?82C@=:?>6>:=:<:B2C:@<@>AB6C:H2:DE B2C:@F@=E>62G2=D6B9252AF@=E>62<9:BC636C2B #:<2CE9E42>AEB2?3292?32<2BE52B2252=29 L 52? AB@C6C <@>AB6C: 36B=2?8CE?8 C642B2 25:232D:< 56?82?    36B2A2<29CE9E42>AEB2?3292? 32<2BD6BC63EDA252<@>AB6C:>22= 200 400 600 4 B. Hukum I Termodinamika -29E<29?52D6?D2?8!E"-6B>@5:?2>:<2.?DE<>6?86D29E:?H2 C:>2<=29EB2:2?36B:2 1. Pengertian Hukum I Termodinamika !E " D6B>@5:?2>:<2 >6?;6=2C<2? 9E3E?82? 2?D2B2 <2=@B H2?8 5:D6B:>2 2D2E <2=@B H2?8 5:=6A2C<2? @=69 C:CD6> <6 =:?8 C6BD2 A6BE3292? 6?6B8: 52=2> H2?8 5:D:>3E= <2??H2&:C2=<2?CE2DEC:CD6>>6?6B:>2<2=@B>2<2<2=@BD6BC63EDD:52< 92?H25:8E?2<2?E?DE<>6?8E3296?6B8:52=2>  D6D2A:;E825:A2<2: E?DE< >6=2=29 6?6B8: D@D2= C6=2=E D6D2A 6B52C2B<2? 9E <6<6<2=2? 6?6B8: !E " -6B>@5:?2>:<2 5:BE>EC<2? C63282: 36B:6>292>:!E"-6B>@5:?2>:<2D6BC63EDA6B92D:<2? ".#"2  )6B;2?;:2? D2?52 E?DE<  52?  A252 ".#"2  252=29 C63282: 36B: >6=2 >6?6B:>2 EC292 ?:=2:  36BD2?52 ?682D:7 O 4 #:<2 C:CD6> >6?6B:>2 <2=@B ?:=2:  36BD2?52 A@C:D:7  5 #:<2 C:CD6> >6=6A2C <2=@B ?:=2:  36BD2?52 ?682D:7 O ?6B8: 52=2> CE2DE 82C :562= >6BEA2<2? E    92?H2 36B82?DE?8 A252 <62522? 2G2= 52? <62522? 2<9:B D:52< 36B82?DE?8 A252 AB@C6C 3282: >2?2 <62522? C:CD6> 36BE329 .?DE< 82C >@?@2D@>:< 56?82? 56B2;2D <63632C2?" A6BE3292?6?6B8:52=2>52A2D5:9:DE?8C63282:36B::< 52? A@=:2D@>:< 72:=:<: 82C D6BC63ED Contoh 8.6 Hubungan sistem dan lingkungan. (a) Sistem menerima kalor sambil melakukan usaha. (b) Sistem melepaskan kalor dan pada sistem dilakukan usaha. (c) Sistem menerima kalor, tetapi tidak melakukan kerja. (d) Sistem melakukan kerja, tetapi tidak ada kalor yang masuk ataupun keluar (adiabatik). ,E2DEC:CD6>>6?H6B2A<2=@B52B:=:?8  ;:<2 2 C:CD6>>6=26=2 "7"# 2 ,:CD6>>6?6B:>2<2=@B  #52?C:CD6>>6=2"-6B>@5:?2>:<2   O  #O  #O # 3 ,:CD6>>6?6B:>2EC29252B:=:?82<25:A6B@=69  O  #OO  # # -2?52A@C:D:7E?DE< >6?E?;E<<2?329G26?6B8:52=2>C:CD6>36BD2>329 C636C2B # 2. Aplikasi Hukum I Termodinamika pada Proses-Proses Termodinamika ,63282:>2?2?52<6D29E:2526>A2D;6?:CAB@C6C52=2>D6B>@5:?2>:<2 H2:DE AB@C6C :C@D6B>2= :C@<9@B:< :C@32B:< 52? 25:232D:< 2=2> 3292C2? :?: 2<2?5:D6B2A<2?!E"-6B>@5:?2>:<2A252AB@C6CAB@C6CD6BC63ED Termodinamika 185 a. Proses Isotermal )B@C6C:C@D6B>2=252=29AB@C6CH2?8D:52<>6?82=2>:A6BE3292?CE9E      C69:?882 A6BE3292? 6?6B8: 52=2>?H2    *       .C292 =E2B H2?8 5:=22<2 A6?6B2A2? !E " -6B>@5:?2>:<2 2<2? >6?892C:=<2?     Pembahasan Soal Suatu sistem mengalami proses adiabatik. Pada sistem dilakukan usaha 100 J. Jika perubahan energi dalam sistem adalah  U dan kalor yang diserap sistem adalah Q, akan berlaku .... a.  U = –1.000 J b.  U = 100 J c.  U = 10 J d. Q = 0 e.  U + Q = – 100 J Soal UMPTN Tahun 1994 Pembahasan: Hukum I Termodinamika: Q = U + W Pada proses adiabatik, tidak ada kalor yang diterima atau diserap sistem. Jadi, Q = 0. Pada sistem dilakukan usaha W = –100 J Jadi, Q = U + W 0 =  U – 100 J  U =100 J Jawaban: b  O  *=?  &23".""/9 >6?E?;E<<2?329G2<2=@BH2?85:36B:<2?<6A252 CE2DE C:CD6> C6=EBE9?H2 5:8E?2<2? E?DE< >6=2:@=69C:CD6>D2?A2252?H2 A6BE3292?F@=E>6 C69:?882EC292@=69C:CD6>82C252=29 ,   )6BE3292?6?6B8:52=2>?H2C6CE2:56?82?A6BC2>22?   * )6?6B2A2?!E"-6B>@5:?2>:<2>6?892C:=<2?*  0          *   O  .?DE<82C:562= *>2<2 O  *  O  #25: <2=@B H2?8 5:36B:<2? <6A252 CE2DE C:CD6> A252 F@=E>6 D6D2A C6=EBE9?H2 5:8E?2<2? E?DE< >6?2:<<2? 6?6B8: 52=2> C:CD6> c. Proses Isobarik )252AB@C6C:C@32B:<C:CD6>D:52<>6?82=2>:A6BE3292?36C2BD6<2?2?  ,    6C2B?H2 EC292 H2?8 5:=26>6?E9: A6BC2>22? , , O )6?6B2A2?!E"-6B>@5:?2>:<2A252 AB@C6C :C@32B:< >6?892C:=<2?     ,   Tugas Anda 8.1 Diskusikanlah bersama teman Anda, apakah ada proses adiabatik di alam ini? O  d. Proses Adiabatik )252 AB@C6C 25:232D:< D:52< D6B;25: A6BDE<2B2? <2=@B 52B: C:CD6> <6 =:?8C6CE2:56?82?A6BC2>22?   * O (=69<2B6?2:DEA6?6B2A2?!E"-6B>@5:?2>:<2 A252 AB@C6C 25:232D:< >6?892C:=<2?   2D2E    O  O *  O 2D2E   *  O  Kata Kunci • • • • adiabatik isobarik isokhorik isotermal 186 O  &23".""/ 9  >6?H2D2<2? 329G2 D:52< 252 <2=@B H2?8 >2CE< <6 52=2> C:CD6> C69:?882 EC292 =E2B H2?8 5:=2 2<2? >6?8EB2?8: 6?6B8:52=2>C:CD6>2B:<66>A2DAB@C6CH2?852A2D5:2=2>:C:CD6>36B?:=2: A@C:D:7 ;:<2 C:CD6> >6?6B:>2 <2=@B 52? ?682D:7 ;:<2 C:CD6> >6=6A2C<2? <2=@B !E " -6B>@5:?2>:<2 52A2D 5:2A=:<2C:<2? A252 C6>E2 AB@C6C D6B>@5:?2>:<2 H2?8 36B9E3E?82? 56?82? <6D:82 36C2B2? H2:DE   52?  Mudah dan Aktif Belajar Fisika untuk Kelas XI Tes Kompetensi Subbab B &2+","/-")%"-".#5,5-"4*)"/     ,E2DE82C>6?H6B2A<2=@B #52?>6=2 C:CD6> 82C D6BC63EDA2<2982CD6BC63ED>6>E2:2D2E5:>2> A2D<2? ,E2DE C:CD6> >6?6B:>2 <2=@B C636C2B  # 52? >6=2C:CD6>D6BC63ED ,632?H2<>@=82C:562=>@?@2D@>:<56?82?CE9E 2G2= L5:?2:<<2?CE9E?H2>6?;25: LA252 D6<2?2?D6D2A6B2A2<29<2=@BH2?85:A6B=E<2?  # >@=$ ,E2DE82CA252D6<2?2?<@?CD2?C636C2BP )2 5:>2>A2D<2?52B:F@=E>6=:D6B>6?;25: =:D6B2=2> AB@C6CD6BC63ED82C>6=6A2C<2=@B ;@E=6 2 6B2A2<29EC292H2?85:=2?H2  #6=2C<2?329G282C52A2D5:A6B=26?H6BEA2: <62522?82C:562=A252AB@C6C:C@D6B>:<:C@32B:<52? :C@F@=E>6 )6B92D:<2?8B27:<36B: 82>32B9:DE?8=29 2 EC292H2?85:=2AB@C6C C. Kapasitas Kalor Gas dan Siklus Termodinamika $2A2C:D2C <2=@B   52B: CE2DE I2D 5:567:?:C:<2? C63282: *4'*4 '(+-* 4*# %,!-(0'* 0*/0' )!*%''* .0$0 5/ /!-.!0/ .!!.-  '!(1%* /0 ./0 !-&/ !(.%0. ,642B2 >2D6>2D:C 5:DE=:C<2?  O   $2A2C:D2C <2=@B E?DE< 82C 252 5E2 >242> H2:DE E?DE< F@=E>6 D6D2A  F 52? E?DE< D6<2?2? D6D2A  A 56?82? A O /  *    1. Kapasitas Kalor untuk Proses Isokhorik (V = tetap) $2A2C:D2C<2=@BE?DE<82CH2?8>6>:=:<:F@=E>6D6D2A52A2D5:9:DE?8 C63282: 36B:@?@2D@>:< Kata Kunci /  *  O  /  * O  .?DE< 82C 5:2D@>:< 2. Kapasitas Kalor untuk Proses Isobarik (p = tetap) $2A2C:D2C<2=@BE?DE<82CH2?8>6>:=:<:D6<2?2?D6D2A52A2D5:9:DE?8 C63282: 36B:@?@2D@>:< A  * .?DE< 82C 5:2D@>:< A *   O  • kapasitas kalor tekanan tetap • kapasitas kalor volume tetap • konstanta Laplace Tantangan untuk Anda Anda pasti tahu apa termos itu. Dapatkah Anda menjelaskan cara kerja termos sehingga air panas dapat tetap panas? Jelaskan hal tersebut dengan konsep termodinamika. O  Termodinamika 187 "#&- -6D2A2?%2A=246   2C 2C -6BD6?DEA252-6<2?2? 2D> 52?,E9E L "3 +*+/+)%' !6=:E>!6 B8@?B %/+)%' ':DB@86?'  (@?@:<   * / "#&- >6?E?;E<<2??:=2:<@?CD2?D2%2A=246E?DE<3636B2A282C A252D6<2?2? 2D>52?CE9E L     Contoh 8.7  Sumber: Fundamental of Physics, 2001 Tantangan untuk Anda Anda pasti pernah mendengar istilah mesin 4 tak dan mesin 2 tak. Selidikilah dan diskusikanlah, apa perbedaan di antara keduanya? Mengapa mesin 2 tak memiliki akselerasi lebih cepat daripada mesin 4 tak? p A Q1 B W D T1 C Q2 T2 V Gambar 8.10 Satu siklus suatu mesin Carnot menggunakan suatu gas ideal sebagai fluida kerja. Grafik AB dan CD menampilkan proses isotermal, grafik BC dan DA menampilkan proses adiabatik. 188 $@?CD2?D2 %2A=246 C642B2 D6@B:D:C 52A2D 5:9:DE?8 C6CE2: 56?82? A6B C2>22? 36B:@?@2D@>:<      * / ,E9E <882C?:DB@86?36B2D>@=6@=5:?2:<<2?52B: L>6?;25: L >6=2=E:AB@C6C:C@32B:<!:DE?8<6?2:<2?6?6B8:52=2>52?EC292H2?85:=2:<CE9EC652?8C69:?882 <2A2C:D2CA2?2C>@=2B82CA252F@=E>6D6D2A52?A252D6<2?2?D6D2A252=29   1   # >@=$ # >@=$ ,     # >@=$  # >@=$ #E>=29>@=82C252=29C2DE2?>2CC2?H292BEC5:E32952=2>8B2> * )   >@=   >@= 8 >@=   :<6D29E:  >@= *  1  # >@=$ ,   # >@=$     $  $     $ $    $O $$    * F   >@= # >@=$$  P #   >@=  # >@=$$ P #  * A     O  P #O  P # P #   ,6@B2?8 :=>EG2? )B2?4:C "%* "2/04  O   >6?H2D2<2? 329G2 C6>E2 A6B86B2<2? 36B9E3E?82? 56?82? <2=@B >:C2=?H2 86B2<2? 86B2<2?H2?8D6B;25:52=2>A6B2=2D2?>6<2?:<C6A6BD:>6C:?5:6C6=>6C:? <2=@B "56 2B?@D >6?H:B2D<2? 329G2 52A2D 5:4:AD2<2? C63E29 >6C:? :562= H2?8 C6=EBE9 6?6B8:?H2 5:8E?2<2? >6?;25: EC292 '2>E? A252 <6?H2D22??H2 92= D6BC63ED CE=:D 5:4:AD2<2? 02=2EAE? 56>:<:2? D6@B: 2B?@D >2C:9 D6D2A 5:A2<2: 9:?882 C22D :?: ,642B2 D6@B:D:C >6C:? 2B?@D >6?E?;E<<2? 3636B2A2 726C:?&6?8E329EC292>6?;25:<2=@B 52A2D 5:=26?6BEC <2? D6D2A: >6?8E329 <2=@B >6?;25: EC292 D:52< 56>:<:2? 92BEC 5:EC292<2? C6;E>=29 82C <6>32=: <6<62522??H2C6>E=2282B82CD6BC63ED52A2D>6=232=: )B@C6C C6A6BD::?: 5:C63ED.%'(0. )252D29E?  2B?@D>6?;6=2C<2?C63E29C:<=ECH2?8D6B5:B:2D2C 6>A2D AB@C6C )6B92D:<2? ".#"2   52? ".#"2   Mudah dan Aktif Belajar Fisika untuk Kelas XI )B@C6C52B:<6252=29AB@C6C632?82? :C@D6B>2= A252 CE9E   )252 AB@C6C :?: 82C >6?H6B2A <2=@B   52B: B6C6BF@:B 36BCE9E D:?88:   52? >6=232?82?25:232D:<,6=2>2AB@C6CCE9E82CDEBE? 52B:   >6?;25:   C2>3:= >6=22>A2D2?:C@D6B>2=A252CE9E 2=2>AB@C6C:?:82C >6=6A2C <2=@B   <6 B6C6BF@:B 36BCE9E B6?529   52? >6=22>A2D2? 25:232D:< ,E9E ?2:< 52B:   <6   C2>3:= >6=26C:?5:6C6=H2:DE>6C:?H2?8A2=:?8 :562=H2?8C6=2?;ED?H25:C63ED>6C:?2B?@D,6=2>2AB@C6CC:<=EC2B?@D 36B=2?8CE?8 82C >6?6B:>2 <2=@B   52B: B6C6BF@:B 36BCE9E D:?88: 52? >6=6A2C <2=@B   <6 B6C6BF@:B 36BCE9E B6?529 .C292 H2?8 5:=2 " -6B>@5:?2>:<2 252=29   2D2E O    O T1 Q1 W (= Q1) Q2 = 0 Gambar 8.11 Siklus mesin ideal Q1 dan suhu fungsi reservoir diubah seluruhnya menjadi usaha W dengan efisiensi 100%. O  $6D6B2?82?   <2=@B H2?8 5:C6B2A 52B: B6C6BF@:B H2?8 36BCE9E D:?88:   <2=@B H2?8 5:=6A2C <6 B6C6BF@:B H2?8 36BCE9E B6?529 3. Efisiensi Mesin )6B92D:<2?".#"2  2>32BD6BC63ED>6?E?;E<<2?C:<=EC<2=@B 5: 52=2> C63E29 >6C:? )6B32?5:?82? 2?D2B2 36C2B?H2 EC292  H2?8 52A2D 5:=2 D6B9252A <2=@B   H2?8 5:C6B2A 52A2D >6?6?DE<2?67:C:6?C:CE2DE>6C:?,642B2>2D6>2D:C67:C:6?C:>6C:?52A2D 5:DE=:C<2? C63282: 36B:6C:? 2B?@D 5:A6B@=69 56?82? 42B2 >6?882?D: EC292  56?82? &23".""/ 9  C69:?882 &23".""/ 9  >6?;25:        P 2D2E      P      O  -6=29 5:3292C 329G2 E?DE< CE2DE 82C :562= 6?6B8: 52=2>  C632?5:?8 56?82? CE9E >ED=2<  C69:?882 E?DE< >6C:? 2B?@D &23".""/ 9  52A2D 5:DE=:C C63282: 36B:6?;25: CE9E >ED=2<  52=2> >6?6?DE<2? 67:C:6?C: C63E29 >6C:? 36B52C2B<2? A252 6?6B8: 52=2> C632?5:?8 56?82? CE9E $6=F:? >6?E?;E<<2? 329G2      T1 Q2 T2 Gambar 8.12 O  Perubahan kalor menjadi kerja: Q1 = kalor masuk; Q2 = kalor dilepaskan; W = usaha yang dilakukan; T1 = suhu reservoir tinggi; dan T2 = suhu reservoir rendah. Termodinamika 189 p A B Q1 D Q2 C V Gambar 8.13 b. Mesin Otto &6C:?(DD@>6BEA2<2?>6C:?<2=@BH2?8AB:?C:A<6B;2?H236B52C2B<2? C:<=EC (DD@ )252 C:<=EC (DD@ D6B52A2D 5E2 AB@C6C 25:232D:< 52? 5E2 AB@C6C :C@<9@B:< )6B92D:<2? ".#"2   )252".#"2 O52?O>6BEA2<2?AB@C6C25:232D:<C652?8<2? O52?O>6BEA2<2?AB@C6C:C@<9@B:<52AE? 252=29<2=@BH2?8 >2CE<52=2>C:CD6>C652?8<2? 252=29<2=@BH2?8<6=E2B5:=6A2C<2? @=69 C:CD6> 7:C:6?C: 52B: C:<=EC (DD@ 5:?H2D2<2? 56?82? A6BC2>22?  Dua proses adiabatik dan dua proses isokhorik pada siklus Otto.          O  ,:<=EC (DD@ 32?H2< 5:2A=:<2C:<2? A252 >6C:? >@D@B 32<2B c. p A D Q1 B Q2 C V Gambar 8.14 Siklus diesel Mesin Diesel &6C:? 5:6C6= >6BEA2<2? >6C:? <2=@B H2?8 AB:?C:A <6B;2?H2 >6?88E?2<2?C:<=EC5:6C6=)252C:<=EC5:6C6=D6B52A2D5E2AB@C6C25:232D:< C2DEAB@C6C:C@32B:<52?C2DEAB@C6C:C@<9@B:< )6B92D:<2? ".#"2   )B@C6C 52B:  <6  >6BEA2<2? AB@C6C :C@32B:< O 52? O >6BEA2<2?AB@C6C25:232D:<52?AB@C6CO>6BEA2<2?AB@C6C:C@<9@B:< )B:?C:A<6B;2>6C:?5:6C6=92>A:BC2>256?82?>6C:?@DD@<2B6?2C6>E2 AB@C6CA252>6C:?5:6C6=C2>256?82?>6C:?@DD@<64E2=:AB@C6C:C@32B:< 7:C:6?C: 3636B2A2 >6C:? 5:DE?;E<<2? A252 "#&-   "#&- 7:C:6?C:636B2A2&6C:? &/*3&3*/ Pembahasan Soal Sebuah mesin Carnot yang menggunakan reservoir suhu tinggi 800 K, memiliki efisiensi 40%. Agar efisiensinya naik menjadi 50%, suhu reservoir suhu tinggi dinaikkan menjadi .... a. 900 K d. 1.180 K b. 960 K e. 1.600 K c. 1.000 K Soal UMPTN Tahun 1990 &6C:?>@3:=36?C:? &6C:?5:6C6= -EB3:?E2AA6>32?8<:D?E<=:B -EB3:?E2AA6>32?8<:D32DE32B2 '*3*&/3* O  O    Contoh 8.8 ,63E29 >6C:? 2B?@D >6>:=:<: 67:C:6?C:   #:<2 CE9E B6C6BF@:B D:?88:   $ D6?DE<2?=2936C2B?H2CE9EB6C6BF@:BD:?88:282B67:C:6?C:>6C:?>6?;25: 56?82? 2?882A2?CE9EB6C6BF@:BB6?529D:52<>6?82=2>:A6BE3292? "7"# )6BD2>2D6?DE<2?CE9EB6C6BF@:BB6?529 A252    Pembahasan: Keadaan 1:  = 40% T1 = 800 K T  = 1 – 2 40% T1 T2 =1– 800 K T2 = 480 K $65E2D6?DE<2?CE9EB6C6BF@:BD:?88: 56?82?>6>A6B8E?2<2? H2?8D6=29 5:9:DE?8D25:E?DE<  Keadaan 2:  = 50% T2 = 480 K T  = 1 – 2 50% T1 480 K =1– T1 T1 = 960 K    $   O   $  $  O       $     O   O     $  $   O Jawaban b 190   #25:CE9EB6C6BF@:BD:?88:H2?85:3EDE9<2?252=29 $ Mudah dan Aktif Belajar Fisika untuk Kelas XI Tes Kompetensi Subbab C &2+","/-")%"-".#5,5-"4*)"/  ,63E29>6C:?2B?@DH2?8>6?88E?2<2?B6C6BF@:B CE9E D:?88:   $ >6>:=:<: 67:C:6?C:  .?DE< >6?2:<<2?67:C:6?C:?H2>6?;25: 36B2A256B2;2D CE9EB6C6BF@:BD:?88:92BEC5:?2:<<2?  &6C:? 2B?@D H2?8 36BCE9E B6C6BF@:B D:?88:  L >6>:=:<:67:C:6?C: 7:C:6?C:52B:>6C:?D6BC63ED 5:D:?8<2D<2? >6?;25:   6B2A2 56B2;2D CE9E B6C6BF@:BD:?88:92BEC5:?2:<<2?  &6C:? 2B?@D >6?6B:>2 <2=@B 52B: B6C6BF@:B H2?8 36BCE9ED:?88: L52?>6=6A2C<2??H2A252CE9E B6?529 L-6?DE<2?67:C:6?C:>6C:?2B?@DD6BC63ED  &6C:? A6?5:?8:? BE2?82? >6?H6B2A <2=@B C636C2B  ;@E=652=2>G2A2DA6>3E2?82?<2=@B252=29 L 6B2A2<2952H2=:CDB:<H2?85:3EDE9<2? ,63E29>6C:?>6?H6B2A<2=@BC636C2B #@E=652B: C63E29B6C6BF@:B36BCE9E $52?>6>3E2?8?H2 C636C2B  ;@E=6A252CE9E $2B:52D2D6BC63ED D6?DE<2?=29 2 67:C:6?C:>6C:?52? 3 EC292H2?852A2D5:=26C:?2B?@D>6>:=:<:67:C:6?C: #:<2CE9E B6C6BF@:BD:?88: $D6?DE<2?=2936C2B?H2CE9E B6C6BF@:B D:?88: 282B 67:C:6?C: >6C:? >6?;25:   56?82? 2?882A2? CE9E B6C6BF@:B B6?529 D:52< >6?82=2>:A6BE3292? Tokoh D. Hukum II Termodinamika !E " -6B>@5:?2>:<2 >6?H2D2<2? D6?D2?8 <6<6<2=2? 6?6B8: H2:DE 6?6B8:D:52<52A2D5:4:AD2<2?2D2E5:>EC?29<2?>6=2:?<2?92?H252A2D5:E329 52B: C2DE 36?DE< 6?6B8: <6 36?DE< 6?6B8: =2:??H2 !E " -6B>@5:?2>:<2 D:52<>6>32D2C:3282:>2?2A6BE3292?6?6B8:D6BC63ED36B=2?8CE?8%2:?92=?H2 56?82?!E""-6B>@5:?2>:<2H2?8>6>:=:<:32D2C2?32D2C2?D6BD6?DE ,63E29 >6C:? 52A2D 36B86B2< 5:C6323<2? 252?H2 6?6B8: <2=@B H2?8 5:36B:<2?A252>6C:?D6BC63EDC642B2D6BEC>6?6BECD6D2A:C632=:E?8<:? 6?6B8: 86B2< EC292 52A2D >6>36B:<2? <2=@B C642B2 D6BEC >6?6BEC )252 <6?H2D22??H2 D:52< 252 C63E29 >6C:? AE? H2?8 36<6B;2 >6?H6B2A 6?6B8: <2=@B 52? >6?8E329 C6=EBE9?H2 >6?;25: EC292 6B:""-6B>@5:?2>:<2 H2?8 >6BEA2<2? <6C:>AE=2? 52B: A6?82>2D2?A6?82>2D2? H2?8 5:=2E?8<:? >6>3E2D >6C:? H2?8 36<6B;2 52=2> CE2DE C:<=EC >6?6B:>2 <2=@B 52B: C2DE B6C6BF@:B 52? >6?8E329 C6=EBE9 <2=@B D6BC63ED >6?;25: EC292  &6?EBED=2EC:ECD:52<>E?8<:?>6>3E2D>6C:?H2?836<6B;252=2> C2DEC:<=EC>6?82>3:=<2=@B52B:B6C6BF@:BH2?8>6>:=:<:CE9EB6?529 52?>6>36B:<2??H2 A252B6C6BF@:B H2?8>6>:=:<: CE9ED:?88: D2?A2 >6>6B=E<2? EC292 52B: =E2B  &6C:?2B?@DH2?836<6B;25:2?D2B2B6C6BF@:BCE9E 52?B6C6BF@:B H2?8 36BCE9E        >6?892C:=<2? 67:C:6?C: H2?8 D:?88: #25: >6?EBED $6=F:? 52? )=2?4< D:52< >E?8<:? CE2DE >6C:? 92?H2 >6>:=:<: C63E29 B6C6BF@:B 52? D:52< >E?8<:? C63E29 >6C:? >6>:=:<: 67:C:6?C: #:<267:C:6?C: <2=@BH2?85:C6B2A52B:=:?86?;25:EC292.C292>6C:?C6>242>:?:5:C63ED >6C:?,-!,!/00))+%(!;6?:C<65E2$6?H2D22??H2D:52<252>6C:?C6A6BD: :DE G2=2EAE? >2C:9 >6>6?E9: !E " -6B>@5:?2>:<2 Nikolaus Otto Sumber: Jendela Iptek: Energi, 1997 Pada 1876, seorang warga negara Jerman, Nikolaus Otto menjadi orang pertama yang membuat dan menjual mesin 4 tak yang kemudian menjadi dasar pembuatan kebanyakan mesin. Ia menamakan mesinnya Silent Otto karena mesin tersebut mampu bekerja tanpa menimbulkan kebisingan. Salah satu ciri mesin 4 tak adalah tekanan kompresinya. Jika bahan bakar berupa gas yang dimampatkan, akan lebih banyak energi yang dilepaskan. Gagasan ini pertama kali dikembangkan oleh Alphone Beau de Rochas (1815– 1891) yang berkewarganegaraan Prancis, tetapi justru Otto yang menyukseskan ide tersebut. Termodinamika 191 &6?EBED =2EC:EC >6C:? C6=2=E >6>6B=E<2? EC292 =E2B 282B 52A2D >6>:?529<2? <2=@B 52B: D6>A2D H2?8 36BCE9E B6?529 <6 D6>A2D H2?8 36BCE9ED:?88:&6C:?C6A6BD::?:5:C63ED>6C:?A6?5:?8:?>:C2=?H2=6>2B: 6C 52? A6?5:?8:? BE2?82? 2D2E  %- +* %/%+*!- 1. Proses Reversibel dan Irreversibel )B@C6CAB@C6CA252>6C:?<2=@B252H2?836BC:72D-!1!-.%!(52?252AE=2 H2?8 36BC:72D %--!1!-.%!( D:52< B6F6BC:36= )B@C6C -!1!-.%!( >6BEA2<2? AB@C6CH2?836B=2?8CE?8C2?82D=2>32DC69:?882AB@C6C?H252A2D5:2?882A C63282: B2?8<2:2? <62522? C6D:>32?8 ,6=EBE9 AB@C6C D6BC63ED 52A2D 5:<6B;2<2?C642B2<632=:<2?D2?A2>6?8E32936C2BEC292H2?85:=2AEB?2D:52<52A2D5:D6?DE<2?52=2><6?H2D22?<2B6?2 AB@C6C:?:D2<D6B32D2C)B@C6C:?:;E82>6?896?52<:D:52<252?H286C6<2? 82?88E2? 2=:B2? E52B2 C6BD2 72:C2=?H2 >2C:9 5:D6>E<2? 86C6<2? H2?8 >6?H6323<2? 252?H2 A2?2C H2?8 9:=2?8 2D2E 2=:B2? 82C H2?8 36BE329 T1 Q1 W Q2 T2 Gambar 8.15 Perubahan kerja menjadi kalor. 2. Mesin Pendingin (Refrigerator) !E""-6B>@5:?2>:<236BA682?8<6A252<646?56BE?82?2=2>:29 C:72D<2=@BH2?8C6=2=E>6B2>32DC642B2CA@?D2?52B:36?5236BCE9ED:?88: <636?52H2?836BCE9EB6?529<64E2=:;:<2252EC292=E2BH2?8>6>26>:?529<2? <2=@B 52B: C:CD6> 36BCE9E B6?529 <6 =:?86C:? A6?5:?8:? C:CD6> >6?82>3:= <2=@B  52?>6=6A2C<2?<2=@B 52AE?EC292H2?85:=26C:? A6?5:?8:? 52A2D 5:=:92D A252 ".#"2   $6D6B2?82? 82>32B   <2=@B H2?8 5:=6A2C<2? A252 CE9E D:?88:   <2=@BH2?85:C6B2AA252CE9EB6?529   EC292 H2?8 5:=26C:? A6?5:?8:? 5:?H2D2<2? 56?82? <@67:C:6? 52H2 8E?2 ,642B2 >2D6>2D:C 52A2D 5:DE=:C<2? C63282: 36B:2B:6C52?A6?5:?8:?BE2?82?>6>:=:<:<@67:C:6?52H28E?252=2> ;2?8<2E2? C2>A2:56?82?,6>2<:?D:?88:?:=2:C6>2<:?32:<>6C:? A6?5:?8:? D6BC63ED Contoh 8.9 -6>A6B2DEB5:52=2>C63E29=6>2B:6C252=29O L=E:52<6B;2H2?85:>2>A2D<2? 5:52=2>?H2>6?86>32?8A252D6>A6B2DEBC636C2B L-6?DE<2?=29<@67:C:6? 52H28E?2=6>2B:6CD6BC63ED "7"# :<6D29E:  O     $      $ 6?82?>6?88E?2<2?A6BC2>22?      192 Mudah dan Aktif Belajar Fisika untuk Kelas XI 5:A6B@=69  $  $    $     $ #25:<@67:C:6?52H28E?2=6>2B:6CD6BC63EDC636C2B Tes Kompetensi Subbab D &2+","/-")%"-".#5,5-"4*)"/    ,E9E5:52=2>C63E29=6>2B:6C252=29OL=E:52 <6B;2H2?85:>2>A2D<2?5:52=2>?H2>6?86>3E? A252CE9E L-6?DE<2?=29<@67:C:6?52H28E?2 =6>2B:6CD6BC63ED ,6;E>=29>2<2?2?52=2>=6>2B:6C>6?892C:=<2? <2=@BC636C2B ##:<2<@67:C:6?52H28E?2=6>2B: 6C D6BC63ED  -6?DE<2?=29 6?6B8: =:CDB:< H2?8 5:A6B=E<2?=6>2B:6CE?DE<>6>:?529<2?<2=@BH2?8 5:92C:=<2?>2<2?2? &6C:?A6?5:?8:?BE2?82?>6?H6B2A<2=@BC636C2B   # 52=2> G2A2DA6>3E2?82?<2=@B252=29 L -6?DE<2?=2952H2=:CDB:<H2?85:3EDE9<2? ,E2DE>6C:?A6?5:?8:?36B52H2<6B;2 G2DD#:<2 CE9EBE2?8A6?5:?8:?OL52?CE9EE52B25:=E2B L2?882A>6C:?:562=36B2A2<2=@B>2E> H2?8 52A2D 5:C6B2A >6C:? A6?5:?8:? 52B: BE2?8 A6?5:?8:??H2C6=2>2 >6?:D ,E2DE32?8E?2?96?52<5:5:?8:?<2?56?82?C63E29 >6C:?A6?5:?8:?:562=,E9E5:=E2B32?8E?2? L52? 5:52=2>32?8E?2? L#:<22=2DA6?5:?8:?D6BC63ED 36B<6 Rangkuman  $2=@B>6BEA2<2?C2=29C2DE36?DE<6?6B8:H2?852A2D 36BA:?52952B:CE2DE=:?82D2E C632=:6=232?82?EC292 36B?:=2:A@C:D:7H2?8>6?H6323<2?F@=E>636BD2>329 2D2E   #:<2 82C 5:>2>A2D<2? EC292 36B?:=2: ?682D:7 %:?86=2C69:?882     2CH2?836B25252=2>BE2?8D6BDEDEA52A2D5:E329 <62522??H2>6=2=E:3636B2A2AB@C6C 2 )B@C6C"C@D6B>2=D6B;25:A252CE9ED6D2A.C292  H2?85:=26D6D2A.C292 H2?85:=282C D:52< >6?82=2>: A6BDE<2B2? <2=@B 56?82? =:?86.C292H2?85:=2"-6B>@5:?2>:<25:BE>EC<2?C63282:36B:=29<2=@BH2?85:36B:<2?<6A252C:CD6>5:A2<2: C6328:2? @=69 C:CD6> E?DE< >6=2256?82?A6BE3292?6?6B8: 52=2>52B:C:CD6>H2:DE    $2A2C:D2C<2=@B52B:CE2DEI2D5:567:?:C:<2?C63282: 32?H26?2:<<2? CE9EI2DD6BC63EDC636C2BC2DE<6=F:?2D2EC2DE56B2;2D 46=C:EC    $2A2C:D2C<2=@BE?DE<AB@C6C:C@<9@B:<1D6D2A / * $2A2C:D2C<2=@BE?DE<AB@C6C:C@32B:< ,D6D2A  A * !E3E?82?2?D2B2 A56?82? F252=29 AO /*  )252C:<=EC2B?@D82C>6?6B:>2<2=@B 52B:B6C6BF@:B 36BCE9ED:?88:52?>6=6A2C<2=@B <6B6C6BF@:B36BCE9E B6?529,:<=EC2B?@D>6BEA2<2?52C2B52B:>6C:?5:6C6= >6C:?2B?@DH2:DE>6C:?H2?8A2=:?8:562= 7:C:6?C:>6C:?>6BEA2<2?A6B32?5:?82?2?D2B236C2B EC292H2?852A2D5:=2D6B9252A<2=@B H2?85:C6B2A Termodinamika 193    !E""-6B>@5:?2>:<2>6>:=:<:<6C:>AE=2?C63282: 36B:E?8<:?>6>3E2DCE2DE>6C:?H2?852A2D >6?8E329 <2=@B H2?8 5:D6B:>2 >6?;25: EC292 C6=EBE9?H252=2>C2DEC:<=EC 3 $2=@BD:52<A6B?29>6?82=:BCA@?D2?52B:36?52 36BCE9EB6?529<636?5236BCE9ED:?88: 4 &6C:?2B?@DH2?836<6B;25:2?D2B2B6C6BF@:B 36BCE9E 52?B6C6BF@:BH2?836BCE9E 56?82?   >2<267:C:6?C:?H2D:?88:   P      P             P         Peta Konsep &2.0%*/".*," >6>3292C )B@C6C "C@D6B>2= !E"-6B>@5:?2>:<2 $2A2C:D2C$2=@B >6>3292C A252 )B@C6C "C@<9@B:< )B@C6C "C@32B:< )B@C6C 5:232D:< -6<2?2? -6D2A ,:<=EC-6B>@5:?2>:<2 !E""-6B>@5:?2>:<2 >6>3292C >6>3292C /@=E>6 -6D2A 76C:6?C:>6C:? )B@C6C+6F6BC:36= A252 )B@C6C"BB6F6BC:36= 4@?D@9?H2 &6C:?2B?@D &6C:?(DD@ &6C:?:6C6= &6C:?)6?5:?8:? Refleksi Setelah mempelajari bab ini, Anda tentu telah memahami Hukum I Termodinamika dan proses-proses yang dapat terjadi di dalamnya. Adapun Hukum II Termodinamika mempelajari tentang perlunya usaha luar dan konsep kapasitas kalor pada proses-proses termodinamika. Dari keseluruhan materi bab ini, bagian 194 Mudah dan Aktif Belajar Fisika untuk Kelas XI manakah yang menurut Anda sulit? Coba diskusikan dengan teman atau guru Fisika Anda. Dari pemahaman yang Anda peroleh, coba sebutkan beberapa manfaat yang dapat diterapkan dalam kehidupan sehari-hari. Tes Kompetensi Bab 8  *-*)-")3"-")3"45+"7"#"/8"/(1"-*/(4&1"4%"/,&2+","/-")1"%"#5,5-"4*)"/        !E"-6B>@5:?2>:<2>6?H2D2<2?329G2 2 <2=@BD:52<52A2D>2CE<<652=2>52?<6=E2B 52B:CE2DEC:CD6> 3 6?6B8:252=29<6<2= 4 6?6B8:52=2>252=29<6<2= 5 CE9E252=29D6D2A 6 C:CD6>D:52<>6?52A2DEC29252B:=E2B ,6;E>=2982C:562=56?82?>2CC2D6BD6?DE>6?82=2>: A6>2>A2D2?C642B225:232D:<#:<2252=29<6B;2 H2?8 5:=2 82C 52?  252=29 A6BE3292?CE9E52B:C:CD6>36B=2@=82C2B8@?>6>E2:C642B2:C@D6B>2=A252CE9E $52B:F@=E>62G2=   > <6F@=E>62<9:B   > .C292H2?85:=2@=$ 2  ;@E=6 5 ;@E=6 3  ;@E=6 6 ;@E=6 4 ;@E=6 ,632?H2<  >  82C 96=:E> H2?8 36BCE9E L 5:A2?2C<2?C642B2:C@32B:<C2>A2: L#:<2D6<2?2? 82C96=:E> P ' > EC292H2?85:=26?H2  >  A6B=292?=292? 5:A2?2C<2?A252D6<2?2?D6D2AC69:?882F@=E>6?H2 >6?;25: > #:<2EC292=E2B82CD6BC63ED P ;@E=6 D6<2?2?82C252=29 2 P ' > 5 P ' >  3 P ' > 6 P ' >  4 P ' > )6B92D:<2?A6B?H2D22?A6B?H2D22?36B:6=26?86>32?8   )252AB@C6C25:32D:<82CC6=2=E>6?86>32?8  )252AB@C6C:C@D6B>:<6?6B8:52=2>82CD6D2A )6B?H2D22?H2?8C6CE2:56?82?<@?C6AD6B>@5:?2>:<2 252=29 2  52?  5   52? 3   52?  6  52? 4  52? #4"/"3  %:>2 =:D6B 82C :562= 52=2> C:=:?56B >6C:? 5:6C6= >6?82=2>:AB@C6C25:232D:<A252D6<2?2?  2D>#:<2 C6D6=29AB@C6C<@>AB6C:5:92C:=<2?F@=E>62<9:B% 56?82?   36C2B?H2D6<2?2?2<9:B252=29 2 2D> 5 2D> 3  2D> 6  2D> 4 2D>  ,6;6?:C82C:562=F@=E>6?H2 %)252CE9E L82C D6BC63ED5:A2?2C<2?A252D6<2?2?D6D2A 2D>C2>A2:CE9E ?H2 L.C292H2?85:=2682C:562=5:A6B36C2B5E2<2=:F@=E>6C6>E=2 52? D6B?H2D2 6?6B8: 52=2>?H2 >6?;25: 6>A2D <2=: C6>E=2D6<2?2?82CD6BC63ED>6?;25: <2=: 5 <2=: <2=: 6 <@?CD2? 4 <2=:  ,6;E>=2982C>6?82=2>:C:<=ECC6A6BD:A25282>32B p (N/m2) 36B:6?E?;E<<2? 9E3E?82? D6<2?2? , D6B9252AF@=E>652B:C6;E>=29>2CC282C:562=.C292 H2?85:=22AB@C6CD6BC63ED252=29 2 # 5 # 3 # 6 # 4 #  )6B92D:<2?8B27:<36B:6?82=2>:AB@C6C $2=@BH2?85:3EDE9<2?E?DE<AB@C6CD6BC63ED252=29 2 ;@E=6 5 ;@E=6 3 ;@E=6 6 ;@E=6 4 ;@E=6 ,E2DEC:CD6>>6?82=2>:AB@C6C25:232D:<)252C:CD6> 5:=2 C:CD6>252=2952?<2=@BH2?85:C6B2AC:CD6>252=29 *5:A6B@=69 2  O  # 5 * # 3   # 6  * # 4   !    )25282C:562=>@?@2D@>:<AB@C6CH2?8D6B;25:A252 36C2B2?36C2B2?7:C:CC642B2:C@32B:<252=29 2   52?   *  3 52?   4  52?   5 * ,  52?   *   6 * ,  52?   .?DE<AB@C6C25:232D:<EC292H2?8D6B;25:A25282C :562=>@?@2D@>:<252=29 2 5  *  3  6 O *  4 ,   ,63E29>6C:?2B?@DC6D:2AC:<=EC?H2>6?6B:>26?6B8: 52B:B6C6BF@:BCE9ED:?88:C636C2B <#52?>6>3E2?8 6?6B8: <#<6B6C6BF@:BCE9EB6?5296C2B67:C:6?C: >6C:?D6BC63ED252=29 2  5  3  6  4   #4"/"3  "7"#-")1&24"/8""/#&2*,54*/*%&/("/4&1"4 ,6;E>=2982C:562=>6?6>A2D:BE2?836BF@=E>6 4>  >2CC282CD6BC63ED 852?36B2D>@=66?82=2>:A6>2?D2A2?C642B225:232D:< C69:?882F@=E>6?H236B6 2G2=?H2  =:D6B 52? D6<2?2??H2  2D>@C76B D6?DE<2?=29D6<2?2?82CD6BC63EDC6D6=29>6?82=2>: A6>2>A2D2?D6D2A2?%2A=246  2=2>CE2DEAB@C6CCE2DE82C>6?6B:>2<2=@B <2=@B:-6B?H2D282C52A2D>6=282C 2C>6=2 82C <2=@B: # 2C>6?6B:>2<2=@B <2=@B:>6?892C:=<2?EC292 C636C2B ;@E=66B2A2A6BE3292?6?6B8:52=2> 82C <2=@B: # Mudah dan Aktif Belajar Fisika untuk Kelas XI  )6B92D:<2?8B27:<,6>6C:?2B?@D36B:6C:?C6D:2AC:<=EC252=29 2   # 5  # 3  # 6  # 4  # #4"/"3   ,63E29>6C:?2B?@DH2?8B6C6BF@:BCE9EB6?529?H2 L >6>:=:<:67:C:6?C: #:<267:C:6?C:5:A6B36C2B>6?;25:  B6C6BF@:BCE9ED:?88:?H292BEC5:?2:<<2?C636C2B 2 $ 5 $ 3  $ 6  $ 4 $  +6C6BF@:B36BCE9ED:?88:A252>6C:?2B?@D252=29  $52?B6C6BF@:BCE9EB6?529?H2 $$2=@BH2?8 5:C6B2A@=69>6C:?52B:B6C6BF@:BCE9ED:?88:C636C2B  ;@E=66C2BEC292H2?85:92C:=<2?>6C:?2B?@D D6BC63ED252=29 2  # 5  # 3  # 6  # 4  #  .C292H2?85:=26?82=2>: AB@C6C:C@<9@B:<52B:D6<2?2?, C2>A2:, 252=29 2 5 , /  3 , / 4 , , / /  6 :28B2>,O36B:6?E?;E<<2?AB@C6CCE2DE82C 52=2>C2DEC:<=EC5:>E=2:52B:52?36B2<9:B5: 4 × 105 1 × 105 p (N/m2) a b d c 1   , ,      3 V(m3) 2B:82>32BD6BC63ED36B2A2<29 2 EC292A252C6D:2AAB@C6C 3 EC292D@D2=82C ,632?H2<>@=82C>6>E2:C642B2:C@D6B>2=A252CE9E $C69:?882F@=E>6?H236BE32952B:4> >6?;25:  4> 6B2A2EC292H2?85:=2CE2DEBE2?8D6BDEDEA>6?82=2>:AB@C6C 52=2>C2DEC:<=EC52B:OOOOC6A6BD:5:28B2> ,636B:6C:?H2?836<6B;2A252 B6C6BF@:BCE9EB6?529L52?B6C6BF@:BCE9ED:?88:  L  ,63E29>6C:?2B?@D36<6B;25:2?D2B2B6C6BF@:BA2?2C L 52? B6C6BF@:B 5:?8:?  #:<2 >6C:? D6BC63ED >6?H6B2A<2=@B  ;@E=652?52A2D>6=26CD6BA6BD2>2H2?8=2=EA252C6>6CD6B:?:?52;E825:DE82C<2? E?DE<>6=26CD6B282BA6>292>2?<@?C6A:C:<2?52C6>2<:? >6?:?8<2D52AE?<68:2D2?C6>6CD6B:?:>6?86?2:7=E:5252?B2?8<2:2?<68:2D2? H2?892BEC?52=22D6>2?C6<6=@>A@<2<2?5:EB2:<2?36B:6?HECE? =2A@B2? 2<9:B A6B4@322? 52? >6>AB6C6?D2C:<2??H25:9252A2?<6=@>A@<=2:?52?8EBE:C:<2?52 Viskositas 5+5"/&(*"4"/ &6?6?DE<2?<@67:C:6?<6<6?D2=2?I2D42:B56?82?>6?88E?2<2?!E,D@<6C -"4%"/")"/  -23E?8,D@<6CD:?88: 4>5:2>6D6B4>A6?H2B:?8 86=2?8A6>32D2C  &:CD2B 4>  &:6D6BC6>  >>  '6B242(92ECC/-%,(!!) 8  8  ):?C6D  @=2A6;2=3292?H2?8C2>256?82?;2B:;2B:36B36523652  /+,2/$  -!+)!/!->2CC2;6?:C 84>   -6B>@>6D6B  %EA 203&%52&2$0#""/  &2$0#""/ &6?6?DE<2?92B82F:C<@C:D2C36B52C2B<2?8B27:</"4 2 .D23E?8CD@<6C56?82?>6?88E?2<2? D6B>@>6D6B8E?2<2?=EA282BA6?8E2CC2;6?:CI2D42:B56?82?>6?88E?2<2?2B6@>6D6B8E?2 <2?=EA282BA6?8EE5:2?E6D6B3@=256?82?>6?88E?2<2?>:6D6BC632?8>2CC23@=2A6;2=H2?82<2?5:8E?2<2?4E2=2DED23E?8CD@<6CH2?8D6=295:36B:I2D42:BH2?82<2? 5:EE5:2?2>2D:86B2<3@=29:?8823@=25:2?882A 36B86B2<=EBEC36B2DEB2? 7 6B:=29D2?5232D2C56?82?86=2?8<2G2DA6BD2>2<6D:<23@=25:2?882A D6=29>6?82=2>:86B2<=EBEC36B2DEB2?N4>5:2D2CA6B>E<22?I2D42:B 8 .2D:456?82?>6>36B:<2?D2?5256?82?86=2?8 <65E2 9 >3:=3@=2H2?8D6=295:>2CE<<2?D:B:C<2?=2=E>2CE<<2?<6>32=:<6 52=2>D23E?8CD@<6C>2D:52?42D2DG2AE93@=2<6D:<2 36B86B2<=EBEC36B2DEB2?C6A2?;2?84 : %26?8E329<65E5E<2?A@C:C:86=2?8<65E2  &2$0#""/ &6?6?DE<2?92B82F:C<@C:D2CI2D42:B36B52C2B<2?8B27:<7E?8C: /"  2 ):=:9 3E293@=256?82?>2CC2;6?:CH2?8C2>2D6B3E2D52B:3292?H2?8 C2>252?;2B:;2B:H2?836B3652 198 Mudah dan Aktif Belajar Fisika untuk Kelas XI 3 4 5 .2CC252?;2B:;2B:C6D:2A3@=2>2C:?8>2C:?84E32D2CA252D23E?8,D@<6C .6?6>AE9;2B2< 2?D2B2<65E286=2?8A6>32D2CH2?8CE5295:D6?DE<2?D6BC63ED &/(0-")"/"4"  6?82?>6?88E?2<2?52D2A6B4@322?A6BD2>23E2D8B27:</"4$6>E5:2? D6?DE<2?<@67:C:6?<6<6?D2=2?I2D42:B36B52C2B<2?8B27:<D6BC63ED   6?82?52D2A6B4@322?<65E23E2D8B27:</" $6>E5:2?D6?DE<2? <@67:C:6?<6<6?D2=2?I2D42:B36B52C2B<2?8B27:<D6BC63ED 2?5:?8<2?92C:=<65E2A6B4@322?D6BC63ED<6>E5:2?36B:<2?A6?;6=2C2??52 >6?86?2:<65E292C:=D6BC63ED ± 5 cm gelang satu y gelang dua Tabung Stokes Proyek Semester 2 199 Tes Kompetensi Fisika Semester 2  *-*)-")3"-")3"45+"7"#"/8"/(1"-*/(4&1"4%"/,&2+","/-")1"%"#5,5-"4*)"/  )6B92D:<2?C:CD6><6C6D:>32?82?A25282>32B36B:32B36B:2CC236?52) 52?) 252=29 2  5  3  6  4  ,63E2936?52>6>:=:<:36B2D '52?5:82?DE?8 52=2> <62522? 5:2> C6A6BD: D2>A2< A252 82>32B 36B:32B36B:32B36B:32B D6BC63ED D6B=6D2<5: 2 3O > 5 3 > 3 3 > 6 3  > 4 3  > )6B92D:<2?82>32B36B:6?292?D682?82?>2< C:>E>  3'36C2B2H2?8>2C:952A2D5:D292? @=69D2=:D6BC63ED252=29 2  ' 5   ' 3  ' 6 ' 4   '  T1 T1 T3  60° T2 m2 6C2B)   <852?<@67:C:6?86C6<CD2D:C2?D2B2 ) 52?>6;2252=29  &2CC2) 252=29 2 <8 5 <8 3 4 200 w = 30 N ,:CD6>A25282>32B36B:<62522? C6D:>32?8 m1  <8 <8 6  <8 Mudah dan Aktif Belajar Fisika untuk Kelas XI B A 2D2?8H2?8A2?;2?8?H2 4>5:36B:3632?5:E;E?8 ?H2C636C2B '#:<2A2?;2?8 4>52?>2CC2 32D2?85:232:<2?36C2BD682?82?D2=:252=29 2 ' 5 ' 3 ' 6  ' 4  ' )6B92D:<2?82>32B36B:E5:2? 52?5:36B:3632?>2C:?8>2C:?82  '52?2   ':<6D29E:  >  >52?  > 36C2BD682?82?D2=:5: 52?5: 252=29 2  '52? ' 5  '52? ' 3  '52? ' 6 '52? ' 4  '52? '  +2A2D>2CC2C68E>A2=6C252=29 <8 >  E>A2=2? 6CH2?8D6B2AE?852=2>2:B2<2?>E?4E=5:2D2CA6B >E<22?2:B56?82?F@=E>6 2   > 3   > 4  > 5 > 6 >  ,63E29A:A232B@>6D6B5:82?D:56?82?A:A2H2?8=E2C A6?2>A2?8?H25E2<2=:?H2)252D6<2?2?E52B2=E2B 2D>@C76BD:?88:B2A:A2252=29 2 4> 3 4> 4 4> 5 4> 6  4>  ,63E29A:A2C:=:?56B=EBEC>6>:=:<:=E2CA6?2>A2?8 >> 52? >> ):A2D6BC63ED5:=6D2<<2?C642B2 9@B:I@?D2=C652?8<2?2:B5:52=2>?H2>6?82=:B52B: 2B29 A6?2>A2?8 36C2B <6 A6?2>A2?8 <64:= #:<2 <646A2D2? 2BEC 5: A6?2>A2?8 36C2B 252=29  > C <646A2D2?2BEC5:A6?2>A2?8<64:=252=29 > C 2  3 > C 4 > C 5 > C 6 > C  ,63E2932=@?E52B236B>2CC2<836B:C:!6=:E>  !6   <8 > #:<232=@?D6BC63ED92BEC>6?82?8<2D 3632? <8  E52B2  <8 > F@=E>632=@?D6BC6 3ED252=29 2  > 3 > 4  > 5  > 6  >  :<6D29E:52D256D2<;2?DE?82EI:<2=:A6B>6?:D 6C2B52H2H2?85:<6=E2B<2?2EI:;:<2;2?DE?8>6>@> A2<2?>%52B2956?82?D6<2?2?B2D2B2D2 >>!8 E?DE<C6D:2A56D2<2?252=29 4>!8  )2 2 G2DD 3 G2DD 4  G2DD 5 G2DD 6 G2DD  ,63E29A@>A2>6?2:<<2?2:BC632?H2<> C6D:?88:  > <6>E5:2? >6?82=:B<2??H2 <6 52=2> A:A2 36BD6<2?2?  <)26C2BEC292252=29 2 P # 3 P # 4  P # 5  P # 6  P #  :<6D29E:>2CC2;6?:C2:B=2ED  8 4> 52?D6<2?2? E52B2=E2B ' > #:<2<2A2=C6=2>36B2525: <652=2>2? >D6<2?2?H2?85:2=2>:<2A2=C6=2> D6BC63ED252=29 2  &A2 3 &A2 4  &A2 5  &A2 6  &A2  )6B92D:<2?82>32B36B:6D6B=E32?8 4>F@=E>62:BH2?8<6=E2B52B: =E32?85:D:D:< C6D:2A>6?:D252=29 2  > A6B>6?:D 3  > A6B>6?:D 4 > A6B>6?:D 5  > A6B>6?:D 6 > A6B>6?:D  ,6D6=29 5:E2?@>6D6B5:<6D29E:D6<2?2?2:B5: 52=2>C63E29D2?8<:252=29 <)2 1 2 )6B92D:<2?82>32B5:C2>A:?8#:<2 D6B;25: <63@4@B2? 5: D:D:<  <646A2D2?2:BH2?8<6=E2B52B:D:D:<D6BC63ED252=29 2 > C 3 > C 4  > C 5  > C 6 > C  E2D23E?85::C:56?82?82C36B3652D6D2A:<65E2?H2 36B252A252CE9EH2?8C2>2:<6D29E: 52? 252=29 36B2D >@=6:<:2?36C2B>@>6?DE>B2D2B2D2>@=62 =2:?>6?EBEDBE>EC 2 , , 3 ,  4 ,       5 ,      6 ,                )2BD:<6=A2BD:<6=82C:562=>6>:=:<:C:72D2?D2B2=2:?   C6=2=E36B86B2<   D:52<C2=:?8D2B:<>6?2B:<   36BDE>3E<2?=6?D:?8C6>AEB?252?  D:52<>6?8:'6GD@?D6?D2?886B2< Tes Kompetensi Fisika Semester 2 201      202 )6B?H2D22?H2?836?2B252=29 2   52?  3  52?  4  52? 5  6 C6>E236?2B )252CE2DEC22D36C2BD6<2?2?E52B2=E2B4>!8 =2DE2?@>6D6BD6B3E<2>6?E?;E< <2?329G2D6<2?2?5:52=2>D2?8<:252=29 4>!8 ,E9E82C52=2>D2?8<:L$6>E5:2?<2B6?2A6>2 ?2C2?CE9ED2?8<:?2:<>6?;25: L-6<2?2?H2?8 5:DE?;E<<2?>2?@>6D6B252=29 2  4>!8 3 4>!8 4  4>!8 5   4>!8 6  4>!8 ,63E29D2?8<:36BF@=E>6 %82C@@=D6<2?2?E52B2=E2B P )2 52? # <>@=$>2CC2@D2?8<: D6BC63ED252=29 2  <8 3  <8 4   <8 5   <8 6  <8 /@=E>6   8 82C @@= A252 <62522??@B>2=252=29 2 P O> 3 P O> 4 P O > 5 P O > 6 P O > ,63E29D23E?8B6256?82? A6?2>A2?836B2DEB2?2<2?5:DEBE?<2?56?82?E;E?8 D6B3E<2<652=2>52?2E2:BD2G2B82BD23E?8D6B:C:2:B C6A6B6>A2D328:2?D23E?8D6BC63ED92BEC5:D6>A2D<2? 5:<652=2>2?D6<2?2?2D>@C76B <)2 2 > 3 > 4 > 5 > 6 > ,63E29>6C:?2B?@DH2?8>6?88E?2<2?B6C6BF@:B CE9ED:?88:36BCE9E $52?>6>:=:<:67:C:6?C:  82B67:C:6?C:?H2>6?;25: CE9EB6C6BF@:BCE9E D:?88:92BEC5:?2:<<2?>6?;25: 2  $ 3  $ 4  $ 5   $ 6  $ Mudah dan Aktif Belajar Fisika untuk Kelas XI  ,:<=EC2B?@D5:32D2C:@=695E282B:CH2:DE   :C@32B:<   25:232D:<   :C@F@=E>6  :C@D6B>:< )6B?H2D22?H2?836?2B252=29 2   52?  3  52?  4  52? 5  6 C6>E236?2B  7:C:6?C:>6C:?2B?@DH2?836B@A6B2C:56?82?CE9EB6?529 <6=F:?52?36BCE9ED:?88:<6=F:?252=29 2  5  3  6  4   &6C:?2B?@D5:@A6B2C:<2?2?D2B25E2B6C6BF@:B<2=@B >2C:?8>2C:?8 36BCE9E   52?   56?82?     7:C:6?C:>6C:?D6BC63ED 52?36C2B?H2  L 82B67:C:6?C:?H2?2:< 36C2BA6BE3292? 252=29 2  $ 3 $ 4  $ 5  $ 6  $ !    ,63E29>6C:?DEB3:?>6>2<2:E2A56?82?CE9E2G2=  L 52? >6>3E2?8?H2 A252 CE9E L 7:C:6?C: >2E>>6C:?DEB3:?D6BC63ED252=29 2  3   4   5   6    )252 CE2DE AB@C6C <2=@B C632?H2<   <2=@B: 5:92?D2B<2?A252C:CD6>C652?8<2?C:CD6>>6=2C:CD6>D6BC63ED252=29 2 <# 3 <# 4 <# 5 <# 6 <#  ,63E29>6C:?A6?825E<36B52H2 G2DD5:A2<2:E?DE< >6?825E<  <8 2:B $6>E5:2? CE9E 2:B ?2:< 2<:32D 252?H286C6<2?5:52=2>2:B6?82?>6?82?882AC6>E2 EC292 >6?;25: <2=@B G26C:? E?DE<36<6B;2282BCE9E2:B?2:<L252=29 2 >6?:D 3 >6?:D 4 >6?:D 5 >6?:D 6 >6?:D  "7"#-")1&24"/8""/#&2*,54*/*%&/("/4&1"4  ,63E29B@52H2?8>@>6?:?6BC:2?H2  <8> 52A2D 36BAED2B3632CA252CE>3E52D2B-2=:5:=:=:D<2?A252 D6A:B@52D6BC63ED52?A252E;E?8D2=:5:82?DE?8<2? 3632? 8#2B:;2B:CE>3EB@52D6BC63ED252=29 4> 68:DE 3632? 5:=6A2C B@52 >E=2: 36BAED2B 6B2A2 ;2E9<29 36?52 D6BC63ED 92BEC ;2DE9 282B B@52 36B<646A2D2? AED2B2? C6<@? ,63E293@=232C<6D>6?886=:?5:?8D2?A2C6=:AA2523:52?8 >:B:?8H2?8A2?;2?8?H2>56?82?CE5ED<6>:B:?82? L#:<2-3@=2 4>) <852?3@=25:=6A2C<2?D2?A2 <646A2D2? 2G2= 52B: E;E?8 2D2C 3:52?8 36B2A2<29 <646A2D2?=:?62B3@=2C22DD:325:E;E?832G293:52?8 ,63E293@=2A6;2=>6?886=:?5:?85:=2?D2:52D2B56?82? 1 > C$6>E5:2?3@=2D6BC63ED>6=6G2D:D2?;2<2? 56?82?CE5ED LD6B9252A3:52?89@B:I@?D2=#:<282H2 86C6<3@=252?=2?D2:5:232:<2?36B2A2<29<6D:?88:2? H2?852A2D5:42A2:3@=2D6BC63ED52B:52C2B=2?D2: .52B2H2?836B>2CC2;6?:C  <8 > 5:=6G2D<2?A252 C63E29A:A2H2?8>6>:=:<:=E2CA6?2>A2?8  4>  #:<25:E>2?@>6D6B252=29 >>-6?DE<2?F@=E>6 E52B2H2?8>6?82=:B52=2>G26?:D     ,6A@D@?8 2=E>:?:E> 52=2> E52B2 36B2D?H2   8   2=E>:?:E>  8 4> #:<236?52D6BC63ED5:82? DE?8<2?A252C6ED2CD2=:52?5:46=EA<2?52=2>>:?H2<   >:?H2< 8 4> 36B2A2<29D682?82?D2=:D6BC63ED  ,63E2932<2:B>6>:=:<:D:?88:>,63E29=E32?8A252 32< D6BC63ED >6>2?42B<2? 2:B C6;2E9  4> #:<2 A6B46A2D2?8B2F:D2C:# > C D6?DE<2?<6D:?88:2? 2:B5:52=2>32<2:BD6BC63ED  -6?DE<2?=29B2A2D>2CC282C>6D2? <8 >@= A252CE9E L52?D6<2?2?2D>  -6?DE<2?1B>C52B:CE2DE82CH2?836B2525:52=2> C63E29D23E?8D6BDEDEA56?82?F@=E>6 =:D6B52? D6<2?2?C636C2B P )2;:<2B2A2D>2CC282CD6BC63ED O 8 4>   2C9:5B@86? <8 >@=52?82C?:DB@86? <8 >@=36B252A252CE9EH2?8C2>2-6?DE<2?=29 A6B32?5:?82? 2  '!  ''52? 3 1B>C!1B>C'  ,63E29A6C2G2DA6?5:?8:?>6>:=:<:<@67:C:6?52H28E?2 C636C2B#:<2D6>A6B2DEBB6C6BF@:BCE9ED:?88:252=29 L9:DE?8=29D6>A6B2DEBB6C6BF@:BCE9EB6?529?H2 Tes Kompetensi Fisika Semester 2 203 Tes Kompetensi Akhir  *-*)-")3"-")3"45+"7"#"/8"/(1"-*/(4&1"4%"/,&2+","/-")1"%"#5,5-"4*)"/   -6B9252A<@@B5:?2D39@B:I@?D2=52?4F6BD:<2=C63E29 36?52H2?836B86B2<>6?8:6> AE?H2:<@>A@?6?<@>A@?6?<646A2D2?H2?8 2 36C2B?H2D6D2AA2522B29352?36BE32936B2DEB2? A2522B294 3 36C2B?H2D6D2AA2522B29452?36BE32936B2DEB2? A2522B293 4 36C2B?H2D6D2A32:<A2522B293>2EAE?A2522B294 5 36C2B?H236BE32936B2DEB2?32:<A2522B293 >2EAE?A2522B294 6 36C2B 52? 2B29?H2 D6BEC>6?6BEC 36BE329 D6B9252AG222? 2J D * DOD +K>,6D6=2936?5236B86B2< C6=2>2 C6<@?<6=2;E2??H2252=29 2 5 > C 3 > C 6  > C 4  > C !      )6B?H2D22? H2?8 D:52< 36?2B >6?86?2: 9E3E?82? 2?D2B2A6B46A2D2?D2?86?C:2=86B2<B@D2C:CE2DEA2BD:<6= 52?36C2B2?36C2B2?CE5ED?H2252=29 2 A6B46A2D2?D2?86?C:2=>6?E?;E<<2?A6BE3292? 36C2B<6=2;E2?=:?62B52B:A2BD:<6= 3 A6B46A2D2?D2?86?C:2=C6=2=E>6>:=:<:A2BD:<6=H2?8 36B86B2<>6=:?8<2B 4 A6B46A2D2? D2?86?C:2= >6>:=:<: A2BD:<6= H2?8 36B86B2<56?82?=2;E=:?62BD6D2A 5 A6B46A2D2? D2?86?C:2= C632?5:?8 56?82? A6B46A2D2?CE5ED52?;2B:;2B: 6 A6B46A2D2?D2?86?C:2=C6=2=E>6?82B29<6AEC2D =:?D2C2?>6=:?8<2B?H2 )@C:C:C63E2936?52H2?85:=6>A2B<2?F6BD:<2=<62D2C 5:?H2D2<2?56?82?A6BC2>22?4 // >56?82? /52=2>C6<@?$646A2D2?2G2=36?52252=29 2 > C 5 > C 3 > C 6 > C 4 > C ,63E2936?52H2?836B2D?H22>6=E?4EB<632G29 56?82?<646A2D2?D6D2AA252CE2DE3:52?8>:B:?8H2?8 <2C2B:52?8>:B:?8D6BC63ED>6>36?DE<CE5ED L D6B9252A9@B:I@?D2=$@67:C:6?86C6<2?2?D2B236?52 52?3:52?8D6BC63ED252=29 2 3 4 204 2 5 6 2 Mudah dan Aktif Belajar Fisika untuk Kelas XI  ,63E2936?5236B>2CC2 <85:5@B@?856?82?82H2  '2B29>6?52D2B$@67:C:6?86C6<2?<6D:<236?52 D6A2D2<2?36B86B2<252=29 2  5  3  6  4   #:<2A6B46A2D2?8B2F:D2C:5:A6B>E<22?E>:#52? ;2B:;2B:E>:>2<2A6B46A2D2?8B2F:D2C:5:CE2DED:D:< H2?836B;2B2<52B:A6B>E<22?E>:252=29 5 # #  3 6 # # 4 #  ,63E29A682C56?82?D6D2A2? ' >5:36B:3632?<8 52?5:D2B:<<62D2C56?82?A6B46A2D2? > C #:<2 # > C >2<2A6BD2>3292?A2?;2?8A682CD6BC63ED 252=29 2  > 5  > 3  > 6 > 4  >  ,6@B2?8A6=2;2BH2?8>2CC2?H2 <836B82?DE?8A252 E;E?8C63E29A682CC69:?882A682C36BD2>329A2?;2?8 4>6?82?56>:<:2?<@?CD2?D2A682C36B?:=2: 2  ' > 5 ' > 3 ' > 6  ' > 4  ' > 2 !    )682C5:CECE?C642B2C6B:52?A2B2=6=C6A6BD:82>32B 36B:236C2B#:<2 <@?CD2?D2A682C' ' ' ''A6B32?5:?82? A6B:@56CECE?2?C6B:52?A2B2=6=252=29 2  5  3  6  4  !    B27:<36B:6?E?;E<<2?86B2<2?C63E2936?52 36B>2CC2 <8A2523:52?852D2BD2?A286C6<2?<2B6?2 A6?82BE982H2H2?836BE329E329 F (N)  :2?D2B236?5236B86B2<36B:6?82=2>:82H2A2=:?836C2B;:<2>6?E>3E<D6>3@< 9:?88236B96?D:252=29 2 36?5236B>2CC2 <856?82?=2;E > C 3 36?5236B>2CC2 <856?82?=2;E > C 4 36?5236B>2CC2 <856?82?=2;E > C 5 36?5236B>2CC2  <856?82?=2;E> C 6 36?5236B>2CC2 <856?82?=2;E> C  balok s (m) #:<2<646A2D2?36?52C22D. 252=29> C>2<2   <646A2D2?36?52C22D.>252=29 > C   A6BE3292?6?6B8:<:?6D:<52B:. C2>A2:56?82? .>252=29;@E=6   36C2BEC29252B:. C2>A2:56?82?.> 252=29;@E=6 )6B?H2D22?5:2D2CH2?836?2B252=29 2   52?  5  C2;2 3  52?  6  52?  4  52?  !    6?5236B>2CC2<85:=6>A2BF6BD:<2=<62D2C56?82? <646A2D2?2G2= > C6C2B?H26?6B8:A@D6?C:2=5: D:D:<D6BD:?88:H2?85:42A2:36?52252=29 2 # 5  # 3  # 6  # 4 #  ,63E29 A682C H2?8 <@?CD2?D2?H2 ' 5:36B: 3632? 36B>2CC2)632?5:86D2B<2?56?82?2>A=:DE5@  ?6B8:A@D6?C:2=3632?:DEA252C22D<646A2D2??H2  <2=:<646A2D2?>2E>252=29 2  ' 5  ' 3  ' 6  ' 4  ' !    ,63E2932=@<36B>2CC2 <85:5@B@?852B:52C2BCE2DE 3:52?8>:B:?8H2?8A2?;2?8?H2>6D6B52?AE?42< 3:52?8>:B:?836B252 >52B:D2?29#:<23:52?8>:B:?8 5:2?882A=:4:?52?A6B46A2D2?8B2F:D2C:E>: > C  EC292H2?892BEC5:=26?5@B@?832=@< 252=29 2 ;@E=6 5  ;@E=6 3  ;@E=6 6  ;@E=6 4  ;@E=6  ,63E29 >@3:= 56?82? >2CC2  D@? 36B86B2< 52B: <62522? 5:2> ,6C22D <6>E5:2? <646A2D2??H2 >6?;25:> C6C2BEC292H2?85:=26C:? >@3:=D6BC63ED252=29 2  # 5  # 3  # 6  # 4  # peluru )6=EBE56?82?>2CC2 8B2>52?<646A2D2?  > C >6?86?2:52?>6?E>3E<C63E2932=@<56?82?>2CC2 <8H2?85:2>5:2D2C3:52?852D2BD2?A286C6<2? $646A2D2?A6=EBEC6D6=29>6?6>3EC32=@<252=29 > C$646A2D2?32=@<<2B6?2D6BD6>3ECA6=EBE 252=29 2  > C 5 > C 3  > C 6  > C 4 > C  @=236B>2CC2<8;2DE9D2?A2<646A2D2?2G2=<6 =2?D2: 52B: <6D:?88:2? $ >6D6B #:<2 A6B46A2D2? 8B2F:D2C:#52?<@67:C6?6=2CD:C:D2C3@=2D6B9252A=2?D2: 252=29  >2<2A6B?H2D22?A6B?H2D22?D6?D2?83@=2 36B:2    #$ > C 3 36C2B <646A2D2? A2?DE=2? H2?8 <65E2   #$ > C 4 D:?88:>22=A2?DE=2?A6BD2>2  $> 5 D:?88:>22=A2?DE=2?<65E2  4 $> 6 <646A2D2?3@=2C22D>6?E>3E<=2?D2: #$ > C  ,63E29A6=EBE36B>2CC2 8B2>5:D6>32<<2?52B: C63E29C6?2A2?<62B29C63E2932=@<36B>2CC2<8 C69:?882A6=EBE36BC2B2?85:52=2>32=@<<2HED6BC63ED 2=@<36B2HE?52??2:<C6D:?88: 4>52B:<62522? C6>E=2#:<2A6B46A2D2?8B2F:D2C: > C <646A2D2? A6=EBEC6D6=29>6?86?2:32=@<252=29 2 > C 5 > C 6 > C 3 > C 4 > C  ,63E293@=2<2CD:36B>2CC2  <852=2><62522?5:2> <6>E5:2?5:AE6=E?4EB56?82?=2;E > C52?A6>E6?H6?DE93@=2C6=2>2  C6<@?6C2B82H2A6>EC69:?882 52=2>G26>:=:<:<646A2D2? B25 C ,63E29D:D:<)36B252A25236?5252?36B;2B2<4> 52B:CE>3EB@D2C:?H2)6B46A2D2?D2?86?C:2=B2D2B2D2 H2?85:>:=:<:D:D:<)D6BC63ED252=29 Tes Kompetensi Akhir 205      5  > C 2  > C 3 > C 6  > C 4 > C )6B92D:<2? 82>32B 5: C2>A:?8 ,63E29 A:B:?82? 9@>@86?H2?8>6>:=:<:>2CC2)52?;2B:;2B:-5:AED2B A252C2=29C2DED:D:<5:82B:CC:?88E?8?H2&@>6?:?6BC:2 52B:A:B:?82?H2?85:AED2BD6BC63ED252=29 )5 )2  )6 )3 4 )- ,63E293@=2A6;2=36B>2CC2<852?36B;2B:;2B:4> @=2D6BC63ED>6?886=:?5:?85:A6B>E<22?;2=2?H2?8 <2C2B2<:32DC63E2982H25@B@?8 '#:<23@=2 >6?886=:?5:?8 C6>AEB?2 >2<2 A6B46A2D2? H2?8 5:2=2>:3@=2A6;2=D6BC63ED252=29 2 > C 5 > C 3  > C 6 > C 4 > C )6B92D:<2?C:CD6>A25282>32B36B:<62522?C6D:>32?8#:<2 #   > C  D682?82?  52? C:?  >2C:?8>2C:?8 252=29  2  '52? 5  '52?   3  '52?  6  '52?   4  '52?  ,63E29A:B:?82?36B36?DE< C:=:?56B9@>@86?36BAED2B r A252 A@B@C?H2 56?82? <646A2D2? 2G2=  B25 C :52?8 A:B:?82? C6;2;2B 3:52?89@B:I@?D2=&2CC2 piringan sumbu A:B:?82? <852?;2B: putar ;2B:A:B:?82? >#:<2 5:2D2CA:B:?82?5:=6D2<<2?4:?4:?36B>2CC2 <8 36B;2B:;2B:  >52?AEC2D4:?4:?D6A2D5:2D2CAEC2D A:B:?82?>2<2<646A2D2?CE5EDA:B:?82?52?4:?4:? <6D:<236BAED2B252=29 2 B25 C 5 B25 C 3 B25 C 6 B25 C 4 B25 C ,63E2932<>2?5:36B36?DE<32=@<>6>:=:<:A2?;2?8 >=632B >52?D:?88: >2<>2?5:D6BC63ED 36B:C: =:D6B2:B %-  <8 > #:<2# > C  D6<2?2?9:5B@CD2D:<A25252C2B32<252=29 2 )2 5  )2 3  )2 6 )2 4 )2  ,63E29A@>A29:5B@=:<>6>:=:<:5E2A6?89:C2AH2?8 36B;2B:;2B: >2C:?8>2C:?8  4> 52?   4> )252 A6?89:C2A<64:=5:<6B;2<2?82H2C636C2B ' 2H2 H2?85:92C:=<2?A252A6?89:C2A36C2B252=29 206 Mudah dan Aktif Belajar Fisika untuk Kelas XI        T 2  '  30 N 3  ' 4  ' 5  ' 4 kg 6  ' 6B:6B?@E==:52=2> <69:5EA2?C692B:92B:'!0(% 2 82H22?8<2DA6C2G2DD6B32?8 3 <2B3EB2D@B>@3:=52?>@D@B 4 A6?H6>AB@D42:B2??H2>E< 5 F6?DEB:>6D6B 6 B6>9:5B@=:< ,63E29=@82>36B36?DE<3@=236B;2B:;2B:4>52? >2CC2;6?:C?H2 8 4> %@82>D6BC63ED;2DE93632C5: 52=2> 32< 36B:C: I2D 42:B H2?8 >6>:=:<: <@67:C:6? F:C<@C:D2C 'C > #:<2>2CC2;6?:CI2D42:B 8 4> 52? A6B46A2D2?8B2F:D2C:E>: > C >2<2<646A2D2?D6B >:?2=3@=2=@82>252=29 2 > C 5 > C 3  > C 6  > C 4  > C ,63E29A:A2H2?8=EBEC>6>AE?H2:5E2A6?2>A2?8 56?82?=E2CA6B>E<22?>2C:?8>2C:?8 > 52?  > H2?85:=6D2<<2?C642B29@B:I@?D2=:B>6?82=:B 52B: A6?2>A2?8 36C2B <6 A6?2>A2?8 <64:= #:<2 <646A2D2?2BECA252A6?2>A2?836C2B> C<646A2D2? 2BEC2:BA252A6?2>A2?8<64:=252=29 2 > C 5 > C 3 > C 6 > C 4 > C #:<2CE2DE82CH2?8>6>6?E9:!E@H=65:;25:<2? C6D6?829?H2>2<2D6<2?2?>6?;25:5E2<2=:?H2!2= :?:5:C6323<2?<2B6?2 2 >@=6@=66B2A2DC69:?882<646A2D2??H2 >6?;25:5E2<2=: 3 >@=6@=6@=6@=66?;25:5E2<2=: 5 32?H2@=66?;25:5E2<2=: 6 6?6B8:<:?6D:<>@=6@=66?;25:5E2<2=: #:<2<@?CD2?D2@=DI>2?'  P O # <>2<2 6?6B8:<:?6D:<C63E292D@>82C96=:E>A252CE9E L 252=29 2  P O # 5  P O # O 3  P # 6  P O # O 4 P # :52=2>BE2?836BF@=E>6 %D6B52A2D >882C 36BD6<2?2? 2D>#:<2 2D> ' > <6=2;E2? B2D2B2D2A2BD:<6=82CD6BC63ED252=29 5  > C 2  > C 3 > C 6 > C 4 > C &2CC2C63E29>@=62CC2 >@=6@=66>:=:<:=2;EB2D2B2D2H2?8C2>256?82?=2;E B2D2B2D2>@=62<252A2D5:A6B<:B2<2? 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C6=2>2 >6?:D252=29 5 P # 2  P #  3  P # 6  P #  4 P #  =E:52:562=56?82?<646A2D2? > C5:52=2>A:A2 36B82B:CD6?8294>>2CE<<652=2>A:A236B82B:C D6?8294>-6?DE<2?=29<646A2D2?2=:B7=E:52A252 A:A2H2?836C2B  2=2>C63E29BE2?8D6BDEDEA36BF@=E>6 =:D6BD6B52A2D >@=82C36BD6<2?2? )2#:<2A2BD:<6=82C>6>:=:<: <6=2;E2?B2D2B2D2  > CD6?DE<2?>2CC282C52? 6?6B8:<:?6D:<B2D2B2D282CD6BC63ED  2C@BE2?8D6BDEDEA36BCE9E L 52?D6<2?2? 2D>C6BD2F@=E>6?H2 %$6>E5:2? 82C@A2: LC69:?882 D6<2?2??H2 ?2:<  2D> -6?DE<2? F@=E>6 82C C6<2B2?8  ,E2DE82C52=2>C:=:?56BD6BDEDEA>6?82=2>:AB@C6C C6A6BD:A2528B27:<36B:6>:=:<:>2CC2) )  <8 36B86B2<C2=:?8>6?56<2D:C6A6BD:A25282>32B 36B:3E<<2?=6?D:?8C6>AEB?2 D6?DE<2?=29<646A2D2?>2C:?8>2C:?836?52C6D6=29 36BDE>3E<<2?52?D6?DE<2?AE=22B29?H2 ,63E2932D2?8),>2CC25:232:<2?A2?;2?8?H2 >)**++,-6?DE<2?>@>6?82H2H2?8 36<6B;2A25232D2?8;:<2 2 AEC2D>@>6?82H25:) 3 AEC2D>@>6?82H25:, B E V(m3) 60 -6?DE<2?EC292H2?85:=26>:=:<: A6BA:?5292? =:?62B C652?8<2? <646A2D2? CE5ED >6>:=:<: A6BA:?5292? B25:2= Tes Kompetensi Subbab A  2 * + 3 >  2 > C 3 > C 4 > C  2 O> C 3 > Tes Kompetensi Subbab B  2 C 3 > 4 >  2 D:D:<D6BD:?88: 3 > C  C  > C Tes Kompetensi Subbab C  O> C*> C  2 > C 3 AED2B2?A6B56D:< 4 C Tes Kompetensi Bab 1 A. Pilihan Ganda  2  2  3  6  3  2  4  4  3  2 B.    208 Soal Uraian 2 > C 3 O > C 4  > C 2 > C 3 > C  > Mudah dan Aktif Belajar Fisika untuk Kelas XI Bab 2 Gaya Tes Kompetensi Awal  $2B6?2D:52<25292>32D2?86C6<2?E52B2  .?DE<C6B:       '. ' ' ' '* .?DE<A2B2=6='A' ' ' '* Tes Kompetensi Subbab A  '  > C   >  > C  2  > C 3    Tes Kompetensi Subbab B  2 ' 3  >52B:3@=2A6BD2>2  P <8 >   C   '  P ' Tes Kompetensi Subbab C   P ' > P O P ' >   P ' >   > ' > Tes Kompetensi Subbab D   '  <8  Tes Kompetensi Bab 2 A. Pilihan Ganda  5  4  6  4  2  2  6  4  2  4  5  4  4 B.     Soal Uraian = C = C ( 1  N ( 2  N = C = C 3= Bab 3 Usaha, Energi, dan Daya Tes Kompetensi Awal L -C181 141<18 @B?C5C DB1>C65B 5>5B79 45>71> =5<921D;1>71H1H1>7=5>H5212;1>D5B:149>H1 @5B@9>4181> L >5B79141<18CE1DE;5=1=@E1>E>DE;=5<1;E ;1>EC181  +52E1825>41H1>749<5=@1B;1>;51D1C;5=E491> :1DE8;5@5B=E;11>E=9 Tes Kompetensi Subbab A  $  $  $ Tes Kompetensi Subbab B  = C   $   Tes Kompetensi Subbab C L !1H1 ;?>C5BF1D96 141<18 71H1 49 =1>1 EC181 1;921D 71H1 D5BC52ED D941; =5>7E218 5>5B79 =5;1>9;C9CD5= L !1H1D941;;?>C5BF1D96141<1871H149=1>1EC181 ?<58 71H1 D5BC52ED 41@1D =5>7E218 5>5B79 =5;1>9;C9CD5=       = C41>  $  1 = C 2  $ Tes Kompetensi Subbab D 8@   G1DD   = C Tes Kompetensi Bab 3 A. Pilihan Ganda 3 3  1  4  2  3  2  5  5  2 B.   Soal Uraian :?E<5 :?E<5 = C   1  :?E<5 2  :?E<5 3  :?E<5 4  = C ( = Bab 4 Momentum, Impuls, dan Tumbukan Tes Kompetensi Awal 01  -;EB1>5<1CD9C9D1C25>41 25>41H1>725BDE=2E;1> Tes Kompetensi Subbab A 1 ( 2 N ( Tes Kompetensi Subbab B 1 = C 2 = C 3  = C  = C Tes Kompetensi Subbab C @  1 = C = C 2  = C= C $ 3 = C= C   $  1 = C 2 $ 3    = C  = C$ Tes Kompetensi Subbab D =  = Tes Kompetensi Subbab E =  = C Tes Kompetensi Subbab F ( Tes Kompetensi Bab 4 A. Pilihan Ganda 1 4  4  4  1  4  4  5  2  2 B.     Soal Uraian  ;7= C 1 = C 2  = C41>= C M= CF5BD9;1<;521G18 = C 1 =5D5B 2  =5D5B 3 Kunci Jawaban 209 Tes Kompetensi Fisika Semester 1 A.       Pilihan 3 2 4 3 1 4 2 2 B.   Soal Uraian = C = C( 1  N ( 2  = C  = C =   Bab 5 Ganda  4  3  1  4  2  5  1 Gerak Rotasi dan Kesetimbangan Benda Tegar Tes Kompetensi Awal L '?=5>71H11D1ED?BC9=5BE@1;1>25C1B1>H1>7 =5>H5212;1>C52E1825>41D571B25>41H1>7 D941;41@1D25BE21825>DE;35>45BE>7E>DE; 25B?D1C9D5B8141@@?B?C>H1 L '?=5>9>5BC91=5BE@1;1>C961D;535>45BE>71> CE1DE25>41E>DE;D5D1@=5=@5BD181>;1>75B1; B?D1C9>H1  %5C5D9=21>71>@14125>41H1>74971>DE>7=5<125>41H1>725B75B1;=5>775<9>49>7 Tes Kompetensi Subbab A 1 B14B14  K  K 2 = 3 B14 C 4 B14 C  B14 C B14 C Tes Kompetensi Subbab B (=  1  (= 2  (=  1 B14 C 2   ( ( Tes Kompetensi Subbab C =   (  (  (K Tes Kompetensi Bab 5 A. Pilihan Ganda 4  4  5  1  3  1 210 Mudah dan Aktif Belajar Fisika untuk Kelas XI B.     Soal Uraian (=  ;7= 1  = C 2 (B14 3 =  (=  C5;?> Bab 6 Fluida Tes Kompetensi Awal "E;E=*1C31< 1B1;5B:1>H145>71>=5>77E>1;1> ;?>C5@D5;1>1>894B?CD1D9;  %1B5>1D5B41@1DD571>71>@5B=E;11>I1D319B Tes Kompetensi Subbab A 1   ( = 2   ( =  1 3= 2 3=  1 =5>71@E>7 2 = 3  ( Tes Kompetensi Subbab B N M== Tes Kompetensi Subbab C = C   (   = C Tes Kompetensi Bab 6 A. Pilihan Ganda 5 2  2  3  5  3  4  4  2  1 B.   Soal Uraian  ;*1 1 = 2 N ( 3 N (  C5;?> Bab 7 Teori Kinetik Gas Tes Kompetensi Awal (9DB?75>?;C975>41>;1B2?>49?;C941 *141;51411> +,*71CD5BC52ED2E;1>=5BE@1;1>71C9451<  1E41B1D5B21>745>71>=5=1>611D;1>=1CC1:5>9C E41B1@1>1CH1>7<5298B9>71>41B9@141E41B12521C Tes Kompetensi Subbab A  *1  =& Tes Kompetensi Subbab B ;);( )( Tes Kompetensi Subbab C    1D=  ;$   N =?<5;E< N M = C = C Tes Kompetensi Bab 7 A. Pilihan Ganda 2 4  3  3  2  1  5  5  1  4 Tes Kompetensi Bab 8 A. Pilihan Ganda 2 4  2  4  4  5  4  2  1  3 B.     Soal Uraian 1D= M $   $ N M$   Tes Kompetensi Fisika Semester 2 A.       Pilihan 4 2 3 3 1 5 3 2 Tes Kompetensi Awal !5<1CD5BC52ED41@1D@5318;1B5>1;5D9;1499C919B@1>1C @5B=E;11>75<1C1;1>=5>71<1=9@5=E191>1;921D @5BE2181>CE8EH1>7D941;=5B1D1  69C95>C941<1=;19D1>>H145>71>;9>5B:1=5C9>141<18 @5B21>49>71>1>D1B1EC181H1>749<1;E;1>45>71> ;5B:1H1>74981C9<;1> B.     Soal Uraian 3= =  ( ;7 = 1 2  Tes Kompetensi Subbab A 1 M;$ 2 ;$  ;*1   $ Tes Kompetensi Akhir B.    Soal Uraian 3= 7 3=  <9D5B <9D5B Bab 8 Termodinamika Ganda  1  1  2  3  3  1  2 A.         Pilihan 1 5 5 1 4 1 2 5 5 1 Tes Kompetensi Subbab C %     1   2  $ B. Tes Kompetensi Subbab D    G1DD   N $  Soal Uraian ( M  3=   = C;5;9B9 M = C;5;1>1>  = C  & Tes Kompetensi Subbab B  $   $  !1C9451<41@1DD5B:149:9;1D941;D5B41@1D@5B@9>4181> @1>1C *5B@9>4181>@1>1CD941;1;1>D5B:149:9;1CE8E D5D1@9C?D5B=1<D5;1>1>D5D1@9C?21B41>F?71> D941;C1=145>71> 81=@9BC1=145>71> 41<1=?B45 C521>49>745>71> <529825C1B41B9@141 <529825C1BC1=145>71> :1E8<529825C1B41B9@141 <5298;539< <5298;539<C1=145>71> :1E8<5298;539<41B9@141  JJ  <9=               9>D57B1< @5BE2181> >9<1912C?45;1D9>?<  DEBE>1>D5B8141@  DEBE>1>@1BC91<D5B8141@ Rumus Trigonometri D1>   D1>   D1> C9>   3?C  C53   D1>   3C3   3?D   C9>    C9> 3?C   3?C   3?C  C9> C9>   3?C 3?C      3?C D1>     3?C  3?C  3?C    C9>  Turunan Fungsi-Fungsi Tertentu   45>71>141<18;?>CD1>D1             C9>   3?C    3?C    C9>    D1>   C53            <>     Rumus-Rumus Integrasi                   212        3?C   C9>   C9>    3?C             <>  Mudah dan Aktif Belajar Fisika untuk Kelas XI  Satuan-Satuan Dasar *1>:1>7 /1;DE '1CC1 '5D5B=141<18:1B1;H1>749D5=@E8?<58 3181H1 49 BE1>7 F1;E= 41<1= G1;DE BEC C5;?>    +5;?> C 141<18 G1;DE H1>7 49@5B E>DE;      C9;725B8E2E>71>45>71>DB1>C9C91>D1B1 4E1D9>7;1D89@5B69>45>71>;51411>41C1B @1411D?= C %941B #>D5B>1C9?>1<E>DE;2?2?D41>E;EB1>H1>7 49C9=@1>49+5FB5C*B1>39C =@5B5141<181BEC@1414E1;1G1D @1>:1>7@1B1<5<H1>7D5B@9C18C5:1E8 =41> =5>9=2E<;1> 71H1 =17>5D9; @5BC1DE1> @1>:1>7C525C1BN M( = ,5=@5B1DEB %5%141<18   41B9D5=@5B1DEB D5B=?49>1=9;1@141  #>D5>C9D1C 1>45<134141<189>D5>C9D1C3181H141<1= 3181H1 1B18D571;25>4189D1= C5E=45>71>D5;1>1> 1D= Satuan-Satuan Turunan !1H1 %5B:1>5B79 1H1 B5;E5>C9 'E1D1><9CDB9; *?D5>C91<<9CDB9; >5GD?>( :?E<5$ G1DD/ 85BDI"I 3?E<9CDB9; %1@1C9D1C<9CDB9; '541>=17>5D 5D #>4E;D1>C9  = C N ;7 N =   =9<  N = C ;/ = ,5;1>1> ?8=   61B14  D5C<1, G525B/2 85>BH"   .     . , ( = /2 ,= " $  Data Terestrial *5B35@1D1>7B1F9D1C9 '1CC1E=9  $1B9 :1B9E=9 B1D1 B1D1 %535@1D1><5@1C    %?>CD1>D1'1D181B9 +E8E41>D5;1>1>CD1>41B+,* ,5=@5B1DEB  ;*1  1D= '1CC1=?<1BE41B1 7 =?< ;7 = '1CC1:5>9CE41B1+,* E41B1 %535@1D1>CE1B1+,*  = C %17E1@1>19B K 1D= '$ ;7  % 1H1B1D1 B1D1H1>7D5B:149@141 =49D1B1E=941>'1D181B9 Data Astronomi '  $1B1;;5E<1> $1B1;;5'1D181B9B1D1 B1D1 %535@1D1>?B29DB1D1 B1D1 &$ '1CC1 $1B9 :1B9  N = N =9< N =  N = C '! '1CC1 $1B9 :1B9 *5B9?45 *5B35@1D1>7B1F9D1C9@141 @5B=E;11> N ;7 N = 81B9 = C N ;7 N = @EC1D;5@EC1D Apendiks 213 Konstanta Fisika %?>CD1>D17B1F9D1C9 %535@1D1>3181H1 'E1D1>5<5;DB?> %?>CD1>D1F?714B? %?>CD1>D171C %?>CD1>D1?> ->9D=1CC1D5B@14E %?>CD1>D1?E781=@1  *5B=5129<9D1CBE1>781=@1  %?>CD1>D1*<1>3;   '1CC15<5;DB?> 5 '1CC1@B?D?> @ '1CC1>5EDB?> > N M  (= N M(  N M$C  N M$C  N M ;7 N M;7 N M;7 Faktor-Faktor Konversi !! ;=  =9< =9<  ;= =  H4 6D9>39 9>393= 6D 9>39 3= H46D 3=  D18E>3181H1 3D18E> N = ?     >= '% = 3= ;=  =9< 81 9>39 3= 6DN M= = 6D 81 6D #=9< 81 ;= "'  = 3= & 3= M= 71<& 71<AD@D ?I 9>39 9>39 3= 6D 9>39&N 3= &' :1= =5>9D;C 81B9:1=  =5>9D;C D18E>81B9 'C #&! ;= :1= = C  =9< :1= =9< :1=  = C  ;= :1= =9< :1= 6D C ''&! #&!''& B14  K B14 K K N MB14 B5F =5>9D  B14 C B14 CB5F =5>9D 214 Mudah dan Aktif Belajar Fisika untuk Kelas XI %% ;7 7 D?> ;7 '7 E  N M;7 ;7 N E C5 <2(  ;7 <2 !! *1 ( = 1D= ;*1  21B 1D= <2 9>39 =="7 D?BB =="7 *1 21B ;*1 !$ ;/8'$ ;1< $ &1D= $ ;1< DE6D<2;1< $ 5.  N M $ E  '5. 5B7 M$ ) 41H1;E41 6D<2 C/ DE =5>9D / /  N M41H1;E41 6D<2 C ! !& ! M, , ! "!'&(&%$  / =%DE9>39 :1=6DK DE9>39 :1=6DK    / =% Senarai A  #&'" C9=@1>71>D5B:1E8@141CE1DE?C9<1C9 1HE>1> %&$"!"  9<=E@5B29>D1>71> )'!!%& 1HE>1>H1>725B6E>7C9E>DE;=5>7E;EB ;535@1D1>75B1;@541H1>725>DE;41>E;EB1>>H1491219;1> !&$ 25>41H1>725>DE;41>E;EB1>>H149@5B 81D9;1> %$!%$ 25C1B1>H1>781>H1=5=9<9;9>9<19 %$!(&"$ 25C1B1>H1>7=5=9<9;9>9<1941>1B18 E %!% %! E;EB1>;9>5B:1C52E18=5C9>H1>7=5BE @1;1>@5B21>49>71>1>D1B15>5B79H1>74981C9<;1> D5B8141@5>5B79H1>74925B9;1> %&%&% ;5=1=@E1>H1>749=9<9;9?<5825>41E>DE; ;5=21<9;525>DE;C5=E<1C5D5<18=5>71<1=971>7 7E1>25>DE; !$!& 5>5B79H1>749=9<9;925>41;1B5>175B1; 1>>H1 !$ ! D?D1<5>5B79;9>5D9;41>5>5B79@?D5>C91< 41B925>41 !$ #"&!% 5>5B79 H1>7 49=9<9;9 25>41 ;1B5>1 ;54E4E;1>>H1 F $'!% :E=<181HE>1> ?C9<1C9H1>7D5B:149@141:1>7;1 G1;DEC1DE45D9; G )% 71H1D1B9; =5>1B9;1>D1B1@1BD9;5<D941; C5:5>9C )%!& 71H175C5;H1>7D9=2E<@141C11D 25>41D5<1825B75B1; ) % %&&% 71H1 75C5; H1>7 D9=2E< @141 C11D 25>41=1C98491= )"% 71H1D1B9; =5>1B9;1>D1B1@1BD9;5<C5:5>9C )"!%$(& 71H1H1>781C9<EC181>H181>H1=5= @5B81D9;1>;54E4E;1>1G1<41>1;89B #$&% 75:1<1>19;>H1I1D319B@141@9@1 @9@1 ;1@9<5B H "%!&$% @1>41>71>H1>7=5>71>771@218G1'1D181B9 141<18@EC1D41B9@5B541B1>25>41<1>79D K $'$&"$ D12E>7@5>31=@EB2181>21;1B@141;5> 41B11>25B=?D?B #&!&$ ! ;535@1D1>;?>CD1>H1>749=9<9;9?<58 25>41H1>7:1DE841<1=CE1DE67=5=9<9;9 ;5;5>D1<1> M !" &$ 1<1DE>DE;=5>7E;EBC5<9C98D5;1>1>I1D319B !%'% '! 25>DE; @5B=E;11> I1D 319B H1>7 35;E>7;5D9;125B14141<1=CE1DEG1418 !%'%  '! 25>DE; @5B=E;11> I1D 319B H1>7 35=2E>7;5D9;125B14141<1=CE1DEG1418 P $""$&%&& G1;DEH1>7492EDE8;1>?<58C1D5<9D E>DE;25B541B@141?B29D>H1C521>H1;C1DE;1<9@E D1B1> $"%%& @B?C5CH1>7D5B:149@141;51411>;17 D5B:149 @141 ;51411> D5;1>1>D5D1@ $"%% %""$ @B?C5C H1>7 D5B:149 @141 ;51411> F?7D5B:149@141;51411>CE8E D5D1@ R $$&"$ =5C9>@5>49>79> %'&! ) 71H1 D?D1< 81C9< @5>:E=<181> 41B9 2525B1@171H1       ;5B5D1=19>1>H1>7=5=1>611D;1>@B9>C9@ ;5;5;1<1>5>5B79=5;1>9;25>41 "&% @5B@ED1B1>25>41@141@?B?C>H1 S %& &$%"% C9CD5=H1>7D941;=5>79I9>;1>@5BDE;1B 1>=1D5B941>;171><9>7;E>71>>H1    B571>71>    D571>71> ''&(% CE4EDH1>74925>DE;?<581B18;535@1D1>1G1< 25>4145>71>1B188?B9I?>D1<@14175B1;@1B12?<1 T !!$"%&& D5;1>1>H1>7491<1=9I1D319B@141 ;541<1=1>D5BD5>DE & "'% #% D9D9; @141 :1B1; C5D5>718 :1B9 :1B9 D5B@1>:1>7@1415<9@C "$% 25C1B1>H1>7=5>H5212;1>25>41D571B35>45BE>7 E>DE;25B?D1C9@141@?B?C>H1 $!%% @5B75C5B1> V !&'$ &$ 1<1DE>DE;=5>7E;EB;535@1D1>1<9B1>71C %"%&% ;5;5>D1<1>I1D319B 215 Indeks 1@85<9?> 25>41D571B            25B1D                                    41H1;E41 45B1:1D;52521C1>      569C95>C9         5<9@C   5>5B79;9>5D9;                                       5>5B79@?D5>C91<            5>DB?@9  6B5;E5>C9  71C9451<                                   71H175C5;     71H1;?85C9     71H1;?>C5BF1D96  71H1C5>DB9@5D1<  "E;E=?H<5         "E;E=##,5B=?49>1=9;1  "E;E=%5;5;1<1>>5B79           "E;E=%5;5;1<1>>5B79'5;1>9;      "E;E=%5;5;1<1>'?=5>DE=             "E;E=%5;5;1<1>'?=5>DE=+E4ED      216 Mudah dan Aktif Belajar Fisika untuk Kelas XI "E;E=#,5B=?49>1=9;1   9=@ED57B1C9   :1DE82521C        :?E<5                        ;11C  ;1@9<1B9D1C      ;535@1D1>B1D1 B1D1     ;535@1D1>C5C11D   ;535@1D1>D5B=9>1<     ;5<1:E1>B1D1 B1D1  ;5<1:E1>C5C11D ;5<5=21=1>  ;5=9B9>71>               ;5B:1                    ;?565C95>B5CD9DEC9  ;?>CD1>D17B1F9D1C9E>9F5BC1<  <1:E1<9B1>     <5>71>         =1CC1                                                                                 =541>7B1F9D1C9  =5C9> 1B>?D             =?=5>9>5BC91                  =?=5>DE=CE4ED          @1>1C                   @1BD9;5<                                         *1C31<        @5B35@1D1>1>7E<1B @5B35@1D1>B1D1 B1D1    @5B35@1D1>C5>DB9@5D1< @5B35@1D1>C5C11D    @5B985<9?> @5B9?45     @5B;1<91>F5;D?B  @5B@9>4181>          *5BC1=11>5B>?E<<9          *5BC1=11>%?>D9>E9D1C          *B9>C9@*1C31<  @B?C5C149121D9;               @EC1D25B1D  @EC1D=1CC1       B56B975B1D?B  B571>71>   +9;?D     C;1<1B  D571>71>@5B=E;11>           D5;1>1>                                                            D5=@5B1DEB             ,5?B9%9>5D9;!1C    ,5B=?49>1=9;1               D?BC9            F5;D?B                    F5;D?B;535@1D1>B1D1 B1D1 F5;D?B@5B@9>4181> F5;D?B@?C9C9   F5;D?BC1DE1> G1DD     Indeks 217 Daftar Pustaka Allonso, M. and Finn 1980. Fundamental Physics, Vol 1and 2. New York: Addision-Wesley Publishing Company Inc. Biryam, M 1992. Hukum-Hukum Kekekalan dalam Mekanika. Jakarta: Departemen Pendidikan dan Kebudayaan. Bueche, Fredrick 1982. Introduction to Physics for Scientist and Insights. New York: Mc Grow Hill Book Company Inc. Dorling Kindsley 1995. Jendela IPTEK, seri 1-4. Jakarta: Balai Pustaka Jakarta. Giancoli, Douglas C. 2000. Physics, 3rd Edition. USA: PrenticeHall International. Grolier International Inc. 1995. Oxford Ensiklopedi Pelajar. Jakarta: PT. Widyadara. Haliday, D, R. Resnick, J. Waker. 2001. Fundamental of Physics, Sixth Edition. USA: John Willey and Sons Inc. Harsanto. 1980. Motor Bakar. Jakarta: Djambatan. Hermawan Edi. 2004. Radar Atmosfer Khatulistiwa. Surakarta: Pabelan. Hewwit, Paul G. 1993. Conceptual Physics, 6th Edition. USA: Harper Collins College Publisher. Hewwit, Paul G. 1998. Conceptual Physics, 8th Edition. USA: Addison Wesley Publishing Company Inc. Kamus Besar Bahasa Indonesia, cetakan ketiga. 2005. Jakarta: PT. Balai Pustaka. Kamus Fisika, cetakan kedua. 2003. Jakarta: PT. Balai Pustaka. Sears, F.W. et.al. 1993. University Physics. USA: Addison Wesley Publishing Company Inc. Tipler, Paul. 1998. Fisika untuk Sains dan Teknik, Jilid 1 (alih bahasa: Prasetyo dan Rahmad W. Adi). Jakarta: Erlangga. Tipler, Paul. 2001. Fisika untuk Sains dan Teknik, Jilid 2 (alih bahasa: Bambang Soegijono). Jakarta: Erlangga. Young, Hugh D. dan Freadman, Roger A. 2001. Fisika Universitas, edisi X. Jakarta: Erlangga. 218 Mudah dan Aktif Belajar Fisika untuk Kelas XI ISBN 978-979-068-816-2 (No. Jld lengkap) ISBN 978-979-068-818-6 Harga Eceran Tertinggi (HET) Rp.14.468,-
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