tag:blogger.com,1999:blog-16692272465326924362024-03-19T14:20:03.578-07:00Bermain Fisikanopinophttp://www.blogger.com/profile/07944999515934940876noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-1669227246532692436.post-69700985813605283522011-11-05T06:14:00.000-07:002011-11-05T06:14:37.608-07:00Biografi Albert EinstenAlbert Einstein (14 Maret 1879–18 April 1955) adalah seorang ilmuwan fisika teoretis yang dipandang luas sebagai ilmuwan terbesar dalam abad ke-20. Dia mengemukakan teori relativitas dan juga banyak menyumbang bagi pengembangan mekanika kuantum, mekanika statistik, dan kosmologi. Dia dianugerahi Penghargaan Nobel dalam Fisika pada tahun 1921 untuk penjelasannya tentang efek fotoelektrik dan "pengabdiannya bagi Fisika Teoretis".<br />
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Setelah teori relativitas umum dirumuskan, Einstein menjadi terkenal ke seluruh dunia, pencapaian yang tidak biasa bagi seorang ilmuwan. Di masa tuanya, keterkenalannya melampaui ketenaran semua ilmuwan dalam sejarah, dan dalam budaya populer, kata Einstein dianggap bersinonim dengan kecerdasan atau bahkan jenius. Wajahnya merupakan salah satu yang paling dikenal di seluruh dunia.<br />
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Pada tahun 1999, Einstein dinamakan "Orang Abad Ini" oleh majalah Time. Kepopulerannya juga membuat nama "Einstein" digunakan secara luas dalam iklan dan barang dagangan lain, dan akhirnya "Albert Einstein" didaftarkan sebagai merk dagang. Untuk menghargainya, sebuah satuan dalam fotokimia dinamai einstein, sebuah unsur kimia dinamai einsteinium, dan sebuah asteroid dinamai 2001 Einstein.<br />
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<span style="font-weight: bold;">1. Masa muda dan universitas</span><br />
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Einstein dilahirkan di Ulm di Württemberg, Jerman; sekitar 100 km sebelah timur Stuttgart. Bapaknya bernama Hermann Einstein, seorang penjual ranjang bulu yang kemudian menjalani pekerjaan elektrokimia, dan ibunya bernama Pauline. Mereka menikah di Stuttgart-Bad Cannstatt. Keluarga mereka keturunan Yahudi; Albert disekolahkan di sekolah Katholik dan atas keinginan ibunya dia diberi pelajaran biola. Pada umur lima, ayahnya menunjukkan kompas kantung, dan Einstein menyadari bahwa sesuatu di ruang yang "kosong" ini beraksi terhadap jarum di kompas tersebut; dia kemudian menjelaskan pengalamannya ini sebagai salah satu saat yang paling menggugah dalam hidupnya. Meskipun dia membuat model dan alat mekanik sebagai hobi, dia dianggap sebagai pelajar yang lambat, kemungkinan disebabkan oleh dyslexia, sifat pemalu, atau karena struktur yang jarang dan tidak biasa pada otaknya (diteliti setelah kematiannya).<br />
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Dia kemudian diberikan penghargaan untuk teori relativitasnya karena kelambatannya ini, dan berkata dengan berpikir dalam tentang ruang dan waktu dari anak-anak lainnya, dia mampu mengembangkan kepandaian yang lebih berkembang. Pendapat lainnya, berkembang belakangan ini, tentang perkembangan mentalnya adalah dia menderita Sindrom Asperger, sebuah kondisi yang berhubungan dengan autisme. Einstein mulai belajar matematika pada umur dua belas tahun. Ada gosip bahwa dia gagal dalam matematika dalam jenjang pendidikannya, tetapi ini tidak benar; penggantian dalam penilaian membuat bingung pada tahun berikutnya. Dua pamannya membantu mengembangkan ketertarikannya terhadap dunia intelek pada masa akhir kanak-kanaknya dan awal remaja dengan memberikan usulan dan buku tentang sains dan matematika. Pada tahun 1894, dikarenakan kegagalan bisnis elektrokimia ayahnya, Einstein pindah dari Munich ke Pavia, Italia (dekat Milan). Albert tetap tinggal untuk menyelesaikan sekolah, menyelesaikan satu semester sebelum bergabung kembali dengan keluarganya di Pavia. Kegagalannya dalam seni liberal dalam tes masuk Eidgenössische Technische Hochschule (Institut Teknologi Swiss Federal, di Zurich) pada tahun berikutnya adalah sebuah langkah mundur;j dia oleh keluarganya dikirim ke Aarau, Swiss, untuk menyelesaikan sekolah menengahnya, di mana dia menerima diploma pada tahun 1896, Einstein beberapa kali mendaftar di Eidgenössische Technische Hochschule. Pada tahun berikutnya dia melepas kewarganegaraan Württemberg, dan menjadi tak bekewarganegaraan.<br />
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Pada 1898, Einstein menemui dan jatuh cinta kepada Mileva Maric, seorang Serbia yang merupakan teman kelasnya (juga teman Nikola Tesla). Pada tahun 1900, dia diberikan gelar untuk mengajar oleh Eidgenössische Technische Hochschule dan diterima sebagai warga negar Swiss pada 1901. Selama masa ini Einstein mendiskusikan ketertarikannya terhadap sains kepada teman-teman dekatnya, termasuk Mileva. Dia dan Mileva memiliki seorang putri bernama Lieserl, lahir dalam bulan Januari tahun 1902. Lieserl, pada waktu itu, dianggap tidak legal karena orang tuanya tidak menikah.<br />
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<span style="font-weight: bold;">2. Kerja dan Gelar Doktor</span><br />
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Pada saat kelulusannya Einstein tidak dapat menemukan pekerjaan mengajar, keterburuannya sebagai orang muda yang mudah membuat marah professornya. Ayah seorang teman kelas menolongnya mendapatkan pekerjaan sebagai asisten teknik pemeriksa di Kantor Paten Swiss dalah tahun 1902. Di sana, Einstein menilai aplikasi paten penemu untuk alat yang memerlukan pengatahuan fisika. Dia juga belajar menyadari pentingnya aplikasi dibanding dengan penjelasan yang buruk, dan belajar dari direktur bagaimana "menjelaskan dirinya secara benar". Dia kadang-kadang membetulkan desain mereka dan juga mengevaluasi kepraktisan hasil kerja mereka. Einstein menikahi Mileva pada 6 Januari 1903. Pernikahan Einstein dengan Mileva, seorang matematikawan, adalah pendamping pribadi dan kepandaian; Pada 14 Mei 1904, anak pertama dari pasangan ini, Hans Albert Einstein, lahir. Pada 1904, posisi Einstein di Kantor Paten Swiss menjadi tetap. Dia mendapatkan gelar doktor setelah menyerahkan thesis "Eine neue Bestimmung der Moleküldimensionen" ("On a new determination of molecular dimensions") dalam tahun 1905 dari Universitas Zürich.<br />
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Di tahun yang sama dia menulis empat artikel yang memberikan dasar fisika modern, tanpa banyak sastra sains yang dapat ia tunjuk atau banyak kolega dalam sains yang dapat ia diskusikan tentang teorinya. Banyak fisikawan setuju bahwa ketiga thesis itu (tentang gerak Brownian), efek fotoelektrik, dan relativitas spesial) pantas mendapat Penghargaan Nobel. Tetapi hanya thesis tentang efek fotoelektrik yang mendapatkan penghargaan tersebut. Ini adalah sebuah ironi, bukan hanya karena Einstein lebih tahu banyak tentang relativitas, tetapi juga karena efek fotoelektrik adalah sebuah fenomena kuantum, dan Einstein menjadi terbebas dari jalan dalam teori kuantum. Yang membuat thesisnya luar biasa adalah, dalam setiap kasus, Einstein dengan yakin mengambil ide dari teori fisika ke konsekuensi logis dan berhasil menjelaskan hasil eksperimen yang membingungkan para ilmuwan selama beberapa dekade. Dia menyerahkan thesis-thesisnya ke "Annalen der Physik". Mereka biasanya ditujukan kepada "Annus Mirabilis Papers" (dari Latin: Tahun luar biasa). Persatuan Fisika Murni dan Aplikasi (IUPAP) merencanakan untuk merayakan 100 tahun publikasi pekerjaan Einstein di tahun 1905 sebagai Tahun Fisika 2005.<br />
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<span style="font-weight: bold;">3. Gerakan Brownian</span><br />
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Di artikel pertamanya di tahun 1905 bernama "On the Motion—Required by the Molecular Kinetic Theory of Heat—of Small Particles Suspended in a Stationary Liquid", mencakup penelitian tentang gerakan Brownian. Menggunakan teori kinetik cairan yang pada saat itu kontroversial, dia menetapkan bahwa fenomena, yang masih kurang penjelasan yang memuaskan setelah beberapa dekade setlah ia pertama kali diamati, memberikan bukti empirik (atas dasar pengamatan dan eksperimen) kenyataan pada atom. Dan juga meminjamkan keyakinan pada mekanika statistika, yang pada saat itu juga kontroversial. Sebelum thesis ini, atom dikenal sebagai konsep yang berguan, tetapi fisikawan dan kimiawan berdebat dengan sengit apakah atom benar suatu benda yang nyata. Diskusi statistik Einstein tentang kelakuan atom memberikan pelaku eksperimen sebuah cara untuk menghitung atom hanya dengan melihat melalui mikroskop biasa. Wilhelm Ostwald, seorang pemimpin sekolah anti-atom, kemudian memberitahu Arnold Sommerfeld bahwa ia telah berkonversi kepada penjelasan komplit Einstein tentang gerakan Brownian.<br />
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<a href="http://elektrokita.blogspot.com/2008/10/biografi-albert-einstein.html"><span style="font-weight: bold;">biografia de albert einstein</span></a> sumber : <a href="http://www.wikipedia.net/">wikipedia</a></div>nopinophttp://www.blogger.com/profile/07944999515934940876noreply@blogger.com0tag:blogger.com,1999:blog-1669227246532692436.post-8663991621164346962011-10-01T00:59:00.001-07:002011-10-01T19:07:58.310-07:00GRAVITASI<m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"></m:narylim></m:intlim></m:wrapindent><br />
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<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Sir Isaac Newton yang terkenal dengan hukum-hukum Newton I, II dan III, juga terkenal dengan hukum <i>Grafitasi Umum</i>. Didasarkan pada partikel-partikel bermassa senantiasa mengadakan gaya tarik menarik sepanjang garis yang menghubungkannya, Newton merumuskan hukumnya tentang grafitasi umum yang menyatakan :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><i><span style="font-size: 12pt; line-height: 125%;">Gaya antara dua partikel bermassa m<sub>1</sub> dan m<sub>2</sub> yang terpisah oleh jarak r adalah gaya tarik menarik sepanjang garis yang menghubungkan kedua partikel tersebut, dan besarnya dapat dinyatakan dengan persamaan :</span></i></div><div class="MsoNormal" style="line-height: 125%; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqoMyz0YZpIEAhRvy0teKH3k9Jbmpjqdamyg8DeNgJ6ImbC7d1HbdG3PQEst43-gd5Pd0X2oDlFK7ig1TIs0Cn8ZQksLMRwqVfWmkoju0JddO1H2rVW0HYd4lIxggs8B6ZbWO2Ec2mgtoI/s1600/1.bmp" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqoMyz0YZpIEAhRvy0teKH3k9Jbmpjqdamyg8DeNgJ6ImbC7d1HbdG3PQEst43-gd5Pd0X2oDlFK7ig1TIs0Cn8ZQksLMRwqVfWmkoju0JddO1H2rVW0HYd4lIxggs8B6ZbWO2Ec2mgtoI/s1600/1.bmp" /></a><i><span style="font-size: 12pt; line-height: 125%;"> </span></i></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">F = Gaya grafitasi, satuan : </span>NEWTON<span style="font-size: 12pt; line-height: 125%;">.</span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">G = Konstanta grafitasi, besarnya :</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUa8du2ZvzhQCBWGnQOuwkRj0dMS834j_3k_rewmLGUHOVIjKezh7o7s0H7Mzpc0ZFiFbzb2OpB1o-cX8wbdqysvKolQulWWBjtbLcyv5PQvjjZlTfFByUckhty3ldB9MysaD_Ob8r2ceF/s1600/2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUa8du2ZvzhQCBWGnQOuwkRj0dMS834j_3k_rewmLGUHOVIjKezh7o7s0H7Mzpc0ZFiFbzb2OpB1o-cX8wbdqysvKolQulWWBjtbLcyv5PQvjjZlTfFByUckhty3ldB9MysaD_Ob8r2ceF/s1600/2.bmp" /></a></div><br />
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<div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> </span> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><br />
<div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">m = massa benda, satuan : </span>KILOGRAM</div><div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">r = jarak antara kedua partikel, satuan : </span>METER</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Gaya grafitasi adalah besaran vektor yang arahnya senantiasa menuju pusat massa partikel.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjabKXAj_Z-Pj4D0SHzL8B8H2WFZ0hDvdN2hitD65YKxu3wAgpP7_dsObfu86M9oJ3dP96neml_1TXnowmot2VNI3ZHLQKkDMbcKVubn7BNFYm385tz0mOBrhM1x4ASB_LWm4XEN2sYUFUI/s1600/3.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjabKXAj_Z-Pj4D0SHzL8B8H2WFZ0hDvdN2hitD65YKxu3wAgpP7_dsObfu86M9oJ3dP96neml_1TXnowmot2VNI3ZHLQKkDMbcKVubn7BNFYm385tz0mOBrhM1x4ASB_LWm4XEN2sYUFUI/s1600/3.bmp" /></a></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Untuk gaya grafitasi yang disebabkan oleh beberapa massa tertentu, maka resultan gayanya ditentukan secara geometris. Misalnya dua buah gaya F<sub>1</sub> dan F<sub>2</sub> yang membentuk sudut </span><span style="position: relative; top: 3pt;"><img height="15" src="file:///C:/DOCUME%7E1/2ITCEN%7E1/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif" width="16" /></span><span style="font-size: 12pt; line-height: 125%;">resultante gayanya dapat ditentukan berdasarkan persamaan :</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhw6-s97tQ9CZz0VW2_1XkQgo0zz8M8Flb9rOopIbbAJZLawe92JEl3_zv9ag16WZ9nzswzpKqWRb_hcpmc2tkGj94fVU5ebjum4BdYPUfHToGju9Gc2YiAKPDUkEqwV4MIaxx6iPp_tHW6/s1600/4.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhw6-s97tQ9CZz0VW2_1XkQgo0zz8M8Flb9rOopIbbAJZLawe92JEl3_zv9ag16WZ9nzswzpKqWRb_hcpmc2tkGj94fVU5ebjum4BdYPUfHToGju9Gc2YiAKPDUkEqwV4MIaxx6iPp_tHW6/s1600/4.bmp" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyPf86H4Z27MB3_VGr26XMNakPzNy7OL9-B6KSDYxj9roBOObTtUwBw8zRiKErsymLMohrgR61TSgB0G_3t8DBQcU2y4-dBIFfs93GQ8ICkk_hI37RA5_cMv_0D82IDFU04l6KTfEAotER/s1600/5.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="102" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyPf86H4Z27MB3_VGr26XMNakPzNy7OL9-B6KSDYxj9roBOObTtUwBw8zRiKErsymLMohrgR61TSgB0G_3t8DBQcU2y4-dBIFfs93GQ8ICkk_hI37RA5_cMv_0D82IDFU04l6KTfEAotER/s400/5.bmp" width="400" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> </span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> </span> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><b><u><span style="font-size: 14pt; letter-spacing: 1pt; line-height: 125%;">MEDAN GRAVITASI</span></u></b></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Kuat medan grafitasi ( intensitas grafitasi ) oleh gaya grafitasi didefinisikan sebagai :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><i><span style="font-size: 12pt; line-height: 125%;">Perbandingan antara gaya grafitasi yang dikerjakan oleh medan dengan massa yang dipengaruhi oleh gaya grafitasi tersebut.</span></i></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Dalam bentuk persamaan, dapat dinyatakan dengan :</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicZszXxYxUtNTBrzjOpw7swfgPcO7N472us9IcLaoCgkteRGUSg-DSORjijClVdbtg-rJYerhRSA1_riy7hilCNGzjbmjy-dym1-iV0wymR4KCtaml7pAAbqnlpAB7hyphenhyphenfp7VC14ZsMzqJu/s1600/7.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicZszXxYxUtNTBrzjOpw7swfgPcO7N472us9IcLaoCgkteRGUSg-DSORjijClVdbtg-rJYerhRSA1_riy7hilCNGzjbmjy-dym1-iV0wymR4KCtaml7pAAbqnlpAB7hyphenhyphenfp7VC14ZsMzqJu/s1600/7.bmp" /></a></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">g = kuat medan grafitasi ; satuan : N.kg<sup>-1</sup></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">F = Gaya grafitasi satuan : N</span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">m = Massa benda satuan : kg</span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 2in;"><b><span style="font-size: 12pt; line-height: 125%;"><br />
</span></b></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></b></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <b><m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent></b> <div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u>KUAT MEDAN GRAVITASI OLEH BENDA BERMASSA</u></b><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Kuat medan grafitasi dapat ditimbulkan oleh suatu benda bermassa. Misalkan dua buah benda bermassa masing-masing m dan m’ terpisah pada jarak r. Maka gaya grafitasi oleh kedua benda itu adalah :</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqoMyz0YZpIEAhRvy0teKH3k9Jbmpjqdamyg8DeNgJ6ImbC7d1HbdG3PQEst43-gd5Pd0X2oDlFK7ig1TIs0Cn8ZQksLMRwqVfWmkoju0JddO1H2rVW0HYd4lIxggs8B6ZbWO2Ec2mgtoI/s1600/1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqoMyz0YZpIEAhRvy0teKH3k9Jbmpjqdamyg8DeNgJ6ImbC7d1HbdG3PQEst43-gd5Pd0X2oDlFK7ig1TIs0Cn8ZQksLMRwqVfWmkoju0JddO1H2rVW0HYd4lIxggs8B6ZbWO2Ec2mgtoI/s1600/1.bmp" /></a></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfG4nxnYz3cb7wHgSPkZhnXZtrFSH_TfO1rF2OIGJPBXx0oWL6HbcZ2NSRdswaBZctCMHb4mN9Sk5kGrF6PZ_yA872FvJ2miJI4ruWgynfs8uuPp_GXEt6bEjHWQ_Mu5bbpTfC78FTLT9y/s1600/9.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Bila kita hitung kuat medan grafitasi yang dilami oleh massa m’ sebagai akibat dari gaya grafitasi di atas, maka di peroleh : </span></div><div class="MsoNormal" style="line-height: 125%; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfG4nxnYz3cb7wHgSPkZhnXZtrFSH_TfO1rF2OIGJPBXx0oWL6HbcZ2NSRdswaBZctCMHb4mN9Sk5kGrF6PZ_yA872FvJ2miJI4ruWgynfs8uuPp_GXEt6bEjHWQ_Mu5bbpTfC78FTLT9y/s1600/9.bmp" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfG4nxnYz3cb7wHgSPkZhnXZtrFSH_TfO1rF2OIGJPBXx0oWL6HbcZ2NSRdswaBZctCMHb4mN9Sk5kGrF6PZ_yA872FvJ2miJI4ruWgynfs8uuPp_GXEt6bEjHWQ_Mu5bbpTfC78FTLT9y/s1600/9.bmp" /> </a></div><div class="MsoNormal" style="line-height: 125%; text-align: center;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: center;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Persamaan di atas menunjukkan kuat medan grafitasi oleh benda bermassa m pada suatu titik berjarak r dari benda itu.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Kuat medan grefitasi adalah suatu besaran vektor yang arahnya senantiasa menuju ke pusat benda yang menimbulkannya. Karena : kuat medan grafitasi di suatu titik oleh beberapa benda bermassa diperoleh dengan menjumlahkan vektor-vektor medan grafitasi oleh tiap-tiap benda.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Sebagai contoh : Kuat medan grafitasi yang disebabkan oleh kedua dua buah benda yang kuat medannya saling membentuk sudut </span><span style="font-family: Symbol; font-size: 12pt; line-height: 125%;">a</span><span style="font-size: 12pt; line-height: 125%;">, dapat dinyatakan dengan persamaan :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRxJMEqQ0ptZY7SGCVxQ1pG65pp1VOnXZ5vXkig7Mp86EC3VH78I-VmF2ZsFRmH6Aasdt6zOLxZooSnumIO_FlsBfHVNPHugeCJkBqsjtfVNAftJx-xSJpGGxBFbhccZX1QLcO8hy2OcJg/s1600/10.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRxJMEqQ0ptZY7SGCVxQ1pG65pp1VOnXZ5vXkig7Mp86EC3VH78I-VmF2ZsFRmH6Aasdt6zOLxZooSnumIO_FlsBfHVNPHugeCJkBqsjtfVNAftJx-xSJpGGxBFbhccZX1QLcO8hy2OcJg/s1600/10.bmp" /> </a></div><div class="separator" style="clear: both; text-align: center;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><b><u><span lang="SV" style="font-size: 14pt; letter-spacing: 1pt; line-height: 125%;">ENERGI POTENSIAL GRAVITASI</span></u></b><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Benda bermassa m yang terletak diluar bumi, energi potensial grafitasinya pada jarak r dari pusat bumi, dinyatakan dengan persamaan :</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxrS2X4JA8VT8BRMTqhiRDKyviTWYvSzm2CcDQWLY4GTd0hleWhACl6oqrRec7ryYbOwi9Za1RuBdOjakycFGFOYWWBAqJ3-5G_B-w4uRdQ9JdXI9lx-QKkUjxKusoOqPqgIK1jnolLx9C/s1600/1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxrS2X4JA8VT8BRMTqhiRDKyviTWYvSzm2CcDQWLY4GTd0hleWhACl6oqrRec7ryYbOwi9Za1RuBdOjakycFGFOYWWBAqJ3-5G_B-w4uRdQ9JdXI9lx-QKkUjxKusoOqPqgIK1jnolLx9C/s1600/1.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"> </span><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="NO-BOK" style="font-size: 12pt; line-height: 125%;">Ep = Energi potensial grafitasi<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">G = Konstanta grafitasi<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">M = massa bumi <o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">m = massa benda<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">r = Jarak pusat benda ke pusat bumi.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Tanda negatif (-) berarti jika benda bergerak di bawah pengaruh gaya grafitasi dari jarak tak terhingga (</span><span style="font-family: Symbol; font-size: 12pt; line-height: 125%;"><span>¥</span></span><span lang="SV" style="font-size: 12pt; line-height: 125%;">) ke jarak r maka energi potensialnya akan berkurang, karena dipergunakan untuk menambah energi kinetik dengan makin besarnya laju benda waktu bergerak mendekati bumi.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Jika mula-mula benda berada di tempat yang jauh tak hingga ( r = </span><span style="font-family: Symbol; font-size: 12pt; line-height: 125%;"><span>¥</span></span><span lang="SV" style="font-size: 12pt; line-height: 125%;"> ) dengan energi kinetik sama dengan nol, maka dalam perjalanan mendekati bumi, medan grafitasi merubah energi potensial menjadi energi kinetik. Pada waktu sampai di bumi energi kinetik benda sama dengan energi potensial grafitasi. Jadi :</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqnvfp3P_1WWqvEhwnszU6zvagmUvoyka6Yrg5_4S55di762qrid5ByvlqH1zOlYNv0exXd-j0eL9sWtS80g57OLLGjehFexhaRbrZYIfJ-dS6sqhMldDgRC2lxaI4pd8QSB10nzeuij3M/s1600/2.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><o:smarttagtype name="City" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:smarttagtype><o:smarttagtype name="place" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:smarttagtype><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><!--[if !mso]><img src="http://img2.blogblog.com/img/video_object.png" style="background-color: #b2b2b2; " class="BLOGGER-object-element tr_noresize tr_placeholder" id="ieooui" data-original-id="ieooui" /> <style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><u><span style="letter-spacing: 1pt;">HUKUM KEKEKALAN ENERGI</span></u><span style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Hukum kekekalan energi mekanik total berlaku untuk <st1:city w:st="on"><st1:place w:st="on">medan</st1:place></st1:city> grafitasi dan harganya adalah :<o:p></o:p></span></div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><div class="separator" style="clear: both; text-align: center;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfRIAbRI7nbHCLRjB4MXp4GG-2lRCGsDRZRs34NJ8QjcgCjkVcUkgGW5IBFFclE0kaQcCxpeAvBsLOXxM5qDrAj9b2uXGgtIpcgCnQoYWFaBnSHi45vjPgZUIe3_N5fV3p5SvvcTyeZz2c/s1600/3.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfRIAbRI7nbHCLRjB4MXp4GG-2lRCGsDRZRs34NJ8QjcgCjkVcUkgGW5IBFFclE0kaQcCxpeAvBsLOXxM5qDrAj9b2uXGgtIpcgCnQoYWFaBnSHi45vjPgZUIe3_N5fV3p5SvvcTyeZz2c/s1600/3.bmp" /></a></div><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Kita dapat mendefinisikan energi potensial sebagai berikut : Jika Ep(A)= energi potensial di titik A dan Ep(B) : energi potensial di titik B, maka beda energi potensialnya : </span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheEr61a6KTHHUHAkWpyRnUpZGopcsmEIDrPG_FGQreS52QDHY8w6MzVFoyjOZY6xSKOHYXBdQm-9EoVfdUmJkwilyeoNhtoAacQJiyICX9HQHQVUwYYsCEaGPaJIB4PR1s4Xd-To-edL0h/s1600/4.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="58" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheEr61a6KTHHUHAkWpyRnUpZGopcsmEIDrPG_FGQreS52QDHY8w6MzVFoyjOZY6xSKOHYXBdQm-9EoVfdUmJkwilyeoNhtoAacQJiyICX9HQHQVUwYYsCEaGPaJIB4PR1s4Xd-To-edL0h/s320/4.bmp" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><br />
<br />
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 14pt; line-height: 125%;">r</span><sub><span style="font-size: 12pt; line-height: 125%;">A</span></sub><span style="font-size: 12pt; line-height: 125%;"> = jarak titik A ke pusat bumi.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 14pt; line-height: 125%;">r</span><sub><span style="font-size: 12pt; line-height: 125%;">B </span></sub><span style="font-size: 12pt; line-height: 125%;">= jarak titik B pusat bumi.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">oleh karena usaha merupakan perubahan energi potensial maka usaha yang dilakukan sepanjang garis dari A ke B dapat dinyatakan dengan :<o:p></o:p></span></div> <span style="font-size: 12pt; line-height: 125%;"></span><br />
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="IT" style="font-size: 12pt; line-height: 125%;">W<sub>A----> B</sub> = Usaha dari A ke B.<o:p></o:p></span></div><br />
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<br />
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</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="IT" style="font-size: 12pt; line-height: 125%;">Potensial grafitasi didefinisikan sebagai :<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><i><span lang="IT" style="font-size: 12pt; line-height: 125%;">Tenaga potensial grafitasi per satuan massa.<o:p></o:p></span></i></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Dapat dinyatakan dengan persamaan :<o:p></o:p></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX4AnFXFo7BvUAEkRT2bikuMzuNv4voROP6qnXlI5cAuSXbdeaZMFB5O63cFM-46hMXDPM2XKTkBez1hcUhO7_sDLhxXkTWfBWaEo6kZY_7md_dkRNQB43fYSGkLjOIgvQpjzvWLFBhK1B/s1600/6.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX4AnFXFo7BvUAEkRT2bikuMzuNv4voROP6qnXlI5cAuSXbdeaZMFB5O63cFM-46hMXDPM2XKTkBez1hcUhO7_sDLhxXkTWfBWaEo6kZY_7md_dkRNQB43fYSGkLjOIgvQpjzvWLFBhK1B/s1600/6.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; margin-left: 144pt; text-align: left;"><span style="position: relative; top: 12pt;"><!--[if gte vml 1]><v:shapetype
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</style> <![endif]--> <div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">v = potensial grafitasi, satuan : Joule/kg.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">Ep = Energi potensial grafitasi, satuan : Joule<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">m = massa benda, satuan : kg.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><u><span lang="SV" style="letter-spacing: 0.5pt;">POTENSIAL GRAFITASI OLEH BENDA BERMASSA<o:p></o:p></span></u></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Energi potensial grafitasi benda bermassa m’ yang terletak pada jarak r dari pusat massa benda bermassa m dapat kita nyatakan dengan persamaan :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDh3tjntMGzH9EpHxSFqWzFYv36Sfj6W4bCvaVUaaD1jYMBXK_TTRCCoa6pxWzHwcUP1RGJd3kLv4uaNsml_iYGlxBeWC9GzeDe5oQctPcLdJWMVYQ-Bjs8twWlaCw-C-WvZp7I3ih_6wh/s1600/7.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDh3tjntMGzH9EpHxSFqWzFYv36Sfj6W4bCvaVUaaD1jYMBXK_TTRCCoa6pxWzHwcUP1RGJd3kLv4uaNsml_iYGlxBeWC9GzeDe5oQctPcLdJWMVYQ-Bjs8twWlaCw-C-WvZp7I3ih_6wh/s1600/7.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Bila massa m’ terletak dititik p maka potensial grafitasi di titik p yang dialami oleh massa m’ dapat ditentukan sebagai berikut :<o:p></o:p></span></div> <span lang="SV" style="font-size: 12pt; line-height: 125%;"><br />
</span><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia-Se-mZXUWBLHTTMPUTxYC8fLZfiHN_y-NCAK6qxMpMTwIYicpyuqpZbw_pWYpeGbepjV9wDl7fQ3-3BnfSuquYzZR-IkDEYG_aJFDlqwaPASqNO88lzWjfwKjLjBrPOnmJWKjRJsOzC5/s1600/8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> </a></div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
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<m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia-Se-mZXUWBLHTTMPUTxYC8fLZfiHN_y-NCAK6qxMpMTwIYicpyuqpZbw_pWYpeGbepjV9wDl7fQ3-3BnfSuquYzZR-IkDEYG_aJFDlqwaPASqNO88lzWjfwKjLjBrPOnmJWKjRJsOzC5/s1600/8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div><br />
<div style="text-align: left;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><o:smarttagtype name="City" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:smarttagtype><o:smarttagtype name="place" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:smarttagtype><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><!--[if !mso]><img src="http://img2.blogblog.com/img/video_object.png" style="background-color: #b2b2b2; " class="BLOGGER-object-element tr_noresize tr_placeholder" id="ieooui" data-original-id="ieooui" /> <style>
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</style> <![endif]--> <div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">V = potensial grafitasi pada jarak r dari <st1:city w:st="on"><st1:place w:st="on">massa</st1:place></st1:city> m<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">m = <st1:city w:st="on"><st1:place w:st="on">massa</st1:place></st1:city> benda<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">r<span> </span>= jarak tempat yang mengalami potensial grafitasi ke benda.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Potensial grafitasi merupakan besaran skalar, karena itu potensial yang disebabkan oleh berapa benda bermassa merupakan jumlah aljabar dari potensial grafitasi masing-masing benda bermassa itu, Jadi :<o:p></o:p></span></div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><span style="font-size: 12pt; line-height: 125%;">V<sub>t</sub><span> </span>=<span> </span>V<sub>1 </sub>+ V<sub>2 </sub>+ V<sub>3 </sub>+ ...... + V<sub>n<o:p></o:p></sub></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Beda potensial antara dua titik dalam medan grafitasi didefinisikan sebagai :<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Potensial di titik yang satu dikurangi dengan potensial ditItik yang lain.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Usaha yang dilakukan untuk mengangkut, massa m dari satu titik ke titik lain lewat sembarang lintasan sama dengan massa benda itu kali beda potensial antara kedua titik itu.<o:p></o:p></span></div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><span lang="IT" style="font-size: 12pt; line-height: 125%;">W<sub>A----> B </sub>=<span> </span>m (V<sub>B</sub> - V<sub>A</sub>)<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="IT" style="font-size: 12pt; line-height: 125%;">W<sub>A----> B</sub> = Usaha dari A ke B.<o:p></o:p></span></div><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia-Se-mZXUWBLHTTMPUTxYC8fLZfiHN_y-NCAK6qxMpMTwIYicpyuqpZbw_pWYpeGbepjV9wDl7fQ3-3BnfSuquYzZR-IkDEYG_aJFDlqwaPASqNO88lzWjfwKjLjBrPOnmJWKjRJsOzC5/s1600/8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> </a></div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia-Se-mZXUWBLHTTMPUTxYC8fLZfiHN_y-NCAK6qxMpMTwIYicpyuqpZbw_pWYpeGbepjV9wDl7fQ3-3BnfSuquYzZR-IkDEYG_aJFDlqwaPASqNO88lzWjfwKjLjBrPOnmJWKjRJsOzC5/s1600/8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div><br />
<div style="text-align: left;"><br />
<m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia-Se-mZXUWBLHTTMPUTxYC8fLZfiHN_y-NCAK6qxMpMTwIYicpyuqpZbw_pWYpeGbepjV9wDl7fQ3-3BnfSuquYzZR-IkDEYG_aJFDlqwaPASqNO88lzWjfwKjLjBrPOnmJWKjRJsOzC5/s1600/8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> </a></div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div style="text-align: left;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> <div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><b><u><span lang="SV" style="font-size: 14pt; letter-spacing: 1pt; line-height: 125%;">HUKUM KEKEKALAN ENERGI</span></u></b><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Untuk gerakan benda dalam medan grafitasi yang tidak sama kekuatan di semua titik, hendaknya dipecahkan dengan perhitungan potensial grafitasi atau tenaga potensial grafitasi. Jika gaya-gaya gesekan diabaikan, dasar persangkutannya hanyalah kekekalan energi, yaitu :<o:p></o:p></span></div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Ek + Ep = konstan.<o:p></o:p></span></div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Ek<sub>(1)</sub> + Ep<sub>(1)</sub> = Ek<sub>(2)</sub> + Ep<sub>(2)</sub><o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Disini pembicaraan akan kita batasi hanya mengenai gerakan massa m dalam medan grafitasi yang ditimbulkan oleh titik tunggal yang tetap atau bola homogen bermassa m. Sehingga :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiakA9xcZO0ftJWuML3EsXZP_LuyLzrkNXYc1OhKP1HGXaf4oT4vBomey0Aa6Unph-Bj0zUaYCZP8c969sqT3ohGE4gOC6e6Wwo9E71dtyUPyu88ERHugsT4kCVCuRh_zRE1WQ6HiZC7Las/s1600/9.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="52" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiakA9xcZO0ftJWuML3EsXZP_LuyLzrkNXYc1OhKP1HGXaf4oT4vBomey0Aa6Unph-Bj0zUaYCZP8c969sqT3ohGE4gOC6e6Wwo9E71dtyUPyu88ERHugsT4kCVCuRh_zRE1WQ6HiZC7Las/s320/9.bmp" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"> </span><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Akhirnya kita dapatkan bahwa :</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCEOcJGdZNPsFd0AhZG6OTnPP15yv5uTymFk8SwLqE2b-5KF8lgSTiYXFgLfQBn0_sNlcbrE2b9HeH12DdUPj6jmffPwDi15oLxTuda_U_EKhyphenhyphen_dv_q6C6sCZvseKQdTa_ka1yR8S0wvtp/s1600/10.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="126" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCEOcJGdZNPsFd0AhZG6OTnPP15yv5uTymFk8SwLqE2b-5KF8lgSTiYXFgLfQBn0_sNlcbrE2b9HeH12DdUPj6jmffPwDi15oLxTuda_U_EKhyphenhyphen_dv_q6C6sCZvseKQdTa_ka1yR8S0wvtp/s320/10.bmp" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%;"><br />
</div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"></div><div class="MsoNormal" style="line-height: 125%;"><br />
</div><div class="MsoNormal" style="line-height: 125%;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"> </span><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><b><u><span style="font-size: 14pt; letter-spacing: 1pt; line-height: 125%;">KELAJUAN LEPAS</span></u></b><span style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Sebuah benda yang dilemparkan lurus ke atas dari permukaan bumi hanya dapat naik sampai jarak tertentu pada waktu energi Kinetik benda sama dengan nol, kemudian akan kembali lagi ke permukaan bumi. Jika suatu benda dilemparkan dari permukaan bumi dengan energi kinetik yang besarnya sama dengan energi potensial dipermukaan bumi, maka energi totalnya sama dengan nol.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Ini berarti benda bergerak ke jauh tak terhingga atau lepas dari bumi. Kelajuan awal agar ini terjadi disebut kelajuan lepas, dan dapat ditentukan dengan persamaan :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4wy6SRlwWcheaDKKkCwydXfWOIFCBJN63miLUiLV8_KbTHfCidNgqjHpZqhXM-5moUNTO9a4JDA14Px6HEBV9E4m9HfyyREU3r1d2NuLl3TmjdKLlbOtKRM5P1twyutKUEL1KsMJVFdrr/s1600/11.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4wy6SRlwWcheaDKKkCwydXfWOIFCBJN63miLUiLV8_KbTHfCidNgqjHpZqhXM-5moUNTO9a4JDA14Px6HEBV9E4m9HfyyREU3r1d2NuLl3TmjdKLlbOtKRM5P1twyutKUEL1KsMJVFdrr/s1600/11.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><br />
<div class="MsoNormal" style="line-height: 125%;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR-H06pna9uKfEFdFadmho0txpL0TQkaudLZunBAIjW29H2d4N3IZyKmiWyL1di9VTLiabB8J3Lxn1E5_jaqfjHx54WYqeJjc-u9Og1s6h99gD2MqWErhzQLKgInC9eVRoH3x5yIQ68N4c/s1600/12.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">v = kelajuan lepas<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">R = jari-jari bumi<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt;"><span style="font-size: 12pt; line-height: 125%;">g = percepatan grafitasi bumi.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%;"><br />
</div><div class="MsoNormal" style="line-height: 125%;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><b><u><span style="font-size: 14pt; letter-spacing: 1pt; line-height: 125%;">GERAKAN PLANET<o:p></o:p></span></u></b></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Menurut Keppler ( hukum Keppler ), perbandingan antara T<sup>2</sup> dari gerakan planet yang mengelilingi matahari terhadap r<sup>3</sup> adalah konstan.<o:p></o:p></span></div><br />
<br />
<br />
<br />
<div style="text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR-H06pna9uKfEFdFadmho0txpL0TQkaudLZunBAIjW29H2d4N3IZyKmiWyL1di9VTLiabB8J3Lxn1E5_jaqfjHx54WYqeJjc-u9Og1s6h99gD2MqWErhzQLKgInC9eVRoH3x5yIQ68N4c/s1600/12.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR-H06pna9uKfEFdFadmho0txpL0TQkaudLZunBAIjW29H2d4N3IZyKmiWyL1di9VTLiabB8J3Lxn1E5_jaqfjHx54WYqeJjc-u9Og1s6h99gD2MqWErhzQLKgInC9eVRoH3x5yIQ68N4c/s1600/12.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"></div><div class="MsoNormal" style="line-height: 125%;"></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"> <link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="PT-BR" style="font-size: 12pt; line-height: 125%;">T = periode<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="PT-BR" style="font-size: 12pt; line-height: 125%;">r = jari-jari lintasan<o:p></o:p></span></div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><span lang="PT-BR" style="font-size: 12pt; line-height: 125%;"><span> </span>( T<sub>1</sub> )<sup>2</sup> : ( T<sub>2</sub> )<sup>2</sup> = ( r<sub>1</sub> )<sup>3</sup> : ( r<sub>2 </sub>)<sup>3</sup><o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Dan dari gerak melingkar beraturan dapat kita peroleh :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNW_uomiF2QDXO2jJin6RclxE_1NgqNP87-BKNEDwDU-aV-265-aU9edkbw1aZDS6NA_mFgtywESLtpq28oF2HmZIzPzVV9JeHl-FD5fzUe6bR0k5mSiPn8iRYOOVqGYcaWPPJ3yfTZpmn/s1600/13.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNW_uomiF2QDXO2jJin6RclxE_1NgqNP87-BKNEDwDU-aV-265-aU9edkbw1aZDS6NA_mFgtywESLtpq28oF2HmZIzPzVV9JeHl-FD5fzUe6bR0k5mSiPn8iRYOOVqGYcaWPPJ3yfTZpmn/s1600/13.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Karena planet bergerak pada lintasan yang tetap maka terdapat gaya centripetal yang mempertahankan planet tetap pada lintasannya.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_YIpQa-idk1kgwJETdCQdpZ1Y0Q_hUUMz99m5tRICiOUfEJZodL3jjqOQFQq816aSKxDnaJftRqxhEii0AQ62HJbV7E_GwIu2CanfhZdLr7IRIDMAD808iZ41Bx3YR-GKidqTF5wqYJNO/s1600/14.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_YIpQa-idk1kgwJETdCQdpZ1Y0Q_hUUMz99m5tRICiOUfEJZodL3jjqOQFQq816aSKxDnaJftRqxhEii0AQ62HJbV7E_GwIu2CanfhZdLr7IRIDMAD808iZ41Bx3YR-GKidqTF5wqYJNO/s1600/14.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"> </span><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><o:smarttagtype name="City" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:smarttagtype><o:smarttagtype name="place" namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:smarttagtype><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><!--[if !mso]><img src="http://img2.blogblog.com/img/video_object.png" style="background-color: #b2b2b2; " class="BLOGGER-object-element tr_noresize tr_placeholder" id="ieooui" data-original-id="ieooui" /> <style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><st1:city w:st="on"><span style="font-size: 12pt; line-height: 125%;">Gaya</span></st1:city><span style="font-size: 12pt; line-height: 125%;"> sentripetal dalam hal ini adalah <st1:city w:st="on"><st1:place w:st="on">gaya</st1:place></st1:city> grafitasi yang dialami oleh planet yang disebabkan oleh matahari.<o:p></o:p></span></div><span lang="SV" style="font-family: "Times New Roman"; font-size: 12pt;">Bila massa planet m dan massa planet m dan massa matahari M maka gaya grafitasi antara planet dan matahari pada jarak r, adalah :</span><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="IT" style="font-size: 12pt; line-height: 125%;">Gaya ini merupakan gaya centripetal. Bila selama mengitari matahari planet bergerak dengan laju tetap sebesar v, maka dapat dinyatakan bahwa :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj23Cu_ln5lVW0F6iY75tl0lGKj3T0Rrz7DZy2vsVAhcOqL_IS955BHEK6IHOtAQfQyom0e0NNDpHSwFXdwTPezuZzJZAx4GYxDQRO_214KJKvn2Op1WZ2buuzGk05ROxJ6zA5xIGIwBIwD/s1600/15.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj23Cu_ln5lVW0F6iY75tl0lGKj3T0Rrz7DZy2vsVAhcOqL_IS955BHEK6IHOtAQfQyom0e0NNDpHSwFXdwTPezuZzJZAx4GYxDQRO_214KJKvn2Op1WZ2buuzGk05ROxJ6zA5xIGIwBIwD/s1600/15.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="IT" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="IT" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div> <span lang="SV" style="font-size: 12pt; line-height: 125%;"><br />
</span><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div> <span lang="SV" style="font-size: 12pt; line-height: 125%;"><br />
</span><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><br />
<div class="MsoNormal" style="line-height: 125%;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"> </span><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--><span lang="SV" style="font-family: "Times New Roman"; font-size: 12pt;">Jika planet bergerak dengan kelajuan sudut </span><span style="font-family: Symbol; font-size: 14pt;"><span>w</span></span><span lang="SV" style="font-family: "Times New Roman"; font-size: 12pt;"> maka dapat dinyatakan suatu persamaan dalam bentuk : </span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLiN1ZOz27Rj3shnYqaQPAwgj3Xfv8PtUANSi37FJ3xrn-5k25FfPQl80Ahvr0B6BLp_8YlvMmnZWrs2qxC66ajWIZrNskI0kQVvenXabbtG-JuFhSXc4uFYVa64UCurmlygD61AJxcxOM/s1600/16.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLiN1ZOz27Rj3shnYqaQPAwgj3Xfv8PtUANSi37FJ3xrn-5k25FfPQl80Ahvr0B6BLp_8YlvMmnZWrs2qxC66ajWIZrNskI0kQVvenXabbtG-JuFhSXc4uFYVa64UCurmlygD61AJxcxOM/s1600/16.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div></div><div style="text-align: left;"><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:PunctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w:DontGrowAutofit/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if gte mso 9]><xml> <w:LatentStyles DefLockedState="false" LatentStyleCount="156"> </w:LatentStyles> </xml><![endif]--><style>
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</style> <![endif]--> </div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span style="font-family: Symbol; font-size: 14pt; line-height: 125%;"><span>w</span></span><span style="font-size: 14pt; line-height: 125%;"> </span><span lang="FI" style="font-size: 12pt; line-height: 125%;"><span> </span>= kelajuan sudut<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">M = massa matahari<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">r = jari-jari lintasan</span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">Semoga membantu :) </span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div> <span lang="SV" style="font-family: "Times New Roman"; font-size: 12pt;"><br />
</span><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></div><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia-Se-mZXUWBLHTTMPUTxYC8fLZfiHN_y-NCAK6qxMpMTwIYicpyuqpZbw_pWYpeGbepjV9wDl7fQ3-3BnfSuquYzZR-IkDEYG_aJFDlqwaPASqNO88lzWjfwKjLjBrPOnmJWKjRJsOzC5/s1600/8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> </a></div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">source : <a href="http://adiwarsito.wordpress.com/2010/11/04/materi-ajar-fisika-sma-kelas-xi-ipa/">from here (just click!)</a><br />
</span></div><div align="center" class="MsoNormal" style="line-height: 125%; text-align: center;"><br />
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<div class="MsoNormal" style="line-height: 125%; margin-left: 1in; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> </span></div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac>nopinophttp://www.blogger.com/profile/07944999515934940876noreply@blogger.com0tag:blogger.com,1999:blog-1669227246532692436.post-61663799408339650332011-09-22T23:48:00.001-07:002011-10-01T17:47:38.207-07:00KINEMATIKA DENGAN ANALISIS VEKTOR<div style="text-align: left;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: center;"><b><u><span style="font-size: 16pt; line-height: 125%;">PERSAMAAN GERAK</span></u></b></div><div class="MsoNormal" style="line-height: 125%; text-align: left;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: left;"><span style="font-size: 12pt; line-height: 125%;">Posisi titik materi dapat dinyatakan dengan sebuah <b><span style="letter-spacing: 1pt;">VEKTOR</span></b>, baik pada suatu bidang datar maupun dalam bidang ruang.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: left;"><span style="font-size: 12pt; line-height: 125%;">Vektor yang dipergunakan untuk menentukan posisi disebut VEKTOR POSISI yang ditulis dalam Vektor satuan.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: left;"><span style="position: relative; top: 5pt;"><br />
</span></div><div class="MsoNormal" style="line-height: 125%; text-align: center;"><b><u><span style="font-size: 12pt; letter-spacing: 1pt; line-height: 125%;">VEKTOR SATUAN</span></u></b><b><span style="font-size: 12pt; letter-spacing: 1pt; line-height: 125%;">.</span></b></div><div class="MsoNormal" style="line-height: 125%; text-align: left;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjzkWj3h6XVW7DIFhX2Zi-fhN4CsSZDkG0Seffh2959tyRlsrBsC28Ici_rKEp6sVw3y9ZuAyEaB3I0WnFW7zCUiZGNyFRZvAKKTX53VWLe7wjtdEykcMWAinmXzdZPOf10MXn_zXbpsa2/s1600/Untitled.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjzkWj3h6XVW7DIFhX2Zi-fhN4CsSZDkG0Seffh2959tyRlsrBsC28Ici_rKEp6sVw3y9ZuAyEaB3I0WnFW7zCUiZGNyFRZvAKKTX53VWLe7wjtdEykcMWAinmXzdZPOf10MXn_zXbpsa2/s1600/Untitled.png" /></a></div><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_editdata.mso" rel="Edit-Time-Data"></link><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_oledata.mso" rel="OLE-Object-Data"></link><style>
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<div class="MsoNormal" style="line-height: 125%;"><b><u><span lang="SV" style="font-size: 12pt; letter-spacing: 1pt; line-height: 125%;">POSISI TITIK MATERI PADA SUATU BIDANG DATAR.</span></u></b><b><span lang="SV" style="font-size: 12pt; line-height: 125%;"><o:p></o:p></span></b></div><div class="MsoNormal" style="line-height: 125%;"><br />
<table cellpadding="0" cellspacing="0" style="margin-left: 0px; margin-right: auto; text-align: left;"><tbody>
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</tbody></table><span lang="SV" style="font-size: 12pt; line-height: 125%;">Posisi titik materi ini dapat dinyatakan dengan :</span><br />
<br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxEq5N1G9Kgn-FfJ9VPr8eGev7asHaapSCJlrjJo1kVLIfbxojy-nIUiucLMPGFeUjBHPNeojurOAsLGTQwnDGOUniaf7ppJsEi0UL3vuTazdhl4hlaido1KjOJqvQT_UEcgpSpfFEJxEK/s1600/2.bmp" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxEq5N1G9Kgn-FfJ9VPr8eGev7asHaapSCJlrjJo1kVLIfbxojy-nIUiucLMPGFeUjBHPNeojurOAsLGTQwnDGOUniaf7ppJsEi0UL3vuTazdhl4hlaido1KjOJqvQT_UEcgpSpfFEJxEK/s1600/2.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%;"><link href="file:///C:%5CDOCUME%7E1%5Cuser%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml" rel="File-List"></link><style>
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</style><span style="font-family: "Times New Roman"; font-size: 12pt;"> </span><span style="font-family: "Times New Roman"; font-size: 12pt;">Contoh : </span><br />
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3yk8Ns2UIraCR8J3J61Ifj0mLMnLwKJWxgSaLz4y6q6BsTZlZxqTQeNqDBmynYAoA2QpvG1OoaPN1f2ARWN8SjS3LOGCOEEdgZLqChzgGhYVXq6NdZ6D5GGMA5l-ZEwZ6pcROcEsjwp3L/s1600/3.bmp" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3yk8Ns2UIraCR8J3J61Ifj0mLMnLwKJWxgSaLz4y6q6BsTZlZxqTQeNqDBmynYAoA2QpvG1OoaPN1f2ARWN8SjS3LOGCOEEdgZLqChzgGhYVXq6NdZ6D5GGMA5l-ZEwZ6pcROcEsjwp3L/s1600/3.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs_H0EB6Uz9AR5kL0gUad_gt9GBqZbHvMCG0ANzk7kLXGypoSlDZJ3ZFmb5MXwpclPcGB1tZDdXGeBst2zHDIF_EBAXLN0cjFK1BXazKIbBelQ8UFWQbdfqtNR1N2rY9N-EcnOH38XCaf-/s1600/4.bmp" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs_H0EB6Uz9AR5kL0gUad_gt9GBqZbHvMCG0ANzk7kLXGypoSlDZJ3ZFmb5MXwpclPcGB1tZDdXGeBst2zHDIF_EBAXLN0cjFK1BXazKIbBelQ8UFWQbdfqtNR1N2rY9N-EcnOH38XCaf-/s1600/4.bmp" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhr8G01NvPc-8YtPf5eD2JYFl_cS3TYJEMkt9SrOJbb-m4gn9iDkmdk3kYseRtoPAqDdXS6anduBwbovOfwC9GEds5u0zyuk7bwGmltqygHQbHEnBu6r9AYQ2v1meJCp5tieRbxRd3NCAMf/s1600/7.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div><br />
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<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u><span lang="FI" style="font-size: 12pt; line-height: 125%;">POSISI TITIK MATERI PADA SUATU RUANG.</span></u></b></div></div><div class="MsoNormal" style="line-height: 125%; text-align: left;">Posisi titik materi ini dapat dinyatakan dengan :</div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixCM-DTJbOFRPQ0sD5IJNGHAnVos-AI1oTbGIWG6Of6dI-pweKkjzv0cPZlMsXTziG_YauOTp6BCCi776Yc7AofRlVM49RC5U_iBt7AoZTGuH-0X28bBKbNYR8JOnl7JKDRmvR1t2niBZQ/s1600/5.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixCM-DTJbOFRPQ0sD5IJNGHAnVos-AI1oTbGIWG6Of6dI-pweKkjzv0cPZlMsXTziG_YauOTp6BCCi776Yc7AofRlVM49RC5U_iBt7AoZTGuH-0X28bBKbNYR8JOnl7JKDRmvR1t2niBZQ/s1600/5.bmp" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioc9Qqz8MO9Qhj8NG63QahbbssBcTT8gSYy8BC_UfmBzZMCnWWxa586Ofx6UsQyG9rpz1oirLzg8RrkEylyOaWAy0sEKhKDDRnH3JAAdIoW5AHb8lZflQDBpqGaV7nunYK-rO334rTGMRg/s1600/6.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div><div class="MsoNormal" style="line-height: 125%; text-align: left;">Contoh : </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaWcuURe4Ya7N9QlYmz4hn28zDqpxnAkaoS5meUlerN94jS-TSr2Bywg8JXwVzOJ4DDfUelzfOn1JM0sT-9SCSlSVBd1Q0KyeIvc2Z_MmgGaN5APz9O_2RqYCX0xSnaReOYordREh0jU5n/s1600/7.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxvZkkf4W5RbDZf0Cs8Hvs391zjwEqDZBMagN5wcEJCFAgQvTafID5Qvpo-Jkq54G5k2CaBgmfYb_4tQ2RU83Hti87Ht05DXlFi97dBFQtPFTYoR1o7TtYAm7SeAaRK9cbKSa2HB2T7nnc/s1600/8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxvZkkf4W5RbDZf0Cs8Hvs391zjwEqDZBMagN5wcEJCFAgQvTafID5Qvpo-Jkq54G5k2CaBgmfYb_4tQ2RU83Hti87Ht05DXlFi97dBFQtPFTYoR1o7TtYAm7SeAaRK9cbKSa2HB2T7nnc/s320/8.bmp" style="cursor: move;" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: left;"><div style="text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioc9Qqz8MO9Qhj8NG63QahbbssBcTT8gSYy8BC_UfmBzZMCnWWxa586Ofx6UsQyG9rpz1oirLzg8RrkEylyOaWAy0sEKhKDDRnH3JAAdIoW5AHb8lZflQDBpqGaV7nunYK-rO334rTGMRg/s1600/6.bmp" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioc9Qqz8MO9Qhj8NG63QahbbssBcTT8gSYy8BC_UfmBzZMCnWWxa586Ofx6UsQyG9rpz1oirLzg8RrkEylyOaWAy0sEKhKDDRnH3JAAdIoW5AHb8lZflQDBpqGaV7nunYK-rO334rTGMRg/s1600/6.bmp" /></a></div><div class="MsoNormal"><div class="separator"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaWcuURe4Ya7N9QlYmz4hn28zDqpxnAkaoS5meUlerN94jS-TSr2Bywg8JXwVzOJ4DDfUelzfOn1JM0sT-9SCSlSVBd1Q0KyeIvc2Z_MmgGaN5APz9O_2RqYCX0xSnaReOYordREh0jU5n/s1600/7.bmp" /> </div><div class=""> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u><span style="font-size: 12pt; letter-spacing: 1pt; line-height: 125%;">KECEPATAN SUATU TITIK MATERI</span></u></b><b><span style="font-size: 12pt; line-height: 125%;">.</span></b></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Gerakan titik materi secara keseluruhan dapat diamati jika posisinya setiap saat diketahui. Seberapa cepat letak titik materi itu berubah setiap saat disebut : <b><i><u><span style="letter-spacing: 1pt;">KECEPATAN</span></u></i><span style="letter-spacing: 1pt;"> .</span></b></span></div><br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitehdtfHyjYXeRLBp_q1SGsrYlO1WZFRSACxgt07CUh4eUgtG2C4okvmVoLk-i1pUMvcT7bLgfAayy4r-dv0OegMPBzFHL5wha8akLKSTN_Cj7f3lu5B0N8EX85skauqNXRwGmcEMojNmY/s1600/9.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitehdtfHyjYXeRLBp_q1SGsrYlO1WZFRSACxgt07CUh4eUgtG2C4okvmVoLk-i1pUMvcT7bLgfAayy4r-dv0OegMPBzFHL5wha8akLKSTN_Cj7f3lu5B0N8EX85skauqNXRwGmcEMojNmY/s320/9.bmp" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"><b><span style="letter-spacing: 1pt;"> </span></b></span> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">Jadi kecepatan sesaat merupakan turunan pertama dari posisi terhadap waktu (t)</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="FI" style="font-size: 12pt; line-height: 125%;">Besarnya kecepatan disebut dengan <b><i>laju</i></b></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBRxgjpOqgn6PGnEuJS2_NKuH1BkF7OLh8LM933wD-dJ3N5UIuUFGi8sNBd4-CbBi2sfiRa-YGlwqJmjEVUupdLZrOGgTJo2Q64lMIythGuIheMP8ACgd_eCneetfyjdbk7FvI_TL_SXJA/s1600/10.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBRxgjpOqgn6PGnEuJS2_NKuH1BkF7OLh8LM933wD-dJ3N5UIuUFGi8sNBd4-CbBi2sfiRa-YGlwqJmjEVUupdLZrOGgTJo2Q64lMIythGuIheMP8ACgd_eCneetfyjdbk7FvI_TL_SXJA/s1600/10.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Laju dapat pula berarti panjang lintasan dibagi waktu yang bersangkutan.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Nilai dari komponen kecepatan sesaat dari suatu titik materi dapat dilihat dari <b><i>kemiringan grafik</i></b> yang dibentuk oleh komponen posisi ( r ) terhadap waktu ( t ).</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXwjKVFxTP15XAZz_CXw3J7GrpWNuAJrqhWUtRkxEqJsY9H0a56TrR6qNuwCwsQboHZDo_48Zf0CHP4_Wore8XfhG4rWotrygz3qjRJRvcYVzbrYUND7JoMdb4RJF348Z611L6VWTSTtfb/s1600/11.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXwjKVFxTP15XAZz_CXw3J7GrpWNuAJrqhWUtRkxEqJsY9H0a56TrR6qNuwCwsQboHZDo_48Zf0CHP4_Wore8XfhG4rWotrygz3qjRJRvcYVzbrYUND7JoMdb4RJF348Z611L6VWTSTtfb/s320/11.bmp" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXfOnvyKSrUijZ1G6b_vkc3AYg69Fhlfv8tleJUI__0SSyzMAX2yT-Lz0xR-uiUcL_qQFy37ephDnILAwZno5-HQ3_kGumoEdEhhDO-3rShrNpRPvUMqMLT1_YpGSBr-zeJW9Jx-JoI_yf/s1600/12.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="125" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXfOnvyKSrUijZ1G6b_vkc3AYg69Fhlfv8tleJUI__0SSyzMAX2yT-Lz0xR-uiUcL_qQFy37ephDnILAwZno5-HQ3_kGumoEdEhhDO-3rShrNpRPvUMqMLT1_YpGSBr-zeJW9Jx-JoI_yf/s320/12.bmp" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Sebaliknya untuk menentukan posisi titik materi jika diketahui fungsi kecepatannya maka dapat diselesaikan dengan <b><i>INTEGRAL</i></b> ( kebalikan dari deferensial ).</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho9-bokZppSwX9lBHkERFrEtbN9mK03VQsMtNLPa9GvtMiS1pM1_TIyL0JOVvRc9nqdzvJ0P2B7b8jXGh4mSM5RW8AnbiQxISQb4mV8uxRXtPy-A71eNANBt_xCTRTA_21jxfhyqSuuvUQ/s1600/13.bmp" /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5XoUyu140lOEzqB2HAkSZAFoPLjol68GVST3vtMfXVnHzkRDHB-Lu7gz40_NJkpVa8UHtIbfRP-xzvL3kBXnrscx2ZmFD3gLTq1u2xbu7R1BOPFjIH1q-T9bXMpnV7JJLUyv2KVoPHc8x/s1600/14.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5XoUyu140lOEzqB2HAkSZAFoPLjol68GVST3vtMfXVnHzkRDHB-Lu7gz40_NJkpVa8UHtIbfRP-xzvL3kBXnrscx2ZmFD3gLTq1u2xbu7R1BOPFjIH1q-T9bXMpnV7JJLUyv2KVoPHc8x/s1600/14.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
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<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><i><span lang="SV" style="font-size: 12pt; line-height: 125%;">Contoh :</span></i><span lang="SV" style="font-size: 12pt; line-height: 125%;"> </span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">v<sub>(t) </sub> = 2 t + 5 m/det</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">maka persamaan posisi titik materi tersebut adalah ......</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieGoelPp7_KL8haXOihH1-HV5HOopRwu0u3IJePSmKTqhyphenhyphenHkfLVE2GbqG_iTVK-RcuzdOp5XjUjQhJTNQ1eSAWJ43k5-yfancgFiPblIUK-kyd1tYgA7UGKcBJy1ALVBE7W46L2vqIKvdI/s1600/15.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieGoelPp7_KL8haXOihH1-HV5HOopRwu0u3IJePSmKTqhyphenhyphenHkfLVE2GbqG_iTVK-RcuzdOp5XjUjQhJTNQ1eSAWJ43k5-yfancgFiPblIUK-kyd1tYgA7UGKcBJy1ALVBE7W46L2vqIKvdI/s1600/15.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
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<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u><span lang="SV" style="font-size: 12pt; line-height: 125%;">PERCEPATAN </span></u></b></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Kecepatan titik materi dapat berubah-ubah setiap saat baik besar, atau arah, ataupun kedua-duanya yang disebabkan oleh karena adanya <b><i>percepatan</i></b> yang dialami oleh titik materi tersebut.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;">Jika pada saat t<sub>1</sub> kecepatan v<sub>1</sub> dan pada saat t<sub>2</sub> kecepatannya v<sub>2</sub>, percepatan rata-ratanya dalam selang waktu </span><span style="font-family: Symbol; font-size: 12pt; line-height: 125%;">D</span><span lang="SV" style="font-size: 12pt; line-height: 125%;"> t = t <sub>2</sub> -t <sub>1</sub> didefinisikan sebagai : (gambar)</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="SV" style="font-size: 12pt; line-height: 125%;"><br />
</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Percepatan sesaatnya : (gambar)</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"><br />
</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Percepatan merupakan tutunan pertama dari kecepatan terhadap waktu (t) atau turunan kedua dari posisi terhadap waktu (t).</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Kecepatan sesaat dari suatu titik materi dapat dilihat dari kemiringan komponen grafik kecepatan (v) terhadap waktu (t).</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">(gambar)</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> </span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="height: 154px; left: 0px; margin-left: 368px; margin-top: 40px; position: absolute; width: 2px; z-index: 251660288;"> </span><span style="height: 154px; left: 0px; margin-left: 368px; margin-top: 40px; position: absolute; width: 2px; z-index: 251660288;"> </span><span lang="IT" style="font-size: 12pt; line-height: 125%;">Percepatan dalam arah masing-masing sumbu dalam bidang/ruang dapat dituliskan sebagai :(gambar)</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span lang="IT" style="font-size: 12pt; line-height: 125%;"> </span> </div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Sebaliknya untuk menentukan kecepatan dari grafik fungsi percepatan terhadap waktu dengan cara <b><i>mengintegralkan : (gambar)</i></b></span><br />
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<i><b>Semoga membantu :)</b></i></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"><b><i><br />
</i></b></span></div>source : <a href="http://adiwarsito.wordpress.com/2010/11/04/materi-ajar-fisika-sma-kelas-xi-ipa/">from here (just click!)</a><br />
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</tbody></table></div></div>nopinophttp://www.blogger.com/profile/07944999515934940876noreply@blogger.com0tag:blogger.com,1999:blog-1669227246532692436.post-38803686593316250442011-09-12T19:50:00.000-07:002011-10-01T17:44:05.225-07:00GERAK HARMONIK<m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <br />
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<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 14pt; line-height: 125%;"> </span><span style="font-size: 12pt; line-height: 125%;">Benda yang melakukan gerak lurus berubah beraturan, mempunyai percepatan yang tetap, Ini berarti pada benda senantiasa bekerja gaya yang tetap baik arahnya maupun besarnya. Bila gayanya selalu berubah-ubah, percepatannyapun berubah-ubah pula.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Gerak yang berulang dalam selang waktu yang sama disebut <b><i>Gerak Periodik.</i></b> Gerak periodik ini selalu dapat dinyatakan dalam fungsi sinus atau cosinus, oleh sebab itu gerak periodik disebut <b><i>Gerak Harmonik.</i></b> Jika gerak yang periodik ini bergerak bolak-balik melalui lintasan yang sama disebut <b><i>Getaran</i></b> atau <b><i>Osilasi.</i></b></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Waktu yang dibutuhkan untuk menempuh satu lintasan bolak-balik disebut <b><i>Periode,</i></b> sedangkan banyaknya getaran tiap satuan waktu disebut <b><i>Frekwensi.</i></b> Hubungan antara periode (T) dan frekwensi (f) menurut pernyataan ini adalah T=1/f</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Satuan frekwensi dalam SI adalah putaran per detik atau Hertz (Hz). Posisi pada saat resultan gaya bekerja pada partikel yang bergetar sama dengan nol disebut posisi seimbang.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Perhatikan sebuah benda massanya m digantungkan pada ujung pegas, pegas bertambah panjang. Dalam keadaan seimbang, gaya berat w sama dengan gaya pegas F, resultan gaya sama dengan nol, beban diam.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDByskIiLVuBBMHHpI9hwXszy0m-xd05QXrBa7UwxuVI75-xkirehV8-ysjdZmrcxKidEsVT39pr8Fc3gcTVjoJS9K6mIXRhpzJUc96cz2-iZ32OA_t1jC531XmrKEzWTKcnstGrAA93tq/s1600/1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="165" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDByskIiLVuBBMHHpI9hwXszy0m-xd05QXrBa7UwxuVI75-xkirehV8-ysjdZmrcxKidEsVT39pr8Fc3gcTVjoJS9K6mIXRhpzJUc96cz2-iZ32OA_t1jC531XmrKEzWTKcnstGrAA93tq/s320/1.bmp" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Dari kesimbangannya beban diberi simpangan y, pada beban bekerja gaya F, gaya ini cenderung menggerakkan beban keatas. Gaya pegas merupakan gaya penggerak, padahal gaya pegas sebanding dengan simpangan pegas.</span></div><span style="font-size: 12pt; line-height: 125%;"> F = - k y ; k tetapan pegas </span><br />
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<m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Mudah dipahami bahwa makin kecil simpangan makin kecil pula gaya penggerak. Gerakan yang gaya penggeraknya sebanding dengan simpangan disebut <i>Gerak Harmonis ( Selaras ).</i></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> Bila beban dilepas dari kedudukan terbawah (A), beban akan bergerak bolak balik sepanjang garis A-O-B. Gerak bolak-balik disebut getaran dan getaran yang gaya penggeraknya sebanding dengan simpangannya disebut : Gerak Harmonis.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Simpangan yang terbesar disebut Amplitudo getaran (A).</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Saat simpangan benda y, percepatannya : </span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDByskIiLVuBBMHHpI9hwXszy0m-xd05QXrBa7UwxuVI75-xkirehV8-ysjdZmrcxKidEsVT39pr8Fc3gcTVjoJS9K6mIXRhpzJUc96cz2-iZ32OA_t1jC531XmrKEzWTKcnstGrAA93tq/s1600/1.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="165" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDByskIiLVuBBMHHpI9hwXszy0m-xd05QXrBa7UwxuVI75-xkirehV8-ysjdZmrcxKidEsVT39pr8Fc3gcTVjoJS9K6mIXRhpzJUc96cz2-iZ32OA_t1jC531XmrKEzWTKcnstGrAA93tq/s320/1.bmp" width="320" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> <sup><br />
</sup></span></div><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Besar energi potensialnya : Ep = ½ ky<sup>2</sup></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Ketika simpangannya terbesar energi kinetiknya Ek = 0, sedangkan energi potensialnya Ep = ½ kA<sup>2</sup> ….. Jadi energi getarannya E = Ep + Ek = ½ kA<sup>2</sup> + 0</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">E = ½ kA<sup>2</sup></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Energi kinetik saat simpangannya y dapat dicari dengan hukum kekekalan energi.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> E = Ep + Ek</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> Ek = E – Ep = ½ kA<sup>2</sup> – ½ ky<sup>2</sup></span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u><span style="font-size: 12pt; line-height: 125%;">FREKUENSI (f)</span></u></b></div><div class="MsoBodyText"> Gerakan dari A-)-B-O-A disebut satu getaran, waktu yang diperlukan untuk melakukan satu getaran disebut PERIODE (T) dan banyaknya getaran yang dilakukan dalam satu detik disebut bilangan getar atau FREKWENSI</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Dalam T detik dilakukan 1 getaran</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Dalam 1 detik dilakukan 1/T getaran</span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Jadi f = 1/T</span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Satuan T dalam detik, f dalam Hertz atau cps (cycles per sekon) atau rps (rotasi per sekon)</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u><span style="font-size: 12pt; line-height: 125%;">PROYEKSI GERAK MELINGKAR BERATURAN.</span></u></b></div><div class="MsoBodyText"> Gerak bolak-balik piston menjadi gerak putaran pada sebuah kendaraan bermotor, gerak putar pada sebuah mesin jahit menjadi gerak bolak-balik jarum mesin jahit, menunjukkan adanya kaitan antara gerak melingkar dengan gerak harmonik.</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"> Gerak melingkar beraturan titik P dalam tiap-tiap saat diproyeksikan pada garis tengah MN, titik proyeksinya yakni titik Q bergerak dari O-M-O-N-O, dengan kata lain titik Q bergerak menyusuri MN bolak-balik. Apakah gerak titik Q gerak harmonik ? akan kita bahas.</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioqNDit1y0sDKUdh4e1tzNkrzRjXk0fBkTgXQWnWujqK58NXQI2XTai3sv6a8oA1GpEnj-3uc325puOx-QMBS4vuSnPXqvvRvlB_lAKlcv_ZCQcvTa5JP6q4umWp-HaxXHkx3Ir-CiC3iH/s1600/3.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioqNDit1y0sDKUdh4e1tzNkrzRjXk0fBkTgXQWnWujqK58NXQI2XTai3sv6a8oA1GpEnj-3uc325puOx-QMBS4vuSnPXqvvRvlB_lAKlcv_ZCQcvTa5JP6q4umWp-HaxXHkx3Ir-CiC3iH/s1600/3.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"><br />
</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Amplitudo gerak titik Q adalah R dan periodenya sama dengan periode gerak melingkar beraturan. Bila dalm t detik titik P menempuh sudut </span><br />
<m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKWg3V7IUfEZufx16TWq1_oqCUS9QHpqus74iQoW1k5GkhfAHOkMqrOaE6WPn40oiZEJ_-J_9szW-Yi5djZXTnddhRMRVlvSnQd0sigNuMpwmDJcZ48DDvobTJe2dXkKRGfeqCAk3Ig1gG/s1600/4.bmp" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKWg3V7IUfEZufx16TWq1_oqCUS9QHpqus74iQoW1k5GkhfAHOkMqrOaE6WPn40oiZEJ_-J_9szW-Yi5djZXTnddhRMRVlvSnQd0sigNuMpwmDJcZ48DDvobTJe2dXkKRGfeqCAk3Ig1gG/s1600/4.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> </span> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Dalam waktu yang sama titik Q mempunyai simpangan : </span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVlkyAIVwrFzGcEGJnnqzuxx6LBdo02AfrQCJGzFig1lWeJ-jc1GJdDohlGpMANl3V1k8ZjdOSGVuofaGBi-LfNHqdMaLoKDXKJ8GKPCUT7ePDitfHQtjShbKQvcSzFwTxhPsPEygr34oO/s1600/5.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVlkyAIVwrFzGcEGJnnqzuxx6LBdo02AfrQCJGzFig1lWeJ-jc1GJdDohlGpMANl3V1k8ZjdOSGVuofaGBi-LfNHqdMaLoKDXKJ8GKPCUT7ePDitfHQtjShbKQvcSzFwTxhPsPEygr34oO/s1600/5.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> </span> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Kecepatannya saat itu :</span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX1sc35Q35KPVH0FhBT2mty70XVDB4XWrd23E4X0Uo8i0_5jpA4nEmxBJwuCvLjZCd9IG3gIBD8NAe0Oa2ns5wyPALyBNfIhJxadVLHEEt548wrxrZDdth8-Ml2CXDyMyTO0VGzbd-oPjE/s1600/6.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="25" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX1sc35Q35KPVH0FhBT2mty70XVDB4XWrd23E4X0Uo8i0_5jpA4nEmxBJwuCvLjZCd9IG3gIBD8NAe0Oa2ns5wyPALyBNfIhJxadVLHEEt548wrxrZDdth8-Ml2CXDyMyTO0VGzbd-oPjE/s320/6.bmp" width="320" /></a></div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div><br />
<br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Percepatan saat itu :</span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3zZIu7_yPAujSlSfH9wwTDx0OaUX63To3hOYqBMB0wTMX1ffQYZ-CBUlSzCFQ4R1iguSe1X-9j6-9Rp3AbSpQF6y9J521VokWHTqz7DkiJ5v_ZDpCxcjv7nl-Gdm5RrFsihdlKWtnsyRo/s1600/7.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3zZIu7_yPAujSlSfH9wwTDx0OaUX63To3hOYqBMB0wTMX1ffQYZ-CBUlSzCFQ4R1iguSe1X-9j6-9Rp3AbSpQF6y9J521VokWHTqz7DkiJ5v_ZDpCxcjv7nl-Gdm5RrFsihdlKWtnsyRo/s1600/7.bmp" /></a></div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Oleh karena arah percepatan ke bawah, tandanya negatif :</span></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTvNNybMYQug_K2IxvgmMY_2JonxCNVYCFhoMTo97wx_08VltAbVgZx1pttSn7MQKmNRCUY3p-VQ4MlW39mdiJMBQx5gzllHLSdpyJPcIOr-ABAKQ8TnBAkEyrT3pUqfQz-pOJi5wAU4sB/s1600/8.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTvNNybMYQug_K2IxvgmMY_2JonxCNVYCFhoMTo97wx_08VltAbVgZx1pttSn7MQKmNRCUY3p-VQ4MlW39mdiJMBQx5gzllHLSdpyJPcIOr-ABAKQ8TnBAkEyrT3pUqfQz-pOJi5wAU4sB/s1600/8.bmp" /></a></div><br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"><sup> </sup></span> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Bila massa titik Q adalah m, besar gaya yang bekerja pada titik itu :</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4lXpfLtjuHWK8r7cNTf7EYgNQEkiBthZCRDtg4VRJJaFK4kfuzKgpztVtz9RFzud_FJ-eHYdulgSwrPdpc_cD7f46Q9f65MR-IhaVz7AMKPQz0z9mnUfdpC7ZnBf7fxShOSicCmYcuwsU/s1600/9.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4lXpfLtjuHWK8r7cNTf7EYgNQEkiBthZCRDtg4VRJJaFK4kfuzKgpztVtz9RFzud_FJ-eHYdulgSwrPdpc_cD7f46Q9f65MR-IhaVz7AMKPQz0z9mnUfdpC7ZnBf7fxShOSicCmYcuwsU/s1600/9.bmp" /></a></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizViyI3IGUFf1otBc93bH5VS7XiUJ78njDuPfnveU_fCZUboV5q9yOnKv2LdbEUfVqtNH56VUWlP1VPK-ZUxbK7AuzPwEMeajVMB29ARSdTh2O4Nx_t7QuQclkNLKiy07lQLfgs_mq8epA/s1600/10.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="30" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizViyI3IGUFf1otBc93bH5VS7XiUJ78njDuPfnveU_fCZUboV5q9yOnKv2LdbEUfVqtNH56VUWlP1VPK-ZUxbK7AuzPwEMeajVMB29ARSdTh2O4Nx_t7QuQclkNLKiy07lQLfgs_mq8epA/s320/10.bmp" width="320" /> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> </m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Persamaan terakhir menyatakan bahwa gaya yang bekerja pada titik Q sebanding dengan simpangannya. Jadi proyeksi gerak melingkar beraturan adalah GERAK HARMONIS.</span></div><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Persamaan di atas gerak mulai dari titik setimbang, jika tidak maka persamaan secara umum ditulis sbb : </span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCyagi3ybXRlxXj8SyNkQNzG77DSEnUxfDeOY3scwVILA6pynkhbtoC8l0p8YCUD9ZmDA4TJij8TrEODMnIABC8eDucozli3YT1NBzjyBf_YorU3qhyphenhyphenOGhnGxoHwyZBhtpDGDO57UZLmrT/s1600/11.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCyagi3ybXRlxXj8SyNkQNzG77DSEnUxfDeOY3scwVILA6pynkhbtoC8l0p8YCUD9ZmDA4TJij8TrEODMnIABC8eDucozli3YT1NBzjyBf_YorU3qhyphenhyphenOGhnGxoHwyZBhtpDGDO57UZLmrT/s1600/11.bmp" /></a></div><br />
<m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <br />
<div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u><span style="font-size: 12pt; line-height: 125%;">PERIODE GERAK HARMONIS.</span></u></b></div><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipwT5Gq82qQh8i1wP5_uipiiHOrE02RxcFUtc6A3G8MZtiW_5EGVzS4HtHTumYJpa4u2EEoEYKY29TXV9IfH1GjBjvF5HKZIiE4BzlrNhY_rjEJG4CAcvFKt1jO0Gt4yVt7hMiXEpVP1UN/s1600/12.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="55" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipwT5Gq82qQh8i1wP5_uipiiHOrE02RxcFUtc6A3G8MZtiW_5EGVzS4HtHTumYJpa4u2EEoEYKY29TXV9IfH1GjBjvF5HKZIiE4BzlrNhY_rjEJG4CAcvFKt1jO0Gt4yVt7hMiXEpVP1UN/s320/12.bmp" width="320" /></a></div><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> </span> <m:smallfrac m:val="off"> <m:dispdef> <m:lmargin m:val="0"> <m:rmargin m:val="0"> <m:defjc m:val="centerGroup"> <m:wrapindent m:val="1440"> <m:intlim m:val="subSup"> <m:narylim m:val="undOvr"> </m:narylim></m:intlim> </m:wrapindent> <br />
<div class="MsoBodyText">m massa benda dalam kg, k tetapan pegas dalam N/m dan T periode getaran dalam detik.</div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u><span style="font-size: 12pt; line-height: 125%;"><span style="text-decoration: none;"><br />
</span></span></u></b></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><b><u><span style="font-size: 12pt; line-height: 125%;">PHASE</span></u></b></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;">Gerak harmonis sederhana akan lebih mudah diketahui bila dikenal keadaannya (phasenya). Phase suatu titik yang bergetar didefinisikan sebagai waktu sejak meninggalkan titik seimbang dibagi dengan periodenya.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwsQtU_S2MIYnhU0S0zN47Z3melZYzDpK8215dJXXjzWIfAan7UsHMTYbQ57l1J0A-O5v4tIXZRC0ZsQMCsK_KqHjOANGzALLXiJDoy2slc4NBjOD8lYCL0gz2eX6boORbFAcLSRxUO_e-/s1600/10.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqF9lMQLDfmlLrtRg-b0Yx1la_O2xfR8l4OY1N-EME1A7ccdHxWKwQ-j6mtFcptWX4Gu7cFTxt97MDkibUvc6IJvpti-c2UsbVx0N3kS9H9swmpUlgqC5qY1SBTsf_5_iye9ofiJ7etvRj/s1600/13.bmp" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqF9lMQLDfmlLrtRg-b0Yx1la_O2xfR8l4OY1N-EME1A7ccdHxWKwQ-j6mtFcptWX4Gu7cFTxt97MDkibUvc6IJvpti-c2UsbVx0N3kS9H9swmpUlgqC5qY1SBTsf_5_iye9ofiJ7etvRj/s1600/13.bmp" /></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><span style="font-size: 12pt; line-height: 125%;"><br />
</span></div><span style="font-size: 12pt; line-height: 125%;"> </span> <span style="font-size: 12pt; line-height: 125%;"> </span></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><div style="text-align: left;"><div style="text-align: left;"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><div class="MsoNormal" style="line-height: 125%; margin-left: 72pt; text-align: justify;">source : <a href="http://www.blogger.com/goog_517229966">from here (just click)</a></div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac><a href="http://www.blogger.com/goog_517229966"><br />
<m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></a></div><a href="http://www.blogger.com/goog_517229966"><br />
<m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></a></div><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><m:smallfrac m:val="off"><m:dispdef><m:lmargin m:val="0"><m:rmargin m:val="0"><m:defjc m:val="centerGroup"><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><a href="http://adiwarsito.wordpress.com/2010/11/04/materi-ajar-fisika-sma-kelas-xi-ipa/"><span style="font-size: 12pt; line-height: 125%;"> </span></a></div><div class="MsoNormal" style="line-height: 125%; text-align: justify;"><br />
</div></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac></m:defjc></m:rmargin></m:lmargin></m:dispdef></m:smallfrac>nopinophttp://www.blogger.com/profile/07944999515934940876noreply@blogger.com0