Belajar tentang momentum dan tumbukan, yuk! Mulai dari pengertian, jenis-jenis, hingga rumus dan contoh soalnya dibahas lengkap di artikel Fisika kelas 10 ini, lho!
—
Siapa yang pernah main bom bom car? Bom bom car atau dikenal juga dengan nama bumper car adalah permainan mobil-mobilan di mana kita akan mengendarai mobil kecil dalam suatu arena yang sengaja dibuat tidak terlalu luas, supaya mobil yang ada dalam arena dapat bertabrakan satu sama lain.
Lho, kok sengaja main tabrak-tabrakan sih? Emangnya nggak bahaya?
Nggak, dong! Wahana bom bom car telah didesain sedemikian rupa agar tetap aman meskipun mobil kita bertabrakan dengan mobil lain. Arena bermain bom bom car biasanya dibuat tidak terlalu luas, agar mobil tidak dapat melaju dengan kecepatan yang terlalu tinggi. Mobil bom bom car pun hanya mampu melaju dengan kecepatan rendah dengan bagian bemper terbuat dari karet yang tebal untuk meminimalisir tumbukan yang terlalu keras apabila mobil saling bertabrakan.
Kamu tipe yang suka nabrak-nabrakin orang nggak, waktu main bom bom car? (Sumber: giphy.com)
Nah, tahu nggak sih, benda yang memiliki massa dan bergerak dengan kecepatan tertentu, seperti halnya mobil yang sedang melaju, memiliki momentum, lho. Apa yang dimaksud dengan momentum?
Momentum adalah besaran yang menunjukkan ukuran kesukaran untuk memberhentikan gerak suatu benda. Untuk menghentikan benda, diperlukan usaha yang besarnya sama dengan perubahan energi mekaniknya.
Baca Juga: Gerak Melingkar Beraturan (GMB): Besaran, Rumus, dan Contoh Soal
Semakin besar massa suatu benda, maka semakin besar pula usaha yang diperlukan untuk menghentikan benda tersebut, atau dengan kata lain, benda semakin sukar untuk dihentikan. Artinya, semakin besar massa benda, maka momentum yang dimiliki benda akan semakin besar pula. Jadi, dapat disimpulkan bahwa momentum berbanding lurus dengan massa, atau dapat digambarkan sebagai berikut:
Momentum ~ Massa
p ~ m
Begitu pula dengan kecepatan. Semakin besar kecepatan suatu benda, maka semakin besar pula usaha yang diperlukan untuk menghentikan benda tersebut, atau dengan kata lain, benda semakin sukar untuk dihentikan. Artinya, semakin besar kecepatan benda, maka momentum yang dimiliki benda akan semakin besar pula. Jadi, dapat disimpulkan bahwa momentum berbanding lurus dengan kecepatan, atau dapat digambarkan sebagai berikut:
Momentum ~ Kecepatan
p ~ v
Jenis-Jenis Momentum
Momentum terdiri atas dua jenis yaitu momentum linear dan momentum angular. Apa itu? Kita bahas satu per satu, ya.
a. Momentum Linear
Momentum linear adalah momentum dari benda yang bergerak secara translasi. Artinya, momentum ini adalah momentum yang dimiliki oleh benda-benda yang bergeraknya lurus.
b. Momentum Angular
Momentum angular adalah momentum dari benda yang bergerak secara rotasi. Artinya, momentum ini adalah momentum yang dimiliki oleh benda-benda yang bergeraknya melingkar atau berputar.
Rumus Momentum
Karena momentum berbanding lurus dengan massa dan kecepatan, maka momentum dapat dirumuskan sebagai berikut:
Keterangan:
p = momentum (kg m/s)
m = massa (kg)
v = kecepatan (m/s)
Baca Juga: Konsep Hukum Gerak Newton dan Contoh Penerapannya
Pengertian Tumbukan
Ketika membahas soal momentum, kita juga tidak terlepas dari pembahasan tentang tumbukan. Tumbukan adalah interaksi dua buah benda atau lebih yang saling bertukar gaya dalam selang waktu tertentu dan memenuhi hukum kekekalan momentum.
Hukum kekekalan momentum berbunyi:
“Jika tidak ada gaya luar yang bekerja pada sistem, maka momentum sebuah sistem akan selalu konstan.”
Benda yang saling bertabrakan akan mengalami tumbukan yang jenisnya berbeda-beda tergantung dari kondisinya. Jenis-jenis tumbukan ini dibedakan berdasarkan perubahan energi yang terjadi.
Jenis-Jenis Tumbukan
Tumbukan terdiri atas tiga jenis, yaitu tumbukan lenting sempurna, tumbukan lenting sebagian, dan tumbukan tidak lenting sama sekali (tidak elastis).
a. Tumbukan Lenting Sempurna
Tumbukan lenting sempurna terjadi jika energi kinetik sebelum tumbukan sama dengan energi kinetik setelah tumbukan. Dengan kata lain, semua energi kinetik di kondisi awal menjadi energi kinetik di kondisi akhir. Pada tumbukan ini berlaku hukum kekekalan energi mekanik.
b. Tumbukan Lenting Sebagian
Tumbukan lenting sebagian terjadi jika energi kinetik sebelum tumbukan berubah menjadi energi panas, gesekan, bunyi, atau deformasi (energi yang mengubah bentuk benda) setelah tumbukan. Pada tumbukan ini tidak berlaku hukum kekekalan energi mekanik.
c. Tumbukan Tidak Lenting Sama Sekali
Tumbukan tidak lenting sama sekali terjadi jika energi kinetik berubah saat tumbukan, sehingga membuat benda menyatu dan bergerak bersama setelah tumbukan. Tumbukan ini terjadi apabila salah satu benda memiliki massa dan kecepatan yang jauh lebih besar dibandingkan massa dan kecepatan benda lainnya, sehingga benda lainnya yang bermassa dan berkecepatan kecil akan ikut terbawa. Pada tumbukan ini tidak berlaku hukum kekekalan energi mekanik.
Baca Juga: Menghitung Gerak Vertikal dalam Permainan Tenis
Rumus Tumbukan
Pada tumbukan, berlaku persamaan sebagai berikut:
Contoh Soal
Sekarang, kita coba kerjakan latihan soal, yuk! Perhatikan contoh soal di bawah ini:
Kira-kira gimana ya, penyelesaiannya? Kita coba kerjakan dengan menulis besaran-besaran yang diketahui dulu, ya.
Penyelesaian:
Diketahui:
m1 = 2000 kg
m2 = 500 kg
v1 = 120 km/jam
v2 = 0 (diam, tidak memiliki kecepatan)
Ditanya:
v’ = ?
Jawab:
m1 . v1 + m2 . v2 = (m1 + m2) . v’
2000 . 120 + 500 . 0 = (2000 + 500) . v’
240.000 = 2.500 v’
v’ = 96 km/jam
Jadi, kecepatan mobil dan becak setelah tumbukan adalah 96 km/jam.
—
Oke, selesai sudah pembahasan kita tentang momentum dan tumbukan, mulai dari pengertian, jenis-jenis, hingga rumus dan contoh soalnya. Gimana? Mudah dipahami, kan? Kalau kamu butuh pembahasan lebih lanjut mengenai momentum dan tumbukan, kamu bisa lho, cek video pembelajaranya di ruangbelajar! Daftar sekarang!
Sumber Gambar:
GIF ‘Bumper Car’ [Daring]. Tautan: https://giphy.com/gifs/ballinthefamily-bitf-1hzAAFIBjBQXyU6xBO (Diakses: 6 April 2022).
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<h1 class="content-title">
Momentum dan Tumbukan: Pengertian, Jenis & Rumus | Fisika Kelas 10 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kenya-swawikanti" class="">Kenya Swawikanti</a> </p>
<p class="content-info"><span>December 4, 2025 • </span> <span>5 minutes read</span></p>
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<p style="font-weight: bold;"><img decoding="async" style="width: 820px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/momentum%20dan%20tumbukan.jpg" alt="momentum dan tumbukan" width="820" /></p>
<blockquote>
<p style="text-align: center;"><em>Belajar tentang momentum dan tumbukan, yuk! Mulai dari pengertian, jenis-jenis, hingga rumus dan contoh soalnya dibahas lengkap di <strong><a href="https://www.ruangguru.com/blog/c/fisika/fisika-sma-kelas-10">artikel Fisika kelas 10</a></strong> ini, lho!</em></p>
<p style="text-align: center;"><span style="color: #000000;"><em><span style="font-weight: 400;">—</span></em></span></p>
</blockquote>
<p> </p>
<p style="text-align: justify;"><span style="font-weight: 400;"><span style="color: #000000;">Siapa yang pernah main <em>bom bom car</em>? <em>Bom bom car </em>atau dikenal juga dengan nama <em>bumper car </em>adalah permainan mobil-mobilan di mana kita akan mengendarai mobil kecil dalam suatu arena yang sengaja dibuat tidak terlalu luas, supaya mobil yang ada dalam arena dapat bertabrakan satu sama lain. </span></span></p>
<p style="text-align: justify;"><span style="font-weight: 400;"><span style="color: #000000;">Lho, kok sengaja main tabrak-tabrakan sih? Emangnya nggak bahaya?</span></span></p>
<p style="text-align: justify;"><span style="font-weight: 400;"><span style="color: #000000;">Nggak, dong! Wahana</span></span><span style="font-weight: 400;"><span style="color: #000000;"> <em>bom bom car </em>telah didesain sedemikian rupa agar tetap aman meskipun mobil kita bertabrakan dengan mobil lain. Arena bermain <em>bom bom car </em>biasanya dibuat tidak terlalu luas, agar mobil tidak dapat melaju dengan kecepatan yang terlalu tinggi. Mobil <em>bom bom car </em>pun hanya mampu melaju dengan kecepatan rendah dengan </span></span><span style="font-weight: 400;"><span style="color: #000000;">bagian <em>bemper</em> terbuat dari karet yang tebal untuk meminimalisir tumbukan yang terlalu keras apabila mobil saling bertabrakan.</span></span></p>
<p><img decoding="async" style="width: 480px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/bumper%20car.gif" alt="bumper car" width="480" /></p>
<p style="text-align: center;"><span style="color: #000000;"><em>Kamu tipe yang suka nabrak-nabrakin orang nggak, waktu main bom bom car? (Sumber: giphy.com)</em></span></p>
<p> </p>
<p style="text-align: justify;"><span style="color: #000000;">Nah, tahu nggak sih, </span><span style="font-weight: 400; color: #000000;">benda yang memiliki <span style="font-weight: bold;">massa</span> dan bergerak dengan <span style="font-weight: bold;">kecepatan</span> tertentu, seperti halnya mobil yang sedang melaju, memiliki <span style="font-weight: bold;">momentum</span><span style="font-weight: normal;">, lho. Apa yang dimaksud dengan momentum?</span></span></p>
<p> </p>
<h2 style="font-weight: bold; font-size: 20px;"><span style="color: #000000; font-size: 18pt;">Pengertian Momentum</span></h2>
<p style="text-align: justify;"><span style="font-weight: 400; color: #000000;"><span style="font-weight: bold;">Momentum adalah</span> besaran yang menunjukkan <span style="font-weight: bold;">ukuran kesukaran</span> untuk <span style="font-weight: bold;">memberhentikan gerak</span> suatu benda. Untuk menghentikan benda, diperlukan <a href="/blog/daya-usaha" rel="noopener"><span style="font-weight: bold;">usaha</span></a> yang <span style="font-weight: bold;">besarnya sama</span> dengan <span style="font-weight: bold;">perubahan energi mekaniknya</span>.</span></p>
<p style="font-weight: bold; text-align: justify;"><span style="color: #000000;">Baca Juga: <a href="/blog/gerak-melingkar-beraturan-dan-penjelasannya" rel="noopener">Gerak Melingkar Beraturan (GMB): Besaran, Rumus, dan Contoh Soal</a></span></p>
<p style="text-align: justify;"><span style="font-weight: 400; color: #000000;"><span style="font-weight: bold;">Semakin besar massa</span> suatu benda, maka <span style="font-weight: bold;">semakin besar pula usaha</span> yang diperlukan untuk menghentikan benda tersebut, atau dengan kata lain, benda semakin sukar untuk dihentikan. Artinya, semakin besar massa benda, maka <span style="font-weight: bold;">momentum</span> yang dimiliki benda akan <span style="font-weight: bold;">semakin besar pula</span>. Jadi, dapat disimpulkan bahwa <span style="font-weight: bold;">momentum berbanding lurus dengan massa</span>, atau dapat digambarkan sebagai berikut:</span></p>
<blockquote>
<p style="text-align: center; font-weight: bold;"><span style="color: #000000; font-size: 14pt;">Momentum ~ Massa</span></p>
<p style="text-align: center; font-weight: bold;"><span style="font-size: 14pt;"><em><span style="color: #000000;">p ~ m</span></em></span></p>
</blockquote>
<p style="text-align: justify;"><span style="font-weight: 400; color: #000000;">Begitu pula dengan kecepatan. <span style="font-weight: bold;">Semakin besar kecepatan</span> suatu benda, maka <span style="font-weight: bold;">semakin besar pula usaha</span> yang diperlukan untuk menghentikan benda tersebut, atau dengan kata lain, benda semakin sukar untuk dihentikan. Artinya, semakin besar kecepatan benda, maka <span style="font-weight: bold;">momentum</span> yang dimiliki benda akan <span style="font-weight: bold;">semakin besar pula</span>. </span><span style="font-weight: 400; color: #000000;">Jadi, dapat disimpulkan bahwa <span style="font-weight: bold;">momentum berbanding lurus dengan kecepatan</span>, atau dapat digambarkan sebagai berikut:</span></p>
<blockquote>
<p style="text-align: center; font-weight: bold;"><span style="color: #000000; font-size: 14pt;">Momentum ~ Kecepatan</span></p>
<p style="text-align: center; font-weight: bold;"><span style="color: #000000; font-size: 14pt;"><em>p ~ v</em></span></p>
</blockquote>
<p> </p>
<h2 style="font-weight: bold; font-size: 20px;"><span style="color: #000000; font-size: 18pt;">Jenis-Jenis Momentum</span></h2>
<p style="text-align: justify;"><span style="font-weight: 400; color: #000000;">Momentum terdiri atas dua jenis yaitu <span style="font-weight: bold;">momentum linear</span> dan <span style="font-weight: bold;">momentum angular</span>. Apa itu? Kita bahas satu per satu, ya.</span></p>
<h3 style="font-weight: bold; font-size: 16px; text-align: justify;"><span style="color: #000000; font-size: 14pt;">a. Momentum Linear</span></h3>
<p style="font-weight: normal; text-align: justify;"><span style="color: #000000;">Momentum linear adalah momentum dari benda yang <span style="font-weight: bold;">bergerak secara translasi</span>. Artinya, momentum ini adalah momentum yang dimiliki oleh benda-benda yang <span style="font-weight: bold;">bergeraknya lurus</span>.</span></p>
<h3 style="font-weight: bold; font-size: 16px; text-align: justify;"><span style="color: #000000; font-size: 14pt;">b. Momentum Angular</span></h3>
<p style="font-weight: normal; text-align: justify;"><span style="color: #000000;">Momentum angular adalah momentum dari benda yang <span style="font-weight: bold;">bergerak secara rotasi</span>. Artinya, momentum ini adalah momentum yang dimiliki oleh benda-benda yang <span style="font-weight: bold;">bergeraknya melingkar atau berputar</span>.</span></p>
<p> </p>
<h2 style="font-weight: bold; font-size: 20px;"><span style="color: #000000; font-size: 18pt;">Rumus Momentum</span></h2>
<p style="text-align: justify;"><span style="font-weight: 400; color: #000000;">Karena momentum berbanding lurus dengan massa dan kecepatan, maka momentum dapat dirumuskan sebagai berikut:</span></p>
<p><span style="font-weight: 400; color: #000000;"><img decoding="async" style="width: 138px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20momentum.png" alt="rumus momentum" width="138" /></span></p>
<p> </p>
<p style="font-weight: bold;"><span style="color: #000000;">Keterangan:</span></p>
<p><span style="color: #000000;"><em><span style="font-weight: 400;">p </span></em><span style="font-weight: 400;">= momentum (kg m/s)</span></span></p>
<p><span style="color: #000000;"><em><span style="font-weight: 400;">m </span></em><span style="font-weight: 400;">= massa (kg)</span></span></p>
<p><span style="color: #000000;"><em><span style="font-weight: 400;">v </span></em><span style="font-weight: 400;">= kecepatan (m/s)</span></span></p>
<p style="font-weight: bold;"><span style="color: #000000;">Baca Juga: <a href="/blog/hukum-gerak-newton" rel="noopener">Konsep Hukum Gerak Newton dan Contoh Penerapannya</a></span></p>
<p> </p>
<h2 style="font-weight: bold; font-size: 20px;"><span style="color: #000000; font-size: 18pt;">Pengertian Tumbukan</span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Ketika membahas soal momentum, kita juga tidak terlepas dari pembahasan tentang tumbukan. <span style="font-weight: bold;">Tumbukan adalah</span> interaksi dua buah benda atau lebih yang saling <span style="font-weight: bold;">bertukar gaya</span> dalam selang <span style="font-weight: bold;">waktu tertentu</span> dan memenuhi <span style="font-weight: bold;">hukum kekekalan momentum</span>. </span></p>
<p style="text-align: justify;"><span style="color: #000000;">Hukum kekekalan momentum berbunyi:</span></p>
<p style="font-weight: bold; text-align: justify;"><span style="color: #000000;">“Jika tidak ada gaya luar yang bekerja pada sistem, maka momentum sebuah sistem akan selalu konstan.”</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Benda yang saling bertabrakan akan mengalami tumbukan yang jenisnya berbeda-beda tergantung dari kondisinya. </span><span style="color: #000000;"><span style="font-weight: bold;">Jenis-jenis tumbukan</span> ini dibedakan berdasarkan <span style="font-weight: bold;">perubahan energi</span> yang terjadi.</span></p>
<p><span style="color: #000000;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/hukum%20kekekalan%20energi.jpg" alt="hukum kekekalan energi" width="600" /></span></p>
<p> </p>
<h2 style="font-weight: bold; font-size: 20px;"><span style="color: #000000; font-size: 18pt;">Jenis-Jenis Tumbukan</span></h2>
<p style="text-align: justify;"><span style="color: #000000;">Tumbukan terdiri atas tiga jenis, yaitu tumbukan <span style="font-weight: bold;">lenting sempurna</span>, tumbukan <span style="font-weight: bold;">lenting sebagian</span>, dan tumbukan <span style="font-weight: bold;">tidak lenting sama sekali </span><span style="font-weight: normal;">(tidak elastis).</span></span></p>
<p> </p>
<h3 style="font-size: 16px; text-align: justify;"><span style="color: #000000; font-size: 14pt;"><span style="font-weight: normal;"><span style="font-weight: bold;">a. Tumbukan</span> <span style="font-weight: bold;">Lenting Sempurna</span></span></span></h3>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: normal;">Tumbukan lenting sempurna terjadi jika <span style="font-weight: bold;"><a href="/blog/hubungan-energi-kinetik-dengan-kecepatan-gerak-partikel" rel="noopener">energi kinetik</a> sebelum tumbukan</span> <span style="font-weight: bold;">sama dengan</span> <span style="font-weight: bold;">energi kinetik setelah tumbukan</span>. Dengan kata lain, <span style="font-weight: bold;">semua energi kinetik di kondisi awal menjadi energi kinetik di kondisi akhir</span>. Pada tumbukan ini <span style="font-weight: bold;">berlaku hukum kekekalan energi mekanik</span>.</span></span></p>
<p> </p>
<h3 style="font-weight: bold; font-size: 16px; text-align: justify;"><span style="color: #000000; font-size: 14pt;">b. Tumbukan Lenting Sebagian</span></h3>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: normal;">Tumbukan lenting sebagian terjadi jika <span style="font-weight: bold;">energi kinetik sebelum tumbukan berubah menjadi energi panas, gesekan, bunyi, atau deformasi</span> (energi yang mengubah bentuk benda) <span style="font-weight: bold;">setelah tumbukan</span>. Pada tumbukan ini <span style="font-weight: bold;">tidak berlaku</span> <span style="font-weight: bold;">hukum kekekalan energi mekanik</span>.</span></span></p>
<p> </p>
<h3 style="font-size: 16px; text-align: justify;"><span style="color: #000000; font-size: 14pt;"><span style="font-weight: normal;"><span style="font-weight: bold;">c. Tumbukan Tidak Lenting Sama Sekali</span></span></span></h3>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: normal;">Tumbukan tidak lenting sama sekali terjadi jika <span style="font-weight: bold;">energi kinetik berubah saat tumbukan</span>, sehingga membuat <span style="font-weight: bold;">benda menyatu dan bergerak bersama setelah tumbukan</span>. Tumbukan ini terjadi apabila <span style="font-weight: bold;">salah satu benda</span> memiliki <span style="font-weight: bold;">massa dan kecepatan</span> yang <span style="font-weight: bold;">jauh lebih besar</span> dibandingkan massa dan kecepatan benda lainnya, sehingga benda lainnya yang bermassa dan berkecepatan kecil akan ikut terbawa. Pada tumbukan ini <span style="font-weight: bold;">tidak berlaku</span> <span style="font-weight: bold;">hukum kekekalan energi mekanik</span>.</span></span></p>
<p style="font-weight: bold; text-align: justify;"><span style="color: #000000;">Baca Juga: <a href="/blog/fisika-kelas-10-menghitung-gerak-vertikal-dalam-permainan-tenis" rel="noopener">Menghitung Gerak Vertikal dalam Permainan Tenis</a></span></p>
<p> </p>
<h2 style="font-weight: bold; font-size: 20px;"><span style="color: #000000; font-size: 18pt;">Rumus Tumbukan</span></h2>
<p><span style="color: #000000;">Pada tumbukan, berlaku persamaan sebagai berikut:</span></p>
<p><span style="color: #000000;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/rumus%20(persamaan)%20yang%20berlaku%20pada%20tumbukan.jpg" alt="rumus (persamaan) yang berlaku pada tumbukan" width="600" /></span></p>
<p> </p>
<h2 style="font-weight: bold; font-size: 20px;"><span style="color: #000000; font-size: 18pt;">Contoh Soal</span></h2>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">Sekarang, kita coba kerjakan latihan soal, yuk! Perhatikan contoh soal di bawah ini:</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/latihan%20soal%20momentum%20dan%20tumbukan.jpg" alt="latihan soal momentum dan tumbukan" width="600" /></span></span></p>
<p> </p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">Kira-kira gimana ya, penyelesaiannya? Kita coba kerjakan dengan menulis besaran-besaran yang diketahui dulu, ya.</span></span></p>
<p style="text-align: justify; font-weight: bold;"><span style="color: #000000;">Penyelesaian:</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">Diketahui:</span></span></p>
<p style="text-align: justify;"><em><span style="color: #000000;"><span style="font-weight: 400;">m<sub>1</sub></span></span></em><span style="color: #000000;"><span style="font-weight: 400;"> = 2000 kg</span></span></p>
<p style="text-align: justify;"><em><span style="color: #000000;"><span style="font-weight: 400;">m<sub>2</sub></span></span></em><span style="color: #000000;"><span style="font-weight: 400;"> = 500 kg</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;"><em>v<sub>1</sub></em> = 120 km/jam</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;"><em>v<sub>2</sub></em> = 0 (diam, tidak memiliki kecepatan)</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">Ditanya:</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;"><em>v’</em> = ?</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">Jawab:</span></span></p>
<p style="text-align: justify;"><em><span style="color: #000000;"><span style="font-weight: 400;">m<sub>1</sub> . v<sub>1</sub> + m<sub>2</sub> . v<sub>2</sub> = (m<sub>1</sub> + m<sub>2</sub>) . v’</span></span></em></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">2000 . 120 + 500 . 0 = (2000 + 500) . <em>v’</em></span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">240.000 = 2.500 <em>v’</em></span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;"><em>v’</em> = 96 km/jam</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">Jadi, kecepatan mobil dan becak setelah tumbukan adalah <span style="font-weight: bold;">96 km/jam</span>.</span></span></p>
<p style="text-align: center;"><span style="color: #000000;"><span style="font-weight: 400;">—</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: 400;">Oke, selesai sudah pembahasan kita tentang momentum dan tumbukan, mulai dari pengertian, jenis-jenis, hingga rumus dan contoh soalnya. Gimana? Mudah dipahami, kan? Kalau kamu butuh pembahasan lebih lanjut mengenai momentum dan tumbukan, kamu bisa lho, cek video pembelajaranya di <a href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener"><span style="font-weight: bold;">ruangbelajar</span></a>! Daftar sekarang!</span></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><a href="https://app.ruangguru.com/ruangbelajar/"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/a2dbab8e-e903-4b70-ae04-39ff5807647e.jpg" alt="CTA ruangbelajar" /></a></span></p>
<p style="font-weight: bold; text-align: left;"><span style="color: #000000;">Sumber Gambar:</span></p>
<p style="font-weight: normal; text-align: left;"><span style="color: #000000;">GIF ‘Bumper Car’ [Daring]. Tautan: https://giphy.com/gifs/ballinthefamily-bitf-1hzAAFIBjBQXyU6xBO (Diakses: 6 April 2022).</span></p>
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<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>