DINAMIKA PARTIKEL

DINAMIKA PARTIKEL

Dinamika partikel adalah cabang mekanika yang mempelajari gerak suatu partikel dengan meninjau penyebab geraknya. Gerak dari suatu partikel dipengaruhi oleh sifat-sifat dan susunan benda lain yang ada disekitarnya. Persoalan pengaruh lingkungan yang mempengaruhi gerak suatu partikel telah dipecahkan oleh Issac Newton (1642-1727) yang digambarkan dengan menggunakan hanya tiga hukum sederhana yang dinamakan dengan hukum Newton tentang gerak.

  1. Hukum I Newton

Hukum pertama Newton menyatakan bahwa sebuah benda dalam keadaan diam atau bergerak dengan kecepatan konstan akan tetap diam atau bergerak dengan kecepatan konstan kecuali ada gaya eksternal yang berpengaruh pada benda tersebut. Kecenderungan dari sifat benda seperti itu disebutkan bahwa benda mempunyai kelembaman, sehubungan dengan itu, hukum I Newton sering disebut hukum kelembaman/inersia. Hukum pertama Newton tidak membuat perbedaan antara benda yang diam dengan benda yang bergerak dengan kecepatan konstan, pertanyaan apakah suatu benda sedang diam atau bergerak denan kecepatan konstan bergantung pada kerangka dimana benda tersebut diamati. Hukum pertama Newton berlaku pada kerangka acuan yang inersial, yaitu kerangka acuan yang bergerak dengan kecepatan konstan atau diam.

  1. Hukum II Newton

Pada hakikatnya, hukum pertama dan hukum kedua Newton dianggap sebagai definisi gaya. Gaya adalah suatu pengaruh pada sebuah benda yang menyebabkan benda mengubah kecepatannya atau mengalami percepatan. Arah gaya sama dengan arah pecepatan yang ditimbulkan oleh gaya tersebut jika gaya itu adalah satu-satunya gaya yang bekerja pada benda yang bermassa. Massa adalah sifat intrinsik sebuah benda yang mengukur resistansinya terhadap percepatan. Jika gaya dikerjakan pada benda bermassa m1, dan menghasilkan percepatan a1, maka

F = m1a1

Jika gaya yang sama dikerjakan pada benda kedua yang massanya mdan menghasilkan percepatan a2 maka

F = m2a2

Dengan menggabungkan kedua persamaan diatas kita dapatkan

F = m1a1m2a2

Atau

Hubungan tersebut dapat digunakan untuk menentukan perbandingan massa-massa partikel yang diukur dari pengukuran yang terjadi pada m1 dan m2. Jika m1dipilih sebagai satuan massa maka massa partikel lain dapat ditentukan. Massa dari benda yang ditentukan dengan cara tersebut dinamakan dengan perbandingan massa Inersia

Dari definisi tentang gaya dan massa diatas, Newton menyatakan dalam hukum II Newton, yaitu “laju perubahan momentum benda terhadap waktu berbanding lurus dengan resultan gaya yang bekerja pada benda dan besarnya sama dengan gaya tersebut

Dari persamaan diatas dapat dilihat bahwa percepatan berbanding lurus dengan gaya yang bekerja dan berbanding terbalik dengan massa benda. Atau dapat dikatakan besar percepatan benda bila dikalikan dengan massanya akan sama dengan besar gaya yang bekerja pada benda tersebut.

Momentum sebuah partikel secara matematis didefinisikan sebagai hasil kali massa dengan kecepatan, sedangkan secara fisisnya momentum sebuah partikel dianggap sebagai ukuran kesulitan untuk mendiamkan suatu benda.

  1. Hukum III Newton

Hukum ketiga Newton kadang-kadang dinamakan hukum interaksi atau aksi reaksi. Hukum ini menggambarkan sifat penting dari gaya, yaitu bahwa gaya selalu terjadi bersama-sama. Misalkan F12 adalah gaya yang dikerjakan oleh partikel 1 pada partikel 2, dan F21 adalah gaya oleh partikel 2 pada partikel 1.

Persamaan ini dikenal dengan Hukum kekekalan momentum, dengan penjelasan “jika resultan gaya eksternal yag bekerja pada sistem sama dengan nol, maka vektor momentum total sistem tetap konstan.

Momentum Sudut

Pada gerak rotasi momen inersia I merupakan analogi dari massa m dan kecepatan sudut merupakan analogi dari kecepatan linear v, maka rumus momentum sudut dapat ditulis sebagai

L = r x p

= r. p sin q

= r . m

= r. mwr

= mr2w

Momentum sudut merupakan besaran vektor. Arah momentum sudut mengikuti aturan tangan kanan, yaitu apabila keempat jari tangan kanan (selain jempol) dikepalkan mengikuti arah rotasi benda, maka jempol yang teracung menunjukkan arah momentum sudut.

Hubungan Momentum Sudut dengan Momen Gaya

Mengingat hubungan impuls dengan momentum Fdt = dp pada gerak linear, maka secara analogi, pada gerak rotasi diperoleh

Ndt=dL

Keterangan :

L = Momentum sudut (kg.m2/s)

I = Momen inersia (kg.m2)

N = Momen gaya (N.m)

Kekekalan Momentum Sudut

F = m.a

 Jika SF = 0 maka dp = 0 atau p = konstanta hukum kekekalan momentum linear dari persamaan diatas dapat diturunkan kaitan momentum sudut dengan momen gaya yaitu:

Jika t = 0 maka L = konstan atau dengan kata lain momentum sudut sistem kekal. Dari persamaan diatas kita peroleh jika tidak ada momen gaya luar yang bekerja pada sistem , maka momentum sudut konstan, atau dengan kata lain dapat disebut prinsip kekekalan momentum sudut. Secara matematis, kekekalan momentum sudut ditulis sebagai

L1=L2

Hubungan Massa dengan Dinamika Partikel

Massa adalah ukuran inersia suatu benda. Makin besar massa yang dimiliki sebuah benda, maka makin sulit merubah keadaan geraknya. Lebih sulit menggerakkannya dari keadaan diam atau memberhentikannya pada waktu sedang bergerak, bahkan sulit merubah gerakannya untuk keluar dari lintasannya yang lurus. Sebuah truk misalnya, akan memiliki inersia yang lebih besar jika dibandingkan dengan sebuah mobil sedan, dan truk itu lebih sulit untuk dipercepat ataupun diperlambat geraknya. Dalam satuan SI, satuan massa adalah kilogram (kg).

Istilah massa dan berat merupakan dua istilah yang berbeda. Jika massa adalah jumlah zat dari suatu benda, maka berat adalah gaya, yaitu gaya gravitasi yang bekerja pada sebuah benda. Sebagai contoh misalnya sebuah benda di bawa ke Bulan. Maka benda tersebut akan mempunyai berat seperenam dari beratnya di bumi, karena gaya gravitasi di bulan lebih lemah, tetapi massa benda tersebut akan tetap sama. Benda tersebut akan tetap memiliki jumlah zat yang sama dan inersia yang sama.

Jenis-Jenis Gaya Dalam Dinamika Partikel

Gaya

Jika kita mendorong atau menarik sebuah benda , maka dapat dikatakan bahwa kita melakukan gaya kepada benda tersebut. Tetapi gaya juga dapat dilakukan oleh bendabenda mati. Seperti pegas yang regang akan melakukan gaya kepada benda-benda yang dikaitkan ke ujung-ujungnya, atau sebuah lokomotif akan melakukan gaya kepada deretan gerbong-gerbong yang sedang ditariknya.

Sebuah gaya memiliki arah dan besar, sehingga gaya merupakan vektor yang mengikuti aturan-aturan penjumlahan vektor. Gaya dapat dinyatakan dengan sebuah garis yang bertanda panah di ujungnya sebagai arah dari gaya tersebut sedangkan panjang garis menyatakan besar gaya tersebut. Dalam satuan SI, satuan gaya adalah Newton (N) atau kg.m/s2.

Gaya Gravitasi

Benda-benda yang dijatuhkan di dekat permukaan bumi akan jatuh dengan percepatan yang sama yaitu sebesar percepatan gravitasi (g = 9,8 m/s2 = 9,8 N/kg dalam satuan SI), jika hambatan udara dapat diabaikan. Gaya yang menyebabkan percepatan ini disebut dengan gaya gravitasi (FG). Maka dapat dikatakan bahwa gaya gravitasi merupakan gaya yang dilakukan oleh bumi terhadap setiap benda yang berada di dekatnya.

Gaya Normal

Gaya normal (N atau FN) merupakan gaya yang timbul jika dua buah benda saling bersentuhan. Arah gaya normal selalu tegak lurus terhadap permukaan yang bersentuhan (bidang singgung) dengan benda tersebut (gambar dibawah). Besar kecilnya gaya normal tergantung pada besar kecilnya gaya tekanan terhadap permukaan kontak (bidang singgung). Jadi jika tangan kita menekan permukaan sebuah meja dengan gaya tekan yang besar, maka gaya normal yang ditimbulkan akan besar. Sedangkan jika kita menekan dengan lembut, maka gaya normal yang ditimbulkan juga akan kecil.

Gaya Gesek

Sebuah benda yang diluncurkan di atas suatu permukaan rata horizontal, maka lajunya akan berkurang dan akhirnya berhenti. Jelas bahwa suatu gaya dalam arah horizontal bekerja pada benda tersebut, dimana arah gaya tersebut berlawanan dengan gerak benda. Gaya ini biasa disebut sebagai gaya gesek (f) yang bekerja pada benda tersebut dan disebabkan oleh permukaan itu. Gaya gesek terjadi jika dua buah benda bergesekan, yaitu permukaan kedua benda tersebut saling bersinggungan pada waktu benda yang satu bergerak terhadap benda yang lainnya dan sejajar dengan permukaan yang saling bersinggungan tersebut. Arah gaya gesek selalu berlawanan arah dengan arah gerak dari benda yang bergerak. Gaya gesek yang bekerja antara dua permukaan yang berada dalam keadaan diam relatif satu dengan lainnya disebut dengan gaya gesek statik (fs). Gaya gesek statik maksimum adalah gaya terkecil yang menyebabkan benda bergerak. Untuk permukaan yang kering dan tidak diberi pelumas, diperoleh bahwa gaya gesek statik maksimum diantara dua permukaan tidak bergantung pada luas permukaan kontak yang saling bergesekan, tetapi sebanding dengan besarnya gaya normal diantara kedua benda yang saling bergesekan. Sekali benda mulai bergerak, gaya gesek yang bekerja akan berkurang besarnya sehingga untuk mempertahankan gerak lurus beraturan dibutuhkan gaya yang lebih kecil. Gaya yang bekerja diantara dua permukaan yang saling bergerak relatif disebut gaya gesek kinetik (fk). Untuk permukaan yang kering dan tidak diberi pelumas, diperoleh bahwa gaya gesek kinetik tidak bergantung pada luas permukaan kontak atau pada kecepatan relatif antara kedua permukaan yang saling bersinggungan, tetapi sebanding dengan besarnya gaya normal diantara kedua benda yang saling bergesekan.

Demikianlah pembahasan tentang Dinamika Partikel, semoga bermanfaat. 🙂

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