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Gerak Partikel Pada Permukaan Bola - Fisika Dasar

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Sebuah partikel bergerak dari keadaan diam sampai posisi P₁ pada suatu permukaan bola yang halus yang memiliki jari-jari R. Pada posisi P₂ partikel tersebut terlepas dari permukaan. Carilah hubungan antara θ₁ dan θ₂.

Solusi

Persoalan di atas bisa digambarkan seperti gambar di bawah.

Karena gaya normal tak melakukan usaha kepada partikel maka energi sistem kekal. Sehingga:

(K + U)_P1 = (K + U)_P2

Atau

Pada posisi P₂, gaya normal yang menekan permukaan hilang dan meninggalkan komponen radial dari berat partikel mg sin θ₂ sebagai gaya sentripetal. Sehingga hukum kedua Newton menjadi:

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