Hukum Newton Tentang Gerak

 

Gaya Sentripetal
A. Percepatan sentripetal

Percepatan sentripetal adalah percepatan yang muncul pada benda yang bergerak melingkar.

Percepatan sentripetal selalu mengarah pada pusat lingkaran.

 

Rendered by QuickLaTeX.com

 

\(a_s = \dfrac {v^2}{R} = \omega^2 \:.\: R\)

B. Gaya sentripetal

Sama seperti percepatan sentripetal, gaya sentripetal juga bekerja pada benda yang bergerak melingkar dan arahnya menuju pusat lingkaran.

 

\(F_s = m \:.\: a_s\)

\(F_s = m \:.\: \dfrac {v^2}{R} = m \:.\: \omega^2 \:.\: R\)

C. Ayunan Konis

Sebuah batu diikat pada ujung tali dan diputar horizontal seperti gambar di bawah ini:

 

Rendered by QuickLaTeX.com

Diagram gaya

Rendered by QuickLaTeX.com

 

 

\begin{equation*} \begin{split} \Sigma F_x & = m \:.\: a_s \\\\ T \sin \theta & = m \:.\: \frac {v^2}{R} \quad {\color {red} \dotso \: (1)} \end{split} \end{equation*}

\begin{equation*} \begin{split} \Sigma F_y & = 0 \\\\ T \cos \theta & = m \:.\: g \quad {\color {red} \dotso \: (2)} \end{split} \end{equation*}

 

 

Eliminasi persamaan (1) dan (2)

\begin{equation*} \begin{split} \frac {\cancel{T} \sin \theta}{\cancel{T} \cos \theta} & = \frac {m \:.\: \dfrac {v^2}{R}}{m \:.\: g } \\\\ \tan \theta & = \frac {\dfrac {v^2}{R}}{g} \\\\ \tan \theta & = \frac {v^2}{g R} \\\\ v^2 & = gR \tan \theta \\\\ v & = \sqrt{gR \tan \theta} \end{split} \end{equation*}

\begin{equation*} \begin{split} \sin \theta & = \frac {R}{L} \\\\ R & = L \sin \theta \end{split} \end{equation*}

D. Tikungan jalan dengan kemiringan θ

 

Rendered by QuickLaTeX.com

Diagram gaya

Rendered by QuickLaTeX.com

 

 

\begin{equation*} \begin{split} \Sigma F_x & = m \:.\: a_s \\\\ N \sin \theta & = m \:.\: \frac {v^2}{R} \quad {\color {red} \dotso \: (1)} \end{split} \end{equation*}

\begin{equation*} \begin{split} \Sigma F_y & = 0 \\\\ N \cos \theta & = m \:.\: g \quad {\color {red} \dotso \: (2)} \end{split} \end{equation*}

 

 

Eliminasi persamaan (1) dan (2)

\begin{equation*} \begin{split} \frac {\cancel{N} \sin \theta}{\cancel{N} \cos \theta} & = \frac {\cancel{m} \:.\: \dfrac {v^2}{R}}{\cancel{m} \:.\: g } \\\\ \tan \theta & = \frac {\dfrac {v^2}{R}}{g} \\\\ \tan \theta & = \frac {v^2}{g \:.\: R} \\\\ v^2 & = g \:.\: R \:.\: \tan \theta \\\\ v & = \sqrt{g \:.\: R \:.\: \tan \theta} \end{split} \end{equation*}

E. Tikungan jalan dengan koefisien gesekan μ

 

Rendered by QuickLaTeX.com

Diagram gaya

Rendered by QuickLaTeX.com

 

 

\begin{equation*} \begin{split} \Sigma F_x & = m \:.\: a_s \\\\ f_s & = m \:.\: a_s \\\\ \mu_s \:.\: N & = m \:.\: \frac {v^2}{R} \quad {\color {red} \dotso \: (1)} \end{split} \end{equation*}

\begin{equation*} \begin{split} \Sigma F_y & = 0 \\\\ N & = m \:.\: g \quad {\color {red} \dotso \: (2)} \end{split} \end{equation*}

 

 

Eliminasi persamaan (1) dan (2)

\begin{equation*} \begin{split} \frac {\mu_s \:.\: \cancel{N}}{\cancel{N}} & = \frac {\cancel{m} \:.\: \dfrac {v^2}{R}}{\cancel{m} \:.\: g } \\\\ \mu_s & = \frac {\dfrac {v^2}{R}}{g} \\\\ \mu_s & = \frac {v^2}{g \:.\: R} \\\\ v^2 & = g \:.\: R \:.\: \mu_s \\\\ v & = \sqrt{g \:.\: R \:.\: \mu_s} \end{split} \end{equation*}

 

SOAL LATIHAN

--- Buka halaman ini ---

Gaya kontak dan tegangan tali (Prev Lesson)
(Next Lesson) Persiapan ulangan 1