From: Andrew Lorimer Date: Tue, 27 Aug 2019 22:58:13 +0000 (+1000) Subject: [spec] variable forces and right angle pulleys X-Git-Tag: yr12~52 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/c0dc70858af633fbee6fd88e78c4f4caef925996?ds=sidebyside [spec] variable forces and right angle pulleys --- diff --git a/spec/dynamics.pdf b/spec/dynamics.pdf index 031b21c..ca06d37 100644 Binary files a/spec/dynamics.pdf and b/spec/dynamics.pdf differ diff --git a/spec/dynamics.tex b/spec/dynamics.tex index 83eb5a2..5891f4e 100644 --- a/spec/dynamics.tex +++ b/spec/dynamics.tex @@ -161,6 +161,7 @@ A mass of \(m\) kg has force of \(mg\) acting on it \begin{itemize} \item \textbf{Suspended pulley:} tension in both sections of rope are equal \item \textbf{Linear connection:} find acceleration of system first + \item \textbf{Pulley on right angle:} \(a = \frac{m_2g}{m_1+m_2}\) where \(m_2\) is suspended (frictionless on both surfaces) \item \textbf{Pulley on edge of incline:} find downwards force \(W_2\) and components of mass on plane \end{itemize} @@ -245,4 +246,8 @@ Three methods: \colorbox{cas}{On CAS:} use Geometry, lock known constants. +\section{Variable forces (DEs)} + +\[ a = \dfrac{d^2x}{dt^2} = \dfrac{dv}{dt} = v\dfrac{dv}{dx} = \dfrac{d}{dx} \left( \frac{1}{2} v^2 \right) \] + \end{document}