From: Andrew Lorimer <andrew@lorimer.id.au>
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}