[spec] variable forces and right angle pulleys

diff --git a/spec/dynamics.pdf b/spec/dynamics.pdf
index 031b21cd32c0cd89736ff69428b20b2166924064..ca06d3747805d82297d78caf4cf3f3f531790f1d 100644 (file)
Binary files a/spec/dynamics.pdf and b/spec/dynamics.pdf differ

diff --git a/spec/dynamics.tex b/spec/dynamics.tex
index 83eb5a2d89055fd231ca350e137ec30554703ddd..5891f4e7195bc967116ba2e5f1aaf8e22b49f49b 100644 (file)
--- 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
 \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}
 
   \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.
 
 
 \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}
 \end{document}