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zu@xrF#N~C0c)8u<+oxgNVq=#*A$~2GyVcI@Ar(RGR?vWRgxKj|WbAoqG@t0;I1H}V zv#i@RgjBjgACG!Ak1He2TKfMJhyug1uc*yqY{UL}!oH@7R9?axbMRFDfPGksf4why z)b-Z!{?5@{!_cxR<_-#ekYv>}(8briL^EoWtfloGUHL8u;ZU1|YCcuCNNCI6zbZ)B zB&K?V*Hw8)$cwLG&Cf8l_K%QUDv>cBidQfg&2-LUkX^|1&GaA~Bwas# zt6E5+h5fYhGt+=X5!bTZ0{;WQb8~kEm^%Dt^dEH{uA955tGl-= Vz!HI-hliJo8-bcyN<|vse*j-OKj{Df 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} -- 2.47.1