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% Document Info
\author{MostAncientDream}
\pdfinfo{
  /Title (alvl-p1-work-energy-and-power-ch6.pdf)
  /Creator (Cheatography)
  /Author (MostAncientDream)
  /Subject (Alvl P1: work, energy and power (ch6) Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Alvl P1: work, energy and power (ch6) Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{MostAncientDream} via \textcolor{DarkBackground}{\uline{cheatography.com/168994/cs/42315/}}}
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\noindent
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}MostAncientDream \\
  \uline{cheatography.com/mostancientdream} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 9th February, 2024.\\
   Updated 8th February, 2024.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
\raggedright
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% Set font size to small. Switch to any value
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% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Work Done and Energy}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Work done is {\bf{maximum}} when cos0 = 0 (the force and distance travelled are therefore parallel) \newline % Row Count 2 (+ 2)
Work done is {\bf{minimum}} when cos0 = 90 (the force and distance travelled are therefore perpendicular) \newline % Row Count 5 (+ 3)
types of energy: \newline % Row Count 6 (+ 1)
- kinetic energy \newline % Row Count 7 (+ 1)
- potential energy \newline % Row Count 8 (+ 1)
- thermal energy (not covered in this spec point) \newline % Row Count 9 (+ 1)
for example: \newline % Row Count 10 (+ 1)
      a ball held at a height will have Ep, when dropped and landing on the ground (assuming there is no energy loss) all the energy will be converted into Ek. \newline % Row Count 14 (+ 4)
	Δ E = W  -{}-\textgreater{} change in energy in a system = work done on a system% Row Count 16 (+ 2)
} \tn 
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Derrivations}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{Gravitational Potential Energy: \newline % Row Count 1 (+ 1)
ΔE = W \newline % Row Count 2 (+ 1)
ΔE = Fxcos0        \newline % Row Count 3 (+ 1)
(work done is force x distance x angle) \newline % Row Count 4 (+ 1)
where F = ma (in this case a is g) \newline % Row Count 5 (+ 1)
and distance is hieght travelled \newline % Row Count 6 (+ 1)
ΔE = mghcos0 \newline % Row Count 7 (+ 1)
as cos0 where 0 is 0' cos0 = 1 so  \newline % Row Count 8 (+ 1)
ΔE = mgh \newline % Row Count 9 (+ 1)
Kinetic Energy: \newline % Row Count 10 (+ 1)
ΔE = W \newline % Row Count 11 (+ 1)
ΔE = Fxcos0        \newline % Row Count 12 (+ 1)
(work done is force x distance x angle) \newline % Row Count 13 (+ 1)
ΔE = Fs  \newline % Row Count 14 (+ 1)
(cos0 = 1) \newline % Row Count 15 (+ 1)
ΔE = mas \newline % Row Count 16 (+ 1)
as v\textasciicircum{}2\textasciicircum{} = u\textasciicircum{}2\textasciicircum{} + 2as \newline % Row Count 17 (+ 1)
rearrange where u = 0  \newline % Row Count 18 (+ 1)
as = v\textasciicircum{}2\textasciicircum{}/2 \newline % Row Count 19 (+ 1)
therefore \newline % Row Count 20 (+ 1)
ΔE = 1/2 mv\textasciicircum{}2\textasciicircum{}% Row Count 21 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{1.44 cm} x{6.56 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Definitions}}  \tn
% Row 0
\SetRowColor{LightBackground}
Work done & product of the force and the distance moved in this direction \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
power & rate of work done \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
 & rate of energy transferred \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{2.32 cm} x{5.68 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Equations}}  \tn
% Row 0
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Work done & Fxcos0  -{}-{}-(where x is distance and 0 is theta between f and x) \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
change in energy & ΔE = W \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
power & W/t \tn 
% Row Count 6 (+ 1)
% Row 3
\SetRowColor{white}
 & Fx/t \tn 
% Row Count 7 (+ 1)
% Row 4
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 & Fv \tn 
% Row Count 8 (+ 1)
% Row 5
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efficiency & useful/total (x100) \tn 
% Row Count 9 (+ 1)
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Conversion of energy}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{8.4cm}}{example of findign resistive forces going down hill \newline % Row Count 2 (+ 2)
-{}-top | v=0   \newline % Row Count 3 (+ 1)
-{}-{}-{}-{}-{}-|  \newline % Row Count 4 (+ 1)
-{}-{}-{}-{}-{}-{}-|  \newline % Row Count 5 (+ 1)
-{}-{}-{}-{}-{}-{}--|  \newline % Row Count 6 (+ 1)
 -{}-bottom | v=8 \newline % Row Count 7 (+ 1)
a ball is roll down from the top to the bottom \newline % Row Count 8 (+ 1)
-length of the ramp is 7m \newline % Row Count 9 (+ 1)
-height is 5m \newline % Row Count 10 (+ 1)
as ΔE = W \newline % Row Count 11 (+ 1)
energy at top (Ep no Ek) then energy at bottom (Ek no Ep) \newline % Row Count 13 (+ 2)
from this we know it is all transferred (assuming no loss to heat) therefore \newline % Row Count 15 (+ 2)
ΔE = mgh - 1/2mv\textasciicircum{}2\textasciicircum{} \newline % Row Count 16 (+ 1)
mgh - 1/2mv\textasciicircum{}2\textasciicircum{} = Fx  \newline % Row Count 17 (+ 1)
(where x is length of ramp)  \newline % Row Count 18 (+ 1)
then just put in numbers to solve for F% Row Count 19 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}