Talk:PlanetPhysics/Power
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[edit source]%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: power %%% Primary Category Code: 40. %%% Filename: Power.tex %%% Version: 6 %%% Owner: bloftin %%% Author(s): bloftin, pahio %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}
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\begin{document}
\section{Power}
Power is the rate of \htmladdnormallink{energy}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} transfer. Since there are several forms of energy, there are several ways of describing power. In general terms of energy, power is defined as
$$P = \frac{dE}{dt}.$$
\subsection{Mechanical Power}
The energy transfer in mechanical \htmladdnormallink{systems}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html} where \htmladdnormallink{work}{http://planetphysics.us/encyclopedia/Work.html} is done by an applied force
$$ P = \frac{dE}{dt} = \frac{dW}{dt}.$$
Using the \htmladdnormallink{relation}{http://planetphysics.us/encyclopedia/Bijective.html} between work and force
$$ dW = {\bf F} \cdot d{\bf r}$$
and then differentiating to get power,
$$P = \frac{dW}{dt} = {\bf F} \cdot \frac{d{\bf r}}{dt} = {\bf F} \cdot {\bf v}.$$
The corresponding form of power in rotation is
$$P = {\bf M} \cdot {\bf \omega},$$
where ${\bf M}$ is the torque and ${\bf \omega}$ the angular \htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html} \htmladdnormallink{vector}{http://planetphysics.us/encyclopedia/Vectors.html}.
\subsection{Electrical Power}
Since energy is transfering from a device storing electrical energy to another device in the circuit that converts to another form of energy, power is the rate of change of electrical potential energy. For a DC circuit
$$P = \frac{dU}{dt} = i V.$$
\subsection{Units}
The SI unit of the power is one joule per second, which is called {\em watt}:
$$\frac{\mathrm{J}}{\mathrm{s}} := \mathrm{W}.$$
The watt is equal to $\mathrm{kg \cdot m^2/s^3}$ in the base units.
The english units of power are
$$ 1 \left [horsepower \right] = 1 \left [hp \right] = 550 \left [\frac{ft \, lb}{s} \right]$$
\begin{table}[t] \begin{center}
\begin{tabular}{ll}
\\ [.3ex] \hline \\ [.3ex]
\hline \\ [.3ex]
1 joule/second & = 1 watt \\ 1,000 watts & = 1 kilowatt \\ 746 watts & = 1 horsepower \\ 550 ft-lb/sec & = 1 horsepower \\ 33,000 ft-lb/min & = 1 horsepower \\ [1ex]
\hline \end{tabular}
\end{center}
\end{table}
\begin{thebibliography}{9} \bibitem{Frye} Frye, Royal M., {\em Applied Physics}. Prentice-Hall, Inc., New York, 1947. \end{thebibliography}
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