Talk:PlanetPhysics/Power

Original TeX Content from PlanetPhysics Archive

%%% 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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