Force and Power

<BODY LANG="EN"> <HR><center> <table border=1> <td><A NAME="tex2html59" HREF="node3.html"><img height=36 width=36 alt="PREVIOUS" src="http://www.cs.utah.edu/icons/latex2html/previous.gif"></A></td> <td><A NAME="tex2html63" HREF="node1.html"><img height=36 width=36 alt="UP" src="http://www.cs.utah.edu/icons/latex2html/up.gif"></A></td> <td><A NAME="tex2html65" HREF="node5.html"><img height=36 width=36 alt="NEXT" src="http://www.cs.utah.edu/icons/latex2html/next.gif"></A></td> <td><a href="contents-node4.html"><img height=36 width=36 alt="CONTENTS" src="http://www.cs.utah.edu/icons/latex2html/toc.gif"></a></td> <td><a href="reset.hamlet"><img height=36 width=36 alt="RESET" src="http://www.cs.utah.edu/icons/latex2html/stop.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="http://www.cs.utah.edu/icons/latex2html/copyright.gif"></a></td> <td><a href="mailto:hamlet@cs.utah.edu"><img height=36 width=36 alt="FEEDBACK" src="http://www.cs.utah.edu/icons/latex2html/feedback.gif"></a></td> <td><a href="http://www.cs.utah.edu/%7Ehamlet/icons.html"><img height=36 width=36 alt="ABOUT" src="http://www.cs.utah.edu/icons/latex2html/about.gif"></a></td> </table> </center> <HR><H2><A NAME="SECTION00013000000000000000">Force and Power</A></H2> <P> Using Newton's <I>F</I> = <I>ma</I>, we know that the force required to produce this acceleration, again as a function of time, is <P> <table><td valign=top><a href="send5.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><code>force := t ->4.5e6 * acceleration(t);</code></td></table> <P> In physics, <EM>work</EM> is a force applied over a distance, and <EM>power</EM> is the rate at which work is done. Put another way, power is the product of force and velocity. Based upon these definitions, we can define a function to calculate the power required to move our destroyer along its trajectory: <P> <table><td valign=top><a href="send6.hamlet"><img height=24 width=24 alt="EXECUTE" src="http://www.cs.utah.edu/icons/latex2html/execute.gif"></a></td><td valign=top><code>power := t -> force(t) * velocity(t);</code></td></table> <P> If mass is expressed in kilograms, position in meters, and time in seconds, then force is expressed in Newtons and power in Watts. The function <TT> power</TT> will tell us the amount of power required at any particular point in time. For example, you'll find that at time 1, the destroyer needs to be generating approximately 91.8 kilowatts of power to produce the desired motion. At time 10, 108 kilowatts are required. <P> As time goes on, more and more power is required because, although the force required to produce the acceleration remains constant, the velocity of the destroyer (the other factor in the power calculation) is steadily increasing. <P> A destroyer has an onboard power plant which, like all power plants, has a peak power production capacity. We will assume that a modern destroyer is capable of producing 5 megawatts of power at any given instant in time. Given this assumption, how long will our destroyer be able to produce the specified motion? How fast will the destroyer be going at that point? <P> <P><A NAME="tex2html8" HREF="answer71.html">Click here for the answer</A><P> <P> These calculations tell us that we will be consuming 5 megawatts of power once the ship reaches approximately 56 meters/second. This translates to over 125 miles/hour, which is a bit much to ask for a destroyer. Evidently, something must be wrong with our model. Can you think of what that might be? <P> <HR><center> <table border=1> <td><A NAME="tex2html59" HREF="node3.html"><img height=36 width=36 alt="PREVIOUS" src="http://www.cs.utah.edu/icons/latex2html/previous.gif"></A></td> <td><A NAME="tex2html63" HREF="node1.html"><img height=36 width=36 alt="UP" src="http://www.cs.utah.edu/icons/latex2html/up.gif"></A></td> <td><A NAME="tex2html65" HREF="node5.html"><img height=36 width=36 alt="NEXT" src="http://www.cs.utah.edu/icons/latex2html/next.gif"></A></td> <td><a href="contents-node4.html"><img height=36 width=36 alt="CONTENTS" src="http://www.cs.utah.edu/icons/latex2html/toc.gif"></a></td> <td><a href="reset.hamlet"><img height=36 width=36 alt="RESET" src="http://www.cs.utah.edu/icons/latex2html/stop.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="http://www.cs.utah.edu/icons/latex2html/copyright.gif"></a></td> <td><a href="mailto:hamlet@cs.utah.edu"><img height=36 width=36 alt="FEEDBACK" src="http://www.cs.utah.edu/icons/latex2html/feedback.gif"></a></td> <td><a href="http://www.cs.utah.edu/%7Ehamlet/icons.html"><img height=36 width=36 alt="ABOUT" src="http://www.cs.utah.edu/icons/latex2html/about.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I><A NAME="tex2html1" HREF="http://www.cs.utah.edu/~zachary">Joseph L. Zachary</A> <BR> <A NAME="tex2html2" HREF="http://www.cs.utah.edu/~hamlet">Hamlet Project</A> <BR> <A NAME="tex2html3" HREF="http://www.cs.utah.edu/">Department of Computer Science</A> <BR> <A NAME="tex2html4" HREF="http://www.utah.edu/ HTML_Docs/UofUHome.html">University of Utah</A></I> </ADDRESS> </BODY>