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<HTML><HEAD><TITLE>new</TITLE><META content="text/html; charset=gb2312" http-equiv=Content-Type><LINK href="text.css" rel=stylesheet type=text/css><META content="Microsoft FrontPage 4.0" name=GENERATOR></HEAD><body leftmargin="15"><center><b><br>2 功</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td width="580" colspan="2"><b><font color="#FF0000">功：</font></b><font color="#800000">力（力偶）在位移上的累積效應。</font></td> </tr> <tr> <td width="20"><font color="#0000FF"><b>一、</b></font></td> <td width="560"><b>功的一般表達式</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">元功：</td> <td width="50%" rowspan="6"> <p align="center"><img border="0" src="pic/3051_248.GIF" width="243" height="185"></td> </tr> <tr> <td width="50%"><img border="0" src="pic/3051_249.GIF" width="296" height="31"></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>功：</td> <td><img border="0" src="pic/3051_5F250.GIF" width="105" height="41"></td> </tr> </table> </td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td bgcolor="#99CCFF">注： <br> 僅僅表示元功,既非變分,也不一定為全微分</td> </tr> </table> </td> </tr> <tr> <td width="50%">直角坐標系下：</td> </tr> <tr> <td width="50%"><img border="0" src="pic/3051_5F251.GIF" width="170" height="24"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><img border="0" src="pic/3051_5F252.GIF" width="198" height="43"></td> </tr> <tr> <td width="20"><font color="#0000FF"><b>二、</b></font></td> <td width="560"><b>幾種常見力的功</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="33%"><font color="#0000FF">1.常力</font></td> <td width="33%"><font color="#0000FF">2.重力</font></td> <td width="34%" rowspan="3"><img border="0" src="pic/3051_5F253.GIF" width="234" height="171"></td> </tr> <tr> <td width="33%"><img border="0" src="pic/3051_5F254.GIF" width="101" height="21"></td> <td width="33%"><img border="0" src="pic/3051_5F255.GIF" width="111" height="26"></td> </tr> <tr> <td width="33%" align="center"><img border="0" src="pic/3051_5F256.GIF" width="199" height="97"></td> <td width="33%" align="center"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><font color="#0000FF">3.彈性力</font></td> <td width="50%"><font color="#0000FF">4.萬有引力</font></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic/3051_5F257.GIF" width="118" height="42"></td> </tr> </table> </td> <td width="50%"><img border="0" src="pic/3051_5F258.GIF" width="131" height="50"></td> </tr> <tr> <td width="50%">δ1、δ2——彈簧初、末時變形。</td> <td width="50%">其中c為引力常數，r<font size="1">1</font>、r<font size="1">2</font>為二星體質心間初末時距離。</td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic/3051_5F259.GIF" width="225" height="210"></td> <td><b>注：</b>對扭轉彈簧，亦如此。<br> </td> </tr> </table> </td> <td width="50%"> <p align="center"><img border="0" src="pic/3051_260.GIF" width="246" height="177"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><font color="#0000FF">5.摩擦力的功</font></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">討論：<br> ①靜滑動摩擦力作功嗎？舉例。<br> ②動滑動摩擦力作功嗎？若是，恒為負嗎？（如書p158所說）。舉例。</td> <td width="50%"> <p align="center"><img border="0" src="pic/3051_261.GIF" width="209" height="66"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560"><font color="#0000FF">6. 力偶與力矩的功：</font></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>力偶：</td> <td><img border="0" src="pic/3051_262.GIF" width="91" height="39"></td> <td bgcolor="#FF6699"> <table border="0" cellspacing="1"> <tr> <td bgcolor="#FFFFFF"><b>注：</b><br> 力偶作用的剛體可作任意運動。</td> </tr> </table> </td> </tr> <tr> <td>力矩：</td> <td><img border="0" src="pic/3051_263.GIF" width="122" height="39"></td> <td bgcolor="#FF6699"> <table border="0" cellspacing="1" width="100%"> <tr> <td bgcolor="#FFFFFF"><b>注：<br> </b>僅限于定軸轉動剛體。</td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560">另注：書上(p159~160)還討論了平面運動剛體上力的功。事實上，書上討論僅限于求虛功（在虛位移原理中），即應用變分原理求功的情況。對一般情況，特別是求有限位移上的功時，沒有實際意義。</td> </tr> <tr> <td width="20"><b><font color="#0000FF">三、</font></b></td> <td width="560"><b>力系的功</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellspacing="0" cellpadding="0"> <tr> <td>功是標量，故</td> <td><img border="0" src="pic/3051_264.GIF" width="83" height="26"></td> <td> </td> <td><img border="0" src="pic/3051_265.GIF" width="64" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">四、</font></b></td> <td width="560"><b>質點系內力的功</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>問題：內力作功嗎？</td> </tr> </table> </td> <td width="50%" rowspan="3"> <p align="center"><img border="0" src="pic/3051_266.GIF" width="260" height="138"></td> </tr> <tr> <td width="50%"><img border="0" src="pic/3051_267.GIF" width="126" height="26"></td> </tr> <tr> <td width="50%">當為剛體（或幾何不變體系）時，內力的功為零。否則不為零，如系統中有彈簧時</td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">五、</font></b></td> <td width="560"><b>約束力的功</b></td> </tr> <tr> <td width="20"></td> <td width="560"> <table border="0" cellpadding="0" cellspacing="0" width="542"> <tr> <td width="123"><font color="#0000FF">①柔性體約束</font></td> <td width="119"><font color="#0000FF">②光滑面約束</font></td> <td width="141"><font color="#0000FF">③鉸鏈約束</font></td> <td width="151"></td> </tr> <tr> <td width="123"><img border="0" src="pic/3051_268.GIF" width="123" height="181"></td> <td width="119"><img border="0" src="pic/3051_269.GIF" width="119" height="88"></td> <td width="141"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic/3051_270.GIF" width="139" height="83"></td> </tr> <tr> <td><img border="0" src="pic/3051_271.GIF" width="52" height="26"></td> </tr> <tr> <td> </td> </tr> <tr> <td> <p align="right"><img border="0" src="pic/3051_272.GIF" width="96" height="26"></td> </tr> </table> </td> <td width="151"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic/3051_273.GIF" width="149" height="88"></td> </tr> <tr> <td><img border="0" src="pic/3051_274.GIF" width="125" height="113"></td> </tr> </table> </td> </tr> <tr> <td width="119"> <p align="center">若限定柔性體約束為質點系內部約束</p> </td> <td rowspan="2" width="119"></td> <td rowspan="2" width="141"></td> <td rowspan="2" width="151"></td> </tr> <tr> <td width="119"> <p align="center"><img border="0" src="../jingli/pic/jian1.GIF" width="20" height="35"></p> </td> </tr> <tr> <td colspan="2" rowspan="3" width="244"><img border="0" src="pic/3051_275.GIF" width="204" height="180"></td> <td width="141"></td> <td width="151"></td> </tr> <tr> <td width="141"><font color="#0000FF">④鏈桿約束</font></td> <td width="151"><font color="#0000FF">⑤固定端約束</font></td> </tr> <tr> <td width="141"><img border="0" src="pic/3051_276.GIF" width="118" height="97"></td> <td width="151"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><img border="0" src="pic/3051_277.jpg" width="54" height="106"></td> <td><img border="0" src="pic/3051_278.GIF" width="52" height="26"></td> </tr> </table> </td> </tr> <tr> <td width="123"> <p align="center"><font color="#0000FF">對于</font><font color="#0000FF">理想約束:</font></td> <td width="119"><img border="0" src="pic/3051_279.GIF" width="79" height="28"></td> <td width="141"></td> <td width="151"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560">在一定意義下，約束力不作功，這給我們分析解決問題帶來很大方便。</td> </tr> <tr> <td width="20"></td> <td width="560"></td> </tr> <tr> <td width="20"></td> <td width="560"></td> </tr> <tr> <td width="580" colspan="2"> <p align="center"> <a href="3051_1.htm"><font color="#FF6666">[ 上一節 ]</font></a> <a href="3051_3.htm"><font color="#00CC00">[ 下一節 ]</font></a> </td> </tr> </table> </BODY></HTML> ?? 快捷鍵說明
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