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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）在位移上的累积效应。</font></td> </tr> <tr> <td width="20"><font color="#0000FF"><b>一、</b></font></td> <td width="560"><b>功的一般表达式</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> 仅仅表示元功,既非变分,也不一定为全微分</td> </tr> </table> </td> </tr> <tr> <td width="50%">直角坐标系下：</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>几种常见力的功</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.弹性力</font></td> <td width="50%"><font color="#0000FF">4.万有引力</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——弹簧初、末时变形。</td> <td width="50%">其中c为引力常数，r<font size="1">1</font>、r<font size="1">2</font>为二星体质心间初末时距离。</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>对扭转弹簧，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%">讨论：<br> ①静滑动摩擦力作功吗？举例。<br> ②动滑动摩擦力作功吗？若是，恒为负吗？（如书p158所说）。举例。</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. 力偶与力矩的功：</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> 力偶作用的刚体可作任意运动。</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>仅限于定轴转动刚体。</td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="560">另注：书上(p159~160)还讨论了平面运动刚体上力的功。事实上，书上讨论仅限于求虚功（在虚位移原理中），即应用变分原理求功的情况。对一般情况，特别是求有限位移上的功时，没有实际意义。</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>功是标量，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>质点系内力的功</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>问题：内力作功吗？</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%">当为刚体（或几何不变体系）时，内力的功为零。否则不为零，如系统中有弹簧时</td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">五、</font></b></td> <td width="560"><b>约束力的功</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柔性体约束</font></td> <td width="119"><font color="#0000FF">②光滑面约束</font></td> <td width="141"><font color="#0000FF">③铰链约束</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">若限定柔性体约束为质点系内部约束</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链杆约束</font></td> <td width="151"><font color="#0000FF">⑤固定端约束</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">对于</font><font color="#0000FF">理想约束:</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">在一定意义下，约束力不作功，这给我们分析解决问题带来很大方便。</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">[ 上一节 ]</font></a> <a href="3051_3.htm"><font color="#00CC00">[ 下一节 ]</font></a> </td> </tr> </table> </BODY></HTML> ⌨️ 快捷键说明
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