📄 3062.htm
字号:
<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 刚体惯性力系的简化</b></center> <table border="0" cellpadding="0" cellspacing="0" width="560"> <tr> <td width="20"><b><font color="#0000FF">一、</font></b></td> <td width="540"><b><font color="#0000FF">平动刚体</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>惯性力系： </td> <td><img border="0" src="pic1/3062.h18.gif" width="93" height="32"></td> </tr> </table> </td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic1/3062.h19.gif" width="179" height="142"></td> </tr> <tr> <td width="50%"><font color="#FF0000">向质心简化：</font></td> </tr> <tr> <td width="50%">主矢：</td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3062.h20.gif" width="231" height="32"></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>即： </td> <td><img border="0" src="pic1/3062.h21.gif" width="86" height="32"></td> <td> ——<b>惯性力</b></td> </tr> </table> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td>主矩：</td> <td> <p align="center"><img border="0" src="pic1/3062.h22.gif" width="476" height="34"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="67%"></td> <td width="33%" valign="top"> <p align="right"><b>——惯性力偶</b></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">所以,平动刚体惯性力只有作用在质心上的惯性力,大小等于MaC ，方向与aC 相反</td> </tr> <tr> <td width="20"><b><font color="#0000FF">二、</font></b></td> <td width="540"><b><font color="#0000FF">转动刚体</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">只讨论平面情形，即绕垂直于质量对称面之轴的转动刚体。</td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic1/3062.h23.gif" width="240" height="158"></td> </tr> <tr> <td width="50%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>任一质点： </td> <td><img border="0" src="pic1/3062.h24.gif" width="60" height="29"></td> <td> <img border="0" src="pic1/3062.h25.gif" width="69" height="29"></td> </tr> <tr> <td>惯性力系： </td> <td><img border="0" src="pic1/3062.h26.gif" width="80" height="29"></td> <td> <img border="0" src="pic1/3062.h27.gif" width="91" height="29"></td> </tr> </table> </td> </tr> <tr> <td width="50%"></td> </tr> <tr> <td width="50%"><font color="#FF0000">方法1：向轴O点简化</font></td> </tr> <tr> <td width="50%">主矢：</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><img border="0" src="pic1/3062.h28.gif" width="397" height="30"></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="10%"> <p align="center">即：</td> <td width="21%"><img border="0" src="pic1/3062.h29.gif" width="86" height="30"></td> <td width="21%"><img border="0" src="pic1/3062.h30.gif" width="86" height="30"></td> <td width="18%"><b>——惯性力</b></td> <td width="30%">注意：作用于轴O</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="493"> <tr> <td width="52">主矩： </td> <td width="437"><img border="0" src="pic1/3062.h31.gif" width="437" height="31"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="285"> <tr> <td width="52"> <p align="center">即：</td> <td width="94"><img border="0" src="pic1/3062.h32.gif" width="94" height="29"></td> <td width="133"> <p align="center"><b>——惯性力偶</b></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><font color="#FF0000">方法2：向质心C简化</font></td> </tr> <tr> <td width="20"></td> <td width="540">主矢——惯性力：完全同上。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="500"> <tr> <td width="52">主矩： </td> <td width="444"><img border="0" src="pic1/3062.h33.gif" width="444" height="32"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="158"> <tr> <td width="51">即：</td> <td width="95"><img border="0" src="pic1/3062.h34.gif" width="94" height="29"></td> <td width="6"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">所以，转动刚体惯性力有两种加法：<br> ①在轴上加惯性力，在刚体上加惯性力偶；<br> ②在质心上加惯性力，在刚体上加惯性力偶。</td> </tr> <tr> <td width="20"><b><font color="#0000FF">三、</font></b></td> <td width="540"><b><font color="#0000FF">平面运动刚体</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="57%">动系：随质心平动。</td> <td width="43%" rowspan="5"> <p align="center"><img border="0" src="pic1/3062.h35.gif" width="198" height="164"></td> </tr> <tr> <td width="57%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>任一质点： </td> <td><img border="0" src="pic1/3062.h36.gif" width="98" height="30"></td> </tr> </table> </td> </tr> <tr> <td width="57%"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>惯性力系： </td> <td><img border="0" src="pic1/3062.h37.gif" width="214" height="33"></td> </tr> </table> </td> </tr> <tr> <td width="57%"><font color="#FF0000">向质心C简化：</font></td> </tr> <tr> <td width="57%"> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><b>主矢：</b> </td> <td><img border="0" src="pic1/3062.h38.gif" width="229" height="33"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td> 即： </td> <td><img border="0" src="pic1/3062.h39.gif" width="87" height="33"></td> <td> <b>——惯性力</b></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td><b>主矩：</b></td> </tr> <tr> <td><img border="0" src="pic1/3062.h40.gif" width="535" height="66"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"><img border="0" src="pic1/3062.h41.gif" width="250" height="34"></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td> 即： </td> <td><img border="0" src="pic1/3062.h42.gif" width="102" height="31"></td> <td> <b>——惯性力偶</b></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">所以,平面运动刚体惯性力是:作用在质心上的惯性力和作用在刚体上的惯性力偶</td> </tr> <tr> <td width="20"></td> <td width="540"><font color="#FF0000">特别注意：</font><br> 关于上述诸式中惯性力和惯性力偶“－”号的处理：<br> <font color="#0000FF">画图时</font>——总是按照质心加速度和刚体角加速度相反方向画出惯性力与惯性力偶;<br> <font color="#0000FF">写公式时</font>——总是只写惯性力与惯性力偶的大小表达式。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">如：图中画出惯性力和惯性力偶，而其表达式为：</td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic1/3062.h43.gif" width="197" height="163"></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3062.h44.gif" width="82" height="28"></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3062.h45.gif" width="83" height="29"></td> </tr> <tr> <td width="50%"><img border="0" src="pic1/3062.h46.gif" width="85" height="29"></td> </tr> <tr> <td width="50%"><b>解题步骤：</b></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">（一）取分离体；<br> （二）画受力图（主动力、约束力、惯性力（偶））；<br> （三）列解平衡方程。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例1</b>（例5-1改，用达朗贝尔原理求解）</td> <td width="50%" rowspan="4"> <p align="center"><img border="0" src="pic1/3062.h47.gif" width="250" height="189"></td> </tr> <tr> <td width="50%">图示系统。均质滚子A、滑轮B重量和半径均为Q和r，滚子纯滚动，三角块固定不动，倾角为α，重量为G，重物重量P。求滚子质心C的加速度和地面给三角块的反力。</td> </tr> <tr> <td width="50%">注：由此可知，达朗贝尔原理与动量定理和动量矩定理等效。故要求用达朗贝尔原理求解问题时，不能用此二定理，但可用动能定理。</td> </tr> <tr> <td width="50%"> </td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%"><b>例2</b>（P244习题5-43）</td> <td width="50%" rowspan="4"> <p align="center"><img border="0" src="pic1/3062.h48.gif" width="233" height="164"></td> </tr> <tr> <td width="50%">质量为m、长为l的均质杆CD，用二绳悬挂于铅直面内，杆在图示位置被无初速度释放，试求此瞬时杆的角加速度及绳AC、BD的张力。</td> </tr> <tr> <td width="50%">先考虑用动力学普遍定理求解，再用达朗贝尔原理解。</td> </tr> <tr> <td width="50%">注：应用达朗贝尔原理列力矩平衡方程时，矩心可任意选，但动量矩定理中矩心不能任意。</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="1" cellpadding="0" cellspacing="0" bordercolor="#008080"> <tr> <td>问题：既然达朗贝尔原理如此好用，是否可不讲三大定理而只讲此原理呢？</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">在求解众多动力学问题中，达朗贝尔原理是好用的。但由于其所用物理概念很少，故定性解释某些问题时受到的局限性也较大，如碰撞问题。三大定理建立了很多概念，故能定性解释许多问题。</td> </tr> <tr> <td width="20"></td> <td width="540"></td> </tr> <tr> <td width="20"></td> <td width="540"></td> </tr> <tr> <td width="560" colspan="2"> <p align="center"> <a href="3061.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a href="3070.htm"><font color="#00CC00">[ 下一节 ]</font></a> </td> </tr></table></BODY></HTML> ⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -