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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>3 动量定理</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">质点的动量定理</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="14%" align="center"><img border="0" src="pic/3052_311.GIF" width="63" height="27"></td> <td width="14%" align="center"><img border="0" src="pic/3052_312.GIF" width="27" height="22"></td> <td width="14%" align="center"><img border="0" src="pic/3052_313.GIF" width="88" height="49"></td> <td width="14%" align="center">或</td> <td width="14%" align="center"><img border="0" src="pic/3052_314.GIF" width="92" height="30"></td> <td width="15%" align="center"><img border="0" src="pic/3052_312.GIF" width="27" height="22"></td> <td width="15%" align="center"><img border="0" src="pic/3052_315.GIF" width="117" height="30"></td> </tr> <tr> <td width="14%" align="center">牛而定律</td> <td width="14%" align="center"></td> <td width="42%" align="center" colspan="3">动量定理的微分形式</td> <td width="15%" align="center"></td> <td width="15%" align="center">动量定理的积分形式(有限形式）</td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">二、</font></b></td> <td width="540"><b><font color="#0000FF">质点系的动量定理</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>任意质点： </td> <td><img border="0" src="pic/3052_316.GIF" width="154" height="48"></td> <td> 前者为外力，后者为内力，且</td> <td><img border="0" src="pic/3052_317.GIF" width="71" height="31"></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td colspan="7">求和：</td> </tr> <tr> <td><img border="0" src="pic/3052_312.GIF" width="27" height="22"></td> <td> 微分形式： </td> <td><img border="0" src="pic/3052_318.GIF" width="91" height="51"></td> <td> <img border="0" src="pic/3052_312.GIF" width="27" height="22"> </td> <td> 积分形式： </td> <td><img border="0" src="pic/3052_319.GIF" width="120" height="29"></td> <td></td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540">反映质系随质心平动部分与所受外力（冲量）主矢之间的关系。</td> </tr> <tr> <td width="20"></td> <td width="540"><b>解题步骤：</b></td> </tr> <tr> <td width="20"></td> <td width="540">(一)取研究对象（取分离体）；</td> </tr> <tr> <td width="20"></td> <td width="540">(二)画受力图、运动图（只画外力、不画内力）；</td> </tr> <tr> <td width="20"></td> <td width="540">(三)列解方程。</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">例1：</td> <td width="50%" rowspan="3"> <p align="center"><img border="0" src="pic/3052_320.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。求地面给三角块的反力。<br> <br> 注：需先用动能定理求各刚体质心加速度，再用下面形式动量定理求反力：</td> </tr> <tr> <td width="50%"> <p align="center"><img border="0" src="pic/3052_321.GIF" width="91" height="51"></td> </tr> </table> </td> </tr> <tr> <td width="20" valign="bottom"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">例2：</td> <td width="50%" rowspan="5"> <p align="center"><img border="0" src="pic/3052_322.GIF" width="201" height="244"></td> </tr> <tr> <td width="50%">理想、定常、不可压缩流体在管道内运动。已知流体密度ρ，两截面流速v1 和v2。求此段流体给管道的附加动压力。<br> （注：附加动压力＝总压力—静压力）</td> </tr> <tr> <td width="50%"></td> </tr> <tr> <td width="50%"></td> </tr> <tr> <td width="50%"></td> </tr> </table> </td> </tr> <tr> <td width="20"><b><font color="#0000FF">三、</font></b></td> <td width="540"><b><font color="#0000FF">动量守恒定理</font></b></td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>动量定理微分形式： </td> <td><img border="0" src="pic/3052_323.GIF" width="91" height="51"></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="11%" rowspan="2" align="center"><img border="0" src="pic/3052_324.GIF" width="38" height="43"></td> <td width="21%" align="center"><img border="0" src="pic/3052_325.GIF" width="76" height="27"></td> <td width="11%" align="center"><img border="0" src="pic/3052_326.GIF" width="27" height="22"></td> <td width="20%" align="center"><img border="0" src="pic/3052_327.GIF" width="85" height="23"></td> <td width="37%" align="center">——质点系动量守恒</td> </tr> <tr> <td width="21%" align="center"><img border="0" src="pic/3052_328.GIF" width="76" height="25"></td> <td width="11%" align="center"><img border="0" src="pic/3052_329.GIF" width="27" height="22"></td> <td width="20%" align="center"><img border="0" src="pic/3052_330.GIF" width="73" height="25"></td> <td width="37%" align="center">——质点系在x方向上动量守恒</td> </tr> <tr> <td width="100%" colspan="5"> <table border="0" cellpadding="0" cellspacing="0"> <tr> <td>动量定理积分形式：</td> <td><img border="0" src="pic/3052_331.GIF" width="120" height="29"></td> </tr> </table> </td> </tr> <tr> <td width="11%" align="center" rowspan="2"><img border="0" src="pic/3052_324.GIF" width="38" height="43"></td> <td width="21%" align="center"><img border="0" src="pic/3052_332.GIF" width="80" height="29"></td> <td width="11%" align="center"><img border="0" src="pic/3052_329.GIF" width="27" height="22"></td> <td width="20%" align="center"><img border="0" src="pic/3052_333.GIF" width="142" height="30"></td> <td width="37%" align="center">——质点系动量守恒</td> </tr> <tr> <td width="21%" align="center"><img border="0" src="pic/3052_334.GIF" width="79" height="33"></td> <td width="11%" align="center"><img border="0" src="pic/3052_329.GIF" width="27" height="22"></td> <td width="20%" align="center"><img border="0" src="pic/3052_335.GIF" width="135" height="28"></td> <td width="37%" align="center">——质点系在x方向上动量守恒</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"></td> </tr> <tr> <td width="20"></td> <td width="540">反例：①光滑水平面上由绳拉住绕定点作匀速圆周运动的小球；<br> ②圆锥摆</td> </tr> <tr> <td width="20"></td> <td width="540"> <table border="0" cellpadding="0" cellspacing="0" width="100%"> <tr> <td width="50%">例3：</td> <td width="50%" rowspan="3"> <p align="center"><img border="0" src="pic/3052_336.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，三角块放在光滑平面上，倾角为α，重量为G，重物重量P。系统初始静止。求重物上升s时，三角块的速度v1。设重物相对三角块铅直运动，滚子与斜面不脱开。</td> </tr> <tr> <td width="50%">注：需综合应用动量守恒和动能定理<br> （详见讲义一稿）</td> </tr> </table> </td> </tr> <tr> <td width="20"></td> <td width="540"></td> </tr> <tr> <td width="560" colspan="2"> <p align="center"> <a href="3052_2.htm"><font color="#FF6666">[ 上一节 ]</font></a> <a 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