{"id":28541,"date":"2024-09-16T15:44:15","date_gmt":"2024-09-16T15:44:15","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28541"},"modified":"2024-09-16T15:44:15","modified_gmt":"2024-09-16T15:44:15","slug":"%e7%89%9b%e9%a1%bf%e5%ae%9a%e5%be%8b","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/zh\/%e7%89%9b%e9%a1%bf%e5%ae%9a%e5%be%8b\/","title":{"rendered":"\u725b\u987f\u5b9a\u5f8b"},"content":{"rendered":"<p><center><\/p>\n<h1>\u725b\u987f\u5b9a\u5f8b<\/h1>\n<p><em><strong>\u6458\u8981\uff1a<\/strong><br \/>\n    \u672c\u8bfe\u8ba8\u8bba\u725b\u987f\u5b9a\u5f8b\u53ca\u5176\u5728\u7269\u4f53\u52a8\u529b\u5b66\u4e2d\u7684\u4f5c\u7528\u3002\u63a2\u8ba8\u4e86\u8d28\u91cf\u548c\u901f\u5ea6\u5982\u4f55\u51b3\u5b9a\u7ebf\u6027\u52a8\u91cf\uff0c\u5e76\u63cf\u8ff0\u4e86\u4e09\u6761\u5b9a\u5f8b\uff1a\u60ef\u6027\uff0c\u5728\u6ca1\u6709\u5916\u529b\u7684\u60c5\u51b5\u4e0b\u4fdd\u6301\u8fd0\u52a8\u72b6\u6001\uff1b\u529b\u548c\u52a0\u901f\u5ea6\u4e4b\u95f4\u7684\u5173\u7cfb\uff1b\u4ee5\u53ca\u7269\u4f53\u4e4b\u95f4\u7684\u4f5c\u7528\u548c\u53cd\u4f5c\u7528\u3002\u901a\u8fc7\u5e73\u9762\u6ed1\u52a8\u548c\u6446\u52a8\u7b49\u5b9e\u4f8b\uff0c\u8bf4\u660e\u4e86\u8fd9\u4e9b\u5b9a\u5f8b\u7684\u5e94\u7528\uff0c\u6700\u540e\u901a\u8fc7\u5b9e\u9645\u7ec3\u4e60\u5de9\u56fa\u5b66\u4e60\u3002<\/em><\/p>\n<p><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n    \u5728\u672c\u8bfe\u7ed3\u675f\u65f6\uff0c\u5b66\u751f\u5c06\u80fd\u591f\uff1a<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>\u7406\u89e3<\/strong>\u725b\u987f\u4e09\u5b9a\u5f8b\u53ca\u5176\u5728\u7269\u4f53\u52a8\u529b\u5b66\u4e2d\u7684\u5e94\u7528\u3002<\/li>\n<li><strong>\u5e94\u7528<\/strong>\u725b\u987f\u5b9a\u5f8b\u5206\u6790\u548c\u89e3\u51b3\u52a8\u529b\u5b66\u95ee\u9898\u3002<\/li>\n<li><strong>\u8bc6\u522b<\/strong>\u8d28\u91cf\u3001\u901f\u5ea6\u548c\u7ebf\u6027\u52a8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u5206\u6790<\/strong>\u60ef\u6027\u89c2\u5bdf\u8005\u5728\u52a8\u529b\u5b66\u7814\u7a76\u4e2d\u7684\u91cd\u8981\u6027\u3002<\/li>\n<li><strong>\u89e3\u91ca<\/strong>\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\u5982\u4f55\u5c06\u529b\u4e0e\u52a0\u901f\u5ea6\u8054\u7cfb\u8d77\u6765\u3002<\/li>\n<li><strong>\u63cf\u8ff0<\/strong>\u60ef\u6027\u8d28\u91cf\u7684\u6982\u5ff5\u53ca\u5176\u5728\u4e0d\u540c\u7269\u4f53\u4e4b\u95f4\u7684\u6bd4\u8f83\u65b9\u6cd5\u3002<\/li>\n<\/ol>\n<p>    <strong>\u5185\u5bb9\u7d22\u5f15<\/strong><br \/>\n    <a href=\"#1\">\u7b80\u4ecb<\/a><br \/>\n    <a href=\"#2\">\u725b\u987f\u5b9a\u5f8b\u4e0e\u7269\u4f53\u52a8\u529b\u5b66<\/a><br \/>\n    <a href=\"#3\">\u5982\u4f55\u4f7f\u7528\u725b\u987f\u5b9a\u5f8b\uff1f<\/a><br \/>\n    <a href=\"#4\">\u4f7f\u7528\u725b\u987f\u5b9a\u5f8b\u89e3\u51b3\u95ee\u9898<\/a><br \/>\n    <\/center><br \/>\n    <a name=\"1\"><\/a><\/p>\n<h2>\u7b80\u4ecb<\/h2>\n<p style=\"text-align: justify;\">\u5982\u679c\u6211\u4eec\u5728<a href=\"https:\/\/toposuranos.com\/posicion-velocidad-y-aceleracion-cinematica\/\" rel=\"noopener\" target=\"_blank\">\u4e4b\u524d\u7684\u8bfe\u7a0b<\/a>\u4e2d\u5b66\u4e60\u7684\u8fd0\u52a8\u5b66\u53ef\u4ee5\u63cf\u8ff0\u7269\u4f53\u7684\u8fd0\u52a8\uff0c\u90a3\u4e48\u901a\u8fc7\u725b\u987f\u5b9a\u5f8b\u6211\u4eec\u83b7\u5f97\u4e86\u80fd\u591f\u63a8\u7406\u8fd0\u52a8\u539f\u56e0\uff08\u6216\u8fd0\u52a8\u72b6\u6001\u53d8\u5316\uff09\u7684\u52a8\u529b\u5b66\u3002\u5728\u8fd9\u91cc\uff0c\u4f4d\u7f6e\u548c\u65f6\u95f4\u7684\u6982\u5ff5\u975e\u5e38\u91cd\u8981\uff0c\u56e0\u4e3a\u6211\u4eec\u901a\u8fc7\u5b83\u4eec\u5b9a\u4e49\u4e86\u901f\u5ea6\u548c\u52a0\u901f\u5ea6\uff0c\u4f46\u8fd8\u6709\u4e00\u4e2a\u989d\u5916\u7684\u56e0\u7d20\uff1a\u8d28\u91cf\u3002<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Tcp_1M1a7H0&amp;t=127s\" target=\"_blank\" rel=\"noopener\"><strong>\u8d28\u91cf\u5bf9\u5b9a\u4e49\u8fd0\u52a8\u72b6\u6001\u975e\u5e38\u91cd\u8981<\/strong><\/a>\uff0c\u5373\u7ebf\u6027\u52a8\u91cf\u3002\u636e\u8bf4\u4e00\u4e2a\u7269\u4f53\u7684\u7ebf\u6027\u52a8\u91cf <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{p}<\/span> \u662f\u8d28\u91cf\u4e0e\u901f\u5ea6\u7684\u4e58\u79ef\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\vec{p}=m\\vec{v}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u8fd0\u52a8\u72b6\u6001\u662f\u725b\u987f\u5b9a\u5f8b\u80cc\u540e\u7684\u5173\u952e\u6982\u5ff5\u3002<\/p>\n<p>    <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/Tcp_1M1a7H0\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>    <a name=\"2\"><\/a><\/p>\n<h2>\u725b\u987f\u5b9a\u5f8b\u4e0e\u7269\u4f53\u52a8\u529b\u5b66<\/h2>\n<h4>\u7b2c\u4e00\u5b9a\u5f8b\uff08\u60ef\u6027\u5b9a\u5f8b\uff09\uff1a<\/h4>\n<p style=\"text-align: center; color: #000080; background-color: #80ff80;\"><strong>\u5728\u6ca1\u6709\u5916\u90e8\u56e0\u7d20\u7684\u60c5\u51b5\u4e0b\uff0c\u6240\u6709\u7269\u4f53\u4fdd\u6301\u5176\u8fd0\u52a8\u72b6\u6001\u4e0d\u53d8\u3002<\/strong><\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Tcp_1M1a7H0&amp;t=208s\" target=\"_blank\" rel=\"noopener\"><strong>\u725b\u987f\u7684\u7b2c\u4e00\u5b9a\u5f8b<\/strong><\/a>\u7684\u5de7\u5999\u4e4b\u5904\u5728\u4e8e\u786e\u7acb\u4e86\u5bf9\u7269\u7406\u5b66\u5177\u6709\u6df1\u8fdc\u91cd\u8981\u6027\u7684\u4e24\u70b9\u3002\u7b2c\u4e00\uff0c\u4e5f\u662f\u6700\u660e\u663e\u7684\uff1a\u5b83\u5c06\u7ebf\u6027\u52a8\u91cf\u8bbe\u5b9a\u4e3a\u5b88\u6052\u91cf\uff1b\u7b2c\u4e8c\uff0c\u540c\u6837\u91cd\u8981\u4f46\u66f4\u4e3a\u9690\u542b\uff1a\u5b83\u8ba9\u6211\u4eec\u5f97\u4ee5\u786e\u7acb\u4ec0\u4e48\u662f<strong>\u60ef\u6027\u89c2\u5bdf\u8005\u3002<\/strong><\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Tcp_1M1a7H0&amp;t=322s\" target=\"_blank\" rel=\"noopener\"><strong>\u6709\u5f88\u591a\u65b9\u5f0f\u5b9a\u4e49\u4e00\u4e2a\u89c2\u5bdf\u8005\uff0c<\/strong><\/a>\u4f46\u5728\u6240\u6709\u89c2\u5bdf\u8005\u4e2d\uff0c\u6709\u4e00\u7c7b\u7279\u6b8a\u7684\u6211\u4eec\u79f0\u4e4b\u4e3a\u60ef\u6027\u89c2\u5bdf\u8005\u3002\u533a\u522b\u5728\u4e8e\uff0c\u4ece\u60ef\u6027\u89c2\u5bdf\u8005\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u5728\u6ca1\u6709\u5916\u90e8\u56e0\u7d20\u7684\u60c5\u51b5\u4e0b\uff0c\u7269\u4f53\u7684\u8fd0\u52a8\u72b6\u6001\u662f\u4e00\u79cd\u5b88\u6052\u91cf\u3002<\/p>\n<h5>\u4ec0\u4e48\u533a\u522b\u4e86\u60ef\u6027\u89c2\u5bdf\u8005\u4e0e\u975e\u60ef\u6027\u89c2\u5bdf\u8005\uff1f<\/h5>\n<p style=\"text-align: justify;\">\u533a\u522b\u5728\u4e8e\uff0c\u4ece\u60ef\u6027\u89c2\u5bdf\u8005\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u5728\u6ca1\u6709\u5916\u90e8\u56e0\u7d20\u7684\u60c5\u51b5\u4e0b\uff0c\u7269\u4f53\u7684\u8fd0\u52a8\u72b6\u6001\u662f\u4e00\u79cd\u5b88\u6052\u91cf\u3002<\/p>\n<h4>\u7b2c\u4e8c\u5b9a\u5f8b\uff08\u529b\u4e0e\u8d28\u91cf\uff09\uff1a<\/h4>\n<p style=\"text-align: center; color: #000080; background-color: #80ff80;\"><strong>\u4ece\u60ef\u6027\u89c2\u5bdf\u8005\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u5916\u90e8\u56e0\u7d20\u5bf9\u7269\u4f53\u65bd\u52a0\u7684\u529b\u7b49\u4e8e\u5176\u8fd0\u52a8\u72b6\u6001\u7684\u53d8\u5316\u3002<\/strong><\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Tcp_1M1a7H0&amp;t=396s\" target=\"_blank\" rel=\"noopener\"><strong>\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c\u5bf9\u7269\u4f53\u65bd\u52a0\u4e00\u4e2a\u529b<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}<\/span>\uff0c\u90a3\u4e48\u5b83\u5c06\u6ee1\u8db3\u4ee5\u4e0b\u5173\u7cfb\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle \\vec{F}=\\frac{d\\vec{p}}{dt}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u4f17\u6240\u5468\u77e5\u7684\u201c\u529b\u7b49\u4e8e\u8d28\u91cf\u4e58\u4ee5\u52a0\u901f\u5ea6\u201d\u5173\u7cfb\uff0c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}=m\\vec{a},<\/span><\/span>\u4e0d\u8fc7\u662f\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\u7684\u4e00\u4e2a\u7ed3\u679c\uff0c\u5b83\u662f\u901a\u8fc7\u5bfc\u6570\u7684\u6027\u8d28\u548c\u8d28\u91cf\u5b88\u6052\u63a8\u5bfc\u51fa\u6765\u7684\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n    \\vec{F} &amp; =\\displaystyle \\frac{d\\vec{p}}{dt} = \\frac{d}{dt}\\left(m\\vec{v} \\right) \\\\ \\\\\n\n    &amp; =\\displaystyle \\underbrace{\\frac{dm}{dt}}_{= 0}\\vec{v} + m \\underbrace{\\frac{d\\vec{v}}{dt}}_{= \\vec{a}} = m\\vec{a}\n\n    \\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u5728\u6700\u540e\u4e00\u6b65\u4e2d\uff0c\u8003\u8651\u4e86 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dm\/dt=0<\/span><\/span>\uff0c\u56e0\u4e3a\u5047\u8bbe\u6ca1\u6709\u589e\u52a0\u6216\u51cf\u5c11\u8d28\u91cf\uff0c\u800c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d\\vec{v}\/dt<\/span><\/span> \u662f\u52a0\u901f\u5ea6\u7684\u5b9a\u4e49\u3002<\/p>\n<h5>\u60ef\u6027\u8d28\u91cf<\/h5>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Tcp_1M1a7H0&amp;t=572s\" target=\"_blank\" rel=\"noopener\"><strong>\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b<\/strong><\/a>\u8fd8\u8ba9\u6211\u4eec\u80fd\u66f4\u6e05\u6670\u5730\u7406\u89e3\u8d28\u91cf\u7684\u6982\u5ff5\u3002\u8fd9\u91cc\u5b83\u88ab\u770b\u4f5c\u529b\u4e0e\u52a0\u901f\u5ea6\u4e4b\u95f4\u7684\u6bd4\u4f8b\u5e38\u6570\u3002\u8d28\u91cf\u8d8a\u5927\uff0c\u4e3a\u8fbe\u5230\u76f8\u540c\u7684\u52a0\u901f\u5ea6\uff0c\u65bd\u52a0\u7684\u529b\u5c31\u5fc5\u987b\u8d8a\u5927\uff1b\u56e0\u6b64\uff0c\u8d28\u91cf\u88ab\u7406\u89e3\u4e3a\u7269\u4f53\u60ef\u6027\u7684\u5ea6\u91cf\uff0c\u56e0\u6b64\u88ab\u79f0\u4e3a<strong>\u60ef\u6027\u8d28\u91cf\u3002<\/strong>\u5982\u679c\u76f8\u5bf9\u4e8e\u60ef\u6027\u89c2\u5bdf\u8005\u7684\u4e24\u4e2a\u7269\u4f53\u5728\u9759\u6b62\u72b6\u6001\u4e0b\u53d7\u5230\u76f8\u540c\u7684\u529b\uff08\u6ca1\u6709\u7269\u8d28\u4ea4\u6362\uff09\uff0c\u90a3\u4e48\u6211\u4eec\u6709<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m_1 \\vec{a}_1 = \\vec{F} = m_2 \\vec{a}_2<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u52a0\u901f\u5ea6\u7684\u91cf\u7684\u6bd4\u503c\u6765\u6bd4\u8f83\u7269\u4f53\u7684\u8d28\u91cf\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{m_1}{m_2} = \\frac{\\|\\vec{a_2}\\|}{\\|\\vec{a_1}\\|}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u56e0\u6b64\uff0c\u5982\u679c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m_2<\/span><\/span> \u662f\u201c\u4e00\u4e2a\u6807\u51c6\u5343\u514b\u201d\uff0c\u90a3\u4e48\u6211\u4eec\u53ea\u9700\u89c2\u5bdf\u6bd4\u503c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\|\\vec{a}_2\\|\/\\|\\vec{a}_1\\|<\/span><\/span> \u6765\u77e5\u9053 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m_1<\/span><\/span> \u7684\u91cd\u91cf\u662f\u591a\u5c11\u3002<\/p>\n<h4>\u7b2c\u4e09\u5b9a\u5f8b\uff08\u4f5c\u7528\u4e0e\u53cd\u4f5c\u7528\uff09\uff1a<\/h4>\n<p style=\"text-align: center; color: #000080; background-color: #80ff80;\"><strong>\u5982\u679c\u7269\u4f53 A \u5bf9\u7269\u4f53 B \u65bd\u52a0\u4e00\u4e2a\u201c\u4f5c\u7528\u201d\u529b\uff0c\u90a3\u4e48 B \u5bf9 A \u65bd\u52a0\u4e00\u4e2a\u5927\u5c0f\u76f8\u7b49\u4f46\u65b9\u5411\u76f8\u53cd\u7684\u201c\u53cd\u4f5c\u7528\u201d\u529b\u3002<\/strong><\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=Tcp_1M1a7H0&amp;t=794s\" target=\"_blank\" rel=\"noopener\"><strong>\u725b\u987f\u7b2c\u4e09\u5b9a\u5f8b\u4e0d\u4ec5\u5141\u8bb8\u6211\u4eec\u66f4\u51c6\u786e\u5730\u8ba8\u8bba<\/strong><\/a>\u529b\uff0c\u8fd8\u660e\u786e\u6307\u51fa\u5916\u90e8\u65bd\u52a0\u529b\u7684\u56e0\u7d20\u4e5f\u662f\u53ef\u80fd\u53d7\u529b\u5f71\u54cd\u7684\u7269\u7406\u5bf9\u8c61\uff1a<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u5916\u90e8\u56e0\u7d20\u662f\u4e00\u4e2a\u53ef\u80fd\u53d7\u529b\u5f71\u54cd\u7684\u7269\u7406\u5bf9\u8c61\u3002<\/li>\n<li>\u529b\u6c38\u8fdc\u4e0d\u4f1a\u5355\u72ec\u5b58\u5728\uff0c\u5b83\u4eec\u603b\u662f\u6210\u5bf9\u51fa\u73b0\uff0c\u79f0\u4e3a\u201c\u4f5c\u7528-\u53cd\u4f5c\u7528\u5bf9\u201d\uff0c\u8fd9\u4e9b\u5bf9\u7684\u77e2\u91cf\u548c\u59cb\u7ec8\u4e3a\u96f6\u3002<\/li>\n<li>\u4f5c\u7528-\u53cd\u4f5c\u7528\u5bf9\u603b\u662f\u53d1\u751f\u5728\u4e0d\u540c\u7684\u7269\u4f53\u4e0a\uff0c\u56e0\u6b64\u7269\u4f53\u4e0a\u7684\u603b\u529b\u4e0d\u4e00\u5b9a\u4e3a\u96f6\u3002<\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u7531\u4e8e\u4f5c\u7528-\u53cd\u4f5c\u7528\u5bf9\u603b\u662f\u6cbf\u76f4\u7ebf\u6267\u884c\uff0c\u8fd9\u5e26\u6765\u4e86\u6211\u4eec\u7a0d\u540e\u5c06\u770b\u5230\u7684\u89d2\u52a8\u91cf\u5b88\u6052\u3002<\/p>\n<p style=\"text-align: justify;\">\u9664\u6b64\u4e4b\u5916\uff0c\u725b\u987f\u7b2c\u4e09\u5b9a\u5f8b\u8fd8\u9690\u542b\u4e86\u5176\u4ed6\u4e00\u4e9b\u5185\u5bb9\uff1a<\/p>\n<ul style=\"text-align: justify;\">\n<li>\u4e3a\u4e86\u5728\u7269\u4f53\u4e0a\u65bd\u52a0\u4e00\u4e2a\u975e\u96f6\u7684\u51c0\u529b\uff0c\u81f3\u5c11\u9700\u8981\u7b2c\u4e8c\u4e2a\u7269\u4f53\u3002<\/li>\n<li>\u4f5c\u7528\u548c\u53cd\u4f5c\u7528\u662f\u540c\u65f6\u53d1\u751f\u7684\u3002\u7531\u4e8e\u4e24\u4e2a\u7269\u4f53\u53ef\u4ee5\u901a\u8fc7\u5f15\u529b\u6216\u7535\u78c1\u529b\u8fdc\u8ddd\u79bb\u76f8\u4e92\u4f5c\u7528\uff0c\u56e0\u6b64\u5728\u725b\u987f\u529b\u5b66\u4e2d\uff0c\u5fc5\u987b\u5b58\u5728\u4e00\u79cd\u4ee5\u65e0\u9650\u901f\u5ea6\u5c06\u4fe1\u606f\u4ece\u4e00\u4e2a\u70b9\u4f20\u9012\u5230\u53e6\u4e00\u4e2a\u70b9\u7684\u65b9\u5f0f\u3002\u6211\u4eec\u77e5\u9053\u8fd9\u79cd\u4e8b\u60c5\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u56e0\u4e3a\u6839\u636e\u72ed\u4e49\u76f8\u5bf9\u8bba\uff0c\u6700\u5927\u901f\u5ea6\u662f\u5149\u5728\u771f\u7a7a\u4e2d\u7684\u901f\u5ea6\uff0c\u56e0\u6b64\u6211\u4eec\u8bf4\u7b2c\u4e09\u5b9a\u5f8b\u662f\u5bf9\u73b0\u5b9e\u7684\u4e00\u79cd\u8fd1\u4f3c\u3002<\/li>\n<\/ul>\n<p>    <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/DuO-cvLNzwQ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>    <a name=\"3\"><\/a><\/p>\n<h2>\u5982\u4f55\u4f7f\u7528\u725b\u987f\u5b9a\u5f8b\uff1f<\/h2>\n<p style=\"text-align: justify;\">\u8981\u7406\u89e3\u5982\u4f55\u4f7f\u7528\u725b\u987f\u5b9a\u5f8b\u4ee5\u6e05\u695a\u5176\u610f\u4e49\uff0c\u6700\u597d\u662f\u901a\u8fc7\u57fa\u4e8e\u5177\u4f53\u60c5\u51b5\u7684\u793a\u4f8b\u4ee5\u53ca\u81ea\u7531\u4f53\u56fe\u7684\u6784\u5efa\u3002<\/p>\n<h3>\u81ea\u7531\u4f53\u56fe<\/h3>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DuO-cvLNzwQ&amp;t=96s\" target=\"_blank\" rel=\"noopener\"><strong>\u81ea\u7531\u4f53\u56fe\u662f<\/strong><\/a>\u4e00\u79cd\u6211\u4eec\u5728\u5176\u4e2d\u8868\u793a\u4f5c\u7528\u5728\u7269\u4f53\u4e0a\u7684\u529b\u7684\u56fe\u793a\u3002\u6839\u636e\u6211\u4eec\u5bf9\u91cd\u91cf\u7684\u7406\u89e3\uff0c\u6211\u4eec\u53ef\u4ee5\u6784\u5efa\u4ee5\u4e0b\u81ea\u7531\u4f53\u56fe\u7684\u793a\u4f8b\u3002<\/p>\n<h4>\u4e00\u4e2a\u7269\u4f53\u653e\u5728\u6c34\u5e73\u9762\u4e0a<\/h4>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DuO-cvLNzwQ&amp;t=180s\" target=\"_blank\" rel=\"noopener\"><strong>\u7531\u4e8e\u91cd\u529b\uff0c\u6240\u6709\u6709\u8d28\u91cf\u7684\u7269\u4f53\u90fd\u4f1a\u611f\u53d7\u5230\u4e00\u4e2a\u6307\u5411\u5730\u9762\u7684\u529b\u3002<\/strong><\/a>\u901a\u8fc7\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\u8be5\u529b\u7531\u8d28\u91cf\u548c\u91cd\u529b\u52a0\u901f\u5ea6\u7684\u4e58\u79ef\u7ed9\u51fa <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{g}=-g\\hat{y},<\/span><\/span> \u5176\u4e2d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g=9.81[m\/s^2].<\/span><\/span><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{\u91cd\u91cf}=m\\vec{g} = -mg\\hat{y}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u6211\u4eec\u6240\u7406\u89e3\u7684\u201c\u91cd\u91cf\u201d\u5b9e\u9645\u4e0a\u662f\u8fd9\u4e2a\u91cd\u91cf\u529b\u7684\u5927\u5c0f\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{\u91cd\u91cf}=\\|\\vec{F}_{\u91cd\u91cf}\\|= mg<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u5f53\u6211\u4eec\u5c06\u4e00\u4e2a\u5757\u653e\u5728\u6c34\u5e73\u9762\u4e0a\u65f6\uff0c\u51fa\u73b0\u4e86\u4e00\u5bf9\u4f5c\u7528-\u53cd\u4f5c\u7528\u529b\uff1a\u5b83\u4eec\u662f\u91cd\u91cf\u548c\u6cd5\u5411\u529b\u3002\u8fd9\u4e9b\u529b\u5728\u5927\u5c0f\u4e0a\u76f8\u7b49\uff0c\u4f46\u65b9\u5411\u76f8\u53cd\uff0c\u4f7f\u5f97\u7269\u4f53\u4e0a\u7684\u529b\u7684\u77e2\u91cf\u548c\u4e3a\u96f6\uff0c\u56e0\u6b64\u5176\u8fd0\u52a8\u72b6\u6001\u5728\u65f6\u95f4\u4e0a\u4fdd\u6301\u4e0d\u53d8\u3002<\/p>\n<p>    <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ylYcrS1tJbw\/YVfZYBYCPjI\/AAAAAAAAFlU\/0mOIkMhF-Hwrysc_WB5o7MLvrQtxQJu2QCLcBGAsYHQ\/s0\/reposo-plano-horizontal.PNG\" width=\"497\" height=\"280\" alt=\"\u653e\u7f6e\u5728\u6c34\u5e73\u9762\u4e0a\u7684\u7269\u4f53\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ylYcrS1tJbw\/YVfZYBYCPjI\/AAAAAAAAFlU\/0mOIkMhF-Hwrysc_WB5o7MLvrQtxQJu2QCLcBGAsYHQ\/s0\/reposo-plano-horizontal.PNG\" width=\"497\" height=\"280\" alt=\"\u653e\u7f6e\u5728\u6c34\u5e73\u9762\u4e0a\u7684\u7269\u4f53\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<h4>\u5728\u6c34\u5e73\u9762\u4e0a\u6ed1\u52a8<\/h4>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DuO-cvLNzwQ&amp;t=343s\" target=\"_blank\" rel=\"noopener\"><strong>\u5047\u8bbe\u73b0\u5728\u8be5\u5757\u88ab\u7cfb\u5728\u4e00\u6839\u7ef3\u5b50\u4e0a<\/strong><\/a>\uff0c\u6211\u4eec\u62c9\u52a8\u5b83\uff0c\u5982\u4ee5\u4e0b\u81ea\u7531\u4f53\u56fe\u6240\u793a\uff1a<\/p>\n<p>    <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-a2GB2RJ7vTY\/YVgEny43ZkI\/AAAAAAAAFlk\/uZ9_XQ3JwVMiiWjZDNC5Y4ePVZ9GH1bngCLcBGAsYHQ\/s0\/fuerza-cuerpo-en-plano-horizontal.PNG\" width=\"793\" height=\"386\" alt=\"\u6c34\u5e73\u9762\u4e0a\u7269\u4f53\u7684\u53d7\u529b\u56fe\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-a2GB2RJ7vTY\/YVgEny43ZkI\/AAAAAAAAFlk\/uZ9_XQ3JwVMiiWjZDNC5Y4ePVZ9GH1bngCLcBGAsYHQ\/s0\/fuerza-cuerpo-en-plano-horizontal.PNG\" width=\"793\" height=\"386\" alt=\"\u6c34\u5e73\u9762\u4e0a\u7269\u4f53\u7684\u53d7\u529b\u56fe\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">\u8fd9\u91cc\u6211\u4eec\u89c2\u5bdf\u5230\u4e24\u4e2a\u4f5c\u7528-\u53cd\u4f5c\u7528\u5bf9\uff1a\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u6709\u4e0e\u7269\u4f53\u7684\u91cd\u91cf\u548c\u6cd5\u5411\u529b\u76f8\u5173\u7684\u5bf9\uff0c\u8fd8\u6709\u4e00\u4e2a\u4f5c\u7528-\u53cd\u4f5c\u7528\u5bf9\u4e0e\u7ef3\u5b50\u7684\u4e24\u7aef\u76f8\u5173\uff0c\u5176\u4e2d\u4eba\u62c9\u52a8\u8be5\u5757\uff0c\u6700\u540e\u8fd8\u6709\u4e00\u4e2a\u4e0e\u65bd\u52a0\u7684\u529b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vec{F}_1<\/span><\/span> \u548c\u6469\u64e6\u529b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{\u6469\u64e6}<\/span><\/span>\u76f8\u5173\u7684\u5bf9\uff0c\u5176\u6700\u5927\u503c\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu\\|\\vec{F}_\\textnormal{\u6b63\u5e38}\\|.<\/span><\/span><\/p>\n<h5>\u6469\u64e6\u7cfb\u6570\u548c\u6469\u64e6\u529b<\/h5>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DuO-cvLNzwQ&amp;t=458s\" target=\"_blank\" rel=\"noopener\"><strong>\u8fd9\u91cc <span class=\"katex-eq\" data-katex-display=\"false\">\\mu<\/span> \u662f\u6469\u64e6\u7cfb\u6570<\/strong><\/a>\uff0c\u5b83\u8868\u793a\u4e24\u4e2a\u8868\u9762\u4e4b\u95f4\u7684\u6ed1\u52a8\u963b\u529b\uff1b\u6469\u64e6\u7cfb\u6570\u6709\u4e24\u79cd\u7248\u672c\uff1a\u4e00\u79cd\u662f\u52a8\u6469\u64e6\u7cfb\u6570\uff08<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu_c<\/span><\/span>\uff09\uff0c\u53e6\u4e00\u79cd\u662f\u9759\u6469\u64e6\u7cfb\u6570\uff08<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu_e<\/span><\/span>\uff09\u3002\u9759\u6469\u64e6\u529b\u51fa\u73b0\u5728\u7269\u4f53\u4fdd\u6301\u9759\u6b62\u65f6\uff0c\u800c\u52a8\u6469\u64e6\u529b\u51fa\u73b0\u5728\u7269\u4f53\u5f00\u59cb\u6ed1\u52a8\u540e\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{lcr}\\mu = \\left\\{\\begin{array}{lll} \\mu_e &amp; ;&amp; \\textnormal{\u7269\u4f53\u5904\u4e8e\u9759\u6b62} \\\\ \\\\ \\mu_c &amp; ;&amp; \\textnormal{\u7269\u4f53\u5904\u4e8e\u8fd0\u52a8} \\end{array}\\right. &amp; ; &amp; \\textnormal{\u5176\u4e2d } \\mu_c \\leq \\mu_e\\end{array}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u6469\u64e6\u529b\u53cd\u5bf9\u7269\u4f53\u7684\u8fd0\u52a8\uff0c\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u516c\u5f0f\uff08\u7b80\u5316\uff09\u8fdb\u884c\u5efa\u6a21\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n        \\vec{F}_\\textnormal{\u6469\u64e6} ( \\vec{F}_1 ) = \\left\\{\n\n            \\begin{array}{lll}\n\n            - \\vec{F}_1 &amp; ; &amp; \\|\\vec{F}_1\\| \\leq \\mu_e \\|\\vec{F}_\\textnormal{\u6b63\u5e38}\\| \\\\ \\\\\n\n            -\\mu_c \\|\\vec{F}_\\textnormal{\u6b63\u5e38}\\|\\hat{x} &amp; ; &amp; \\mu_e \\|\\vec{F}_\\textnormal{\u6b63\u5e38}\\| \\lt \\|\\vec{F}\\|\n\n            \\end{array}\n\n    \\right.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u5f53\u65bd\u52a0\u7684\u529b\u5c0f\u4e8e\u6216\u7b49\u4e8e\u6700\u5927\u9759\u6469\u64e6\u529b\u65f6\uff0c\u7269\u4f53\u76f8\u5bf9\u4e8e\u5730\u9762\u4fdd\u6301\u9759\u6b62\u3002\u5982\u679c\u65bd\u52a0\u7684\u529b\u8d85\u8fc7\u9759\u6469\u64e6\u529b\uff0c\u7269\u4f53\u5f00\u59cb\u8fd0\u52a8\uff0c\u6469\u64e6\u53d8\u4e3a\u52a8\u6469\u64e6\uff1b\u7269\u4f53\u4e0a\u7684\u51c0\u529b\u56e0\u6b64\u4e3a\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{\u51c0} = \\vec{F}_1 - \\mu_c\\|\\vec{F}_\\textnormal{\u6b63\u5e38}\\|\\hat{x},<\/span><\/span>\u56e0\u6b64\uff0c\u4ee5\u52a0\u901f\u5ea6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{a} = \\vec{F}_{\u51c0}\/M<\/span><\/span> \u79fb\u52a8\u3002\u5982\u679c\u7269\u4f53\u5f00\u59cb\u8fd0\u52a8\u540e\uff0c\u65bd\u52a0\u7684\u529b\u7b49\u4e8e\u52a8\u6469\u64e6\u529b\uff0c\u90a3\u4e48\u7269\u4f53\u4ee5\u6052\u5b9a\u901f\u5ea6\u79fb\u52a8\u3002<\/p>\n<h4>\u5728\u659c\u9762\u4e0a\u6ed1\u52a8<\/h4>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DuO-cvLNzwQ&amp;t=753s\" target=\"_blank\" rel=\"noopener\"><strong>\u5f53\u7269\u4f53\u6cbf\u659c\u9762\u6ed1\u52a8\u65f6<\/strong><\/a>\uff0c\u5728\u89d2\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span> \u5904\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u53d7\u529b\u56fe\uff1a<\/p>\n<p>    <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-vMApZqsSDs0\/YVjUkV187NI\/AAAAAAAAFls\/eZ2DPO6f54AKJDtB7-y1DP3TFjIMZjT7ACLcBGAsYHQ\/s0\/diagrama%2Bde%2Bfuerzas%2Ben%2Bplano%2Binclinado.PNG\" width=\"823\" height=\"554\" alt=\"\u659c\u9762\u4e0a\u6ed1\u52a8\u7684\u53d7\u529b\u56fe\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-vMApZqsSDs0\/YVjUkV187NI\/AAAAAAAAFls\/eZ2DPO6f54AKJDtB7-y1DP3TFjIMZjT7ACLcBGAsYHQ\/s0\/diagrama%2Bde%2Bfuerzas%2Ben%2Bplano%2Binclinado.PNG\" width=\"823\" height=\"554\" alt=\"\u659c\u9762\u4e0a\u6ed1\u52a8\u7684\u53d7\u529b\u56fe\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">\u8fd9\u91cc\u4e3a\u4e86\u65b9\u4fbf\uff0c\u6211\u4eec\u9009\u62e9\u4e86\u4e00\u4e2a\u53c2\u8003\u7cfb\uff0c\u4f7f\u6c34\u5e73\u5750\u6807\u4e0e\u6ed1\u52a8\u5e73\u9762\u5bf9\u9f50\u3002\u5728\u8fd9\u4e2a\u56fe\u4e2d\uff0c\u91cd\u529b\u88ab\u5206\u89e3\u4e3a\u4e24\u4e2a\u5206\u91cf\uff1a\u4e00\u4e2a\u5e73\u884c\u4e8e\u8fd0\u52a8\uff0c\u53e6\u4e00\u4e2a\u5782\u76f4\u4e8e\u8fd0\u52a8\u3002<\/p>\n<ul>\n<li><strong>\u5e73\u884c\u5206\u91cf\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{\\textnormal{\u91cd\u91cf},x}=mg\\sin(\\alpha)\\hat{x}<\/span><\/span><\/li>\n<li><strong>\u5782\u76f4\u5206\u91cf\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{\u91cd\u91cf,y}=-mg\\cos(\\alpha)\\hat{y}<\/span><\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify;\">\u6469\u64e6\u529b\u51fa\u73b0\u5728\u4e0e\u91cd\u91cf\u529b\u7684\u5e73\u884c\u5206\u91cf\u7684\u53cd\u4f5c\u7528\u4e0b\uff0c\u6cd5\u5411\u529b\u4f5c\u4e3a\u91cd\u91cf\u529b\u7684\u5782\u76f4\u5206\u91cf\u7684\u53cd\u4f5c\u7528\u3002\u5982\u679c\u91cd\u91cf\u529b\u7684\u6c34\u5e73\u5206\u91cf\u8d85\u8fc7\u6700\u5927\u9759\u6469\u64e6\u529b\uff0c\u5757\u7684\u8fd0\u52a8\u72b6\u6001\u5c06\u4ee5\u52a0\u901f\u5ea6\u6539\u53d8\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\vec{a} = mg\\left(\\frac{\\sin(\\alpha) - \\mu_c \\cos(\\alpha)}{m}\\right)\\hat{x}<\/span><\/span><\/p>\n<h4>\u60ac\u6302\u8d28\u91cf<\/h4>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DuO-cvLNzwQ&amp;t=1085s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e00\u4e2a\u8d28\u91cf\u60ac\u6302\u5728\u8fde\u63a5\u5230\u5929\u82b1\u677f\u7684\u7ef3\u5b50\u4e0a<\/strong><\/a>\u5e76\u4e14\u4fdd\u6301\u9759\u6b62\uff0c\u5b83\u7684\u81ea\u7531\u4f53\u56fe\u5982\u4e0b\uff1a<\/p>\n<p>    <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-jWSXd7lQhiw\/YVjpzr8z-pI\/AAAAAAAAFl0\/sZ955vFZz3Y-MtKXQQK8UFPRAaHhgxyPgCLcBGAsYHQ\/s0\/masa-colgante.PNG\" width=\"555\" height=\"521\" alt=\"\u60ac\u6302\u8d28\u91cf\u7684\u81ea\u7531\u4f53\u56fe\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-jWSXd7lQhiw\/YVjpzr8z-pI\/AAAAAAAAFl0\/sZ955vFZz3Y-MtKXQQK8UFPRAaHhgxyPgCLcBGAsYHQ\/s0\/masa-colgante.PNG\" width=\"555\" height=\"521\" alt=\"\u60ac\u6302\u8d28\u91cf\u7684\u81ea\u7531\u4f53\u56fe\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">\u4e00\u4e2a\u8d28\u91cf\u60ac\u6302\u5728\u8fde\u63a5\u5230\u5929\u82b1\u677f\u7684\u7ef3\u5b50\u4e0a\u5e76\u4e14\u4fdd\u6301\u9759\u6b62\uff0c\u5b83\u7684\u81ea\u7531\u4f53\u56fe\u5982\u4e0b\uff1a<\/p>\n<p style=\"text-align: justify;\">\u5728\u7ef3\u5b50\u4e0a\uff0c\u6709\u4e00\u5bf9\u6211\u4eec\u79f0\u4e4b\u4e3a\u201c\u5f20\u529b\u201d\u7684\u529b\uff0c\u5982\u679c\u7ef3\u5b50\u662f\u4e0d\u53ef\u4f38\u5c55\u7684\uff0c\u8fd9\u4e9b\u529b\u76f8\u7b49\u4e14\u76f8\u53cd\u3002\u5728\u5757\u4e0a\uff0c\u8fd8\u6709\u4e00\u5bf9\u529b\uff1a\u91cd\u91cf\u548c\u7ef3\u5b50\u7684\u5f20\u529b\u3002\u5982\u679c\u5757\u4fdd\u6301\u60ac\u6302\u548c\u9759\u6b62\uff0c\u90a3\u4e48\u91cd\u91cf\u548c\u5f20\u529b\u76f8\u53cd\u4e14\u5927\u5c0f\u76f8\u7b49\u3002\u8fd9\u91cc\u8fd8\u6709\u7b2c\u56db\u4e2a\u529b\u6ca1\u6709\u663e\u793a\uff0c\u5373\u5c06\u7ef3\u5b50\u56fa\u5b9a\u5728\u5929\u82b1\u677f\u4e0a\u7684\u529b\uff1b\u8fd9\u56db\u4e2a\u529b\u5f62\u6210\u4e86\u4e24\u4e2a\u4f5c\u7528-\u53cd\u4f5c\u7528\u5bf9\u3002<\/p>\n<h4>\u7b80\u5355\u6446\u7684\u8fd0\u52a8<\/h4>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=DuO-cvLNzwQ&amp;t=1158s\" target=\"_blank\" rel=\"noopener\"><strong>\u4e00\u4e2a\u8d28\u91cf\u8fde\u63a5\u5230\u4e00\u6839\u4e0d\u53ef\u4f38\u5c55\u7684\u7ef3\u5b50\u4e0a\uff0c\u7ef3\u5b50\u8fde\u63a5\u5230\u5929\u82b1\u677f\u4e0a<\/strong><\/a>\uff0c\u5b83\u5728\u5176\u81ea\u8eab\u91cd\u91cf\u7684\u5f71\u54cd\u4e0b\u56f4\u7ed5\u5e73\u8861\u4f4d\u7f6e\u6446\u52a8\uff0c\u8fd9\u5c31\u662f\u6211\u4eec\u6240\u8bf4\u7684\u7b80\u5355\u6446\u3002\u4e0b\u9762\u662f\u5b83\u7684\u81ea\u7531\u4f53\u56fe\u3002<\/p>\n<p>    <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-KEfWZhZZNl8\/YVkYdDhxLcI\/AAAAAAAAFl8\/CXQTZSVYbxIDw9G_JaVtV9VaG-ruwqHewCLcBGAsYHQ\/s0\/pendulo%2Bsimple.PNG\" width=\"366\" height=\"452\" alt=\"\u7b80\u5355\u6446\u7684\u81ea\u7531\u4f53\u56fe\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-KEfWZhZZNl8\/YVkYdDhxLcI\/AAAAAAAAFl8\/CXQTZSVYbxIDw9G_JaVtV9VaG-ruwqHewCLcBGAsYHQ\/s0\/pendulo%2Bsimple.PNG\" width=\"366\" height=\"452\" alt=\"\u7b80\u5355\u6446\u7684\u81ea\u7531\u4f53\u56fe\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center><\/p>\n<p style=\"text-align: justify;\">\u7531\u4e8e\u7ef3\u5b50\u662f\u4e0d\u53ef\u4f38\u5c55\u7684\uff0c\u56e0\u6b64\u5f84\u5411\u52a0\u901f\u5ea6\u4e3a\u96f6\uff0c\u56e0\u800c\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_{p,\\parallel} + T = ma_{\\parallel}(t) = 0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u53e6\u4e00\u65b9\u9762\uff0c\u5bf9\u4e8e\u5782\u76f4\u4e8e\u7ef3\u5b50\u7684\u5206\u91cf\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F_{p,\\bot}=-mg\\sin(\\theta) = ma_{\\bot}(t)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u4ece\u8fd9\u4e2a\u6700\u540e\u7684\u8868\u8fbe\u5f0f\u4e2d\uff0c\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4e00\u4e2a\u5fae\u5206\u65b9\u7a0b\u6765\u63cf\u8ff0\u7b80\u5355\u6446\u7684\u89d2\u4f4d\u7f6e <span class=\"katex-eq\" data-katex-display=\"false\">\\theta<\/span> \u968f\u65f6\u95f4\u7684\u53d8\u5316\u3002<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d^2\\theta(t)}{dt^2} + \\frac{g}{l}\\sin(\\theta) = 0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">\u4f46\u662f\u63a8\u5bfc\u8fd9\u4e2a\u65b9\u7a0b\u4ee5\u53ca\u6211\u4eec\u53ef\u4ee5\u4ece\u4e2d\u505a\u51fa\u7684\u63a8\u8bba\u5c06\u5728\u7a0d\u540e\u8be6\u7ec6\u8ba8\u8bba\u3002<\/p>\n<p>    <a name=\"4\"><\/a><\/p>\n<h2>\u4f7f\u7528\u725b\u987f\u5b9a\u5f8b\u89e3\u51b3\u95ee\u9898<\/h2>\n<p style=\"text-align: justify;\">\u4f7f\u7528\u725b\u987f\u5b9a\u5f8b\u89e3\u51b3\u4ee5\u4e0b\u95ee\u9898\uff1a<\/p>\n<ol style=\"text-align: justify;\">\n<li>\u4e00\u4e2a <span class=\"katex-eq\" data-katex-display=\"false\">15[kg]<\/span> \u7684\u5757\u88ab\u653e\u7f6e\u5728\u6c34\u5e73\u8868\u9762\u4e0a\u3002\u5757\u548c\u8868\u9762\u4e4b\u95f4\u6709\u9759\u6469\u64e6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu_e=0.55<\/span><\/span> \u548c\u52a8\u6469\u64e6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu_c=0.31<\/span><\/span>\n<ol>\n<li type=\"a\">\u4f7f\u5757\u79fb\u52a8\u6240\u9700\u7684\u6700\u5c0f\u529b\u662f\u591a\u5c11\uff1f<\/li>\n<li type=\"a\">\u5f53\u5b83\u7531\u4e8e\u5148\u524d\u83b7\u5f97\u7684\u529b\u800c\u5f00\u59cb\u79fb\u52a8\u65f6\uff0c\u8ba1\u7b97\u5757\u7684\u52a0\u901f\u5ea6\u3002<\/li>\n<\/ol>\n<\/li>\n<li>\u4e00\u4e2a <span class=\"katex-eq\" data-katex-display=\"false\">12[kg]<\/span> \u7684\u5757\u88ab\u653e\u7f6e\u5728\u53ef\u503e\u659c\u7684\u5e73\u9762\u4e0a\u3002\u5982\u679c\u9759\u6469\u64e6\u7cfb\u6570\u662f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu_e=0.03,<\/span><\/span> \u786e\u5b9a\u5757\u4fdd\u6301\u9759\u6b62\u7684\u6700\u5927\u503e\u659c\u89d2\u3002<\/li>\n<li>\u4e00\u4e2a <span class=\"katex-eq\" data-katex-display=\"false\">75[kg]<\/span> \u7684\u5757\u7531\u4e8e\u5bf9\u5176\u6c34\u5e73\u65bd\u52a0\u7684\u529b\u4ee5\u6052\u5b9a\u901f\u5ea6\u4e0a\u5347\uff0c\u5728\u76f8\u5bf9\u4e8e\u6c34\u5e73\u9762\u7684 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">30^o<\/span><\/span> \u659c\u9762\u4e0a\u3002\u5982\u679c\u5757\u548c\u5e73\u9762\u8868\u9762\u4e4b\u95f4\u7684\u52a8\u6469\u64e6\u7cfb\u6570\u4e3a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu_c=0.21,<\/span><\/span> \u786e\u5b9a\u65bd\u52a0\u7684\u529b\u7684\u5927\u5c0f\u3002<\/li>\n<p>    <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/kQaZdNm-iDQ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<li>\u8003\u8651\u4e24\u4e2a\u8d28\u91cf <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m_1<\/span><\/span> \u548c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m_2<\/span><\/span> \u901a\u8fc7\u4e00\u4e2a\u4e0d\u53ef\u4f38\u5c55\u3001\u65e0\u8d28\u91cf\u7684\u7ef3\u5b50\u8fde\u63a5\uff0c\u5e76\u901a\u8fc7\u4e00\u4e2a\u6ed1\u8f6e\uff0c\u5982\u56fe\u6240\u793a\u3002\u8ba1\u7b97\u4e24\u4e2a\u8d28\u91cf\u7684\u52a0\u901f\u5ea6\u3002\n<p>    <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEg6YZ3Pc3UlsxceJu3isovO7by4X1DHEtV-82DhHMl7FLepZDp8YQt4DAGxlQGSCemJE1Ai-SS4OdSMoJUc66U2cEKTuSbCbM_MhX-8jTElj2kwGK589fba-JoIcF9fDw_v36cKBD9OPrPJ6ZaXp4tKhK7qvNftjVQDoIyQDgGUlKXHLj_T3LOgT-rNyw\" width=\"298\" height=\"345\" alt=\"\u963f\u7279\u4f0d\u5fb7\u673a\u5668\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEg6YZ3Pc3UlsxceJu3isovO7by4X1DHEtV-82DhHMl7FLepZDp8YQt4DAGxlQGSCemJE1Ai-SS4OdSMoJUc66U2cEKTuSbCbM_MhX-8jTElj2kwGK589fba-JoIcF9fDw_v36cKBD9OPrPJ6ZaXp4tKhK7qvNftjVQDoIyQDgGUlKXHLj_T3LOgT-rNyw\" width=\"298\" height=\"345\" alt=\"\u963f\u7279\u4f0d\u5fb7\u673a\u5668\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center>\n    <\/li>\n<li>\u4e00\u6839\u8d28\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">M<\/span> \u7684\u67d4\u6027\u7ef3\u5b50\u60ac\u6302\u5728\u4e24\u5835\u5899\u4e4b\u95f4\uff0c\u5728\u8fde\u63a5\u70b9\u5f62\u6210\u4e00\u4e2a\u89d2\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span>\u3002\u8ba1\u7b97\u7ef3\u5b50\u5728\u6700\u4f4e\u70b9\u7684\u5f20\u529b\u3002\n<p>    <center><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEh3rmFCklJ9Z7Hb6M5Nb_lREohLFKZNhujGlrx1m8aUKGvr4RnoB0w3H2wQj1VHo6or-UgVj7_CtuBiL-mIs17CGJT4FF9gVPXPEKR34_6sRLW50L8q8bb5vby23Lby4xLzX92nfDvUnWnJsxtuTzehTRw-N3NJq9R91n-UFXzCgksrGooUWFGX8D1VLA\" width=\"343\" height=\"281\" alt=\"\u60ac\u6302\u7684\u7ef3\u5b50\" class=\"alignnone size-full lazyload\" \/><noscript><img decoding=\"async\" src=\"https:\/\/blogger.googleusercontent.com\/img\/a\/AVvXsEh3rmFCklJ9Z7Hb6M5Nb_lREohLFKZNhujGlrx1m8aUKGvr4RnoB0w3H2wQj1VHo6or-UgVj7_CtuBiL-mIs17CGJT4FF9gVPXPEKR34_6sRLW50L8q8bb5vby23Lby4xLzX92nfDvUnWnJsxtuTzehTRw-N3NJq9R91n-UFXzCgksrGooUWFGX8D1VLA\" width=\"343\" height=\"281\" alt=\"\u60ac\u6302\u7684\u7ef3\u5b50\" class=\"alignnone size-full lazyload\" \/><\/noscript><\/center>\n    <\/li>\n<li>\u4e00\u4e2a\u8d28\u91cf\u4e3a <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u7684\u7269\u4f53\u4ee5\u534a\u5f84 <span class=\"katex-eq\" data-katex-display=\"false\">R<\/span> \u548c\u6052\u5b9a\u89d2\u901f\u5ea6 <span class=\"katex-eq\" data-katex-display=\"false\">\\omega<\/span> \u5728 <span class=\"katex-eq\" data-katex-display=\"false\">x,y<\/span> \u5e73\u9762\u4e0a\u7ed5\u5708\u3002\u8ba1\u7b97\u65bd\u52a0\u5728\u8d28\u91cf\u4e0a\u7684\u529b\u3002<\/li>\n<p>    <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/D3fnVM-HKJ4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u725b\u987f\u5b9a\u5f8b \u6458\u8981\uff1a 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