{"id":29391,"date":"2023-11-27T15:54:01","date_gmt":"2023-11-27T07:54:01","guid":{"rendered":"http:\/\/www.qiusir.com\/?p=29391"},"modified":"2023-11-27T15:54:01","modified_gmt":"2023-11-27T07:54:01","slug":"%e6%88%91%e4%bb%ac%e8%a6%81%e5%8f%98%e5%a5%bd","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=29391","title":{"rendered":"\u6211\u4eec\u8981\u53d8\u66f4\u597d\/\u5355\u6446"},"content":{"rendered":"<p><center><img decoding=\"async\" alt=\"\u200e\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/net\/Nobelnote.jpeg\" width=\"480\" class=\"framed\" \/><\/center><br \/>\n\u201c\u4e16\u754c\u4f1a\u4e0d\u4f1a\u53d8\u597d\u4e0d\u91cd\u8981\uff0c\u6211\u4eec\u8981\u53d8\u597d\u624d\u91cd\u8981\u3002\u201d\u7f51\u4e0a\u6ca1\u67e5\u5230\u662f\u4e0d\u662f\u8bfa\u8d1d\u5c14\u8bf4\u7684\uff0c\u4e0d\u8fc7\u8fd9\u8bdd\u5bf9\u83ab\u540d\u7126\u8651\u7684\u4eba\u6765\u8bf4\u4e5f\u4e0d\u662f\u6ca1\u6709\u4e00\u70b9\u9053\u7406:)<br \/>\n\u4e0a\u8bfe\u5e26\u9886\u5b66\u751f\u63a8\u53cc\u661f\u7684\u516c\u5f0f\uff0c$$\\frac{L^3}{T^2}=\\frac{G(m_1+m_2)}{4\\pi^2}$$\uff0c\u7c7b\u6bd4\u5f00\u666e\u52d2\u7b2c\u4e09\u5b9a\u5f8b\u5f88\u5bb9\u6613\u8bb0\u5fc6&#8230;\u800c\u5bf9\u5730\u7403\u8d34\u5730\u536b\u661f\u5468\u671f\u516c\u5f0f\u5316\u7b80\uff0c$$\\frac{R^3}{T_1^2}=\\frac{GM}{4\\pi^2}$$\uff0c$$T_1=2\\pi \\sqrt{\\frac{R^3}{GM}}$$\uff0c$$T_1=2\\pi \\sqrt{\\frac{R}{g}}$$<br \/>\n\u7c7b\u6bd4\u5355\u6446\u7684\u516c\u5f0f\uff0c$$T=2\\pi \\sqrt{\\frac{l}{g}}$$\uff0c\u4ee5\u53ca\u5706\u9525\u6446\u7684\u5468\u671f\u516c\u5f0f$$T=2\\pi \\sqrt{\\frac{lcos\\theta}{g}}$$\uff0c\u5f88\u5bb9\u6613\u5efa\u7acb\u8d77\u5173\u8054\u3002\u5de7\u5999\u7684\u662f$$T=2\\pi \\sqrt{\\frac{R}{g}}$$\u4e5f\u662f\u5730\u7403\u4e0a\u6446\u957f\u65e0\u9650\u7684\u5355\u6446\u5468\u671f\uff0c\u8fd9\u4e2a\u65f6\u95f4\u8fd8\u662f\u7a7f\u8d8a\u5730\u5fc3\u96a7\u9053\uff08\u7b80\u8c10\u632f\u52a8\uff09\u65f6\u95f4\u7684\u4e8c\u500d\u3002<br \/>\n<center><img decoding=\"async\" alt=\"\u200e\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/epqneycc.png\" width=\"480\" class=\"framed\" \/><\/center><br \/>\n\u548c\u7b80\u8c10\u632f\u52a8\u4e00\u7ae0\u63a8\u5230\u5355\u6446\u7684\u5468\u671f\u5f88\u63a5\u8fd1\uff0c\u8bbe\u60f3\u5730\u9762\u4e0a\uff08\u53ef\u4ee5\u8bbe\u60f3\u662f\u5728\u5f88\u9ad8\u5efa\u7b51\u4e0a\uff09\u60ac\u70b9o\u60ac\u6302\u6446\u957fl\u7684\u5355\u6446\uff08\u6446\u89d2\u5f88\u5c0f\uff0c\u4e00\u6837\u80fd\u8fd1\u4f3c\u7b80\u632f\u7684\uff09\uff0c\u4e07\u6709\u5f15\u529b\u7684\u5207\u5411\u5206\u529b\u63d0\u4f9b\u56de\u590d\u529b\u3002<br \/>\n\u6446\u7403\u5728\u5730\u8868\uff0c\u6240\u6709\u6709$$\\frac{GMm}{R^2}=mg$$\uff0c$$F_t=mgsin(\\alpha+\\beta)$$\uff0c\u5229\u7528\u5c0f\u89d2\u5ea6$$sin\\theta\\approx\\theta$$\uff0c$$F_t=mg(\\alpha+\\beta)$$\uff0c\u56e0\u4e3a\u5c0f\u89d2\u5ea6\uff0c\u4f4d\u79fb\u5927\u5c0f\u8fd1\u4f3c\u5f27\u957f\u4e5f\u8fd1\u4f3c\u6c34\u5e73&#8230;$$F_t=-mg(\\frac{1}{R}+\\frac{1}{l})x$$<br \/>\n\u5957\u7528\u5f39\u7c27\u632f\u5b50\u5468\u671f\u516c\u5f0f\uff0c$$T=2\\pi\\sqrt{\\frac{m}{k}}$$\uff0c\u5f97$$T=2\\pi\\sqrt{\\frac{Rl}{g(R+l)}}$$<br \/>\n\u5e26\u5165\u7279\u6b8a\u503c\u5230\u4e0a\u8ff0\u516c\u5f0f\uff0c\u6bd4\u5982\u6446\u957f\u8fdc\u5c0f\u4e8e\u5730\u7403\u534a\u5f84\uff0c$$T=2\\pi \\sqrt{\\frac{l}{g}}$$(l=1m,T\u7ea62s)\uff1b\u6bd4\u5982\u6446\u957f\u4e3a\u5730\u7403\u534a\u5f84\uff0c$$T=2\\pi \\sqrt{\\frac{R}{2g}}$$\uff081h\uff09\uff1b\u6bd4\u5982\u6446\u957f\u8fdc\u5927\u4e8e\u5730\u7403\u534a\u5f84\uff0c$$T=2\\pi \\sqrt{\\frac{R}{g}}$$(1.4h)&#8230;<br \/>\n<center><img decoding=\"async\" alt=\"\u200e\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/eqbzh.jpg\" width=\"480\" class=\"framed\" \/><\/center><br \/>\n\u5173\u4e8e\u8d2f\u7a7f\u5730\u7403\u7684\u5730\u4e0b\u94c1\u901a\u884c\u65f6\u95f4\u7684\u63a8\u7b97\uff0c\u4e5f\u662f\u7528\u7b80\u8c10\u632f\u52a8\u7684\u5468\u671f\u3002\u7531\u4e8e\u7403\u58f3\u5bf9\u7403\u58f3\u5185\u7269\u4f53\u7684\u4e07\u6709\u5f15\u529b\u4e3a\u96f6\uff0c\u6240\u4ee5\u7269\u4f53\u7a7f\u884c\u5730\u7403\u65f6\u6240\u53d7\u7684\u4e07\u6709\u5f15\u529b\u4ec5\u4e0e\u6b64\u5904\u5185\u90e8\u7403\u4f53\u6709\u5173\uff0c$$F=\\frac{GMm}{r^2}=\\frac{Gm\\rho\\frac{4}{3}\\pi r^3}{r^2}$$\uff0c$$F_x=-Gm\\rho\\frac{4}{3}\\pi rsin\\alpha=-kx$$&#8230;<br \/>\n\u7ee7\u7eed\u5957\u7528\u5f39\u7c27\u632f\u5b50\u5468\u671f\u516c\u5f0f\uff0c$$T=2\\pi\\sqrt{\\frac{m}{k}}$$\uff0c\u4e14$$gR^2=GM=G\\rho\\frac{4}{3}\\pi R^3$$\uff0c\u5316\u7b80\u540e\uff0c$$G\\rho\\frac{4}{3}\\pi=\\frac{g}{R}$$\uff0c\u5f97$$T=2\\pi \\sqrt{\\frac{R}{g}}$$\uff0c\u4e14\u4e0e$$\\theta$$\u65e0\u5173\u3002<br \/>\n\u5982\u679c\u662f\u6a2a\u8d2f\u5730\u5fc3\u7684\u5730\u4e0b\u94c1\uff0c\u4e0d\u4ec5\u65f6\u95f4\u548c\u8d34\u5730\u536b\u661f\u5468\u671f\u76f8\u540c\uff0c\u66f4\u662f\u5927\u6492\u5fc3\u5fc3\u76f8\u6620\u7684\u72d7\u7cae\uff08\u5706\u5468\u8fd0\u52a8\u7684\u6295\u5f71\u70b9\uff09&#8230;<br \/>\n\u5f53\u7136\uff0c\u8fd9\u4e2a\u5468\u671f\u4e5f\u662f\u548c\u5730\u7403\u534a\u5f84\uff08\u5927\u5c0f\uff09\u65e0\u5173\u7684\uff0c\u7531Kepler&#8217;s Law III\uff0c$$T=\\sqrt{\\frac{3\\pi}{G\\rho}}$$\u3002\u5730\u7403\u7684\u5e73\u5747\u5bc6\u5ea6\u5927\u6982\u662f\u6c34\u76845.5\u500d\uff0c\u5bf9\u4e8e\u66f4\u9ad8\u5bc6\u5ea6\u7684\u661f\u4f53\uff0c\u8fd9\u4e2a\u8fd0\u884c\u5468\u671f\u8981\u5c0f\u5f97\u591a\uff0c\u5982\u679c\u662f\u4e2d\u5b50\u661f\u5185\u90e8\u7684\u96a7\u9053&#8230;<br \/>\nX\u4e0a\u770b\u5230\u8fd9\u79cd\u63a8\u5bfc&#8230;<br \/>\n<center><img decoding=\"async\" alt=\"\u200e\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/fpninp.jpg\" width=\"480\" class=\"framed\" \/><\/center><br \/>\n<center><img decoding=\"async\" alt=\"\u200e\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/net\/tmpmyg.JPG\" width=\"480\" class=\"framed\" \/><\/center><br \/>\n\u7269\u7406\u4f5c\u4e3a\u9ad8\u8003\u7406\u79d1\u7684\u4e3b\u529b\u662f\u8981\u80cc\u5f88\u591a\u7684\u9505\uff0c\u4e0d\u5355\u662f\u8ba1\u7b97\u4e0d\u51c6\u7684\u6570\u5b66\u9505\uff0c\u8fd8\u6709\u5ba1\u9898\u5931\u8bef\u7684\u8bed\u6587\u9505\uff0c\u4ee5\u53ca\u57fa\u7840\u77e5\u8bc6\u76f8\u5173\u7684\u5730\u7406\u9505\u3001\u5316\u5b66\u9505\u7b49\u7b49\uff0c\u751a\u81f3\u5076\u6709\u7b26\u53f7\u4e71\u7528\u7684\u82f1\u8bed\u9505&#8230; \u200b<br \/>\n<center><img decoding=\"async\" alt=\"\u200e\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/net\/pmgmeme.JPG\" width=\"480\" class=\"framed\" \/><\/center><br \/>\n\u6570\u5b66L\u8001\u5e08\u5c31\u66fe\u63d0\u51fa\u8fc7[<a href=\"http:\/\/www.qiusir.com\/?p=29102\" rel=\"noopener\" target=\"_blank\">?<\/a>]\u4e0a\u9762\u6897\u56fe\u7684\u56f0\u60d1\u3002\u5730\u7403\u81ea\u8f6c\u7684\u7ebf\u901f\u5ea6$$v_0=\\frac{2\\pi R}{T_0}$$=0.464km\/s\uff0c1670km\/h&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u201c\u4e16\u754c\u4f1a\u4e0d\u4f1a\u53d8\u597d\u4e0d\u91cd\u8981\uff0c\u6211\u4eec\u8981\u53d8\u597d\u624d\u91cd\u8981\u3002\u201d\u7f51\u4e0a\u6ca1\u67e5\u5230\u662f\u4e0d\u662f\u8bfa\u8d1d\u5c14\u8bf4\u7684\uff0c\u4e0d\u8fc7\u8fd9\u8bdd\u5bf9\u83ab\u540d\u7126\u8651\u7684\u4eba\u6765\u8bf4\u4e5f\u4e0d\u662f\u6ca1\u6709\u4e00 &#8230; <a title=\"\u6211\u4eec\u8981\u53d8\u66f4\u597d\/\u5355\u6446\" class=\"read-more\" href=\"https:\/\/www.qiusir.com\/?p=29391\" aria-label=\"\u9605\u8bfb \u6211\u4eec\u8981\u53d8\u66f4\u597d\/\u5355\u6446\">\u9605\u8bfb\u66f4\u591a<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[5,8],"tags":[259,14,247],"class_list":["post-29391","post","type-post","status-publish","format-standard","hentry","category-physics","category-idea","tag-class","tag-neyc","tag-physics"],"_links":{"self":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/29391","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=29391"}],"version-history":[{"count":0,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/29391\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=29391"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=29391"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=29391"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}