{"id":20075,"date":"2021-05-14T07:35:51","date_gmt":"2021-05-13T23:35:51","guid":{"rendered":"http:\/\/www.qiusir.com\/?p=20075"},"modified":"2026-06-25T14:06:16","modified_gmt":"2026-06-25T06:06:16","slug":"%e5%b8%a6%e7%94%b5%e7%b2%92%e5%ad%90%e5%9c%a8%e7%94%b5%e5%ae%b9%e5%99%a8%e9%87%8c%e7%9a%84%e8%bf%90%e5%8a%a8","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=20075","title":{"rendered":"\u5e26\u7535\u7c92\u5b50\u5728\u7535\u5bb9\u5668\u91cc\u7684\u8fd0\u52a8"},"content":{"rendered":"<p>\u5e26\u7535\u7c92\u5b50\uff08\u4e0d\u8ba1\u91cd\u529b\uff09\u4ece\u5e73\u884c\u677f\u7535\u5bb9\u5668\u4e2d\u95f4\u6c34\u5e73\u5165\u5c04\uff0c\u7535\u5bb9\u5668\u4e24\u677f\u4e4b\u95f4\u52a0\u65b9\u6ce2\u7535\u538b\uff08<del datetime=\"2025-05-30T00:40:03+00:00\">\u9759\u6001\u770b\uff0c\u4e5f\u53ef\u4ee5\u6682\u65f6\u628a\u7535\u538b\u8003\u8651\u6210\u7535\u91cf\uff0c\u4f46\u7535\u91cf\u7684\u597d\u5904\u662f\u8c03\u6574\u677f\u95f4\u8ddd\u79bb\u7535\u573a\u529b\u4e0d\u53d8\uff0c\u52a0\u901f\u5ea6\u4e0d\u53d8<\/del>\uff09\uff0c\u4e14$v_0=\\frac{L}{T}$\uff0c\u5373\u5e26\u7535\u7c92\u5b50\u5728\u7535\u5bb9\u5668\u5185\u7a7f\u884c\u7684\u65f6\u95f4\u4e3a\u4e00\u4e2a\u5468\u671f$T$&#8230;\uff08\u53e6\u4e00\u7c7b\u9898\u76ee\u662f\u521d\u901f\u5ea6\u5f88\u5927\uff0c\u5373$\\frac{L}{v_0}\\sim 0$\uff0c\u5e26\u7535\u7c92\u5b50\u5728\u7535\u5bb9\u91cc\u8fd0\u52a8\u770b\u4f5c\u7c7b\u5e73\u629b&#8230;\uff09<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/va11.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n\u4ee5\u6b63\u8d1f\u7535\u538b\u76f8\u7b49\u4e3a\u4f8b\uff0c\u7535\u538b\u56fe\u50cf\u53ef\u4ee5\u8f6c\u5316\u4e3a\u52a0\u901f\u5ea6\u65f6\u95f4\u56fe\u50cf\uff0c\u7531\u4e8e\u8fd0\u884c\u65f6\u95f4\u4e3a\u4e00\u4e2a\u5468\u671f\uff0c\u901f\u5ea6\u53d8\u5316\u91cf\u76f8\u540c\uff0c\u6216\u8005\u8bf4\u7528\u7ad6\u76f4\u65b9\u5411\u52a8\u91cf\u5b9a\u7406\uff08\u6216\u4ece\u52a0\u901f\u5ea6\u65f6\u95f4\u56fe\u50cf\u7684\u9762\u79ef\u4e0d\u53d8\u6765\u8003\u8651\uff09\uff0c\u51fa\u5c04\u7c92\u5b50\u7ad6\u76f4\u901f\u5ea6\u4e3a\u96f6\uff0c\u5373\u7c92\u5b50\u90fd\u6c34\u5e73\u5c04\u51fa\u3002<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/xy11.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n\u800c\u5bf9\u4e8e\u7c92\u5b50\u7684\u8fd0\u52a8\u8f68\u8ff9\uff0c\u9664\u4e86\u672b\u901f\u5ea6\u6c34\u5e73\u4ee5\u5916\uff0c\u51fa\u5c04\u70b9\u4f4d\u7f6e\u5173\u4e8e$\\frac{T}{2}$\u5bf9\u79f0\uff0c\u4e14\u4e3a\u7ebf\u6027\u3002\u4ee5\u7c92\u5b50\u5165\u5c04\u65f6\u523b$\\frac{T}{2}\\pm t$\uff0c$y=\\frac{4aTt-aT^2}{4}$\uff08\u8fd9\u662f\u5c04\u51fa\u65f6\u6570\u503c\u504f\u79fb\u91cf\uff0c\u4f46\u672a\u5fc5\u662f\u6700\u5927\u6570\u503c\u504f\u79fb\u91cf\uff0c\u540e\u9762\u7528\u5230\u3002\uff09<\/p>\n<p>\u6709\u8da3\u7684\u662f\uff0c\u524d\u9762\u7684\u7ed3\u8bba\u5728\u66f4\u4e00\u822c\u4e00\u70b9\u7684\u60c5\u51b5\u4e0b\u4e5f\u6709\u6210\u7acb\uff0c\u5982\u679c\u628a\u6b63\u5411\u7535\u538b$U_1$\u8f6c\u5316\u4e3a$a_1$\uff0c\u53cd\u5411\u7535\u538b$U_2$\u8f6c\u5316\u4e3a$a_2$\uff0c\u534a\u5468\u671f\u8fd8\u662f\u5bf9\u7b49\uff0c\u8fd0\u884c\u65f6\u95f4\u8fd8\u662f\u4e00\u4e2a\u5468\u671f\uff0c\u90a3\u5c04\u51fa\u901f\u5ea6$v_y=(a_1-a_2)\\frac{T}{2}$\uff0c$y=\\frac{a_1T^2-3a_2T^2+4(a_1+a_2)Tt}{8}$<\/p>\n<p><center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/va21.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n\u4ece\u521d\u8bbe\u8f68\u8ff9\u4e0a\u80fd\u5f88\u76f4\u89c2\u770b\u5230\uff0c\u5c04\u51fa\u7c92\u5b50\u901f\u5ea6\u76f8\u540c\uff0c\u5165\u5c04\u65f6\u95f4\u5173\u4e8e$\\frac{T}{2}$\u5bf9\u79f0\u65f6\uff0c\u4e5f\u5982\u524d\u9762\uff0c\u8fd0\u884c\u8f68\u8ff9\u4e0d\u540c\u4f46\u51fa\u5c04\u70b9\u4f4d\u7f6e\u76f8\u540c\u3002<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/xy12.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n\u5bf9\u4e8e\u6b63\u53cd\u7535\u538b\u76f8\u540c\u7684\u60c5\u51b5\u4e0b\uff0c\u4e2d\u95f4\u5165\u5c04\u7684\u7c92\u5b50\u4ecd\u4ece\u4e2d\u95f4\u5c04\u51fa\uff0c\u5165\u5c04\u65f6\u95f4\u5206\u522b\u662f$\\frac{1}{4}T$\u548c$\\frac{3}{4}T$\uff0c\u800c\u5bf9\u4e8e\u5bf9\u4e8e\u6b63\u7535\u538b\u662f\u53cd\u7535\u538b2\u500d\u7684\u60c5\u51b5\u4e0b\uff0c\u4e2d\u95f4\u5165\u5c04\u7684\u7c92\u5b50\u4ecd\u4ece\u4e2d\u95f4\u5c04\u51fa\uff0c\u5165\u5c04\u65f6\u95f4\u5206\u522b\u662f$\\frac{5}{12}T$\u548c$\\frac{7}{12}T$\uff08\u6b63\u53cd\u7535\u538b\u4e0d\u540c\u662f\u4e00\u9053\u4e0d\u662f\u5f88\u8f7b\u677e\u7684\u8ba1\u7b97\u9898\u76ee\uff0c\u8981\u52a8\u7b14\u7b97\u7b97\uff09\u3002\u4f46\u90fd\u662f\u5173\u4e8e$\\frac{1}{2}T$\u5bf9\u79f0\u7684\u3002<\/p>\n<p>\u771f\u6b63\u4fc3\u4f7f\u6211\u7528\u6574\u6574\u4e00\u4e2a\u665a\u81ea\u4e60\u6765\u6574\u7406\u76f8\u5173\u5185\u5bb9\uff0c\u8fd8\u662f\u90a3\u4f4d\u559c\u6b22\u6253\u7bee\u7403\u4e14\u7bee\u7403\u6253\u5f97\u5f88\u597d\u7684\u738b\u540c\u5b66\u95ee\u7684\u4e00\u9053\u770b\u8d77\u6765\u4e0d\u96be\u7684\u95ee\u9898\uff0c\u6211\u4e00\u76f4\u6000\u7591\u662f\u4e0d\u662f\u4ec0\u4e48\u7ade\u8d5b\u9898\u76ee\u3002\u4e3b\u8981\u7684\u662f\u5bf9\u8fd9\u4e2a\u95ee\u9898\u89e3\u51b3\u7684\u8fc7\u7a0b\u4e2d\uff0c\u590d\u4e60\u4e86\u4e0d\u5c11\u8fd0\u52a8\u5b66\u77e5\u8bc6\uff0c\u4e5f\u9047\u5230\u4e00\u4e9b\u4e3b\u52a8\u7684\u95ee\u9898\u3002<\/p>\n<blockquote><p>\u6b63\u53cd\u7535\u538b\u540c\u4e3a$U_0$\uff0c\u7c92\u5b50\u4ece\u7535\u5bb9\u5668\u4e24\u677f<strong>\u4e2d\u95f4<\/strong>\u5165\u5c04\uff0c\u4e14\u7c92\u5b50\u5728\u7535\u5bb9\u5668\u5185\u90e8\u8fd0\u884c\u7684\u65f6\u95f4\u6b63\u597d\u662f\u4e00\u4e2a\u5468\u671f\uff08\u5982\u524d\u9762\u8ba8\u8bba\u7684$T=\\frac{L}{v_0}$\uff09\uff0c\u95ee\u677f\u95f4\u8ddd\u79bb\u662f\u591a\u5c11\u80fd\u4f7f\u5165\u5c04\u7c92\u5b50\u768450%\u4ece\u7535\u5bb9\u5668\u53e6\u4e00\u7aef\u5c04\u51fa\u3002<\/p><\/blockquote>\n<p>\u8981\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u5148\u8981\u601d\u8003\u5982\u4e0b\u51e0\u4e2a\u5c0f\u95ee\u9898\u3002<br \/>\n1\u3001\u4fdd\u8bc1$\\frac{T}{4}$\u65f6\u523b\u5165\u5c04\u7684\u7c92\u5b50\u8fd8\u80fd\u4ece\u7535\u5bb9\u5668\u53e6\u4e00\u7aef\u7684\u4e2d\u95f4\u5c04\u51fa\uff0c\u677f\u95f4\u8ddd\u79bb\u662f\u591a\u5c11\u3002$d=\\frac{1}{2}a{(\\frac{T}{4}})^2\\times2\\times2$<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/max1.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n2\u3001\u4e2d\u95f4\u5165\u5c04\u7684\u7c92\u5b50\u80fd\u4ece\u7535\u5bb9\u5668\u53e6\u4e00\u7aef\u5c04\u51fa\uff0c\u677f\u95f4\u8ddd\u79bb\u662f\u5426\u6709\u6700\u5c0f\u503c\u3002<br \/>\n\u8fd9\u4e2a\u95ee\u9898\u6700\u5148\u662f\u6ea2\u6210\u540c\u5b66\u6700\u5148\u5728\u8bfe\u4e0a\u63d0\u51fa\uff0c\u82e5\u4e91\u6700\u5148\u662f\u76f4\u89c9\u5224\u65ad\u90a3\u4e24\u4e2a\u4e09\u89d2\u5f62\u9762\u79ef\u4e3a1\uff1a2\u65f6\uff0c\u5373\u5411\u4e0a\u548c\u5411\u4e0b\u504f\u79bb\u5165\u5c04\u65b9\u5411\u76f8\u540c\u7684\u65f6\u5019\u677f\u95f4\u8ddd\u79bb\u6700\u4e0b\uff0c\u5355\u4e00\u540c\u5b66\u7ed9\u51fa\u5f88\u597d\u7684\u51e0\u4f55\u89e3\u91ca\uff0c\u5d14\u5218\u540c\u5b66\u4e5f\u72ec\u7acb\u7ed9\u51fa\u6c42\u89e3\u3002\u73b0\u5728\u770b\uff0c\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u4e8c\u6b21\u51fd\u6570\u4e0e\u4e00\u4e2a\u4e00\u6b21\u51fd\u6570\u53d6\u5927\u7684\u4ea4\u70b9\u6765\u6c42\u89e3\u3002\uff08\u7c92\u5b50\u662f\u4ece\u4e2d\u95f4\u5165\u5c04\uff0c\u5411\u4e0a\u504f\u6216\u5411\u4e0b\u504f\u79fb\u7684\u8ddd\u79bb\u90fd\u5f97\u6ee1\u8db3\u624d\u53ef\uff09\uff08\u5165\u5c04\u5411\u4e0a\u504f\u79fb\u7684\u8ddd\u79bb\u662f\u548c\u5165\u5c04\u65f6\u523b\u7684\u5173\u7cfb\u662f\u4e8c\u6b21\u51fd\u6570\uff0c\u5165\u5c04\u5230\u51fa\u5c04\u6574\u4e2a\u8fc7\u7a0b\u7684\u6570\u503c\u4f4d\u79fb\u662f\u548c\u5165\u5c04\u65f6\u523b\u7684\u4e00\u6b21\u51fd\u6570\uff09<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/20220507.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n\uff08\u5206\u6bb5\u53d6\u6700\u5927\u7684\u95ee\u9898\uff09\uff08\u95f4\u8ddd\u6781\u503c\u95ee\u9898\uff0c\u8d34\u8fb9\u5165\u5c04\u548c\u4e2d\u70b9\u5165\u5c04\u3002\u4e00\u4e2a\u662f$\\frac{T}{4}$\uff0c\u4e00\u4e2a\u662f$\\frac{2-\\sqrt{2}}{2}T$\uff09<br \/>\n3\u3001\u6c34\u5e73\u5165\u5c04\u7684\u7c92\u5b50\u80fd\u591f\u51fa\u5c04\uff0c\u677f\u95f4\u8ddd\u79bb\u6700\u5c0f\u503c\u662f\u591a\u5c11\u3002\uff08\u5e76\u6ca1\u6709\u5165\u5c04\u7c92\u5b50\u5728\u4e2d\u95f4\u8fd9\u4e2a\u524d\u63d0\uff09\uff08\u5411\u4e0a\u504f\u79fb\u548c\u5411\u4e0b\u504f\u79fb\u7684\u548c\u7684\u6781\u5c0f\u503c\u3002\uff09<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/vaxy50pc.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n4\u3001\u5982\u679c\u4ece\u65f6\u95f4\u5206\u5e03\u4e0a\u770b\uff0c\u51fa\u5c04\u7c92\u5b50\u504f\u79bb\u5165\u5c04\u65b9\u5411\u6700\u8fd1\u768450%\uff0c\u6709\u4e00\u534a\u5bf9\u5e94\u7684\u662f$\\frac{1}{8}T$\u5230$\\frac{3}{8}T$\uff0c\u800c\u8fd9\u6837\u8003\u8651\uff0c\u9996\u5148\u80fd\u60f3\u5230\u7684\u9519\u8bef\u662f\uff0c\u7c92\u5b50\u5728\u7ad6\u76f4\u65b9\u5411\u504f\u79bb\u7684\u6700\u5927\u4f4d\u7f6e\u662f\u5728\u5c04\u51fa\u524d\u51fa\u73b0\uff08\u7ad6\u76f4\u901f\u5ea6\u4e3a\u96f6\u7684\u4f4d\u7f6e\u4e5f\u662f\u7ad6\u76f4\u6700\u5927\u8ddd\u79bb\u5904\uff09\uff0c\u5bf9\u5e94\u524d\u9762\u7684\u4e8c\u6b21\u4ef6\u6570\u4e0e\u4e00\u6b21\u51fd\u6570\u7684\u8868\u8fbe\uff0c\u5bb9\u6613\u7406\u89e3\u4e00\u70b9\u3002<br \/>\n5\u3001\u665a\u81ea\u4e60\u63a8\u8350\u7ed9\u7269\u7ade\u7684\u6b23\u7136\u540c\u5b66\uff0c\u65e9\u4e0a\u4ed6\u4e00\u6b21\u6027\u7ed9\u51fa\u4e86\u5f88\u5b8c\u5907\u7684\u89e3\u91ca\uff0c\u5411\u540c\u5b66\u6700\u65e9\u6709\u81ea\u5df1\u7684\u6b63\u786e\u7684\u60f3\u6cd5\uff0c\u5f15\u53d1\u4e86\u6211\u66f4\u591a\u7684\u8003\u8651\uff0c\u82e5\u4e91\u540c\u5b66\u7ed9\u51fa\u66f4\u591a\u89e3\u91ca\u548c\u6b63\u786e\u548c\u5de5\u6574\u7684\u8ba1\u7b97\uff0c\u5e86\u6797\u540c\u5b66\u4e5f\u7ed9\u51fa\u6b63\u786e\u8ba1\u7b97\u3002\u5f53\u7136\u8fd9\u4e2a\u95ee\u9898\u7684\u6838\u5fc3\u5728\u7ad6\u76f4\u504f\u79bb\u7684\u6700\u5927\u4f4d\u7f6e\u5173\u4e8e\u5165\u5c04\u65f6\u95f4\u7684\u5173\u7cfb\u662f\u4e00\u4e2a\u4e8c\u6b21\u51fd\u6570\u4e0e\u4e00\u6b21\u51fd\u6570\u7684\u6700\u5927\u95ee\u9898\u3002<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/50perc.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n\u5b8b\u660e\u5c7f\u540c\u5b66\u4e00\u65e9\u7b97\u51fa\uff1a$t_1=\\frac{2-\\sqrt{3}}{2}T$\uff08$t_2=t_1+\\frac{1}{4}T$\uff0c\u53e6\u4e00\u90e8\u5206\u662f\u5ef6\u540e$\\frac{1}{2}T$\u5c04\u5165\uff09\uff0c\u677f\u95f4\u6700\u5c0f\u8ddd\u79bb$d=(2-\\sqrt{3})\\frac{U_0q}{md}T^2$\u3002\u5b59\u6d5a\u8c6a\u540c\u5b66\u548c\u900d\u9065\u8001\u5e08\u73ed\u4e0a\u7684\u540c\u5b66\u4e5f\u7ed9\u51fa\u76f8\u540c\u7684\u7ed3\u679c\u3002<br 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\/>\n8\u3001\uff08\u5f53\u521d\u8bb0\u5f55\u7684\u5c31\u4e0d\u6761\u7406\uff0c\u9664\u4e86\u5207\u5165\u9898\u76ee\u96be\u4e4b\u5916\uff0c\u4e5f\u662f\u9057\u5fd8\u7b49\u56e0\u7d20\u3002\u4e00\u5e74\u540e\u518d\u6b21\u505a\u4e86\u8fd9\u4e2a\u9898\u76ee\u4e5f\u4e0d\u662f\u5f88\u5bb9\u6613\uff0c\u5f53\u7136\u6700\u4e3b\u8981\u7684\u539f\u56e0\u662f\u5bf9\u4e8e\u4ee3\u6570\u8ba1\u7b97\u7684\u91cd\u89c6\u4e0d\u591f\uff0c\u60f3\u901a\u8fc7\u56fe\u50cf\u4e00\u8e74\u800c\u5c31\u53cd\u800c\u589e\u52a0\u4e86\u8ba4\u77e5\u96be\u5ea6\u300220220505\uff09<br \/>\n\u5728\u6574\u7406\u8fd9\u9053\u9898\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6253\u5b8c\u7fbd\u6bdb\u7403\u7684\u5bb6\u9e9f\u540c\u5b66\u6765\u529e\u516c\u5ba4\u63a8\u8350\u4e00\u9053\u7269\u7406\u9898\uff0c\u7136\u540e\u4e00\u8d77\u4f5c\u56fe\u4f11\u606f\uff0c\u4ed6\u508d\u665a\u8981\u6a21\u8003\u4e24\u79d1\uff0c\u4e0b\u73ed\u8def\u4e0a\uff0c\u738b\u8001\u5e08\u56b7\u7740\u8bf4\u90a3\u672c\u7ec3\u4e60\u518c\u7279\u522b\uff0c\u5176\u4e2d\u4e5f\u6709\u8fd9\u9053\u9898\u76ee\uff0c\u54c8\u54c8\u54c8<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/jialinandqiusir.png\" width=\"580\" class=\"framed\" \/><\/center><br \/>\n\u9644\u5b8b\u660e\u5c7f\u540c\u5b66\u7684\u8ba1\u7b97\u8fc7\u7a0b[<a href=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/mysong2021.png\" target=\"_blank\">?<\/a>]\uff1a<br \/>\n<center><img decoding=\"async\" alt=\"2021\" src=\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/mysong2021.jpg\" width=\"580\" class=\"framed\" \/><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5e26\u7535\u7c92\u5b50\uff08\u4e0d\u8ba1\u91cd\u529b\uff09\u4ece\u5e73\u884c\u677f\u7535\u5bb9\u5668\u4e2d\u95f4\u6c34\u5e73\u5165\u5c04\uff0c\u7535\u5bb9\u5668\u4e24\u677f\u4e4b\u95f4\u52a0\u65b9\u6ce2\u7535\u538b\uff08\u9759\u6001\u770b\uff0c\u4e5f\u53ef\u4ee5\u6682\u65f6\u628a\u7535\u538b\u8003\u8651\u6210\u7535\u91cf\uff0c &#8230; <a title=\"\u5e26\u7535\u7c92\u5b50\u5728\u7535\u5bb9\u5668\u91cc\u7684\u8fd0\u52a8\" class=\"read-more\" href=\"https:\/\/www.qiusir.com\/?p=20075\" aria-label=\"\u9605\u8bfb 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