![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/pdqljpf.jpg\")
<\/center>\n\u5927\u6982\u8bfb\u8fc7\u4e94\u516d\u4e2a\u7248\u672c\u7684\u53f0\u6e7e\u7269\u7406\u6559\u79d1\u4e66\uff0c\u6700\u8fd1\u770b\u4e86\u65e5\u672c\u7684\uff0c\u5f88\u662f\u611f\u6168\u3002\u53c8\u8981\u88ab\u53eb\u79cb\u6851\u4e86…
\n\uff08\u5c11\u513f\u90e8\u5b66\u751f\u5199\u7684\u6807\u8bed\uff0c\u4e7e\u5764\u672a\u5b9a\u4f60\u6211\u7686\u662f\u9ed1\u9a6c\uff0c\u4e7e\u5764\u5df2\u5b9a\uff0c\u90a3\u5c31\u626d\u8f6c\u4e7e\u5764\u3002\uff09
\n\u963f\u4fee\u7f57\u4e4b\u624b\u3001\u826f\u95ee\u4e4b\u98ce\u3001\u540d\u95ee\u4e4b\u68ee<\/p>\n
\u78b0\u649e\u540e\u901f\u5ea6\uff0c\u548c\u5207\u9762\u5e73\u884c\u65b9\u5411\u4e0d\u53d8u\u2192u\uff0c\u5782\u76f4\u65b9\u5411v\u2192ev<\/strong> \u8584\u819c\u5e72\u6d89\u5929\u6587\u95f4\u8ddd$\\frac{\\lambda}{2}=\\Delta x tan\\theta$\u7531\u4e8e\u5c0f\u89d2\u5ea6\uff0c$\\Delta x=\\frac{\\lambda}{2\\theta}$ \u5149\u6ed1\u6c34\u5e73\u9762\u4e0am\u4ee5v\u7684\u521d\u901f\u5ea6\u5728M\u4e0a\u8868\u9762\u6ed1\u884c\u4ece\u76f8\u5bf9\u8fd0\u52a8\u8ba1\u7b97\uff08$t=\\frac{Mv_0}{(m+M)\\mu g}$\uff09\uff08$l=\\frac{Mv_0^2}{2(m+M)\\mu g}$\uff09\uff08\u76f8\u5bf9\u9759\u6b62\u7684\u65f6\u95f4\u548c\u76f8\u5bf9\u6ed1\u884c\u7684\u8ddd\u79bb\u4ece\u52a8\u91cf\u5b9a\u7406\u548c\u6469\u64e6\u751f\u70ed\uff0c\u51fa\u73b0\u8d28\u91cf\u4e92\u6362\u548c\u6469\u64e6\u589e\u52a0\u7684\u9519\u89c9\uff09 \u5927\u6982\u8bfb\u8fc7\u4e94\u516d\u4e2a\u7248\u672c\u7684\u53f0\u6e7e\u7269\u7406\u6559\u79d1\u4e66\uff0c\u6700\u8fd1\u770b\u4e86\u65e5\u672c\u7684\uff0c\u5f88\u662f\u611f\u6168\u3002\u53c8\u8981\u88ab\u53eb\u79cb\u6851\u4e86… \uff08\u5c11\u513f\u90e8\u5b66\u751f\u5199\u7684\u6807 … \u9605\u8bfb\u66f4\u591a<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[5],"tags":[256,313,247,263],"class_list":["post-31451","post","type-post","status-publish","format-standard","hentry","category-physics","tag-book","tag-japan","tag-physics","tag-teach"],"_links":{"self":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/31451","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=31451"}],"version-history":[{"count":2,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/31451\/revisions"}],"predecessor-version":[{"id":43857,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/31451\/revisions\/43857"}],"wp:attachment":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=31451"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=31451"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=31451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\u4e0d\u5728\u4e00\u6761\u76f4\u7ebf\u4e0a\u7684\u901f\u5ea6\u53d8\u5316\u91cf\uff0c\u5148\u4e8e\u529b\u5b66\u7684\u4e09\u89d2\u5f62\u5b9a\u52192\u51fa\u73b0
\n\u7ef3\u7684\u62c9\u529b\u8fd9\u91cc\u53eb\u5f20\u529b<\/strong>
\n\u9759\u6469\u64e6\u7cfb\u6570$\\mu$\u548c\u52a8\u6469\u64e6\u7cfb\u6570$\\mu’$\uff0c\u652f\u6301\u529b\u548c\u6469\u64e6\u529b\u7684\u5408\u529b\u79f0\u6297\u529b<\/strong>
\n\u5bf9\u4e8e\u5f39\u7c27\u5f39\u529b\uff0c\u7528\u56fe\u793a\u8868\u660e\u62c9\u4f38\u548c\u538b\u7f29\u76f8\u540c\u5f39\u529b\u5927\u5c0f\u76f8\u540c\uff1b\u5bf9\u4e8e\u7b49\u6548\u5f39\u6027\u7cfb\u6570\u8fd9\u4e48\u597d\u7684\u7ed3\u8bba\u81ea\u7136\u4e0d\u80fd\u9519\u8fc7\uff0c\u76f4\u5217$\\frac{1}{k_T}=\\frac{1}{k_1}+\\frac{1}{k_2}+\\cdot\\cdot\\cdot$\uff0c\u5e76\u5217…\u800c\u4e14\u5728\u7b80\u8c10\u632f\u52a8\u90e8\u5206\u7528\u5230\u3002\uff08\u53ef\u548c\u521d\u4e2d\u7535\u963b\u3001\u9ad8\u4e2d\u7535\u5bb9\u4e32\u5e76\u8054\u7b49\u7c7b\u6bd4\uff0c\u751a\u81f3\u6269\u5927\u5230\u5bc6\u5ea6\u548c\u901f\u5ea6\uff09\uff08\u7528\u4e0a\u6211\u7684\u901a\u5206\u5b50\u8ba1\u7b97\u66f4\u5feb\uff09
\n\u8865\u5145\u4e86\u6d6e\u529b\uff08\u51e0\u4f55\u5149\u5b66\u4e2d\u4e5f\u7279\u522b\u8bb2\u4e86\u900f\u955c\uff09\uff08\u6d6e\u529b\u548c\u900f\u955c\u4e0d\u80fd\u7b80\u5355\u5f52\u4e3a\u521d\u4e2d\u77e5\u8bc6\uff09
\n\u8d28\u5fc3($\\frac{m_1x_1+m_2x_2+\\cdot\\cdot\\cdot}{m_1+m_2+\\cdot\\cdot\\cdot}$,$\\frac{m_1y_1+m_2y_2+\\cdot\\cdot\\cdot}{m_1+m_2+\\cdot\\cdot\\cdot}$)
\n\u4f5c\u7528\u00b7\u53cd\u4f5c\u7528\u6cd5\u5219\u76f4\u63a5\u63d0\u4f9b\u4e07\u6709\u5f15\u529b\u548c\u5e93\u4ed1\u529b\u7684\u8303\u4f8b
\n\u7814\u7a76\u5bf9\u8c61\u8fd9\u91cc\u662f\u6ce8\u76ee\u7269\u4f53<\/strong>
\n\u62c9\u4e24\u4e2a\u7269\u4f53\u548c\u63a8\u4e24\u4e2a\u7269\u4f53\uff0c\u4e24\u7269\u4f53\u89c1\u7684\u4f5c\u7528\u529b$\\frac{m_2}{m_1+m_2}F$\uff08\u5206\u6bcd\u662f\u6ca1\u76f4\u63a5\u53d7\u5916\u529b\u7684\u7269\u4f53\u8d28\u91cf\uff09
\n\u5149\u6ed1\u6c34\u5e73\u9762\u4e0am\u4ee5v\u7684\u521d\u901f\u5ea6\u5728M\u4e0a\u8868\u9762\u6ed1\u884c\u4ece\u76f8\u5bf9\u8fd0\u52a8\u8ba1\u7b97\uff08$t=\\frac{Mv_0}{(m+M)\\mu g}$\uff09\uff08$l=\\frac{Mv_0^2}{2(m+M)\\mu g}$\uff09\uff08\u76f8\u5bf9\u9759\u6b62\u7684\u65f6\u95f4\u548c\u76f8\u5bf9\u6ed1\u884c\u7684\u8ddd\u79bb\u4ece\u52a8\u91cf\u5b9a\u7406\u548c\u6469\u64e6\u751f\u70ed\uff0c\u51fa\u73b0\u8d28\u91cf\u4e92\u6362\u548c\u6469\u64e6\u589e\u52a0\u7684\u9519\u89c9\uff09
\n\uff08\u6b64\u90e8\u5206\u5f88\u5999\uff0c\u91cd\u65b0\u63a8\u5230\u4e86\u5149\u6ed1\u6c34\u5e73\u9762\u4e0a\u53e0\u653e\u7684\u4e24\u7269\u4f53\u5206\u522b\u5177\u6709\u51fa\u901f\u901f\uff0c\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u540c\u6837\u6210\u7acb\uff0c\u53ea\u662f\u901f\u5ea6\u66ff\u6362\u4e3a\u76f8\u5bf9\u901f\u5ea6\uff0c\u800c\u4e14\uff0c\u5173\u4e8e\u70ed\u80fd\u95ee\u9898\uff0c\u53ef\u4ee5\u5f15\u5165\u7ea6\u5316\u8d28\u91cf\uff09
\n\u673a\u68b0\u80fd\u5b88\u6052\u5b9a\u5f8b—\u529b\u5b66\u80fd\u4fdd\u5b58\u5219<\/strong>=\u4e00\u5b9a<\/strong>\uff08\u5f88\u597d\u5947\u8fd9\u91cc\u4e0d\u7528cons.\uff09
\n\u8fd0\u52a8\u91cf\/\u52a8\u91cf \u5b9a\u7406\u76f4\u63a5\u7528\u5411\u91cf\u65b9\u5f0f
\n![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/bdqljpf2.jpg\")
<\/center>
\n\u8fd0\u52a8\u91cf\u4fdd\u5b58\u5219\uff08\u5de7\u7528\u5e73\u884c\u56db\u8fb9\u5f62\u89e3\u91ca\u975e\u5bf9\u5fc3\u78b0\u649e<\/strong>\uff09\uff08\u6b64\u5904\u5e94\u8be5\u914d\u81ea\u5df1\u7ed8\u5236\u7684\u56fe\uff09\uff08\u529b\u5b66\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u5b9a\u5219\u5230\u901f\u5ea6\u7684\u5408\u6210\u518d\u5230\u52a8\u91cf\u7684\u5206\u89e3\u4ee5\u53ca\u52a8\u91cf\u5b9a\u7406\u7684\u8fd0\u7528\u548c\u725b\u987f\u7b2c\u4e09\u5b9a\u5f8b\u3002\uff09
\n\u53cd\u767a\u7cfb\u6570\u5728\u738b\u806a\u65b9\u6cd5\u4e0a\u7684\u5e94\u7528\uff08\u5e94\u8be5\u5355\u72ec\u6574\u7406\uff09
\n$v_1=\\frac{m_1-em_2}{m_1+m_2}v_0$\uff0c$v_2=\\frac{(1+e)m_1}{m_1+m_2}v_0$\uff08$\\Delta E_k=\\frac{1}{2}(1-e^2)\\frac{m_1m_2}{m_1+m_2}v_0^2$\uff09
\n\uff08\u5f39\u7c27\u6700\u5927\u5f62\u53d8\u91cf\u7684\u7ea6\u5316\u8d28\u91cf\uff08\u7c7b\u4f3c\u7b49\u6548\u7535\u963b\uff09\u6c42\u89e3$\\frac{1}{2}kl^2=\\frac{1}{2}\\frac{m_1m_2}{m_1+m_2}(v_1-v_2)^2$\uff09
\n\uff08\u5bf9\u4e24\u7269\u4f53\u7684\u5b8c\u5168\u975e\u5f39\u6027\u78b0\u649e\uff0c$m_1v_1+m_2v_2=(m_1+m_2)v$\uff0c$v=\\frac{m_1v_1+m_2v_2}{m_1+m_2}$\uff0c\u800c\u8d28\u5fc3\u7684\u901f\u5ea6\u6c42\u89e3\uff0c$x_G=\\frac{m_1x_1+m_2x_2}{m_1+m_2}$\uff0c$v_G=\\frac{dx_G}{dt}=\\frac{m_1\\frac{dx_1}{dt}+m_2\\frac{dx_2}{dt}}{m_1+m_2}=\\frac{m_1v_1+m_2v_2}{m_1+m_2}$\uff09
\n\u60ef\u6027\u529b\u7684\u5f15\u5165\u4f7f\u52a8\u529b\u5b66\u95ee\u9898\u8f6c\u5316\u4e3a\u9759\u529b\u5b66\u95ee\u9898\uff08\u6c34\u5e73\u52a0\u901f\u8fd0\u52a8\u7684\u8f66\u4e0a\u7684\u676f\u5b50\u4e2d\u6c34\u9762\u65b9\u5411\u548c\u7b49\u6548\u91cd\u529b\u5782\u76f4\uff09\uff0c\u800c\u8fdc\u5fc3\u529b<\/strong>\u7684\u5f15\u5165\u5bf9\u6709\u7684\u5706\u5468\u8fd0\u52a8\u7b80\u5316\u3002
\n\u590d\u539f\u529b<\/strong>($\\omega=\\sqrt{\\frac{k}{m}}$\uff0c$x=Acos\\sqrt{\\frac{k}{m}}t$)
\n$\\frac{1}{2}mv^2+mgh+\\frac{1}{2}kx^2$=\u4e00\u5b9a $\\frac{1}{2}mv^2+\\frac{1}{2}kx^2$=\u4e00\u5b9a \u524d\u8005x\u4e3a\u5f39\u7c27\u5f62\u53d8\u91cf\uff0c\u540e\u8005x\u4e3a\u7b80\u8c10\u632f\u52a8\u7684\u4f4d\u79fb
\n\u6c34\u5e73\u632f\u5b50\u6709\u6469\u64e6\u529b\u7684\u5e73\u8861\u4f4d\u7f6e\u8df3\u52a8\uff08\u9700\u8981\u518d\u7814\u7a76\uff09
\n\u5f15\u529b\u52bf\u80fd\u3001\u529b\u5b66\u80fd\u8868\u8fbe\u5f0f…
\n\u7c97\u7ec6\u5747\u5300\u7684\u6728\u68d2\u5728\u6c34\u4e2d\u7684\u7b80\u8c10\u632f\u52a8\u5468\u671f$T=2\\pi\\sqrt{\\frac{m}{k}}=2\\pi\\sqrt{\\frac{h}{g}}$\uff08\u9759\u6b62\u65f6\u6ca1\u5165\u7684\u6df1\u5ea6\uff0c\u7528\u5230\u6d6e\u529b\u66ff\u6362\u4e24\u4e2a\u5bc6\u5ea6\u7684\u5173\u7cfb\uff0c\u81f3\u6b64\u5468\u671f\u7684\u4e13\u9898\u5e94\u8be5\u62d3\u5c55\u4e00\u4e2a\uff09
\n\u6ca1\u6709\u76f4\u63a5\u5f15\u5165\u89d2\u52a8\u91cf\u5b88\u6052\uff0c\u7528\u9762\u79ef\u5b9a\u5f8b\u5f97\u51fa\u7ed3\u8bba $\\Delta S=\\frac{1}{2}r(v\\Delta t)sin\\theta$\uff0c$\\frac{\\Delta S}{\\Delta t}=\\frac{1}{2}rvsin\\theta$\uff08\u6b64\u5904\u5706\u9525\u66f2\u7ebf\u51e0\u4f55\u6027\u8d28\u5f15\u5165\uff09
\n![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/jppbdql1.jpg\")
<\/center>
\n\u7eb5\u6ce2\u7684\u758f\u90e8\u5bc6\u90e8\u548c\u6a2a\u6ce2\u7684\u5e73\u8861\u4f4d\u7f6e\u5bf9\u5e94\u7684\u56fe\u793a\uff08\u5f88\u8d5e\uff09\uff08\u4e24\u76f8\u90bb\u52a0\u5f3a\u70b9\u8ddd\u79bb$\\frac{1}{2}\\lambda$\uff09
\n\u5b9a\u957f\u6ce2<\/strong>\uff08\u9a7b\u6ce2\uff09
\n\u591a\u666e\u52d2\u6548\u5e94\u516c\u5f0f\u63a8\u5bfc
\n\uff08\u5982\u679c\u4f60\u8bf4\u7684\u4e1c\u897f\u7ed9\u522b\u4eba\u8bb2\u8fc7\u591a\u904d\uff0c\u90a3\u4e48\u8fd9\u4e2a\u89c2\u70b9\u624d\u7b97\u662f\u6210\u719f\u7684\uff1f\uff09
\n$f’=\\frac{v\\pm v_o}{v\\mp v_s}f$
\nf’\u4e3a\u89c2\u5bdf\u5230\u7684\u9891\u7387\uff1b
\nf\u4e3a\u53d1\u5c04\u6e90\u4e8e\u8be5\u4ecb\u8d28\u4e2d\u7684\u539f\u59cb\u53d1\u5c04\u9891\u7387\uff1b
\nv\u4e3a\u6ce2\u5728\u8be5\u4ecb\u8d28\u4e2d\u7684\u884c\u8fdb\u901f\u5ea6\uff1b
\n$v_o$\u4e3a\u89c2\u5bdf\u8005\u76f8\u5bf9\u4e8e\u4ecb\u8d28\u7684\u79fb\u52a8\u901f\u5ea6\uff0c\u82e5\u63a5\u8fd1\u53d1\u5c04\u6e90\u5219\u524d\u65b9\u8fd0\u7b97\u7b26\u53f7\u4e3a+\u53f7\uff0c\u53cd\u4e4b\u5219\u4e3a\u2212\u53f7\uff1b
\n$v_s$\u4e3a\u53d1\u5c04\u6e90\u76f8\u5bf9\u4e8e\u4ecb\u8d28\u7684\u79fb\u52a8\u901f\u5ea6\uff0c\u82e5\u63a5\u8fd1\u89c2\u5bdf\u8005\u5219\u524d\u65b9\u8fd0\u7b97\u7b26\u53f7\u4e3a\u2212\u53f7\uff0c\u53cd\u4e4b\u5219\u4e3a+\u53f7\u3002
\n\u51b2\u51fb\u6ce2\uff08shock wave\uff09$sin\\theta=\\frac{V}{v}$
\n\u900f\u955c\u6210\u50cf\u7684\u51e0\u4f55\u7ed3\u8bba\u4e0d\u5e94\u8be5\u4e24\u4e0d\u7ba1\u3002<\/p>\n
\n\u8ddd\u79bb\u5dee\u5230\u76f8\u4f4d\u5dee\u7684\u8f6c\u6362$\\lambda$\u2192$2\\pi$ x\u2192$2\\pi\\frac{x}{\\lambda}$
\n\u65f6\u95f4\u5dee\u5230\u76f8\u4f4d\u5dee\u7684\u8f6c\u6362T\u2192$2\\pi$ t\u2192$2\\pi\\frac{t}{T}$
\n![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/jppbdql2.jpg\")
<\/center>
\n\u5149\u7a0b\u5dee$2ndcos\\theta$
\n![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/net\/pdaoqljp1.jpg\")
<\/center><\/p>\n\u5e74\u7ec8\u56de\u987e<\/del>
\n\u60ef\u6027\u6cd5\u5219\uff08\u5b9a\u5f8b\uff09\u8fd0\u52a8\u7b2c\u4e09\u6cd5\u5219
\n\u652f\u6301\u529b\u548c\u6469\u64e6\u529b\u7684\u5408\u529b\u79f0\u6297\u529b
\n\u6ce8\u76ee\u7269\u4f53<\/p>\n
\n\uff08\u6b64\u90e8\u5206\u5f88\u5999\uff0c\u91cd\u65b0\u63a8\u5230\u4e86\u5149\u6ed1\u6c34\u5e73\u9762\u4e0a\u53e0\u653e\u7684\u4e24\u7269\u4f53\u5206\u522b\u5177\u6709\u51fa\u901f\u901f\uff0c\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u540c\u6837\u6210\u7acb\uff0c\u53ea\u662f\u901f\u5ea6\u66ff\u6362\u4e3a\u76f8\u5bf9\u901f\u5ea6\uff0c\u800c\u4e14\uff0c\u5173\u4e8e\u70ed\u80fd\u95ee\u9898\uff0c\u53ef\u4ee5\u5f15\u5165\u7ea6\u5316\u8d28\u91cf$Q=\\frac{1}{2}\\frac{Mm}{(m+M)}(v_1+v_2)^2$\uff09
\n\u5173\u4e8e\u6062\u590d\u7cfb\u6570\uff0c\u7c7b\u6bd4\u5f39\u7c27\uff0c\u5f62\u53d8\u91cf\u5e73\u6cd5\u548c\u5f39\u6027\u52bf\u80fd\u6210\u6bd4\u4f8b\uff0c\u8fd9\u6837\u7684\u903b\u8f91\uff0c\u635f\u5931\u52a8\u80fd\u7684\u8868\u8fbe\u5f0f\u5bb9\u6613\u63a8\u5bfc\u4e00\u4e9b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"