{"id":48063,"date":"2013-10-29T17:53:01","date_gmt":"2013-10-29T09:53:01","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=48063"},"modified":"2021-10-06T16:19:43","modified_gmt":"2021-10-06T08:19:43","slug":"%e7%9b%b8%e5%b0%8d%e8%ab%96%e6%80%a7%e8%b3%aa%e9%87%8ftransverse-and_longitudinal-mass","status":"publish","type":"post","link":"http:\/\/localhost\/%e7%9b%b8%e5%b0%8d%e8%ab%96%e6%80%a7%e8%b3%aa%e9%87%8ftransverse-and_longitudinal-mass\/","title":{"rendered":"\u76f8\u5c0d\u8ad6\u6027\u8cea\u91cf(Transverse and Longitudinal Mass)"},"content":{"rendered":"

\u76f8\u5c0d\u8ad6\u6027\u8cea\u91cf(Transverse and Longitudinal Mass)<\/span>
\n\u570b\u7acb\u81fa\u7063\u5927\u5b78\u7269\u7406\u7814\u7a76\u6240\u5f90\u9298\u9375<\/span><\/strong><\/strong><\/p>\n

\u81ea\u5f9e\u611b\u56e0\u65af\u5766\u767c\u73fe\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u4e4b\u5f8c\uff0c\u4eba\u5011\u4e86\u89e3\u5230\u8cea\u91cf\u548c\u80fd\u91cf\u6709\u7dca\u5bc6\u7684\u95dc\u4fc2\uff0c\u8457\u540d\u7684\u8cea\u80fd\u4e92\u63db\u516c\u5f0f(mass-energy equivalence)\u70ba<\/p>\n

$$E=\\sqrt{(m_0c^2)^2+(pc)^2}\\equiv mc^2$$<\/p>\n

\u5176\u4e2d $$p$$\u00a0<\/i>\u662f\u7269\u9ad4\u7684\u52d5\u91cf\uff0c$$c$$\u00a0<\/i>\u662f\u5149\u901f\uff0c$$m_0$$\u00a0<\/i>\u662f\u975c\u6b62\u8cea\u91cf(rest mass; \u4e5f\u662f\u4e00\u822c\u4eba\u6240\u719f\u77e5\u7684\u8cea\u91cf)\uff0c$$m$$\u00a0<\/i>\u7a31\u70ba\u76f8\u5c0d\u8ad6\u6027\u8cea\u91cf(relativistic mass)\uff0c\u5b83\u53ef\u4ee5\u8aaa\u662f\u76f4\u63a5\u5f9e\u80fd\u91cf $$E$$\u00a0<\/i>\u9664\u4ee5\u5b9a\u7fa9 $$c^2$$\u00a0<\/i>\u800c\u4f86\u3002<\/p>\n

\u9019\u516c\u5f0f\u8868\u793a\u4e86\u6211\u5011\u6240\u719f\u77e5\u7684\u80fd\u91cf\uff0c\u9664\u4e86\u5305\u62ec\u52d5\u80fd\u3001\u4f4d\u80fd\u3001\u71b1\u80fd…\u4e4b\u5916\uff0c\u7e3d\u80fd\u91cf\u7684\u4e00\u90e8\u5206\u4f86\u81ea\u65bc\u6216\u8ca2\u737b\u7d66\u7269\u9ad4\u7684\u8cea\u91cf $$m_0$$\u00a0<\/i>\u672c\u8eab\uff0c\u9019\u88e1\u7684\u8cea\u91cf\u6307\u975c\u6b62\u8cea\u91cf\uff0c\u4e4b\u6240\u4ee5\u7a31\u975c\u6b62\u8cea\u91cf\u662f\u56e0\u70ba\u6b64\u4e43\u7269\u9ad4(\u6216\u7cfb\u7d71)\u975c\u6b62\u6642\uff0c\u5373\u52d5\u91cf $$p=0$$\u00a0<\/i>\u6642\u6240\u6e2c\u5f97\u7684\u8cea\u91cf\uff0c\u6b64\u6642\u80fd\u91cf\u4e26\u6c92\u6709\u6574\u500b\u7cfb\u7d71\u52d5\u80fd\u7684\u8ca2\u737b\uff1b\u975c\u6b62\u8cea\u91cf\u53c8\u7a31\u7f85\u502b\u8332\u4e0d\u8b8a\u8cea\u91cf(invariant mass)\uff0c\u662f\u56e0\u70ba\u4e0d\u8ad6\u662f\u54ea\u4e00\u500b\u6163\u6027\u5ea7\u6a19\u89c0\u5bdf\u8005\uff0c\u5404\u81ea\u6e2c\u91cf\u5230\u80fd\u91cf $$E$$\u00a0<\/i>\u8ddf\u52d5\u91cf $$p$$\uff0c\u5fc5\u53ef\u5f9e\u95dc\u4fc2\u5f0f $$E^2-(pc)^2=m_0^2c^4$$ \u5f97\u5230 $$m_0$$\u00a0<\/i>\u70ba\u4e0d\u8b8a\u7684\u8cea\u91cf\u5e38\u6578\u3002<\/p>\n

\u7531\u65bc\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u6307\u660e\uff0c\u901f\u7387\u70ba $$u$$\u00a0\u7684\u7269\u9ad4\u4e4b\u52d5\u91cf\u53ef\u4ee5\u5beb\u6210 $$p=\\gamma m_0u$$\uff0c\u5176\u4e2d $$\\gamma=1\/\\sqrt{1-u^2\/c^2}$$\uff0c\u6240\u4ee5\u6709\u6642\u4eba\u5011\u6703\u8aaa\u904b\u52d5\u4e2d\u7269\u9ad4\u7684\u8cea\u91cf\u6703\u589e\u52a0\u70ba $$m=m_0\\gamma$$\uff0c\u9019\u500b $$m$$\u00a0<\/i><\/b>\u6070\u70ba\u4e0a\u9762\u6240\u8ff0\u7684\u76f8\u5c0d\u8ad6\u6027\u8cea\u91cf\u3002<\/p>\n

\u4f46\u8cea\u91cf\u4e5f\u53ef\u4ee5\u5f9e\u7269\u9ad4\u88ab\u52a0\u901f\u6642\u5176\u6240\u53d7\u4f5c\u7528\u529b\u8207\u52a0\u901f\u5ea6\u7684\u6bd4\u503c(\u9019\u4ee3\u8868\u67d0\u7a2e\u62b5\u6297\u53d7\u529b\u7684\u7a0b\u5ea6)\u4f86\u5b9a\u7fa9\uff0c\u5373 $$m=\\frac{F}{a}$$\u00a0\u516c\u5f0f\u3002\u800c\u72f9\u7fa9\u76f8\u5c0d\u8ad6\u544a\u8a34\u4e86\u6211\u5011\u6642\u9593\u548c\u7a7a\u9593\u5176\u5be6\u662f\u5f88\u96e3\u5340\u5206\u7684\uff0c\u5169\u500b\u4e0d\u540c\u7684\u6163\u6027\u5ea7\u6a19\u89c0\u5bdf\u8005\uff0c\u5404\u81ea\u6e2c\u91cf\u5230\u7684\u6642\u9593\u548c\u7a7a\u9593\u5ea7\u6a19\uff0c\u4e0d\u518d\u662f\u6642\u9593\u548c\u7a7a\u9593\u5404\u81ea\u7368\u7acb\uff0c\u5176\u8f49\u63db\u5f0f\u6703\u5c07\u6642\u9593\u548c\u7a7a\u9593(\u6642\u7a7a)\u6df7\u5408\u3002<\/p>\n

\u66f4\u5177\u9ad4\u7684\u8aaa\uff0c\u5047\u8a2d\u76f8\u5c0d\u65bc\u89c0\u5bdf\u8005 $$A$$\uff0c\u89c0\u5bdf\u8005 $$B$$ \u6cbf\u8457 $$x$$\u00a0<\/i><\/b>\u65b9\u5411\u4ee5\u56fa\u5b9a\u901f\u5ea6 $$u$$\u00a0<\/i><\/b>\u4f86\u79fb\u52d5\uff0c\u5247 $$B$$ \u6e2c\u91cf\u5230\u7684\u67d0\u7269\u9ad4\u7684\u6642\u7a7a\u5ea7\u6a19 $$(t’,x’,y’,z’)$$\u00a0\u548c $$A$$ \u6240\u6e2c\u91cf\u5230\u7684\u540c\u4e00\u7269\u9ad4\u7684\u6642\u7a7a\u5ea7\u6a19 $$(t,x,y,z)$$\u00a0\u5f7c\u6b64\u6709\u4e00\u500b\u95dc\u4fc2<\/p>\n

$$\\displaystyle\\begin{cases}t’=\\gamma(t-\\displaystyle\\frac{u}{c^2}x)\\\\ x’=\\gamma(x-ut)\\\\ y’=y\\\\ z’=z \\end{cases}$$<\/p>\n

\u5176\u4e2d $$\\gamma=1\/\\sqrt{1-u^2\/c^2}$$ \u70ba\u5e38\u6578\u3002<\/p>\n

\u7279\u5225\u8981\u6ce8\u610f\u7684\u662f\u53ea\u6709\u6cbf\u8457\u904b\u52d5\u65b9\u5411\u7684\u5ea7\u6a19(\u6b64\u4f8b\u5b50\u70ba $$x$$\u00a0<\/i><\/b>\u65b9\u5411)\u548c\u6642\u9593\u5ea7\u6a19\u6df7\u548c\uff0c\u800c\u5782\u76f4\u65b9\u5411($$y$$\u00a0<\/i><\/b>\u548c $$z$$\u00a0<\/i><\/b>\u65b9\u5411)\u5ea7\u6a19\u5247\u4ecd\u662f\u7368\u7acb\u7684\u3002\u4f46\u56e0\u901f\u5ea6\u6d89\u53ca\u8ddd\u96e2\u5c0d\u6642\u9593\u7684\u8b8a\u5316\uff0c\u6240\u4ee5\u4e0d\u8ad6 $$x,y,z$$\u00a0<\/i><\/b>\u65b9\u5411\u6e2c\u91cf\u5230\u7684\u7269\u9ad4\u901f\u5ea6\uff0c\u90fd\u662f\u6642\u9593\u548c\u7a7a\u9593\u6df7\u5408\u7684\u5f62\u5f0f\u3002<\/p>\n

\u800c\u660e\u986f\u7684\uff0c\u5e73\u884c\u904b\u52d5\u65b9\u5411($$x$$\u00a0<\/i><\/b>\u65b9\u5411)\u7684\u901f\u5ea6\uff0c\u548c\u5782\u76f4\u904b\u52d5\u65b9\u5411($$y,z$$\u00a0<\/i><\/b>\u65b9\u5411)\u7684\u901f\u5ea6\uff0c\u5176\u6642\u7a7a\u6df7\u548c\u7684\u5f62\u5f0f\u662f\u4e0d\u540c\u7684\u3002\u540c\u7406\uff0c\u52a0\u901f\u5ea6\u7684\u5e73\u884c\u65b9\u5411\u548c\u5782\u76f4\u65b9\u5411\u7684\u5f62\u5f0f\u4e5f\u662f\u4e0d\u540c\u7684\u3002\u4f9d\u76f8\u5c0d\u8ad6\u6027\u7684\u539f\u7406\uff0c\u6211\u5011\u4e5f\u53ef\u63a8\u5f97\u96fb\u78c1\u5834\u5c0d\u5e36\u96fb\u7c92\u5b50\u7684\u65bd\u529b\u5728\u4e0d\u540c\u5ea7\u6a19\u4e4b\u9593\u7684\u8f49\u63db\u5f0f\uff0c\u5176\u5e73\u884c\u89c0\u5bdf\u8005\u904b\u52d5\u65b9\u5411\u548c\u5782\u76f4\u65b9\u5411\u4e5f\u662f\u4e0d\u540c\u7684\u3002<\/p>\n

\u7d9c\u5408\u4ee5\u4e0a\u6240\u8ff0\uff0c\u6211\u5011\u5fc5\u9808\u4fee\u6539\u725b\u9813\u529b\u5b78\u7684 $$F=ma$$\u00a0<\/i><\/b>\u516c\u5f0f\uff0c\u4f7f\u5176\u5340\u5206\u5e73\u884c\u904b\u52d5\u65b9\u5411\u548c\u5782\u76f4\u65b9\u5411\u3002\u5047\u8a2d\u6211\u5011\u89c0\u5bdf\u4ee5\u56fa\u5b9a\u901f\u5ea6 $$u$$\u00a0<\/i><\/b>\u6cbf\u8457 $$x$$\u00a0<\/i><\/b>\u65b9\u5411\u904b\u52d5\u4e2d\u7684\u7269\u9ad4\uff0c\u5176\u53d7\u529b\u548c\u52a0\u901f\u5ea6\u7684\u95dc\u4fc2\u70ba\uff0c<\/p>\n

$$\\begin{cases}f_x=m_La_x,~m_L=\\gamma^3m_0\\\\ f_y=m_Ta_y,~m_T=\\gamma m_0\\\\f_z=m_Ta_z,~m_T=\\gamma m_0\\\\\\end{cases}$$<\/p>\n

\u91cd\u9ede\u5728\u65bc\uff0c\u5e73\u884c\u65b9\u5411\u8ddf\u5782\u76f4\u65b9\u5411\u7684\u52a0\u901f\u5ea6\u5c0d\u65bd\u529b\u7684\u62b5\u6297\u7a0b\u5ea6\u4e0d\u540c\uff0c\u5373\u5e73\u884c\u65b9\u5411\u70ba $$m_L$$\u00a0<\/i><\/b>\u7a31\u70ba\u5e73\u884c\u8cea\u91cf(longitudinal mass)\uff0c\u5782\u76f4\u65b9\u5411\u70ba $$m_T$$\u00a0<\/i><\/b>\u7a31\u70ba\u5782\u76f4\u8cea\u91cf(transverse mass)\uff0c\u5169\u8005\u90fd\u548c\u975c\u6b62\u8cea\u91cf\u6709\u95dc\uff0c\u5176\u95dc\u4fc2\u5f0f\u5982\u516c\u5f0f\u6240\u8ff0\uff0c\u800c\u5e73\u884c\u8cea\u91cf\u548c\u5782\u76f4\u8cea\u91cf\u53ea\u6709\u5728\u7269\u9ad4\u904b\u52d5\u901f\u5ea6 $$u=0$$\u00a0(\u6b64\u6642 $$\\gamma=1$$)\u6642\u76f8\u540c\uff0c\u96a8\u8457\u901f\u5ea6 $$u$$\u00a0<\/i>\u6108\u63a5\u8fd1\u5149\u901f $$(\\gamma \\to \\infty)$$\uff0c\u5e73\u884c\u8cea\u91cf\u548c\u5782\u76f4\u8cea\u91cf\u6108\u4f86\u6108\u5927\uff0c\u6240\u4ee5\u6211\u5011\u6703\u767c\u73fe\u8d8a\u4f86\u8d8a\u96e3\u63a8\u52d5\u6b64\u7269\u9ad4(\u548c\u7cfb\u7d71)\uff0c\u800c\u5e73\u884c\u8cea\u91cf\u589e\u52a0\u7684\u6bd4\u4f8b\u5927\u65bc\u5782\u76f4\u8cea\u91cf\u96a8\u901f\u5ea6 $$u$$\u00a0<\/i>\u589e\u52a0\u7684\u6bd4\u4f8b\uff0c\u5373\u5169\u8005\u662f\u4e0d\u76f8\u7b49\u7684\u3002<\/p>\n

\u5e73\u884c\u8cea\u91cf\u4ee5\u53ca\u5782\u76f4\u8cea\u91cf\u7684\u5340\u5225\u591a\u898b\u65bc\u8f03\u820a\u7684\u6587\u737b\u4e2d\u3002\u73fe\u4ee3\u5c0d\u65bc\u8cea\u91cf\u7684\u898b\u89e3\uff0c\u5247\u50be\u5411\u65bc\u5c07\u4e4b\u5b9a\u7fa9\u70ba\u7269\u9ad4\u5f9e\u975c\u6b62\u4e2d\u88ab\u52a0\u901f<\/b>\u6642\uff0c\u4f5c\u7528\u529b\u8207\u52a0\u901f\u5ea6\u7684\u6bd4\u503c\uff0c\u4ea6\u5373 $$m=F\/a$$\u3002\u5982\u524d\u6240\u8ff0\uff0c\u9019\u500b\u8aaa\u6cd5\u6240\u5b9a\u7fa9\u51fa\u4f86\u7684\u8cea\u91cf\u5373\u662f\u975c\u6b62\u8cea\u91cf $$m_0$$\uff0c\u5b83\u662f\u4e0d\u6703\u96a8\u5ea7\u6a19\u7cfb\u800c\u6539\u8b8a\u3002<\/p>\n

\u53c3\u8003\u8cc7\u6599\uff1a<\/p>\n

    \n
  1. Wikipedia:\u00a0 Mass in special relativity<\/li>\n
  2. Kevin Brown, Reflections on Relativity<\/i>, Publisher: Lulu.com,( ISBN-13: 9781257033027)
    \n\u53ef\u53e6\u53c3\u8003 http:\/\/www.mathpages.com\/rr\/rrtoc.htm<\/a><\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u76f8\u5c0d\u8ad6\u6027\u8cea\u91cf(Transverse and Longitudinal Mass) \u570b\u7acb\u81fa\u7063\u5927\u5b78\u7269\u7406\u7814\u7a76\u6240\u5f90\u9298\u9375…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107,36,32],"tags":[5743,5742,5745,2236,5741,5744],"class_list":["post-48063","post","type-post","status-publish","format-standard","hentry","category-physics00","category-physics07-04","category-physics07","tag-5743","tag-5742","tag-5745","tag-2236","tag-5741","tag-5744","loop-entry","cat-107","cat-36","cat-32","no-thumbnail"],"views":8199,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/48063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=48063"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/48063\/revisions"}],"predecessor-version":[{"id":87316,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/48063\/revisions\/87316"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=48063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=48063"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=48063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}