{"id":22203,"date":"2011-03-25T09:55:46","date_gmt":"2011-03-25T01:55:46","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=22203"},"modified":"2021-10-06T16:28:13","modified_gmt":"2021-10-06T08:28:13","slug":"%e7%89%9b%e9%a0%93%e6%93%ba%ef%bc%88newtons-cradle%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e7%89%9b%e9%a0%93%e6%93%ba%ef%bc%88newtons-cradle%ef%bc%89\/","title":{"rendered":"\u725b\u9813\u64fa"},"content":{"rendered":"

\u725b\u9813\u64fa (Newton’s Cradle)
\n<\/span>\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u66fe\u923a\u6f54\u78a9\u58eb\u751f\/\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u8521\u5fd7\u7533\u6559\u6388\u8cac\u4efb\u7de8\u8f2f
\n<\/span><\/strong>
\n\u725b\u9813\u64fa\u662f\u4e00\u500b\u5e38\u898b\u7684\u684c\u9762\u6f14\u793a\u88dd\u7f6e\uff0c\u7531\u4e94\u500b\u8cea\u91cf\u76f8\u540c\u7684\u7403\u9ad4\u7531\u540a\u7e69\u56fa\u5b9a\uff0c\u5f7c\u6b64\u7dca\u5bc6\u6392\u5217\u3002<\/p>\n

\"\"<\/p>\n

<\/p>\n

\u725b\u9813\u64fa\u6700\u65e9\u662f\u5728 1676 \u5e74\u7531\u6cd5\u570b\u7269\u7406\u5b78\u5bb6\u57c3\u5fb7\u59c6\uff0e\u99ac\u7565\u7279\uff08Edme Mariotte\uff09\u63d0\u51fa\uff0c\u800c\u5728 1960 \u5e74\u4ee3\u767c\u660e\u7684\u684c\u9762\u6f14\u793a\u88dd\u7f6e\u3002\u56e0\u70ba\u8a72\u88dd\u7f6e\u5229\u7528\u5805\u56fa\u7684\u540a\u7e69\u540a\u8d77\u4e94\u500b\u8cea\u91cf\u76f8\u540c\u7684\u7403\u9ad4\uff0c\u800c\u5c07\u7403\u9ad4\u7684\u904b\u52d5\u9650\u5236\u5728\u4e00\u7dad\u4e0a\u904b\u52d5\uff0c\u6240\u4ee5\u7576\u6700\u53f3\u5074\u7684\u7403\u88ab\u62c9\u9ad8\u4e26\u81ea\u7531\u91cb\u653e\u5f8c\uff0c\u5728\u56de\u64fa\u81f3\u539f\u4f4d\u7f6e\u6642\u6703\u8207\u7b2c\u4e8c\u9846\u7403\u78b0\u649e\uff0c\u800c\u5947\u5999\u7684\u4e8b\u60c5\u5c31\u9019\u9ebc\u767c\u751f\u4e86\u2014\u4e2d\u9593\u7dca\u5bc6\u6392\u5217\u7684\u7403\u4e26\u6c92\u6709\u56e0\u70ba\u78b0\u649e\u800c\u64fa\u76ea\u7684\u73fe\u8c61\uff0c\u53ea\u6709\u6700\u5de6\u5074\u7684\u7403\u6703\u88ab\u5f48\u51fa\uff0c\u4e14\u5728\u6700\u5de6\u5074\u7684\u7403\u56de\u64fa\u5f8c\u767c\u751f\u540c\u6a23\u7684\u4e8b\u60c5\u2014\u50c5\u6709\u6700\u53f3\u5074\u7684\u7403\u9ad4\u5f48\u51fa\uff0c\u4e2d\u9593\u7dca\u5bc6\u6392\u5217\u7684\u7403\u7d72\u6beb\u4e0d\u52d5\u3002<\/p>\n

\u70ba\u4ec0\u9ebc\u725b\u9813\u64fa\u6703\u5c55\u73fe\u9019\u9ebc\u5947\u7279\u7684\u73fe\u8c61\u5462\uff1f\u4ed4\u7d30\u56de\u60f3\u725b\u9813\u64fa\u88dd\u7f6e\u7684\u9650\u5236\uff0c\u5c31\u6703\u77e5\u9053\u5b83\u5176\u5be6\u53ef\u4ee5\u7528\u7c21\u55ae\u7684\u4e00\u7dad\u5f48\u6027\u78b0\u649e\u89e3\u91cb\u3002<\/p>\n

\u4e00\u7dad\u7684\u5f48\u6027\u78b0\u649e\uff0c\u6703\u9075\u5b88\u529b\u5b78\u80fd\u5b88\u6046\u3001\u52d5\u91cf\u5b88\u6046\u3002\u4e00\u822c\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n

\"\"<\/a><\/p>\n

\u52d5\u91cf\u5b88\u6046\uff1a$$m_1v_1+m_2v_2=m_1v^{‘}_1+m_2v^{‘}_2$$<\/p>\n

\u529b\u5b78\u80fd\u5b88\u6046\uff1a$$\\frac{1}{2}m_1v^2_1+\\frac{1}{2}m_2v^2_2=\\frac{1}{2}m_1{v^{‘}_1}^2+\\frac{1}{2}m_2{v^{‘}_2}^2$$<\/p>\n

\u7d93\u904e\u89e3\u806f\u7acb\u65b9\u7a0b\u5f8c\u53ef\u5f97\u7d50\u679c\uff1a<\/p>\n

$$v^{‘}_1=\\displaystyle\\frac{m_1-m_2}{m_1+m_2}v_1+\\frac{2m_2}{m_1+m_2}v_2$$\uff0c$$v^{‘}_2=\\displaystyle\\frac{2m_1}{m_1+m_2}v_1+\\frac{m_2-m_1}{m_1+m_2}v_2$$<\/p>\n

\u82e5\u5169\u7403\u8cea\u91cf\u76f8\u540c $$m_1=m_2$$\uff0c\u53ef\u5f97\u5230\u7c21\u55ae\u7684\u7d50\u679c\uff1a$$v^{‘}_1=v_2$$\u3001$$v^{‘}_2=v_1$$\u3002<\/p>\n

\u56de\u982d\u770b\u725b\u9813\u64fa\u88dd\u7f6e\uff0c\u7403\u9ad4\u4e0d\u50c5\u9650\u5236\u5728\u4e00\u7dad\u4e0a\u904b\u52d5\uff0c\u9084\u662f\u4e94\u500b\u8cea\u91cf\u76f8\u540c\u7684\u7403\u9ad4\uff08$$m_1=m_2=m_3=m_4=m_5$$\uff09\uff0c\u56e0\u6b64\u53ef\u4ee5\u5927\u5927\u6e1b\u5316\u78b0\u649e\u7684\u60c5\u5f62\uff08\u5982\u5716\u4e09\uff09\uff1a<\/p>\n

    \n
  1. \u525b\u958b\u59cb\u62c9\u8d77\u6700\u53f3\u5074\u7684 $$1$$ \u865f\u7403\uff0c\u7576\u7403\u9ad4\u843d\u4e0b\u78b0\u649e\u5230 $$2$$ \u865f\u7403\u524d\uff0c\u5177\u6709\u901f\u5ea6 $$v_1$$\uff0c\u540c\u6642 $$2$$ \u865f\u7403\u4e4b\u901f\u5ea6 $$v_2=0$$\u3002<\/li>\n
  2. \u7576 $$1$$ \u865f\u3001$$2$$ \u865f\u5169\u7403\u767c\u751f\u78b0\u649e\u5f8c\uff0c\u56e0\u70ba\u5169\u7403\u8cea\u91cf\u76f8\u540c\uff0c\u6545\u53ef\u5f97 $$v^{‘}_1=v_2=0$$\u3001$$v^{‘}_2=v_1$$\u3002<\/li>\n
  3. \u7531\u65bc\u7403\u9ad4\u5f7c\u6b64\u7dca\u5bc6\u6392\u5217\uff0c\u7576 $$2$$ \u865f\u7403\u64c1\u6709\u5411\u5de6\u7684\u901f\u5ea6 $$v^{‘}_2$$\u00a0\u6642\uff0c\u96a8\u5373\u8207 $$3$$ \u865f\u7403\uff08\u901f\u5ea6 $$v_3=0$$\uff09\u7522\u751f\u78b0\u649e\u3002\u540c\u6a23\u56e0\u70ba\u5169\u7403\u8cea\u91cf\u76f8\u540c\uff0c\u6545 $$v^{”}_2=v_3=0$$\u3001$$v^{‘}_3=v_1$$\u3002<\/li>\n
  4. $$4$$ \u865f\u7403\u7684\u60c5\u6cc1\u4e5f\u662f\u5982\u6b64\uff0c\u76f4\u5230\u7b2c $$5$$ \u865f\u7403\uff0c\u7576\u548c $$4$$ \u865f\u7403\u78b0\u649e\u5f8c\u5f97\u5230\u901f\u5ea6 $$v^{‘}_5=v_1$$\u00a0\u5f8c\uff0c\u56e0\u70ba\u5de6\u5074\u518d\u4e5f\u6c92\u6709\u7403\u9ad4\u8207\u4e4b\u78b0\u649e\uff0c\u6240\u4ee5\u5c07\u4ee5\u901f\u5ea6 $$v_1$$\u00a0\u4f5c\u904b\u52d5\u800c\u5411\u4e0a\u64fa\u76ea\u3002<\/li>\n<\/ol>\n

    \"\"<\/a><\/p>\n

    \u7576\u660e\u767d\u725b\u9813\u64fa\u53ef\u4ee5\u7c21\u55ae\u7684\u4ee5\u4e00\u7dad\u5f48\u6027\u78b0\u649e\u89e3\u91cb\u5f8c\uff0c\u662f\u5426\u6703\u597d\u5947\u5982\u679c\u540c\u6642\u62c9\u8d77\u5169\u9846\u7403\u9ad4\u5c07\u4e4b\u81ea\u7531\u91cb\u653e\uff0c\u539f\u672c\u975c\u6b62\u7684\u7403\u9ad4\u9084\u53ef\u4ee5\u7e7c\u7e8c\u4fdd\u6301\u975c\u6b62\u55ce\uff1f\u4f9d\u985e\u63a8\u7684\u65b9\u5f0f\u53ef\u4ee5\u731c\u6e2c\u6700\u4e2d\u9593\u7684\u7403\u4ecd\u4fdd\u6301\u975c\u6b62\uff0c\u800c\u53e6\u4e00\u5074\u7684\u5169\u9846\u7403\u6703\u540c\u6642\u649e\u8d77\u2026\u3002\u90a3\u62c9\u8d77\u4e09\u9846\u7403\u5462\uff1f\u56db\u9846\u7403\u5462\uff1f\u597d\u50cf\u8b8a\u8907\u96dc\u4e86\u5462\u2026\u4e0d\u5982\u770b\u770b\u5be6\u969b\u725b\u9813\u64fa\u64fa\u76ea\u7684\u60c5\u6cc1\uff0c\u9a57\u8b49\u4e00\u4e0b\u731c\u6e2c\u7684\u7d50\u679c\u5427\uff01
    \n    http:\/\/140.122.141.9\/~haha90\/content\/fun_exp\/index.htm<\/a>
    \n\uff08\u8acb\u9ede\u9078\u5de6\u5074\u9078\u9805\uff1a— \u52d5\u529b\u5b78 — \u725b\u9813\u64fa\u3002\u6e90\u81ea\u65bc\uff1a\u597d\u597d\u73a9\u7269\u7406\u7db2\u00a0\u00a0\u6f58\u51a0\u9321\u8001\u5e2b\u7684\u7db2\u7ad9\uff09<\/p>\n

    \u770b\u5b8c\u4e86\u5f71\u7247\u5f8c\uff0c\u662f\u5426\u89ba\u5f97\u548c\u60f3\u50cf\u4e2d\u7684\u6709\u4e9b\u8a31\u5dee\u8ddd\u5462\uff1f\u5176\u5be6\u5be6\u969b\u7684\u725b\u9813\u64fa\u7121\u6cd5\u5b8c\u5168\u505a\u5230\u5404\u500b\u7403\u9ad4\u8cea\u91cf\u76f8\u7b49\uff0c\u9019\u5f71\u97ff\u8457\u7406\u8ad6\u8a08\u7b97\u4e2d\uff0c\u539f\u672c\u4fdd\u6301\u975c\u6b62\u7684\u7403\u9ad4\u4e5f\u8ddf\u8457\u64fa\u52d5\uff08\u5e36\u6709\u901f\u5ea6\uff09\uff0c\u78b0\u649e\u7684\u516c\u5f0f\u5c31\u6703\u8b8a\u5f97\u8907\u96dc\uff0c\u751a\u81f3\u6703\u6709\u76f8\u9130\u5169\u7403\u901f\u5ea6\u65b9\u5411\u76f8\u53cd\u800c\u5c0d\u649e\u7684\u60c5\u6cc1\u767c\u751f\u3002\u82e5\u89ba\u5f97\u96e3\u4ee5\u60f3\u50cf\uff0c\u4e0d\u59a8\u9ede\u9078\u4ee5\u4e0b\u806f\u7d50–
    \n    http:\/\/www.phy.ntnu.edu.tw\/demol … pic.php?topic=19870<\/a>
    \n\uff08\u6e90\u81ea\u65bc\uff1a\u9ec3\u798f\u5764\u6559\u6388\uff0c\u570b\u7acb\u53f0\u7063\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u00a0\u00a0\u7269\u7406\u6559\u5b78\u793a\u7bc4\u5be6\u9a57\u6559\u5ba4\u00a0\u00a0\u7269\u7406\u554f\u984c\u8a0e\u8ad6\u5340\uff09
    \n\u9019\u88e1\u80fd\u6539\u8b8a\u53c3\u6578\u52a0\u4ee5\u63a7\u5236\uff0c\u6a21\u64ec\u51fa\u7406\u8ad6\u8207\u771f\u5be6\u60c5\u6cc1\u7684\u52d5\u756b\uff0c\u52d5\u756b\u4e2d\u9084\u9644\u4e0a\u7403\u9ad4\u78b0\u649e\u524d\u5f8c\u7684\u901f\u5ea6\uff08\u4ee5\u7bad\u865f\u8868\u793a\uff09\uff0c\u4ee5\u6700\u76f4\u63a5\u7684\u65b9\u6cd5\u62c6\u89e3\u725b\u9813\u64fa\u7684\u904b\u52d5\u65b9\u5f0f\u3002<\/p>\n

    \n

    \u53c3\u8003\u8cc7\u6599<\/strong>
    \n1.\u7dad\u57fa\u767e\u79d1–\u725b\u9813\u64fa\u00a0\u00a0    http:\/\/zh.wikipedia.org\/zh-tw\/\u725b\u9813\u64fa<\/a>
    \n2.\u725b\u9813\u64fa\uff0c\u4e2d\u8208\u5927\u5b78\u7269\u7406\u7cfb\u00a0\u00a0\u666e\u7269\u6f14\u793a\u5ef3\u00a0\u00a0    http:\/\/ezphysics.nchu.edu.tw\/physiweb\/device\/exp3.htm<\/a>
    \n3.\u597d\u597d\u73a9\u7269\u7406\u7db2\u00a0\u00a0\u6f58\u51a0\u9321\u8001\u5e2b\u7684\u7db2\u7ad9 \u2192 \u8da3\u5473\u5be6\u9a57 \u2192 — \u52d5\u529b\u5b78 — \u725b\u9813\u64fa\uff0c    http:\/\/140.122.141.9\/~haha90\/content\/fun_exp\/index.htm<\/a>
    \n4.\u725b\u9813\u64fa\u6a21\u64ec\u52d5\u756b\uff0c\u9ec3\u798f\u5764\uff0c\u570b\u7acb\u53f0\u7063\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u00a0\u00a0\u7269\u7406\u6559\u5b78\u793a\u7bc4\u5be6\u9a57\u6559\u5ba4\u2192\u7269\u7406\u554f\u984c\u8a0e\u8ad6\u5340\u2192\u7269\u7406\u52d5\u756b\u2192\u52d5\u529b\u5b78\u2192\u725b\u9813\u64fa\u6a21\u64ec\u52d5\u756b\u00a0\u00a0    http:\/\/www.phy.ntnu.edu.tw\/demol … pic.php?topic=19870<\/a><\/p>\n

     <\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u725b\u9813\u64fa (Newton’s Cradle) \u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u66fe\u923a\u6f54\u78a9\u58eb\u751f\/\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u7269…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107,13,3],"tags":[706,10250,690,10252,2104,471,10251,2165],"class_list":["post-22203","post","type-post","status-publish","format-standard","hentry","category-physics00","category-physics01-10","category-physics01","tag-collision","tag-elastic-collision","tag-newton","tag-newtons-cradle","tag-2104","tag-471","tag-10251","tag-2165","loop-entry","cat-107","cat-13","cat-3","no-thumbnail"],"views":14560,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/22203","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=22203"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/22203\/revisions"}],"predecessor-version":[{"id":88751,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/22203\/revisions\/88751"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=22203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=22203"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=22203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}