{"id":16744,"date":"2010-12-02T17:38:40","date_gmt":"2010-12-02T09:38:40","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=16744"},"modified":"2021-10-06T16:30:24","modified_gmt":"2021-10-06T08:30:24","slug":"%e8%ae%8a%e8%b3%aa%e9%87%8f%e9%81%8b%e5%8b%95-%e7%81%ab%e7%ae%ad%ef%bc%88rocket%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e8%ae%8a%e8%b3%aa%e9%87%8f%e9%81%8b%e5%8b%95-%e7%81%ab%e7%ae%ad%ef%bc%88rocket%ef%bc%89\/","title":{"rendered":"\u8b8a\u8cea\u91cf\u904b\u52d5\u2014\u706b\u7bad\uff08Rocket\uff09"},"content":{"rendered":"

\u8b8a\u8cea\u91cf\u904b\u52d5\u2014\u706b\u7bad\uff08Rocket\uff09<\/span>
\n\u570b\u7acb\u5f70\u5316\u9ad8\u7d1a\u4e2d\u5b78\u7269\u7406\u79d1\u8cf4\u6587\u54f2\u8001\u5e2b\/\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u8521\u5fd7\u7533\u6559\u6388\u8cac\u4efb\u7de8\u8f2f<\/span>
\n<\/strong>
\n\u5047\u8a2d\u706b\u7bad\u5728\u4e0d\u53d7\u91cd\u529b\u53ca\u7a7a\u6c23\u963b\u529b\u4f5c\u7528\u4e0b\uff0c\u4f5c\u4e00\u7dad\u52a0\u901f\u5ea6\u904b\u52d5\uff0c\u4ee4\u4efb\u4e00\u6642\u9593 $$t$$\u00a0\u7684\u706b\u7bad\u8cea\u91cf\u70ba $$m$$\u00a0\u901f\u5ea6\u70ba $$v$$\uff0c\u7d93\u904e\u6642\u9593 $$dt$$\u00a0\u5f8c\uff0c\u706b\u7bad\u8cea\u91cf\u70ba $$m+dm$$\u00a0\u901f\u5ea6\u70ba $$v+dv$$\uff0c\u706b\u7bad\u5ee2\u6c23\u5674\u51fa\u7684\u901f\u5ea6\u76f8\u5c0d\u65bc\u6163\u6027\u5ea7\u6a19\u89c0\u5bdf\u8005\u7684\u901f\u5ea6\u70ba $$u$$\uff0c\u7531\u5674\u6c23\u524d\u5f8c\u52d5\u91cf\u5b88\u6046\uff0c\uff08$$v_{rel}$$\u3001$$u$$\u3001$$v$$\u00a0<\/i><\/span>\u7b26\u865f\u6cd5\u5247\u76f8\u540c\uff0c$$dm$$\u00a0<\/i><\/span>\u70ba\u8ca0\u503c\u3001$$dv$$\u00a0<\/i><\/span>\u70ba\u6b63\u503c\uff09<\/p>\n

$$mv=(m+dm)\\times(v+dv)-dm\\times u$$<\/p>\n

\u7531\u76f8\u5c0d\u901f\u5ea6\u95dc\u4fc2\uff0c\u8a2d\u706b\u7bad\u76f8\u5c0d\u65bc\u5ee2\u6c23\u7684\u901f\u5ea6\u662f $$v_{rel}$$<\/p>\n

$$v+dv=u+v_{rel}$$\uff0c\u4ee5 $$u=v+dv-v_{rel}$$\u00a0\u4ee3\u5165\u4e0a\u5f0f<\/p>\n

$$mv=mv+mdv+vdm+dm\\times dv-dm\\times(v+dv-v_{rel})-v_{rel}dm=mdv$$<\/p>\n

\u5169\u908a\u540c\u9664\u4ee5 $$dt$$<\/p>\n

$$\\displaystyle -\\frac{dm}{dt}v_{rel}=m\\frac{dv}{dt}$$<\/p>\n

\u5c07\u706b\u7bad\u55ae\u4f4d\u6642\u9593\u640d\u5931\u7684\u8cea\u91cf $$-\\frac{dm}{dt}$$ \u8a08\u70ba $$R$$\uff0c$$\\frac{dv}{dt}$$ \u70ba\u52a0\u901f\u5ea6 $$a$$<\/p>\n

$$Rv_{rel}=ma=F$$\uff0c\u6b64\u4f5c\u7528\u529b\u7a31\u70ba\u706b\u7bad\u5f15\u64ce\u7684\u63a8\u529b\uff0c\u6b64\u63a8\u529b\u8207\u55ae\u4f4d\u6642\u9593\u7684\u5674\u6c23\u91cf\u4ee5\u53ca\u6c23\u9ad4\u7684\u5674\u767c\u901f\u7387\u6709\u95dc\uff0c\u9019\u5169\u500b\u7269\u7406\u91cf\u6108\u5927\uff0c\u5f15\u64ce\u63a8\u529b\u5c31\u6108\u5927\u3002<\/p>\n

\u56fa\u614b\u71c3\u6599\u706b\u7bad<\/strong>\u4e0d\u9700\u8981\u984d\u5916\u7684\u71c3\u6599\u69fd\uff0c\u4e5f\u4e0d\u9700\u8981\u8f38\u9001\u6216\u52a0\u58d3\u7684\u7ba1\u7dda\uff0c\u5728\u69cb\u9020\u4e0a\u56fa\u9ad4\u706b\u7bad\u767c\u52d5\u6a5f\u6bd4\u6db2\u614b\u706b\u7bad\u767c\u52d5\u6a5f\u8981\u7c21\u55ae\u8a31\u591a\uff0c\u71c3\u6599\u4f54\u706b\u7bad\u8cea\u91cf\u7684\u6bd4\u4f8b\u4e5f\u6bd4\u8f03\u5927\uff0c\u591a\u534a\u4f7f\u7528\u5728\u63a8\u529b\u9700\u6c42\u8f03\u70ba\u56fa\u5b9a\uff0c\u4e00\u7d93\u555f\u52d5\u5c31\u4e0d\u9700\u8981\u505c\u6b62\u7684\u8a2d\u8a08\u4e0a\u9762\uff0c\u5176\u7f3a\u9ede\u662f\uff0c\u4e00\u65e6\u9ede\u71c3\u5f8c\u5373\u7a69\u5b9a\u71c3\u71d2\u81f3\u71c3\u6599\u7528\u5b8c\uff0c\u4e2d\u9014\u96e3\u4ee5\u63a7\u5236\u6539\u8b8a\u5176\u63a8\u529b\u5927\u5c0f\u3002<\/p>\n

\u6db2\u614b\u71c3\u6599\u706b\u7bad<\/strong>\u7684\u71c3\u6599\u548c\u6c27\u5316\u5291\u662f\u4ee5\u6db2\u614b\u7684\u65b9\u5f0f\u5132\u5b58\uff0c\u4f7f\u7528\u7684\u6642\u5019\u624d\u4ee5\u6c23\u614b\u7684\u65b9\u5f0f\u6df7\u5408\uff0c\u71c3\u71d2\u7522\u751f\u63a8\u529b\uff0c\u5728\u69cb\u9020\u4e0a\u8f03\u8907\u96dc\uff0c\u4f46\u5177\u6709\u53ef\u8abf\u6574\u63a8\u529b\u7684\u512a\u9ede\u3002<\/p>\n

\u518d\u7531 $$\\displaystyle dv=-v_{rel}\\frac{dm}{m}$$<\/p>\n

\u7a4d\u5206\u53ef\u5f97 $$\\displaystyle \\int^{v_f}_{v_i}dv=-v_{rel}\\int^{m_f}_{m_i}\\frac{dm}{m}$$<\/p>\n

$$\\displaystyle v_f-v_i=v_{rel}\\ln\\frac{m_i}{m_f}$$<\/p>\n

\u7531\u4e0a\u662f\u53ef\u77e5\uff0c\u71c3\u6599\u4f54\u706b\u7bad\u8cea\u91cf\u7684\u6bd4\u4f8b\u6108\u5927\uff0c\u706b\u7bad\u7684\u901f\u5ea6\u8b8a\u5316\u91cf\u4e5f\u6108\u5927\u3002<\/p>\n

\u706b\u7bad\u7684\u8a2d\u8a08\u53ef\u5206\u70ba\u55ae\u7bc0\u706b\u7bad\u8207\u591a\u7bc0\u706b\u7bad\uff0c\u55ae\u7bc0\u706b\u7bad<\/strong>\u69cb\u9020\u7c21\u55ae\uff0c\u4f46\u662f\u5f80\u5f80\u5916\u6bbc\u6240\u4f54\u8cea\u91cf\u904e\u5927\uff0c\u71c3\u6599\u8017\u76e1\u5f8c $$m_f$$\u00a0\u4ecd\u5f88\u5927\uff0c\u4ee5\u81f4\u65bc\u7121\u6cd5\u5f97\u5230\u8db3\u5920\u7684\u672b\u901f $$v_f$$\u3002<\/p>\n

\u591a\u7bc0\u706b\u7bad<\/strong>\u53ef\u9678\u7e8c\u62cb\u68c4\u7528\u76e1\u7684\u71c3\u6599\u8259\u4f86\u6e1b\u5c0f\u706b\u7bad\u8cea\u91cf\uff0c\u8f03\u6709\u6548\u5f97\u5230\u63a8\u9032\u7684\u6548\u679c\u3002\u4f46\u591a\u7bc0\u706b\u7bad\u9664\u9020\u50f9\u6602\u8cb4\u4e4b\u5916\uff0c\u5728\u62cb\u68c4\u7528\u76e1\u7684\u71c3\u6599\u8259\u6642\u4e5f\u662f\u4e00\u500b\u5f88\u95dc\u9375\u7684\u6280\u8853\uff0c\u82e5\u4e0d\u80fd\u9806\u5229\u812b\u96e2\uff0c\u5c07\u9020\u6210\u6574\u500b\u767c\u5c04\u5de5\u4f5c\u6bc0\u65bc\u4e00\u65e6\u3002<\/p>\n

\u592a\u7a7a\u68ad\u7cfb\u7d71\u7e3d\u5171\u4f7f\u7528\u4e94\u5177\u767c\u52d5\u6a5f\u4f86\u5b8c\u6210\u8d77\u98db\u7684\u52d5\u4f5c\uff0c\u5176\u4e2d\u4e09\u5177\u4e3b\u5f15\u64ce\u5728\u8ecc\u9053\u904b\u884c\u5668\u7684\u5f8c\u9762\uff0c\u53ef\u7522\u751f\u7d04 $$5\\times 10^5~kgw$$\u00a0\u7684\u63a8\u529b\uff1b\u53e6\u5916\u9084\u6709\u5169\u5177\u5916\u639b\u5728\u5916\u90e8\u71c3\u6599\u7bb1\u65c1\u908a\u7684\u56fa\u614b\u706b\u7bad\u52a9\u63a8\u5668\uff0c\u53ef\u7522\u751f\u7d04$$2\\times 10^6~kgw$$\u00a0\u5678\u7684\u63a8\u529b\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u9084\u6709\u5169\u5177\u5c0f\u7684\u8ecc\u9053\u904b\u884c\u767c\u52d5\u6a5f\u548c\u82e5\u5e72\u500b\u5c0f\u578b\u5674\u5c04\u63a8\u9032\u5668\u3002<\/p>\n

\u53c3\u8003\u8cc7\u6599\uff1a<\/strong>
\n1.\u7dad\u57fa\u767e\u79d1–\u56fa\u614b\u71c3\u6599\u706b\u7bad\u00a0\u00a0http:\/\/en.wikipedia.org\/wiki\/Solid-fuel_rocket<\/a>
\n2.\u7dad\u57fa\u767e\u79d1–\u6db2\u614b\u71c3\u6599\u706b\u7bad\u00a0\u00a0http:\/\/en.wikipedia.org\/wiki\/Liquid-propellant_rocket<\/a>
\n3.\u7dad\u57fa\u767e\u79d1–\u591a\u7bc0\u706b\u7bad\u00a0\u00a0http:\/\/en.wikipedia.org\/wiki\/Multistage_rocket<\/a><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

\u8b8a\u8cea\u91cf\u904b\u52d5\u2014\u706b\u7bad\uff08Rocket\uff09 \u570b\u7acb\u5f70\u5316\u9ad8\u7d1a\u4e2d\u5b78\u7269\u7406\u79d1\u8cf4\u6587\u54f2\u8001\u5e2b\/\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u7269\u7406\u7cfb\u8521\u5fd7\u7533\u6559\u6388\u8cac\u4efb\u7de8\u8f2f …<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,107,3],"tags":[2215,2214],"class_list":["post-16744","post","type-post","status-publish","format-standard","hentry","category-physics01-05","category-physics00","category-physics01","tag-2215","tag-2214","loop-entry","cat-8","cat-107","cat-3","no-thumbnail"],"views":13410,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/16744","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=16744"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/16744\/revisions"}],"predecessor-version":[{"id":89260,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/16744\/revisions\/89260"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=16744"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=16744"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=16744"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}