{"id":1043,"date":"2025-11-25T11:16:04","date_gmt":"2025-11-25T02:16:04","guid":{"rendered":"http:\/\/saegil-lab.kr\/?p=1043"},"modified":"2026-03-11T19:32:59","modified_gmt":"2026-03-11T10:32:59","slug":"emc2-fracm_0-c2sqrt1-v2-c2","status":"publish","type":"post","link":"https:\/\/saegil-lab.kr\/?p=1043","title":{"rendered":"\"E=mc^2 = \frac{m_0 c^2}{\sqrt{1-v^2/c^2}}\""},"content":{"rendered":"\n

  <\/span>   <\/span>\"\[ E=mc^2 \]\"<\/p><\/p>\n\n\n\n

\uc2dc\uac04\uc5d0 \ub530\ub978 \uc5d0\ub108\uc9c0\uc758 \ubcc0\ud654\ub7c9\uc740 \uc77c\ub960\uacfc \uac19\uc73c\ubbc0\ub85c \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\begin{equation*}\begin{aligned}\frac{dE}{dt} &= c^2 \frac{dm}{dt} \\&= \bf{F} \cdot \bf{v} \\&=\it \frac{d\bf{p}}{\it dt} \cdot \bf{v} \\&= \it \frac{dm}{dt} \bf{v} \cdot v + \it m \frac{d\bf{v}}{dt} \cdot \bf{v} \\&= \it \frac{dm}{dt} v^{\rm 2} + \frac{m}{\rm{2}} \frac{dv^{\rm 2}}{dt} \end{aligned}\end{equation*}\"<\/p><\/p>\n\n\n\n

\uc704 \uc2dd\uc744 \ub2e4\uc2dc \uc815\ub9ac\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[(c^2 - v^2) \frac{dm}{dt} = \frac{m}{2} \frac{dv^2}{dt}\]\"<\/p><\/p>\n\n\n\n

\uc591\ubcc0\uc758 \"dt\"\ub97c \uc81c\uac70\ud558\uace0 \uc67c\ucabd\uc740 \ubcc0\uc218 \"m\"\uc73c\ub85c, \uc624\ub978\ucabd\uc740 \ubcc0\uc218 \"v^2\"\uc73c\ub85c \ubcc0\uc218\ub97c \ubd84\ub9ac\ud558\uc5ec \ud45c\ud604\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \frac{dm}{m} = \frac{dv^2}{2(c^2 - v^2)}\]\"<\/p><\/p>\n\n\n\n

\"c^2 - v^2 = x\"\ub77c\uace0 \ud558\uba74 \"-dv^2 = dx\"\uc774\ubbc0\ub85c \uc704\uc758 \ubbf8\ubd84 \ubc29\uc815\uc2dd\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\frac{dm}{m} = - \frac{dx}{2x}\]\"<\/p><\/p>\n\n\n\n

\"v=0\"\uc77c \ub54c \"m=m_0\", \"x=c^2\"\uc774\uace0, \uc18d\ub825\uc774 \"v\"\uc77c \ub54c \uc9c8\ub7c9\uc740 \"m\", \"x = c^2 - v^2\"\uc774\ubbc0\ub85c \ub2e4\uc74c\uacfc \uac19\uc774 \uc801\ubd84\ud560 \uc218 \uc788\ub2e4.<\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\int_{m_0}^m \frac{dm}{m} = -\int_{c^2}^{c^2 - v^2} \frac{dx}{2x} = \int_{c^2 - v^2}^{c^2} \frac{dx}{2x}\]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[\ln \left( \frac{m}{m_0}\right) = \frac{1}{2} \ln \left( \frac{c^2}{c^2 - v^2}\right) = \ln \sqrt{\frac{c^2}{{c^2 - v^2}}} = \ln \frac{1}{\sqrt{1 - v^2/c^2}}\]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \therefore \quad m = \frac{m_0}{\sqrt{1-v^2/c^2}}\]\"<\/p><\/p>\n\n\n\n

  <\/span>   <\/span>\"\[ \therefore \quad E=mc^2 = \frac{m_0 c^2}{\sqrt{1-v^2/c^2}}\]\"<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

    \uc2dc\uac04\uc5d0 \ub530\ub978 \uc5d0\ub108\uc9c0\uc758 \ubcc0\ud654\ub7c9\uc740 \uc77c\ub960\uacfc \uac19\uc73c\ubbc0\ub85c \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.     \uc704 \uc2dd\uc744 \ub2e4\uc2dc \uc815\ub9ac\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \uc4f8 \uc218 \uc788\ub2e4.     \uc591\ubcc0\uc758 \ub97c \uc81c\uac70\ud558\uace0 \uc67c\ucabd\uc740 \ubcc0\uc218 \uc73c\ub85c, \uc624\ub978\ucabd\uc740 \ubcc0\uc218 \uc73c\ub85c \ubcc0\uc218\ub97c \ubd84\ub9ac\ud558\uc5ec \ud45c\ud604\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4. … \uacc4\uc18d \uc77d\uae30 →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[79,78],"class_list":["post-1043","post","type-post","status-publish","format-standard","hentry","category-5","tag-emc2","tag-78"],"_links":{"self":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/1043","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1043"}],"version-history":[{"count":24,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/1043\/revisions"}],"predecessor-version":[{"id":1068,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=\/wp\/v2\/posts\/1043\/revisions\/1068"}],"wp:attachment":[{"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/saegil-lab.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}