{"id":190,"date":"2015-05-19T12:32:47","date_gmt":"2015-05-19T12:32:47","guid":{"rendered":"http:\/\/phd-kawamura.jp\/wordpress\/?p=190"},"modified":"2015-05-19T18:07:01","modified_gmt":"2015-05-19T18:07:01","slug":"cit-qa150514-1","status":"publish","type":"post","link":"http:\/\/phd-kawamura.jp\/wordpress\/cit-qa150514-1\/","title":{"rendered":"\u6559\u990a\u306e\u7269\u7406\uff5e5\/14\u5206\u306e\u30a2\u30f3\u30b1\u30fc\u30c8\u306b\u95a2\u3057\u3066"},"content":{"rendered":"

\u30fb\u6b21\u5143\u306e\u899a\u3048\u65b9\u3092\u6559\u3048\u3066\u4e0b\u3055\u3044\u3002
\n\u30fb\u6b21\u5143\u306b\u3064\u3044\u3066\u306e\u30a4\u30e1\u30fc\u30b8\u304c\u63b4\u307f\u96e3\u304f\u3066\u308f\u304b\u3089\u306a\u3044\u3067\u3059\u3002
\n
\n\u6b21\u5143\u89e3\u6790\u3068\u306f\u7269\u7406\u91cf\u3092$[\\mathrm{L}][\\mathrm{T}][\\mathrm{M}]$\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u3067\u3059\u3002
\n\u305d\u308c\u305e\u308c\u306e\u7269\u7406\u91cf\u306f\u300c\u3069\u306e\u3088\u3046\u306a\u8981\u7d20\u304b\u3089\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u306e\u304b\uff1f\u300d\u3092
\n\u8003\u3048\u308b\u3046\u3048\u3067\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002
\n\u307e\u305f\u3001\u5358\u4f4d\u3092\u7d44\u307f\u7acb\u3066\u308b\u6642\u306b\u3082\u6709\u7528\u3067\u3059\u3002<\/p>\n

\u305d\u308c\u305e\u308c\u306e\u7269\u7406\u91cf\u306f\u3001\u5b9a\u7fa9\u5f0f\u3084\u6cd5\u5247\u304b\u3089\u5c0e\u304d\u51fa\u3055\u308c\u3066\u3044\u307e\u3059\u3002
\n\u305d\u306e\u5f0f\u306b$[\\mathrm{L}][\\mathrm{T}][\\mathrm{M}]$\u3092\u5f53\u3066\u306f\u3081\u3066\u8003\u3048\u308c\u3070\u826f\u3044\u306e\u3067\u3059\u3002<\/p>\n

\u4f8b\u3048\u3070\u3001\u901f\u5ea6\u306f<\/p>\n

\\begin{eqnarray*}
\nv= \\frac{\\mathrm{d} x}{\\mathrm{d} t}
\n\\end{eqnarray*}<\/p>\n

\u3068\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002
\n\u3088\u3063\u3066\u3001\u901f\u5ea6\u306e\u6b21\u5143\u306f<\/p>\n

\\begin{eqnarray*}
\n\\biggl[\\frac{\\mathrm{L}}{\\mathrm{T} } \\biggr]
\n\\end{eqnarray*}<\/p>\n

\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n

\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092$x$\u3067\u7a4d\u5206\u3057\u305f\u6642\u306b\u51fa\u3066\u304f\u308b<\/p>\n

\\begin{eqnarray*}
\n\\int \\frac{\\mathrm{d}}{\\mathrm{d} t} \\Bigl( \\frac{1}{2}mv^2 \\Bigr) dt & = \\int F dx
\n\\end{eqnarray*}<\/p>\n

\u5de6\u8fba\u306e\u90e8\u5206\u306e$ \\frac{1}{2}mv^2$\u3067\u3059\u3002<\/p>\n

\u3088\u3063\u3066\u3001\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u6b21\u5143\u306f<\/p>\n

\\begin{eqnarray*}
\n[\\mathrm{M}] \\biggl( \\biggl[\\frac{\\mathrm{L}}{\\mathrm{T} } \\biggr] \\biggl)^2 =
\n\\biggl[\\frac{\\mathrm{M}\\mathrm{L}^2}{\\mathrm{T}^2 } \\biggr]
\n\\end{eqnarray*}<\/p>\n

\u3068\u306a\u308a\u307e\u3059\u3002
\n\u3053\u306e\u6642\u3001\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u8981\u7d20\u3060\u3051\u3092\u8003\u3048\u308b\u306e\u3067\u4fc2\u6570\u306e$\\frac{1}{2}$\u306f\u95a2\u4fc2\u306a\u3044\u3067\u3059\u3002<\/p>\n

\u3053\u306e\u69d8\u306b\u3001\u5f0f\u304b\u3089\u9806\u3092\u8ffd\u3063\u3066\u8003\u3048\u308c\u3070\u3088\u3044\u306e\u3067\u3059\u3002
\n<\/font><\/p>\n

\u30fb$\\frac{\\mathrm{d}}{\\mathrm{d} t}\\Bigl( \\frac{1}{2}mv^2 \\Bigr) =\\frac{1}{2}m \\cdot 2vv’$ \u306e$v’$\u304c\u51fa\u3066\u304f\u308b\u306e\u304c\u306a\u305c\u304b\u89e3\u3089\u306a\u304b\u3063\u305f\u3002
\n\u30fb\u5408\u6210\u95a2\u6570\u306f\u7fd2\u3063\u3066\u3044\u306a\u3044\u306e\u3067\u308f\u304b\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002
\n
\n\u5408\u6210\u95a2\u6570\u306e\u5fae\u5206\u6cd5\u306f
\n$y=f(g(x)), \\quad g(x)=u$\u3068\u3057\u305f\u3068\u304d<\/p>\n

\\begin{eqnarray*}
\n\\frac{\\mathrm{d}y}{\\mathrm{d} x} = \\frac{\\mathrm{d}y}{\\mathrm{d} u} \\cdot \\frac{\\mathrm{d}u}{\\mathrm{d} x}
\n\\end{eqnarray*}<\/p>\n

\u6216\u3044\u306f<\/p>\n

\\begin{eqnarray*}
\n{f(g(x))}’=f'(g(x)) \\cdot g'(x)
\n\\end{eqnarray*}<\/p>\n

\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n

\u7d30\u304b\u304f\u306f\u6570\u5b66\u306e\u6559\u79d1\u66f8\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002
\n<\/font><\/p>\n

\u30fb\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f$ma=F$\u3060\u3063\u305f\u306e\u3060\u304c\u3001\u5f0f\u3092\u4f7f\u3046\u6642\u306b$ma=-mg$\u306b\u5909\u308f\u3063\u305f\u306e\u3067\u3061\u3087\u3063\u3068\u3084\u3084\u3053\u3057\u304b\u3063\u305f\u3002
\n<\/p>\n

\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f$ma=F$\u3068\u8868\u3057\u307e\u3059\u304c\u3001F\u3068\u3044\u3046\u306e\u306f\u305d\u306e\u8ef8\u306b\u6cbf\u3063\u3066\u50cd\u3044\u3066\u3044\u308b\u529b\u306e\u5168\u3066\u3092\u6307\u3057\u3066\u3044\u307e\u3059\u3002
\n\u3088\u3063\u3066\u3001\u7d30\u304b\u304f\u66f8\u304f\u3068<\/p>\n

\\begin{eqnarray*}
\nma=f_1+f_2+ \\cdots + f_n
\n\\end{eqnarray*}<\/p>\n

\u3068\u306a\u308a\u307e\u3059\u3002
\n$f_1,f_2, \\cdots , f_n$\u306b\u306f\u305d\u308c\u305e\u308c\u306e\u529b\u304c\u5bfe\u5fdc\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002
\n\u8ef8\u306e\u5411\u304d\u306b\u6ce8\u610f\u3057\u3066\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u7acb\u3066\u308c\u3070\u826f\u3044\u306e\u3067\u3059\u3002
\n<\/font><\/p>\n

\u30fb\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u548c\uff1d0 \u4e00\u5b9a\u304c\u826f\u304f\u308f\u304b\u3089\u306a\u3044\u3002
\n\u30fb\u5fae\u5206\u3057\u30660 \u4e00\u5b9a\u3068\u304b
\n
\n\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u3084\u904b\u52d5\u91cf\u4fdd\u5b58\u3092\u8868\u3059\u65b9\u6cd5\u306e\u8868\u73fe\u306b\u3064\u3044\u3066\u3067\u3059\u3002
\n\u7269\u7406\u5b66\u3067\u4fdd\u5b58\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u610f\u5473\u306f\u3001\u300c\u6642\u9593\u304c\u7d4c\u3063\u3066\u3082\u5909\u5316\u3057\u306a\u3044\u300d\u300c\u6642\u9593\u306b\u4f9d\u5b58\u3057\u306a\u3044\u300d
\n\u3068\u8a00\u3046\u3053\u3068\u3092\u6307\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n

\u5f93\u3063\u3066\u3001\u4fdd\u5b58\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u306b\u306f<\/p>\n

\u30fb\u6642\u9593\u3067\u5fae\u5206\u3057\u3066\u307f\u305f\u3089\u30bc\u30ed\u3060\u3063\u305f\u3002
\n\u30fb\u5b9f\u969b\u306b\u8a08\u7b97\u3057\u3066\u307f\u305f\u3089$t$\u3092\u542b\u307e\u306a\u3044\u91cf\u306b\u306a\u3063\u305f\u3002<\/p>\n

\u3068\u8a00\u3046\u3053\u3068\u3092\u793a\u305b\u3070\u826f\u3044\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

\u8cea\u554f\u306e\u6307\u3057\u3066\u3044\u308b\u30e2\u30c7\u30eb\u306f\u304a\u305d\u3089\u304f\u8b1b\u7fa9\u3067\u6271\u3063\u305f\u81ea\u7531\u843d\u4e0b\u306e\u30e2\u30c7\u30eb\u306e\u4e8b\u3060\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n

\u8b1b\u7fa9\u3067\u306f\u5b9f\u969b\u306b\u8a08\u7b97\u3057\u305f\u5834\u5408\u3092\u6271\u3063\u305f\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n

\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc$K(t)$\u306f<\/p>\n

\\begin{eqnarray*}
\nK(t)=\\frac{1}{2}mv^2=\\frac{1}{2} m (-gt)^2 = \\frac{1}{2}mg^2 t^2
\n\\end{eqnarray*}<\/p>\n

\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc$U(t)$\u306f<\/p>\n

\\begin{eqnarray*}
\nU(t)=mgx =mg \\Bigl(-\\frac{1}{2} gt^2 \\Bigr) = -\\frac{1}{2}mg^2 t^2
\n\\end{eqnarray*}<\/p>\n

\u3068\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002
\n\u3088\u3063\u3066\u5168\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc$E(t)$\u306f<\/p>\n

\\begin{eqnarray*}
\nE(t)= K(t)+U(t) =\\frac{1}{2}mg^2 t^2 + \\Bigl( -\\frac{1}{2}mg^2 t^2 \\Bigr) =0
\n\\end{eqnarray*}<\/p>\n

\u3068\u306a\u308a\u307e\u3059\u3002
\n\u3088\u3063\u3066\u3001\u3053\u306e\u30e2\u30c7\u30eb\u3067\u306f$E(t)$\u306f$t$\u3092\u542b\u307e\u306a\u3044\u5b9a\u6570\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002
\n\u5f93\u3063\u3066\u300c$E(t)$\u306f\u6642\u9593\u306b\u4f9d\u3089\u305a\u4fdd\u5b58\u3057\u3066\u3044\u308b\u300d\u3068\u3044\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n

\u300c\u6642\u9593\u3067\u5fae\u5206\u3057\u3066\u307f\u305f\u3089\u30bc\u30ed\u3060\u3063\u305f\u3002\u300d\u3068\u3044\u3046\u65b9\u6cd5\u3067\u793a\u3059\u5834\u5408\u306f
\n\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u5909\u5f62\u3057\u3066\u3044\u304f\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n

\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n

\\begin{eqnarray*}
\nm a &= -mg \\\\
\nm \\frac{\\mathrm{d} v}{\\mathrm{d} t} &=-mg
\n\\end{eqnarray*}<\/p>\n

\u3067\u3059\u3002
\n\u3053\u306e\u4e21\u8fba\u306b$v=\\frac{\\mathrm{d} x}{\\mathrm{d} t}$\u3092\u304b\u3051\u308b\u3068<\/p>\n

\\begin{eqnarray*}
\nm \\frac{\\mathrm{d} v}{\\mathrm{d} t} v &=& -mg \\frac{\\mathrm{d} x}{\\mathrm{d} t} \\\\
\n\\frac{\\mathrm{d}}{\\mathrm{d} t}\\Bigl( \\frac{1}{2}mv^2 \\Bigr) &=& \\frac{\\mathrm{d}}{\\mathrm{d} t}\\Bigl( -mgx \\Bigr) \\\\
\n\\frac{\\mathrm{d}}{\\mathrm{d} t}\\Bigl( \\frac{1}{2}mv^2 +mgx\\Bigr) &=&0
\n\\end{eqnarray*}<\/p>\n

\u3068\u306a\u308a\u307e\u3059\u3002
\n\u3053\u3053\u3067\u3053\u306e\u5f0f\u3092\u3088\u304f\u898b\u3066\u307f\u308b\u3068\u3001$(\\qquad )$\u306e\u4e2d\u306e\u90e8\u5206\u304c\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc$K(t)$\u3068\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc$U(t)$\u306e\u548c\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002
\n\u3088\u3063\u3066\u3001\u5168\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc$E(t)$\u3092$t$\u3067\u5fae\u5206\u3057\u305f\u3089\u30bc\u30ed\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3067\u3001$E(t)$\u306f\u6642\u9593\u3092\u542b\u307e\u306a\u3044\u91cf\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002
\n\u5f93\u3063\u3066\u300c$E(t)$\u306f\u6642\u9593\u306b\u4f9d\u3089\u305a\u4fdd\u5b58\u3057\u3066\u3044\u308b\u300d\u3068\u3044\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n

\u3044\u305a\u308c\u306e\u65b9\u6cd5\u3067\u3082\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002
\n<\/font><\/p>\n

\u30fb\u659c\u885d\u7a81\u304c\u3088\u304f\u308f\u304b\u3089\u306a\u304b\u3063\u305f\u3002
\n
\n\u659c\u3081\u306b\u885d\u7a81\u3059\u308b\u5834\u5408\u306f\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u8003\u3048\u308b\u65b9\u6cd5\u3068\u3001
\n\u6210\u5206\u306b\u5206\u89e3\u3057\u3066\u8003\u3048\u308b\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002
\n\u8b1b\u7fa9\u3067\u6271\u3063\u305f\u4f8b\u306f\u6210\u5206\u306b\u5206\u89e3\u3057\u3066\u8003\u3048\u308b\u65b9\u6cd5\u3067\u3059\u3002
\n\u6210\u5206\u306b\u5206\u89e3\u3057\u3066\u8003\u3048\u308b\u5834\u5408\u306f\u3001\u8ef8\u306e\u5411\u304d\u3068\u305d\u308c\u305d\u308c\u306e\u6210\u5206\u306b\u5206\u89e3\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002
\n<\/font><\/p>\n

\u30fb\u6388\u696d\u306e\u5185\u5bb9\u306e\u9032\u307f\u5177\u5408\u304c\u65e9\u304f\u3001\u5185\u5bb9\u3092\u7406\u89e3\u3059\u308b\u524d\u306b\u6b21\u306e\u5185\u5bb9\u306b\u9032\u3080\u306e\u3067\u5185\u5bb9\u304c\u982d\u306b\u5165\u3089\u306a\u304b\u3063\u305f\u3002
\n\u30fb\u805e\u3044\u3066\u3044\u3066\u3082\u3088\u304f\u308f\u304b\u3089\u306a\u3044\u3053\u3068\u304c\u591a\u304f\u3066\u5c11\u3057\u4e0d\u5b89\u3067\u3059\u3002
\n
\n\u5bb6\u3067\u306e\u5fa9\u7fd2\u306e\u6642\u9593\u3092\u53d6\u308a\u307e\u3057\u3087\u3046\u3002
\n\u5fa9\u7fd2\u3057\u3066\u308f\u304b\u3089\u306a\u3044\u90e8\u5206\u306b\u3064\u3044\u3066\u306f\u6b21\u56de\u306e\u8b1b\u7fa9\u306e\u6642\u306b\u8cea\u554f\u3092\u3057\u307e\u3057\u3087\u3046\u3002
\n\u3069\u306e\u79d1\u76ee\u3067\u3082\u540c\u69d8\u306e\u4e8b\u304b\u3068\u601d\u3044\u307e\u3059\u304c\u3001\u524d\u306e\u8b1b\u7fa9\u3092\u524d\u63d0\u3068\u3057\u3066
\n\u6b21\u306e\u8b1b\u7fa9\u306e\u5185\u5bb9\u306b\u306a\u308a\u307e\u3059\u3002
\n\u524d\u306e\u6bb5\u968e\u3067\u7a74\u304c\u3042\u308b\u3068\u5224\u3089\u306a\u3044\u90e8\u5206\u304c\u5e83\u304c\u3063\u3066\u3069\u3053\u304b\u3089\u624b\u3092\u3064\u3051\u305f\u3089\u3088\u3044\u304b
\n\u308f\u304b\u3089\u306a\u304f\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002
\n\u65e9\u3044\u6bb5\u968e\u3067\u7a74\u306f\u57cb\u3081\u3066\u304a\u304b\u306a\u3044\u3068\u5927\u5909\u306a\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3088\u3002
\n<\/font><\/p>\n

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