![\"cit-qa150910-7\"](\"http:\/\/phd-kawamura.jp\/wordpress\/wp-content\/uploads\/2015\/09\/cit-qa150910-7.png\")
<\/a><\/p>\n\u30fb\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u8a08\u7b97\u3057\u305f\u7d50\u679c\u304c\u5b9a\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059<\/p>\n
\u4e0a\u5411\u304d\u3092\u6b63\u306b\u8ef8\u3092\u53d6\u308a\u3001\u7269\u4f53\u306b\u4f5c\u7528\u3059\u308b\u529b\u306f\u91cd\u529b$mg$\u3067\u3042\u308b\u304b\u3089
\n\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n
\\begin{eqnarray*}
\nma=-mg\\\\
\nm\\frac{dv}{dt}=-mg
\n\\end{eqnarray*}<\/p>\n
\u3067\u3042\u308b\u3002
\n\\begin{eqnarray*}
\n\\frac{dv}{dt}=-g
\n\\end{eqnarray*}<\/p>\n
\u3088\u308a\u3001
\n\\begin{eqnarray*}
\n\\frac{dv}{dt}&=&-g \\\\
\nv&=&-gt+C
\n\\end{eqnarray*}<\/p>\n
\u521d\u901f\u5ea6\u306f\u7121\u3044\u81ea\u7531\u843d\u4e0b\u306a\u306e\u3067$t=0$\u3067$v=0$\u3088\u308a<\/p>\n
\\begin{eqnarray*}
\nv(0)=-g\\cdot 0+C &=&0 \\\\
\nC&=&0
\n\\end{eqnarray*}<\/p>\n
\u3088\u3063\u3066
\n\\begin{eqnarray*}
\nv(t)=-gt
\n\\end{eqnarray*}<\/p>\n
\u3055\u3089\u306b\u3001$x$\u306f<\/p>\n
\\begin{eqnarray*}
\nv= \\frac{dx}{dt} &=&-gt \\\\
\nx &=& -gt^2 \\cdot \\frac{1}{2} +C’
\n\\end{eqnarray*}<\/p>\n
\u539f\u70b9\u30b9\u30bf\u30fc\u30c8\u3068\u3059\u308b\u3068\u3001$t=0$\u3067$x=0$\u3088\u308a<\/p>\n
\\begin{eqnarray*}
\nx(0)=-\\frac{1}{2} g \\cdot 0^2 +C’ &=&0 \\\\
\nC’ &=&0
\n\\end{eqnarray*}<\/p>\n
\u3088\u3063\u3066
\n\\begin{eqnarray*}
\nx(t)=-\\frac{1}{2}gt^2
\n\\end{eqnarray*}<\/p>\n
\u3053\u308c\u3067\u6e96\u5099\u304c\u3067\u304d\u305f\u306e\u3067$K,U$\u306b\u4ee3\u5165\u3059\u308b\u3068<\/p>\n
\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc$K$\u306f
\n\\begin{eqnarray*}
\nK(t)=\\frac{1}{2}mv^2 &=& \\frac{1}{2}m (-gt)^2 \\\\
\n &=& \\frac{1}{2} mg^2 t^2
\n\\end{eqnarray*}<\/p>\n
\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc$U$\u306f
\n\\begin{eqnarray*}
\nU(t)=mgx &=& mg \\Bigl( -\\frac{1}{2}gt^2 \\Bigr) \\\\
\n &=& -\\frac{1}{2} mg^2 t^2
\n\\end{eqnarray*}<\/p>\n
\u3088\u3063\u3066\u3001\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc$E$\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) \\\\
\n &=& 0
\n\\end{eqnarray*}<\/p>\n
\u3068\u5b9a\u6570\u306b\u306a\u308a\u3001\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u4fdd\u5b58\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u30fb\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092\u5909\u5f62\u3057\u3066\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u6642\u9593\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3053\u3068\u3092\u793a\u3059\u3002<\/p>\n
\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n
\\begin{eqnarray*}
\nm\\frac{dv}{dt}=-mg
\n\\end{eqnarray*}<\/p>\n
\u3067\u3042\u308b\u3002
\n\u3053\u306e\u4e21\u8fba\u306b$v=\\frac{dx}{dt}$\u3092\u304b\u3051\u308b\u3068<\/p>\n
\\begin{eqnarray*}
\nm\\frac{dv}{dt} \\cdot v &=& -mg\\frac{dx}{dt} \\\\
\n\\frac{d}{dt} \\Bigl( \\frac{1}{2}mv^2 \\Bigr) &=& -\\frac{d}{dt}(mgx) \\\\
\n\\frac{d}{dt} \\Bigl( \\frac{1}{2}mv^2 + mgx \\Bigr ) &=& 0
\n\\end{eqnarray*}<\/p>\n
\u3053\u306e$(\\ \\ \\ )$\u5185\u306f\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u4f4d\u7f6e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5408\u8a08\u306b\u306a\u3063\u3066\u3044\u3066\u3001
\n\u305d\u308c\u3092\u6642\u9593\u3067\u5fae\u5206\u3059\u308b\u3068\u30bc\u30ed\u306b\u306a\u308b\u4e8b\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002
\n\u6642\u9593\u3067\u5fae\u5206\u3059\u308b\u3068\u30bc\u30ed\u306b\u306a\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u3001
\n$(\\ \\ \\ )$\u5185\u306f\u6642\u9593\u306b\u4f9d\u5b58\u3057\u306a\u3044\u5024\u3067\u3042\u308b\u3053\u3068\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n
\u5f93\u3063\u3066\u3001\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u6642\u9593\u306b\u4f9d\u3089\u305a\u4e00\u5b9a\u3067\u3042\u308a\u3001\u4fdd\u5b58\u3057\u3066\u3044\u308b\u3068\u8a00\u3048\u307e\u3059\u3002<\/p>\n
\u30fb\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092$x$\u3067\u7a4d\u5206\u3057\u3066\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u5b9a\u6570\u306b\u306a\u308b\u4e8b\u3092\u793a\u3059\u3002<\/p>\n
\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n
\\begin{eqnarray*}
\nm\\frac{dv}{dt}=-mg
\n\\end{eqnarray*}<\/p>\n
\u3067\u3042\u308b\u3002
\n\u3053\u306e\u5f0f\u3092$x$\u3067\u7a4d\u5206\u3059\u308b\u3068<\/p>\n
\\begin{eqnarray*}
\n\\int m\\frac{dv}{dt} dx &=& \\int -mg dx \\\\
\n\\int m\\frac{dv}{dt} v dt &=& \\int -mg dx \\\\
\n\\int m v dv &=& \\int -mg dx \\\\
\n\\frac{1}{2}mv^2 &=& -mgx +C” \\\\
\n\\frac{1}{2}mv^2 +mgx &=&C”
\n\\end{eqnarray*}<\/p>\n
\u3053\u306e\u72b6\u614b\u3067\u3082$C”$\u306f\u5b9a\u6570\u306a\u306e\u3067\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u4fdd\u5b58\u3057\u3066\u3044\u308b\u3068\u8a00\u3048\u307e\u3059\u304c\u3001
\n\u521d\u671f\u6761\u4ef6\u3088\u308a\u3001$t=0$\u3067$v=0,x=0$\u3067\u3042\u308b\u306e\u3067<\/p>\n
\\begin{eqnarray*}
\nE(0)=\\frac{1}{2}m \\cdot 0^2 + mg \\cdot 0 &=&C” \\\\
\n C” &=&0
\n\\end{eqnarray*}
\n\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n
\u5f93\u3063\u3066\u3001
\n\\begin{eqnarray*}
\nE(t)=\\frac{1}{2}mv^2 + mgx &=& 0 \\\\
\n\\end{eqnarray*}<\/p>\n
\u3068\u306a\u308b\u306e\u3067\u3001\u529b\u5b66\u7684\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u4fdd\u5b58\u3057\u3066\u3044\u308b\u3002<\/p>\n
\u3044\u305a\u308c\u306e\u65b9\u6cd5\u3082\u7406\u89e3\u3057\u3001\u8eab\u306b\u7740\u3051\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002
\n<\/font><\/p>\n","protected":false},"excerpt":{"rendered":"
\u6559\u990a\u306e\u7269\u7406\uff5e4\/23\u30fb5\/7\u5206 \u30fb\u6700\u5f8c\u306e\u6469\u64e6\u306e\u95a2\u4fc2\u304c\u89e3\u3089\u306a\u304b\u3063\u305f \u30fb\u6297\u529bR\u304c\u3088\u304f\u308f\u304b\u3089\u306a\u304b\u3063\u305f \u6297\u529b$R$\u306f\u63a5\u89e6\u3057\u3066\u3044\u308b\u9762\u304b\u3089\u53d7\u3051\u308b\u529b\u3067\u3059\u3002 \u3053\u306e\u9762\u304b\u3089\u53d7\u3051\u308b\u529b\u306f\u3001\u63a5\u89e6\u9762\u3092\u62e1\u5927\u3057\u3066\u307f\u308b\u3068 \u9762\u3092\u69cb\u6210\u3057\u3066 … <\/p>\n","protected":false},"author":1,"featured_media":91,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/posts\/444"}],"collection":[{"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/comments?post=444"}],"version-history":[{"count":7,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/posts\/444\/revisions"}],"predecessor-version":[{"id":458,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/posts\/444\/revisions\/458"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/media\/91"}],"wp:attachment":[{"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/media?parent=444"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/categories?post=444"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/phd-kawamura.jp\/wordpress\/wp-json\/wp\/v2\/tags?post=444"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\"cit-qa150910-\uff11\"](\"http:\/\/phd-kawamura.jp\/wordpress\/wp-content\/uploads\/2015\/09\/cit-qa150910-\uff11.png\")
<\/a><\/p>\n