{"id":50797,"date":"2024-02-07T21:14:41","date_gmt":"2024-02-07T21:14:41","guid":{"rendered":"https:\/\/science-hub.click\/%E5%8A%9B%E3%81%AE%E5%83%8D%E3%81%8D-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-02-07T21:14:41","modified_gmt":"2024-02-07T21:14:41","slug":"%E5%8A%9B%E3%81%AE%E5%83%8D%E3%81%8D-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=50797","title":{"rendered":"\u529b\u306e\u50cd\u304d – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>

\u529b\u306e\u4ed5\u4e8b\u306f\u3001\u529b\u306e<\/b>\u4f5c\u7528\u70b9\u304c\u79fb\u52d5\u3059\u308b (\u529b\u3092\u53d7\u3051\u308b\u7269\u4f53\u304c\u79fb\u52d5\u307e\u305f\u306f\u5909\u5f62\u3059\u308b) \u3068\u304d\u306b\u3001\u3053\u306e\u529b\u306b\u3088\u3063\u3066\u63d0\u4f9b\u3055\u308c\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u8eca\u3092\u62bc\u3059\u5834\u5408\u3001\u63a8\u529b<\/a><\/span>\u306e\u4ed5\u4e8b\u306f\u3001\u3053\u306e\u63a8\u529b\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u308b\u30a8\u30cd\u30eb\u30ae\u30fc<\/a><\/span>\u3067\u3059\u3002\u3053\u306e\u540d\u524d\u3092\u6301\u3064\u3053\u306e\u6982\u5ff5\u306f\u3001\u30ac\u30b9\u30d1\u30fc\u30eb\u30fb\u30ae\u30e5\u30b9\u30bf\u30fc\u30f4\u30fb\u30b3\u30ea\u30aa\u30ea<\/a><\/span>\u306b\u3088\u3063\u3066\u5c0e\u5165\u3055\u308c\u307e\u3057\u305f\u3002\u4ed5\u4e8b\u306f\u30b8\u30e5\u30fc\u30eb ( J<\/b> ) \u3067\u8868\u3055\u308c\u3001\u4ed5\u4e8b<\/i>\u3092\u610f\u5473\u3059\u308b\u82f1\u8a9e\u306eWork<\/i>\u306e\u982d\u6587\u5b57\u3067\u3042\u308bW<\/i>\u3067\u8868\u3055\u308c\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002<\/p>

\n\"\u529b\u306e\u50cd\u304d<\/figure>

\u610f\u5473<\/h2>

\u4e00\u5b9a\u306e\u529b<\/a><\/span>

$$ {\\vec{F}} $$<\/div>\u3053\u308c\u306f\u76f4\u7dda\u30d1\u30b9\u3092\u79fb\u52d5\u3059\u308b\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306b\u9069\u7528\u3055\u308c\u307e\u3059
$$ {\\vec{u}} $$<\/div>\u306f\u3001\u6a5f\u68b0<\/a><\/span>\u30b7\u30b9\u30c6\u30e0\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5909\u5316\u306b\u5bfe\u5fdc\u3059\u308b\u4ed5\u4e8bW \u3092<\/i>\u63d0\u4f9b\u3057\u307e\u3059\u3002 <\/p>
$$ {W = \\vec{F}\\cdot \\vec{u}} $$<\/div><\/dd><\/dl>

\u306e\u6210\u5206\u306e\u307f\u3067\u3042\u308b\u3053\u3068\u306b\u6c17\u4ed8\u304d\u307e\u3059\u3002

$$ {\\vec{F}} $$<\/div>\u3068\u5e73\u884c\u3057\u3066\u3044\u308b\u306e\u306f
$$ {\\vec{u}} $$<\/div>\u306f\u6a5f\u80fd\u3057\u307e\u3059\uff08\u30b9\u30ab\u30e9\u30fc\u7a4d\u306e\u7279\u6027: 2 \u3064\u306e\u76f4\u4ea4\u3059\u308b\u529b\u306e\u30b9\u30ab\u30e9\u30fc\u306f\u30bc\u30ed\u3067\u3059\uff09\u3002<\/p>

\u7d4c\u8def\u4e2d\u306b\u529b\u304c\u5909\u5316\u3059\u308b\u5834\u5408\u3001\u307e\u305f\u306f\u7d4c\u8def\u304c\u76f4\u7dda\u7684\u3067\u306a\u3044\u5834\u5408\u306f\u3001\u529b\u304c\u4e00\u5b9a\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u3066\u7d4c\u8def\u304c\u79fb\u52d5\u3059\u308b\u77ed\u3044\u6301\u7d9a\u6642\u9593dt<\/i>\u306b\u77ed\u7e2e\u3055\u308c\u307e\u3059\u3002

$$ {\\vec{du}} $$<\/div>\u76f4\u7dda\u7684 (\u66f2\u7dda\u306b\u63a5\u3059\u308b) \u3068\u307f\u306a\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u57fa\u672c\u7684\u306a\u4ed5\u4e8b\u306f\u03b4 W<\/i><\/span>\u3067\u793a\u3055\u308c\u3001\u6b21\u306e\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>
$$ {\\delta W = \\vec{F} \\cdot \\vec{du}} $$<\/div> \u3002<\/dd><\/dl>

\u305d\u306e\u5f8c\u3001\u529b\u306b\u3088\u3063\u3066\u884c\u308f\u308c\u305f<\/a><\/span>\u4ed5\u4e8b\u306e\u5408\u8a08<\/a><\/span>\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059

$$ {\\vec{F}} $$<\/div> \u3001\u8ecc\u9053\u4e0a\u306e\u4ed5\u4e8b\u3092\u5408\u8a08\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066
$$ {\\mathcal{C}} $$<\/div>\u306e\u7533\u8acb\u5730\u70b9\u3092\u7d4c\u7531\u3057\u3066\u65c5\u884c\u3055\u308c\u305f
$$ {\\vec{F}} $$<\/div> : <\/p>
$$ {W=\\int_{\\mathcal{C}}\\vec{F}\\cdot\\vec{du}} $$<\/div><\/dd><\/dl>

\u8ecc\u9053\u304c\u5186\u5f62\u306e\u5834\u5408\uff08\u529b\u306e\u4f5c\u7528\u70b9\u304c\u8ef8\u306e\u5468\u308a\u3092<\/a><\/span>\u56de\u8ee2\u3057\u3066\u3044\u308b\u5834\u5408\u306a\u3069\uff09

$$ {(\\Delta)\\,} $$<\/div> \uff09\u3001\u305d\u306e\u7d50\u679c\u5f97\u3089\u308c\u308b\u77ac\u9593\u306e\u57fa\u672c\u7684\u306a\u4f5c\u696d\u306b\u306f\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059
$$ {\\delta W = \\vec{M} \\cdot \\vec{d\\theta}\\,} $$<\/div> \u3001 \u307e\u305f\u306f
$$ {\\vec{M}} $$<\/div>\u306b\u95a2\u3059\u308b\u529b\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u3067\u3059
$$ {(\\Delta)\\,} $$<\/div>\u305d\u3057\u3066
$$ {\\vec{d\\theta}} $$<\/div>\u77ed\u671f\u9593\u306b\u56fa\u4f53\u304c\u79fb\u52d5\u3057\u305f\u89d2\u5ea6dt<\/i> \u3002<\/p>

\u4fdd\u5b88\u7684\u306a\u529b\u306e\u4ed5\u4e8b: \u91cd\u91cf\u306e\u4f8b<\/h2>

\u4fdd\u5b88\u52e2\u529b\u3068\u306f\u3001\u5b9a\u7fa9\u4e0a\u3001\u305d\u306e\u6d3b\u52d5\u304c\u305f\u3069\u308b\u9053\u306b\u4f9d\u5b58\u3057\u306a\u3044\u52e2\u529b\u3067\u3042\u308b\u3002\u91cd\u91cf\u306f\u4e00\u4f8b\u3067\u3059\u3002<\/p>

\u30ac\u30ea\u30ec\u30aa\u7cfb<\/span>\u3067\u8cea\u91cf<\/a><\/span>m \u306e\u7269\u4f53\u304c A \u304b\u3089 B \u306b\u79fb\u52d5\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u307e\u3059\u3002

$$ {\\left (O,\\vec{x},\\vec{y},\\vec{z} \\right )} $$<\/div> \u3001\u8ef8
$$ {\\vec{z}} $$<\/div>\u5782\u76f4\u3067\u91cd\u529b\u306e\u53cd\u5bfe<\/span>\u65b9\u5411\u306b\u5411\u3044\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002
$$ {\\vec{g}=-g\\vec{z}} $$<\/div> \u3002\u3053\u306e\u5834\u5408\u3001\u91cd\u307f\u306e\u4ed5\u4e8b\u306b\u306f\u6b21\u306e\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002 <\/p>
$$ {W = \\vec{P}\\cdot \\vec{AB} = m\\vec{g}\\cdot\\vec{AB}= -mg\\vec{z}\\cdot\\vec{AB}} $$<\/div><\/dd><\/dl>

\u6ce8\u610f\u3059\u308c\u3070

$$ {\\left ( x_A,y_A,z_A \\right )} $$<\/div>\u3053\u306e\u5ea7\u6a19\u7cfb\u306e\u70b9 A \u306e\u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u3001\u304a\u3088\u3073
$$ {\\left ( x_B,y_B,z_B \\right )} $$<\/div> B \u306e\u5ea7\u6a19\u3001\u6b21\u306b\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19
$$ {\\vec{P}} $$<\/div>\u305d\u3057\u3066
$$ {\\vec{AB}} $$<\/div>\u30ac\u30ea\u30ec\u30aa\u53c2\u7167\u7cfb\u3067\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>

\u305d\u3057\u3066\u3001\u30b9\u30ab\u30e9\u30fc\u7a4d\u306e\u5b9a\u7fa9\u306b\u3088\u308a\u3001\u91cd\u307f\u306e\u4ed5\u4e8b\u306f\u6b21\u306e\u3088\u3046\u306b\u5358\u7d14\u5316\u3055\u308c\u307e\u3059\u3002<\/p>

\u3057\u305f\u304c\u3063\u3066\u3001\u7269\u4f53\u306e\u91cd\u91cf\u306e\u4ed5\u4e8b\u306f\u3001\u305d\u306e\u79fb\u52d5<\/a><\/span>\u4e2d\u306b\u305f\u3069\u308b\u7d4c\u8def\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3042\u308a\u3001\u3053\u306e\u7269\u4f53\u306e\u91cd\u5fc3\u306e<\/a><\/span>\u9ad8\u5ea6<\/a><\/span>\u306e\u5909\u5316\u306b\u306e\u307f\u4f9d\u5b58\u3057\u307e\u3059\u3002<\/p>

\n\"\u529b\u306e\u50cd\u304d<\/figure>

\u8a08\u7b97\u4f8b<\/span><\/h3>

\u4f53\u91cd80kg<\/span>\u306e\u4eba\u304c\u9ad8\u305550cm<\/span>\u306e\u6905\u5b50\u306b\u76f4\u7acb\u3057\u307e\u3059\u3002\u3053\u306e\u4eba\u306e\u4f53\u91cd\u3067\u3069\u308c\u3060\u3051\u306e\u4ed5\u4e8b\u304c\u884c\u308f\u308c\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f

$$ {W = -m \\ g \\left ( z_B-z_A \\right )} $$<\/div> \u3001 \u3069\u3061\u3089\u304b
$$ {W = – 80 \\times 9,81 \\times ( 0,5 – 0 ) = – 392,4 \\ J} $$<\/div>\u3053\u3053\u3067\u30019.81 \u306f\u5730\u7403\u306e\u5b9a\u6570 g \u7279\u6027 (\u30cb\u30e5\u30fc\u30c8\u30f3\/\u30ad\u30ed\u30b0\u30e9\u30e0) \u3092\u8868\u3057\u300180 \u306f\u8cea\u91cf (\u30ad\u30ed\u30b0\u30e9\u30e0)\u30010.5 \u306f\u9ad8\u3055<\/a><\/span>(\u30e1\u30fc\u30c8\u30eb)<\/a><\/span>\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u4f53\u91cd\u306f\u62b5\u6297\u529b\u3067\u3059\uff08\u4eba\u306e\u52d5\u304d\u306b\u300c\u62b5\u6297\u300d\u3057\u307e\u3059\uff09\u3002<\/p>
\n\"\u529b\u306e\u50cd\u304d<\/figure>

\u5177\u4f53\u7684\u306a\u4e8b\u4f8b<\/h2>

\u529b\u3092\u8003\u3048\u308b

$$ {\\vec{F}} $$<\/div>\u76f4\u7dda\u8ecc\u9053\u4e0a\u3092\u79fb\u52d5\u3059\u308b\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306b\u9069\u7528\u3055\u308c\u308b\u5b9a\u6570 (\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306b\u4f5c\u7528\u3059\u308b\u4ed6\u306e\u529b\u306f\u3042\u308a\u307e\u305b\u3093)\u3002\u3044\u304f\u3064<\/a><\/span>\u304b\u306e\u7279\u5b9a\u306e\u4e8b\u4f8b\u306b\u3088\u3063\u3066\u3001\u529b\u306e\u4ed5\u4e8b\u306e\u6982\u5ff5\u3092\u8aac\u660e\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002<\/p>