{"id":39326,"date":"2025-11-24T09:37:23","date_gmt":"2025-11-24T01:37:23","guid":{"rendered":"http:\/\/www.qiusir.com\/?p=39326"},"modified":"2025-11-24T09:37:23","modified_gmt":"2025-11-24T01:37:23","slug":"%e4%bb%8e%e8%b4%a8%e5%bf%83%e4%bd%8d%e7%bd%ae%e5%8f%98%e5%8c%96%e7%9c%8b%e9%9d%9e%e5%bc%b9%e6%80%a7%e7%a2%b0%e6%92%9e","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=39326","title":{"rendered":"\u4ece\u8d28\u5fc3\u4f4d\u7f6e\u53d8\u5316\u770b\u975e\u5f39\u6027\u78b0\u649e"},"content":{"rendered":"

JQX\/\u8fdb\u53d6\u82af \u5e2d\u660e\u7eb3\u7b2c20\u671f\uff082025.11.13\uff09
\n

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\n\u4ece\u8d28\u5fc3\u4f4d\u7f6e\u53d8\u5316\u770b\u975e\u5f39\u6027\u78b0\u649e<\/strong><\/center>
\n\u4e00\u3001\u4e00\u5343\u514b\u7684\u7269\u4f53\u4ece\u9ad8\u4e8c\u5341\u7c73\u7684\u9ad8\u5ea6\u81ea\u7531\u4e0b\u843d\uff0c\u843d\u5730\u540e\u4e0e\u5730\u9762\u63a5\u89e6\u65f6\u95f4\u4e3a0.1\u79d2\uff0c\u5f39\u8d77\u9ad8\u5ea6\u4e3a5\u7c73\u3002\u5047\u8bbe\u5730\u9762\u4e3a\u521a\u4f53\uff0c\u5730\u9762\u5bf9\u7269\u4f53\u7684\u652f\u6301\u529b\u4e3a\u6052\u529b\u3002\u6c42\u5730\u9762\u5bf9\u7269\u4f53\u7684\u652f\u6301\u529b\u5927\u5c0f\u3002
\n\"\"
\n\u65b9\u6cd51\uff1a
\n\u4e0b\u843d\u65f6\u95f4 \\( t_1 = \\sqrt{\\frac{2 h_1}{g}} = 2 \\, \\text{s} \\)
\n\u4e0a\u5347\u65f6\u95f4 \\( t_2 = \\sqrt{\\frac{2 h_2}{g}} = 1.5 \\, \\text{s} \\)
\n\u6839\u636e\u52a8\u91cf\u5b9a\u7406\uff1a\\( m g (t_1 + t_2 + \\Delta t) + F_N \\cdot \\Delta t = 0 \\)
\n\u89e3\u5f97\u652f\u6301\u529b\u4e3a \\( F_N = -310 \\, \\text{N} \\)<\/p>\n

\u65b9\u6cd52\uff1a
\n\u4f7f\u7528\u81ea\u7531\u843d\u4f53\u516c\u5f0f\u8ba1\u7b97\u5c0f\u7403\u4e0b\u843d\u524d\u7684\u901f\u5ea6\uff1a
\n\\( v_1 = \\sqrt{2 g h_1} = \\sqrt{2 \\cdot 10 \\cdot 20} = 20 \\, \\text{m\/s} \\)
\n\\( v_2 = \\sqrt{2 g h_2} = \\sqrt{2 \\cdot 10 \\cdot 5} = 10 \\, \\text{m\/s} \\)
\n\u6839\u636e\u52a8\u91cf\u5b9a\u7406\uff1a\\( (m g + F_N) \\Delta t = m v_2 – m v_1 \\)
\n\u89e3\u5f97\u652f\u6301\u529b\u4e3a \\( F_N = -310 \\, \\text{N} \\)\uff0c\u8d1f\u53f7\u8868\u793a\u652f\u6301\u529b\u7684\u65b9\u5411\u4e0e\u91cd\u529b\u76f8\u53cd\u3002<\/p>\n

\u65b9\u6cd53\uff1a
\n\u6574\u4e2a\u8fc7\u7a0b\u652f\u6301\u529b\u548c\u91cd\u529b\u90fd\u662f\u6052\u529b\uff0c\u6240\u4ee5\u5c0f\u7403\u505a\u5300\u53d8\u901f\u8fd0\u52a8\uff0c\u52a0\u901f\u5ea6\u4e3a\uff1a
\n\\( a = \\frac{\\Delta v}{\\Delta t} = \\frac{30 \\, \\text{m\/s}}{0.15 \\, \\text{s}} = 200 \\, \\text{m\/s}^2 \\)
\n\u6839\u636e\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\uff1a\\( F = F_N – mg = ma = 300 \\, \\text{N} \\)<\/p>\n

\u65b9\u6cd54\uff1a<\/p>\n

\u7531\u4e8e\u652f\u6301\u529b\u4e0e\u91cd\u529b\u90fd\u662f\u6052\u529b\uff0c\u7269\u4f53\u5408\u5916\u529b\u4e0d\u53d8\uff0c\u56e0\u6b64\u505a\u5300\u53d8\u901f\u8fd0\u52a8\u3002\u4f4d\u79fb \\( \\Delta x = \\frac{v_1 + v_2}{2} \\cdot \\Delta t = 0.5 \\, \\text{m} \\)\uff0c\u5176\u4e2d \\( v_1 \\) \u548c \\( v_2 \\) \u662f\u7269\u4f53\u7684\u521d\u672b\u901f\u5ea6\uff0c\\( \\Delta t \\) \u662f\u78b0\u649e\u65f6\u95f4\u3002
\n\u6839\u636e\u52a8\u91cf\u5b9a\u7406\uff1a\\( m g (h_1 + \\Delta x – h_2) + F_N \\cdot \\Delta x = 0 \\)
\n\u89e3\u5f97\uff1a\\( F_N = 310 \\, \\text{N} \\)<\/p>\n

\u65b9\u6cd55\uff1a<\/p>\n

\u540c\u65b9\u6cd5\u56db\uff0c\u4ec5\u5bf9\u78b0\u649e\u524d\u540e\u5217\u52a8\u80fd\u5b9a\u7406\uff0c\u540c\u6837\u53ef\u4ee5\u6c42\u51fa\u652f\u6301\u529b\u7684\u5927\u5c0f\u3002
\n

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\n\u4e8c\u3001\u5982\u56fe\u6240\u793a\uff0c\u8d28\u91cf\u4e3a \\(M\\) \u7684\u5c0f\u8f66\u5728\u5149\u6ed1\u7684\u6c34\u5e73\u9762\u4e0a\u4ee5\u901f\u5ea6 \\(v_0\\) \u5411\u53f3\u8fd0\u52a8\uff0c\u4e00\u8d28\u91cf\u4e3a \\(m\\) \u7684\u5c0f\u7403\uff08\\(m \\ll M\\)\uff09\u4ece\u9ad8\u5904\u81ea\u7531\u4e0b\u843d\uff0c\u4e0e\u5c0f\u8f66\u78b0\u649e\u540e\uff08\u78b0\u649e\u65f6\u95f4\u672a\u77e5\uff09\uff0c\u53cd\u5f39\u4e0a\u5347\u7684\u6700\u5927\u9ad8\u5ea6\u4e3a \\(\\frac{1}{4}h\\)\u3002\u7403\u4e0e\u8f66\u4e4b\u95f4\u7684\u6469\u64e6\u53ef\u89c6\u4e3a\u6ed1\u52a8\u6469\u64e6\uff0c\u5176\u52a8\u6469\u64e6\u56e0\u6570\u4e3a \\(\\mu\\)\uff0c\u91cd\u529b\u52a0\u901f\u5ea6\u4e3a \\(g\\)\uff0c\u4e0d\u8ba1\u7a7a\u6c14\u963b\u529b\u3002\u5219\u5c0f\u7403\u5f39\u8d77\u540e\u6c34\u5e73\u65b9\u5411\u7684\u6700\u5927\u901f\u5ea6\u4e3a\uff1a
\n\u89e3\u9898\u8fc7\u7a0b\uff1a
\n\u9996\u5148\u5047\u8bbe\u5728\u78b0\u649e\u8fc7\u7a0b\u4e2d\u5c0f\u7403\u4e0e\u5c0f\u8f66\u5728\u6c34\u5e73\u65b9\u5411\u59cb\u7ec8\u6ca1\u6709\u5171\u901f\uff0c\u6469\u64e6\u529b\u59cb\u7ec8\u4e3a\u6ed1\u52a8\u6469\u64e6\u529b\u3002\u5bf9\u78b0\u649e\u8fc7\u7a0b\u4e2d\u7684\u5c0f\u7403\u5728\u7ad6\u76f4\u65b9\u5411\u5217\u52a8\u91cf\u5b9a\u7406\uff0c\u8fd9\u91cc\u8ba4\u4e3a\u652f\u6301\u529b\u7684\u51b2\u91cf\u8fdc\u5927\u4e8e\u91cd\u529b\u7684\u51b2\u91cf\uff0c\u56e0\u6b64\u6709\uff1a\\( F_N \\cdot t = m \\left( \\sqrt{2g h^{1\/4}} – \\sqrt{2g h} \\right) = \\frac{3}{2} m \\sqrt{2g h} \\)
\n\u5bf9\u5c0f\u7403\u5728\u6c34\u5e73\u65b9\u5411\u4e0a\u5217\u52a8\u91cf\u5b9a\u7406\uff1a\\(\\mu F_N \\cdot t = \\frac{3}{2} \\mu m \\sqrt{2g h} = m v_x\\)
\n\u89e3\u5f97\uff1a\\( v_x = \\frac{3}{2} \\mu \\sqrt{2gh} \\)
\n\u7531\u4e8e\u53ef\u80fd\u5728\u78b0\u649e\u7ed3\u675f\u524d\u5c0f\u7403\u5df2\u7ecf\u4e0e\u5c0f\u8f66\u5171\u901f\uff0c\u5c0f\u7403\u6c34\u5e73\u65b9\u5411\u7684\u901f\u5ea6\u53d6\u503c\u8303\u56f4\u4e3a\uff1a\\( v_0 \\leq v_x \\leq \\frac{3}{2} \\mu \\sqrt{2gh} \\)
\n
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\n\u4e09\u3001\u5982\u56fe\u6240\u793a\uff0c\u8d28\u91cf\u4e3a \\(M = 2 \\, \\text{kg}\\) \u7684\u957f\u6728\u677f\u5728\u5149\u6ed1\u7684\u6c34\u5e73\u9762\u4e0a\u4ee5 \\(v_0 = 6 \\, \\text{m\/s}\\) \u7684\u901f\u5ea6\u6ed1\u884c\uff0c\u5176\u4e0a\u65b9 \\(h_0 = 5 \\, \\text{m}\\) \u9ad8\u5904\u6709\u4e00\u8d28\u91cf\u4e3a \\(m = 2 \\, \\text{kg}\\) \u7684\u5c0f\u7269\u5757\uff08\u8d28\u70b9\uff09\uff0c\u5c06\u5c0f\u7269\u5757\u7531\u9ad8\u5904\u81ea\u7531\u91ca\u653e\uff0c\u649e\u5230\u6728\u677f\u540e\u5f39\u8d77\u7684\u6700\u5927\u9ad8\u5ea6\u4e3a \\(h = 3.2 \\, \\text{m}\\)\u3002\u5df2\u77e5\u5c0f\u7269\u5757\u4e0e\u6728\u677f\u95f4\u7684\u6469\u64e6\u56e0\u6570\u4e3a 0.2\uff0c\u6b64\u6b21\u78b0\u649e\u65f6\u7684\u65f6\u95f4\u4e3a 0.2s\u3002\u5219\u6b64\u78b0\u649e\u8fc7\u7a0b\u4e2d\u7684\uff1a
\nA.\u6728\u677f\u4e0e\u5730\u9762\u95f4\u7684\u5e73\u5747\u5f39\u529b\u5927\u5c0f\u4e3a 200 N
\nB.\u6728\u677f\u5bf9\u7269\u5757\u505a\u6b63\u529f\uff0c\u56e0\u6b64\u7269\u5757\u7684\u673a\u68b0\u80fd\u589e\u52a0
\nC.\u82e5\u5c0f\u7269\u5757\u548c\u6728\u677f\u95f4\u7684\u6469\u64e6\u56e0\u6570\u589e\u5927\uff0c\u5219\u7269\u5757\u5f39\u8d77\u65f6\u7684\u6c34\u5e73\u901f\u5ea6\u589e\u5927
\nD.\u7269\u5757\u5bf9\u6728\u677f\u505a\u8d1f\u529f\uff0c\u6700\u5927\u503c\u4e3a 27J<\/p>\n

\u89e3\u9898\u8fc7\u7a0b\uff1a
\n1.\u5173\u4e8e\u652f\u6301\u529b\uff0c\u548c\u524d\u9762\u7684\u7b2c\u4e00\u9898\u4e00\u6837\uff0c\u6709\u5f88\u591a\u79cd\u65b9\u6cd5\uff0c\u8fd9\u91cc\u7528\u76f8\u5bf9\u7b80\u4fbf\u7684\u6c42\u52a0\u901f\u5ea6\u7684\u65b9\u6cd5\uff0c\u5bf9\u4e8e\u78b0\u649e\u524d\u540e\u77ac\u95f4\u7684\u901f\u5ea6\u5206\u522b\u4e3a\uff1a\\(v_1 = \\sqrt{2 g h_0}\\)\uff0c\\(v_2 = \\sqrt{2 g h_1}\\)\u3002\u5c06\u652f\u6301\u529b\u770b\u4e3a\u6052\u529b\uff0c\u5c0f\u7403\u505a\u5300\u52a0\u901f\u8fd0\u52a8\uff1a\\(a_y = \\frac{v_2 – v_1}{\\Delta t} = 90 \\, \\text{m\/s}^2\\)\u3002\u5bf9\u78b0\u649e\u8fc7\u7a0b\u4e2d\u7684\u5c0f\u7403\u5217\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\uff1a\\(F_N – mg = m a_y\\)\u3002\u89e3\u5f97\uff1a\\(F_N = 200 \\, \\text{N}\\)\u3002\u7531\u4e8eA\u9009\u9879\u95ee\u7684\u662f\u5730\u9762\u5bf9\u957f\u6728\u677f\u7684\u652f\u6301\u529b\uff0c\u56e0\u6b64\u8fd8\u8981\u8003\u8651\u957f\u6728\u677f\u7684\u91cd\u529b\uff0c\u56e0\u6b64A\u9009\u9879\u9519\u8bef\u3002<\/p>\n

2.\u5c0f\u7403\u5728\u6c34\u5e73\u65b9\u5411\u7684\u6700\u7ec8\u901f\u5ea6\uff1a\u6839\u636e\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\uff0c\u7269\u4f53\u5728\u6c34\u5e73\u65b9\u5411\u4e0a\u7684\u52a0\u901f\u5ea6\u4e3a \\(a_x = \\frac{\\mu F_N}{m} = 20 \\, \\text{m\/s}^2\\)\uff0c\u6c34\u5e73\u65b9\u5411\u52a8\u91cf\u5b88\u6052\uff0c\u82e5\u7269\u4f53\u548c\u6728\u677f\u80fd\u591f\u5171\u901f\uff0c\u6839\u636e\u52a8\u91cf\u5b9a\u7406\uff0c\u7269\u4f53\u548c\u6728\u677f\u7684\u6700\u7ec8\u901f\u5ea6\u4e3a \\(M v_0 = (m + M) v_f\\)\uff0c\u89e3\u5f97 \\(v_f = 3 \\, \\text{m\/s}\\)\u3002\u6839\u636e\u52a0\u901f\u5ea6\u516c\u5f0f \\(a_x \\cdot t = v_f\\)\uff0c\u7269\u4f53\u52a0\u901f\u5230 3 m\/s \u9700\u8981\u65f6\u95f4 \\(t = 0.15 \\, \\text{s} < 0.25 \\, \\text{s}\\)\uff0c\u56e0\u6b64\u5728 15s \u65f6\u5df2\u7ecf\u5171\u901f\uff0c\u901f\u5ea6\u5927\u5c0f\u4e3a 3 m\/s\u3002<\/p>\n

3.\u7269\u4f53\u5bf9\u957f\u6728\u677f\u505a\u7684\u529f\uff1a\u53ef\u4ee5\u4ece\u6469\u64e6\u529b\u505a\u529f\u548c\u52a8\u80fd\u5b9a\u7406\u4e24\u4e2a\u89d2\u5ea6\u6765\u5206\u6790\u8fd9\u4e2a\u95ee\u9898\u3002\u4ece\u6469\u64e6\u529b\u505a\u529f\u7684\u89d2\u5ea6\uff1a\\( W = \\mu F_N x = \\mu F_N \\cdot \\frac{v_0 + v_f}{2} = -27 \\, \\text{J} \\) \u5bf9\u5c0f\u6728\u5757\u5217\u52a8\u80fd\u5b9a\u7406\uff1a\\( W = \\frac{1}{2} M v_f^2 – \\frac{1}{2} M v_0^2 = -27 \\, \\text{J} \\),\u4e5f\u53ef\u4ee5\u7528\u6469\u64e6\u529b\u4e58\u4ee5\u76f8\u5bf9\u4f4d\u79fb\u7684\u89d2\u5ea6\uff0c\u4ece\u901f\u5ea6\u65f6\u95f4\u56fe\u50cf\u6c42\u51fa\u957f\u6728\u677f\u7684\u4f4d\u79fb\uff0c\u518d\u7528\u6469\u64e6\u529b\u4e58\u4ee5\u957f\u6728\u677f\u4f4d\u79fb\u6c42\u7269\u4f53\u5bf9\u957f\u6728\u677f\u505a\u7684\u529f\u3002<\/p>\n

4.\u957f\u6728\u677f\u5bf9\u7269\u4f53\u505a\u7684\u529f\uff1a** \u7528\u5e73\u5747\u901f\u5ea6\u8ba1\u7b97\u7ad6\u76f4\u65b9\u5411\u4f4d\u79fb\uff1a\\(\\Delta x = \\frac{v_0 + v_f}{2} \\Delta t = 0.2 \\, \\text{m}\\)\uff0c\u5782\u76f4\u65b9\u5411\u7684\u529f\uff1a\\(W_y = – F_N \\cdot \\Delta x = -40 \\, \\text{J}\\)\uff0c\u6c34\u5e73\u65b9\u5411\u7684\u529f\uff1a\\(W_x = \\frac{1}{2} m v^2 = 9 \\, \\text{J}\\)\uff0c\u603b\u529f\uff1a\\(W = W_x + W_y = -31 \\, \\text{J}\\)\u3002\u4e5f\u53ef\u4ee5\u4ece\u80fd\u91cf\u7684\u89d2\u5ea6\uff0c\u6574\u4e2a\u8fc7\u7a0b\u4e2d\u7269\u4f53\u80fd\u91cf\u7684\u53d8\u5316\u4e3a\uff1a\\(\\Delta E_p + \\Delta E_k = -mg(\\Delta y_1 + \\Delta y_2 – \\Delta y_1) + \\frac{1}{2} M V^2 = -31 \\, \\text{J}\\)\u3002
\n


\nJQX|Xiao<\/center>
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