![\"\"](\"https:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/20260326jqx.jpg\")
\u8fd0\u52a8\u5408\u6210\u5206\u89e3\u7684\u8fdb\u9636\u5e94\u7528
![\"\"](\"http:\/\/www.qiusir.com\/wp-content\/gallery\/MPO\/Jinqc.jpeg\")
JQX|Jin<\/center>
\n\u4e00\u3001\u53d7\u7a7a\u6c14\u963b\u529b\u7684\u629b\u4f53\u8fd0\u52a8\u5206\u6790
\n\u4f8b\u9898\uff1a\u4e00\u5c0f\u7403\u5728\u8ddd\u5730\u9762\u9ad8\u5ea6$h$\u5904\u4ee5\u521d\u901f\u5ea6$v_0$\u6cbf\u6c34\u5e73\u629b\u51fa\uff0c\u7a7a\u6c14\u963b\u529b\u5927\u5c0f\u4e0e\u901f\u5ea6\u6210\u6b63\u6bd4\uff0c\u65b9\u5411\u4e0e\u901f\u5ea6\u76f8\u53cd\u7ecf$t$\u65f6\u95f4\u540e\u843d\u5730\uff0c\u843d\u5730\u65f6\u901f\u5ea6\u65b9\u5411\u4e0e\u6c34\u5e73\u5939\u89d2\u4e3a$\\theta$\uff0c\u91cd\u529b\u52a0\u901f\u5ea6\u4e3a$g$\uff0c\u6c42\u843d\u5730\u901f\u5ea6\u548c\u6c34\u5e73\u4f4d\u79fb\u3002
![\"\"](\"https:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/jqx28-1.jpeg\")
\n\u672c\u9898\u7684\u5173\u952e\u5728\u4e8e\u963b\u529b\u4e5f\u53ef\u4ee5\u5206\u89e3\u4e3a\u6c34\u5e73\u7ad6\u76f4\u4e24\u4e2a\u65b9\u5411\uff0c\u4e14\u4e24\u4e2a\u65b9\u5411\u7684\u963b\u529b\u5927\u5c0f\u4f9d\u7136\u5c31\u4e24\u4e2a\u65b9\u5411\u901f\u5ea6\u6210\u6b63\u6bd4\u3002
\uff081\uff09\u843d\u5730\u901f\u5ea6
\u5bf9\u7ad6\u76f4\u65b9\u5411\u52a8\u91cf\u5b9a\u7406\u5206\u6790\uff0c\u5411\u4e0b\u4e3a\u6b63\u3002
$mv_0\\sin\\theta – 0 = mgt – \\sum kv_y\\Delta t = mgt – kh$ \u5373\u53ef\u89e3\u51fa\u901f\u5ea6\u3002
\uff082\uff09\u6c34\u5e73\u4f4d\u79fb
$mv\\cos\\theta – mv_0 = -\\sum kv_x\\Delta t = -kx$ \u5373\u53ef\u89e3\u51fa\u6c34\u5e73\u4f4d\u79fb\u3002
\u8fd9\u91ccqiusir\u8865\u5145\u4e86\u4e00\u4e2a\u5f88\u5e05\u7684\u4f8b\u9898\uff1a
\n[\u6e56\u53572025\u9ad8\u80039\u9898]\u5982\u56fe\uff0c\u5173\u4e8e$x$\u8f74\u5bf9\u79f0\u7684\u5149\u6ed1\u5bfc\u8f68\u56fa\u5b9a\u5728\u6c34\u5e73\u9762\u5185\uff0c\u5bfc\u8f68\u5f62\u72b6\u4e3a\u629b\u7269\u7ebf\uff0c\u9876\u70b9\u4f4d\u4e8e$O$\u70b9\u3002\u4e00\u8db3\u591f\u957f\u7684\u91d1\u5c5e\u6746\u521d\u59cb\u4f4d\u7f6e\u4e0e$y$\u8f74\u91cd\u5408\uff0c\u91d1\u5c5e\u6746\u7684\u8d28\u91cf\u4e3a$m$\uff0c\u5355\u4f4d\u957f\u5ea6\u7684\u7535\u963b\u4e3a$r_0$\u3002\u6574\u4e2a\u7a7a\u95f4\u5b58\u5728\u7ad6\u76f4\u5411\u4e0a\u7684\u5300\u5f3a\u78c1\u573a\uff0c\u78c1\u611f\u5e94\u5f3a\u5ea6\u4e3a$B$\u3002\u73b0\u7ed9\u91d1\u5c5e\u6746\u4e00\u6cbf$x$\u8f74\u6b63\u65b9\u5411\u7684\u521d\u901f\u5ea6$v_0$\uff0c\u91d1\u5c5e\u6746\u8fd0\u52a8\u8fc7\u7a0b\u4e2d\u59cb\u7ec8\u4e0e$y$\u8f74\u5e73\u884c\uff0c\u4e14\u4e0e\u7535\u963b\u4e0d\u8ba1\u7684\u5bfc\u8f68\u63a5\u89e6\u826f\u597d\u3002\u4e0b\u5217\u8bf4\u6cd5\u6b63\u786e\u7684\u662f\uff08\u3000\u3000\uff09
\n
![\"\"](\"https:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/jqx28-2.jpeg\")
\nA\uff0e\u91d1\u5c5e\u6746\u6cbf$x$\u8f74\u6b63\u65b9\u5411\u8fd0\u52a8\u8fc7\u7a0b\u4e2d\uff0c\u91d1\u5c5e\u6746\u4e2d\u7535\u6d41\u6cbf$y$\u8f74\u8d1f\u65b9\u5411
B\uff0e\u91d1\u5c5e\u6746\u53ef\u4ee5\u5728\u6cbf$x$\u8f74\u6b63\u65b9\u5411\u7684\u6052\u529b\u4f5c\u7528\u4e0b\u505a\u5300\u901f\u76f4\u7ebf\u8fd0\u52a8
C\uff0e\u91d1\u5c5e\u6746\u505c\u6b62\u8fd0\u52a8\u65f6\uff0c\u4e0e\u5bfc\u8f68\u56f4\u6210\u7684\u9762\u79ef\u4e3a$\\frac{mv_0r_0}{B^2}$
D\uff0e\u82e5\u91d1\u5c5e\u6746\u7684\u521d\u901f\u5ea6\u51cf\u534a\uff0c\u5219\u91d1\u5c5e\u6746\u505c\u6b62\u8fd0\u52a8\u65f6\u7ecf\u8fc7\u7684\u8ddd\u79bb\u5c0f\u4e8e\u539f\u6765\u7684\u4e00\u534a
\u8fd9\u91cc\u6211\u4eec\u5206\u6790C\u9009\u9879\u3002
\u6c34\u5e73\u65b9\u5411\u5217\u52a8\u91cf\u5b9a\u7406$-\\sum BIL\\Delta t = 0 – mv_0$
\u5e26\u5165\u7535\u6d41\u8868\u8fbe\u5f0f$-\\sum B \\cdot \\frac{BLv}{r_0 \\cdot L} \\cdot L\\Delta t = -mv_0$
\u6c42\u548c\u53ef\u5f97$\\sum \\frac{B^2L\\Delta x}{r_0} = mv_0$ \u8fd9\u91cc\u957f\u5ea6\u968f\u4f4d\u79fb\u662f\u53d8\u91cf\uff0c\u4e0e\u5c0f\u6bb5\u4f4d\u79fb\u6c42\u548c\u5373\u4e3a\u9762\u79ef\u3002
\u5373$\\frac{B^2S}{r_0} = mv_0$\uff0c\u89e3\u5f97$S = \\frac{mv_0r_0}{B^2}$
\n\u4e8c\u3001\u9760\u5899\u659c\u6746\u4e2d\u70b9\u7684\u8fd0\u52a8\u5206\u6790<\/strong>
\n[2025-2026\u5b66\u5e74\u5ea612\u6708\u4efdT8\u8003\u8bd5]\u4e00\u8f7b\u8d28\u6746AB\uff0c\u521d\u59cb\u65f6\u7d27\u9760\u5728\u5149\u6ed1\u7684\u7ad6\u76f4\u5899\u9762\u4e0a\u7ad6\u76f4\u9759\u6b62\u653e\u7f6e\uff0c\u6746\u957f\u4e3a$2l$\uff0c\u5728\u5176\u4e2d\u70b9C\u5904\u56fa\u5b9a\u4e00\u4e2a\u8d28\u91cf\u4e3a$m$\u7684\u5c0f\u7403\uff0c\u73b0\u4f7fA\u7aef\u4e0d\u8131\u79bb\u5899\u9762\uff0cB\u7aef\u6cbf\u7740\u5149\u6ed1\u5730\u9762\u4ee5\u901f\u5ea6$v$\u5411\u53f3\u5300\u901f\u8fd0\u52a8\uff0c\u5f53\u6746\u4e0e\u5730\u9762\u6210$\\alpha$\u89d2\u65f6\uff0c\u5219
\n
![\"\"](\"https:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/jqx28-3.jpeg\")
\nA\uff0e\u5c0f\u7403\u7684\u901f\u5ea6\u5927\u5c0f\u4e3a$\\frac{v}{2\\cos\\alpha}$
B\uff0e\u5c0f\u7403\u505a\u5300\u901f\u5706\u5468\u8fd0\u52a8
C\uff0e\u5f53$\\alpha=45^\\circ$\u65f6\uff0c\u6746\u5bf9\u5c0f\u7403\u7684\u4f5c\u7528\u529b\u5927\u5c0f\u4e3a$\\frac{mv^2}{2l}$
D\uff0e\u5f53$\\alpha=45^\\circ$\u65f6\uff0c\u6746\u5bf9\u5c0f\u7403\u505a\u7684\u529f\u4e3a$\\frac{mv^2}{4}$
\uff081\uff09\u6c42\u5c0f\u7403\u7684\u901f\u5ea6
\u6cd51\uff1a\u7531\u4e8e\u4e2d\u70b9\u5230O\u70b9\u7684\u8ddd\u79bb\u59cb\u7ec8\u4e0d\u53d8\uff0c\u6240\u4ee5\u8fd0\u52a8\u7684\u8def\u5f84\u662f\u5706\u5468\uff0c\u901f\u5ea6\u65b9\u5411\u65f6\u523b\u5782\u76f4\u4e8e\u4e0eO\u70b9\u8fde\u7ebf\u3002\u6839\u636e\u901f\u5ea6\u5173\u8054\uff0c\u6cbf\u6746\u901f\u5ea6\u4e3a$v\\cos\\alpha$\uff0c\u7531\u56fe\u4e2d\u51e0\u4f55\u5173\u7cfb\u5f97\uff0c\u5c0f\u7403\u5728 $C$ \u70b9\u901f\u5ea6\u65b9\u5411\u4e0e\u6746\u7684\u5939\u89d2\u4e3a $|2\\alpha-90^\\circ|$\uff0c\u6cbf\u6746\u65b9\u5411\u7684\u5206\u901f\u5ea6\u4e3a $v_C\\cos|2\\alpha-90^\\circ|$\uff0c\u5219\u6709 $v\\cos\\alpha=v_C\\cos|2\\alpha-90^\\circ|$ \u89e3\u5f97 $v_C=\\dfrac{v}{2\\sin\\alpha}$
\u6cd52\uff1a\u77ac\u5fc3\u6cd5
\u521a\u4f53\u5e73\u9762\u8fd0\u52a8\u4e2d\uff0c\u67d0\u4e00\u77ac\u65f6\u901f\u5ea6\u4e3a\u96f6\u7684\u70b9\uff0c\u79f0\u4e3a\u521a\u4f53\u5728\u8be5\u77ac\u65f6\u7684\u8f6c\u52a8\u77ac\u5fc3\uff08\u77ac\u65f6\u901f\u5ea6\u4e2d\u5fc3\uff0c\u7b80\u79f0\u77ac\u5fc3\uff09\u3002\u5bf9\u505a\u5e73\u9762\u8fd0\u52a8\u7684\u6746\u6765\u8bf4\uff0c\u5b83\u7684\u8fd0\u52a8\u53ef\u4ee5\u5206\u89e3\u4e3a\u968f\u57fa\u70b9\u7684\u5e73\u52a8\u548c\u7ed5\u57fa\u70b9\u7684\u8f6c\u52a8\uff1b\u800c\u77ac\u5fc3\u7684\u672c\u8d28\uff0c\u662f\u5728\u8fd9\u4e00\u77ac\u95f4\uff0c\u6574\u4e2a\u6746\u53ef\u4ee5\u88ab\u770b\u4f5c\u7eaf\u7ed5\u77ac\u5fc3\u505a\u5b9a\u8f74\u8f6c\u52a8\u3002
\u8fd9\u91cc\u9700\u8981\u6ce8\u610f\u7684\u662f\u77ac\u5fc3\u662f\u4e00\u4e2a\u4e0d\u65ad\u53d8\u5316\u7684 \u201c\u77ac\u65f6\u201d \u70b9\uff0c\u4f1a\u968f\u7740\u8fd0\u52a8\u8fdb\u884c\u4f4d\u7f6e\u7684\u6539\u53d8\u7684\u3002
\u6746\u4e0a\u5404\u70b9\u7684\u901f\u5ea6\u65b9\u5411\uff0c\u90fd\u5782\u76f4\u4e8e\u8be5\u70b9\u5230\u77ac\u5fc3\uff0c\u8fde\u7ebf\u6746\u4e0a\u4efb\u610f\u4e00\u70b9\u7684\u901f\u5ea6\u5927\u5c0f\u4e3a $v=\\omega \\cdot r$\uff08$r$ \u662f\u8be5\u70b9\u5230\u77ac\u5fc3\u7684\u8ddd\u79bb\uff0c$\\omega$ \u662f\u6746\u7684\u89d2\u901f\u5ea6\uff09\uff0c\u65b9\u5411\u4e0e\u8fde\u7ebf\u5782\u76f4\uff0c\u6307\u5411\u8f6c\u52a8\u65b9\u5411\u3002
\u90a3\u4e48\uff0c\u6211\u4eec\u8be5\u5982\u4f55\u5224\u65ad\u77ac\u5fc3\u7684\u4f4d\u7f6e\u5462\uff1f
\u6c42\u77ac\u5fc3\u6cd51\uff1a\u4e24\u70b9\u901f\u5ea6\u5782\u7ebf\u6cd5
\u5df2\u77e5\u6746\u4e0a\u4e24\u70b9 A\u3001B \u7684\u901f\u5ea6 $v_A$\u3001$v_B$ \u65b9\u5411\uff0c\u5206\u522b\u8fc7 A\u3001B \u4f5c\u901f\u5ea6\u65b9\u5411\u7684\u5782\u7ebf\uff0c\u4e24\u6761\u5782\u7ebf\u7684\u4ea4\u70b9\u5c31\u662f\u8be5\u77ac\u65f6\u7684\u77ac\u5fc3 P\u3002\u82e5 $v_A$\u3001$v_B$ \u5e73\u884c\u4e14\u5927\u5c0f\u76f8\u7b49\uff1a\u6746\u6b64\u65f6\u505a\u77ac\u65f6\u5e73\u52a8\uff0c\u89d2\u901f\u5ea6 $\\omega=0$\uff0c\u6ca1\u6709\u6709\u9650\u4f4d\u7f6e\u7684\u77ac\u5fc3\uff08\u53ef\u8ba4\u4e3a\u77ac\u5fc3\u5728\u65e0\u7a77\u8fdc\u5904\uff09\u3002
\u6c42\u77ac\u5fc3\u6cd52\uff1a\u901f\u5ea6\u5206\u89e3\u6cd5
\u4ee5\u6746\u4e0a\u4efb\u610f\u4e00\u70b9\u4e3a\u57fa\u70b9\uff08\u6bd4\u5982 A\uff09\uff0c\u6746\u4e0a\u53e6\u4e00\u70b9 B \u7684\u901f\u5ea6\u6ee1\u8db3\uff1a$v_B = v_A + v_{B\u76f8\u5bf9A}$\uff0c\u5176\u4e2d $v_{B\u76f8\u5bf9A}$ \u662f B \u7ed5 A \u8f6c\u52a8\u7684\u901f\u5ea6\uff0c\u65b9\u5411\u5782\u76f4\u4e8e\u6746\u3002\u901a\u8fc7\u77e2\u91cf\u5408\u6210\u627e\u5230\u901f\u5ea6\u4e3a\u96f6\u7684\u70b9\uff0c\u5373\u4e3a\u77ac\u5fc3\u3002
\u90a3\u4e48\uff0c\u672c\u9898\u4e2d\u77ac\u5fc3\u4e3a\u9ed1\u677f\u4e2dO’\u70b9\uff0c
\u5bf9\u5e94\u7684\u89d2\u901f\u5ea6$\\omega = \\frac{v}{L \\cdot \\sin\\alpha}$
\u53ef\u6c42\u4e2d\u70b9\u7684\u77ac\u65f6\u901f\u5ea6 $v = \\omega \\cdot \\frac{L}{2} = \\frac{v}{2\\sin\\alpha}$
\u6cd53\uff1a\u901f\u5ea6\u6bd4\u4f8b\u6cd5
\u5728\u6c34\u5e73\u65b9\u5411\u4e0a\uff0c\u4e2d\u70b9C\u7684\u4f4d\u7f6e\u6c38\u8fdc\u662fB\u70b9\u7684\u4e00\u534a\uff0c\u90a3\u4e48\u6c34\u5e73\u901f\u5ea6\u6c38\u8fdc\u662fB\u70b9\u901f\u5ea6\u7684\u4e00\u534a\u3002
\u540c\u7406\uff0c\u5728\u7ad6\u76f4\u65b9\u5411\u4e0a\uff0c\u4e2d\u70b9C\u7684\u4f4d\u7f6e\u6c38\u8fdc\u662fA\u70b9\u7684\u4e00\u534a\uff0c\u90a3\u4e48\u7ad6\u76f4\u901f\u5ea6\u6c38\u8fdc\u662fA\u70b9\u901f\u5ea6\uff08\u6839\u636e\u901f\u5ea6\u5173\u8054\u53ef\u6c42\uff09\u7684\u4e00\u534a\u3002
\u90a3\u4e48\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u6c34\u5e73\u7ad6\u76f4\u7684\u8fd0\u52a8\u5408\u6210\u6c42\u51fa\u901f\u5ea6\u5927\u5c0f\u3002
\uff082\uff09\u6c42\u6746\u5bf9\u7403\u7684\u4f5c\u7528\u529b
\u6839\u636e\u4e0a\u4e00\u95ee\u6cd53\u5206\u6790\uff0c\u5c0f\u7403\u6c34\u5e73\u65b9\u5411\u5300\u901f\uff0c\u53ef\u5f97\u6746\u5bf9\u5c0f\u7403\u7684\u4f5c\u7528\u529b\u5fc5\u987b\u6cbf\u7740\u7ad6\u76f4\u65b9\u5411\uff0c\u7531\u6307\u5411\u5706\u5fc3\u7684\u5408\u5916\u529b\u63d0\u4f9b\u5411\u5fc3\u529b\uff0c\u5373
$F_N – mg = m\\frac{v_C^2}{l}$ \u5f97 $F_N = mg + m\\frac{v^2}{4l\\cos^2\\alpha}$
\uff083\uff09\u6c42\u6574\u4e2a\u6746\u4e0a\u901f\u5ea6\u6700\u5c0f\u7684\u70b9
\u6cd51\uff1a\u6cbf\u6746\u901f\u5ea6\u4e3a$v\\cos\\alpha$\uff0c\u5f53\u5782\u76f4\u6746\u901f\u5ea6\u4e3a0\u65f6\uff0c\u603b\u901f\u5ea6\u6700\u5c0f\u3002
\u6cd52\uff1a\u5b9a\u4e49\u77ac\u5fc3\u540e\uff0c\u6746\u4e0a\u6240\u6709\u70b9\u5bf9\u77ac\u5fc3\u89d2\u901f\u5ea6\u76f8\u540c\uff0c\u6240\u4ee5\u8fc7\u77ac\u5fc3\u5bf9\u6746\u505a\u5782\u7ebf\uff0c\u5782\u8db3\u5904\u901f\u5ea6\u6700\u5c0f\u3002
\n\u4e09\u3001\u4f38\u7f29\u67b6\u4e0a\u70b9\u7684\u8fd0\u52a8\u5206\u6790<\/strong>
\n\u4f8b\u9898\uff1a\u5982\u56fe\u6240\u793a\uff0c\u4f38\u7f29\u67b6\u7531\u4e24\u4e2a\u5149\u6ed1\u94f0\u63a5\u7684\u6b63\u65b9\u5f62\u7ec4\u6210\uff0c\u5de6\u4fa7\u6b63\u65b9\u5f62\u8fb9\u957f\u4e3a $2l$\uff0c\u53f3\u4fa7\u6b63\u65b9\u5f62\u8fb9\u957f\u4e3a $l$\u3002\u6841\u67b6\u7684\u5de6\u7aef\u70b9\u56fa\u5b9a\u5728 O \u70b9\uff0c\u5728\u6700\u53f3\u7aef D \u70b9\u65bd\u52a0\u6052\u5b9a\u6c34\u5e73\u62c9\u529b\uff0c\u4f7f D \u70b9\u901f\u5ea6\u4fdd\u6301\u4e3a $v$\u3002\u67d0\u65f6\u523b\u6841\u67b6\u6240\u6709\u5185\u89d2\u5747\u4e3a\u76f4\u89d2\uff0c\u6c42\u6b64\u65f6 A \u70b9\u7684\u901f\u5ea6 $v_A$ \u548c B \u70b9\u7684\u901f\u5ea6 $v_B$ \u7684\u5927\u5c0f\u4e0e\u65b9\u5411\u3002
\n
![\"\"](\"https:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/jqx28-4.jpeg\")
\n\uff081\uff09A \u70b9\u7684\u901f\u5ea6 $v_A$
\u4e24\u4e2a\u6b63\u65b9\u5f62\u7684\u516c\u5171\u94f0\u63a5\u70b9\u4e3a C\uff0c\u5916\u529b\u4f5c\u7528\u70b9\u4e3a\u53f3\u7aef\u70b9 D\u3002
\u7531\u51e0\u4f55\u5173\u7cfb\uff0c\u6b64\u65f6 O \u5230 C \u7684\u6c34\u5e73\u8ddd\u79bb $x_C = \\frac{2}{3}x_D$\uff0c\u5bf9\u65f6\u95f4\u6c42\u5bfc\u53ef\u5f97\uff1a
$v_C = \\frac{2}{3}v$
A \u70b9\u7ed5 O \u70b9\u505a\u5706\u5468\u8fd0\u52a8\uff0c\u56e0\u6b64\u901f\u5ea6\u65b9\u5411\u5fc5\u7136\u5782\u76f4\u4e8e\u6746 OA\u3002
\u6cbf\u6746\u65b9\u5411\u7684\u5206\u901f\u5ea6\u4e3a\uff1a
$v_{C\\parallel} = v_C \\cos45^\\circ = \\frac{2}{3}v \\cdot \\frac{\\sqrt{2}}{2} = \\frac{\\sqrt{2}}{3}v$
A \u70b9\u7684\u901f\u5ea6 $v_A$ \u5782\u76f4\u4e8e\u6746 OA\uff0c\u5176\u6cbf\u6746 AC \u65b9\u5411\u7684\u5206\u901f\u5ea6\u7b49\u4e8e $v_{C\\parallel}$\uff0c\u56e0\u6b64\uff1a
$v_A = \\frac{v_{C\\parallel}}{\\cos45^\\circ} = \\frac{\\frac{\\sqrt{2}}{3}v}{\\frac{\\sqrt{2}}{2}} = \\frac{\\sqrt{2}}{2} \\cdot \\frac{2}{3}v = \\frac{\\sqrt{2}}{3}v$
\u65b9\u5411\uff1a\u5782\u76f4\u4e8e\u6746 OA\uff0c\u659c\u5411\u5de6\u4e0a\u65b9\uff08\u4e0e\u6c34\u5e73\u65b9\u5411\u5939\u89d2 $135^\\circ$\uff09\u3002
\uff082\uff09B \u70b9\u7684\u901f\u5ea6 $v_B$
\u6cd5\u4e00\uff1a
B\u70b9\u540c\u65f6\u5c5e\u4e8e\u6746CB\u548c\u6746BD\uff0c\u9700\u4e24\u6b21\u5229\u7528\u201c\u6746\u4e24\u7aef\u901f\u5ea6\u6cbf\u6746\u5206\u91cf\u76f8\u7b49\u201d\u7684\u7ea6\u675f\u5173\u7cfb\uff1a
C\u70b9\u901f\u5ea6$v_C$\u6c34\u5e73\u5411\u53f3\uff0c\u4e0eCB\u6746\u5939\u89d2\u4e3a$45^\\circ$\uff0c\u5176\u6cbfCB\u6746\u7684\u5206\u91cf\u4e3a\uff1a
$v_{C\\parallel} = v_C \\cos45^\\circ = \\frac{2}{3}v \\times \\frac{\\sqrt{2}}{2} = \\frac{\\sqrt{2}}{3}v$
\u56e0\u6b64B\u70b9\u901f\u5ea6\u6cbfCB\u6746\u7684\u5206\u91cf\u4e3a\uff1a
$v_1 = v_{C\\parallel} = \\frac{\\sqrt{2}}{3}v$<\/p>\n
D\u70b9\u901f\u5ea6$v$\u6c34\u5e73\u5411\u53f3\uff0c\u4e0eBD\u6746\u5939\u89d2\u4e3a$45^\\circ$\uff0c\u5176\u6cbfBD\u6746\u7684\u5206\u91cf\u4e3a\uff1a
$v_{D\\parallel} = v \\cos45^\\circ = v \\times \\frac{\\sqrt{2}}{2} = \\frac{\\sqrt{2}}{2}v$
\u56e0\u6b64B\u70b9\u901f\u5ea6\u6cbfBD\u6746\u7684\u5206\u91cf\u4e3a\uff1a
$v_2 = v_{D\\parallel} = \\frac{\\sqrt{2}}{2}v$<\/p>\n
\u7531\u4e8eCB\u6746\u4e0eBD\u6746\u4e92\u76f8\u5782\u76f4\uff0c\u5206\u91cf$v_1$\u4e0e$v_2$\u4e92\u76f8\u5782\u76f4\uff0c\u56e0\u6b64B\u70b9\u7684\u5408\u901f\u5ea6\u5927\u5c0f\u4e3a\uff1a \u56db\u3001\u5f39\u6027\u7ef3\u672b\u7aef\u7684\u8fd0\u52a8\u5206\u6790 A\u9009\u9879\uff1a\u4ee5B\u70b9\u4e3a\u539f\u70b9\uff0c\u5411\u53f3\u4e3a$x$\u8f74\u6b63\u65b9\u5411\uff0c\u5411\u4e0b\u4e3a$y$\u8f74\u6b63\u65b9\u5411\uff0c\u5bf9\u5c0f\u7403\u5728\u6c34\u5e73\u65b9\u5411\u7684\u53d7\u529b\u4e3a$F_x = -k(x + \\frac{l}{2})$\uff0c\u7ad6\u76f4\u65b9\u5411\u7684\u53d7\u529b\u4e3a$F_y = -ky + mg$\uff0c \u3010\u4e0b\u671f\u9884\u544a\u3011\u4e0b\u4e00\u671f\uff0cK2304\u73ed\u5f20\u8018\u94ed\u540c\u5b66\u5e26\u6765\u8fd1\u671f\u7684\u4e2a\u4eba\u7814\u7a76\u6210\u679c\uff1a\u5300\u53d8\u901f\u66f2\u7ebf\u8fd0\u52a8\u4e2d\u5e73\u5747\u901f\u5ea6\u7684\u5e94\u7528<\/p>\n","protected":false},"excerpt":{"rendered":" JQX\/\u8fdb\u53d6\u82af \u5e2d\u660e\u7eb3\u7b2c28\u671f\uff082026.03.26\uff09 \u8fd0\u52a8\u5408\u6210\u5206\u89e3\u7684\u8fdb\u9636\u5e94\u7528JQX|Jin \u4e00\u3001\u53d7\u7a7a\u6c14\u963b\u529b\u7684 … \u9605\u8bfb\u66f4\u591a<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[9],"tags":[460,247],"class_list":["post-45435","post","type-post","status-publish","format-standard","hentry","category-jqx","tag-jqx","tag-physics"],"_links":{"self":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/45435","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=45435"}],"version-history":[{"count":24,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/45435\/revisions"}],"predecessor-version":[{"id":47026,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/45435\/revisions\/47026"}],"wp:attachment":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=45435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=45435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=45435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
$v_B = \\sqrt{v_1^2 + v_2^2}$
\u4ee3\u5165$v_1 = \\frac{\\sqrt{2}}{3}v$\u3001$v_2 = \\frac{\\sqrt{2}}{2}v$\uff1a
$v_B = \\frac{\\sqrt{26}}{6}v$
\u901f\u5ea6\u65b9\u5411\uff1a\u4e0eCB\u6746\u65b9\u5411\u7684\u5939\u89d2$\\theta$\u6ee1\u8db3$\\tan\\theta = \\frac{v_2}{v_1} = \\frac{\\frac{\\sqrt{2}}{2}v}{\\frac{\\sqrt{2}}{3}v} = \\frac{3}{2}$\uff0c\u5373$\\theta = \\arctan\\frac{3}{2}$\u3002
\n[\u601d\u8003]\u6cd51\u80fd\u76f4\u63a5\u5408\u6210\u7684\u539f\u56e0\uff0c\u662f\u672c\u9898\u4e24\u4e2a\u65b9\u5411\u901f\u5ea6\u4e92\u76f8\u5782\u76f4\u3002\u5982\u679c\u672c\u9898\u672b\u6001\u4e24\u4e2a\u6746\u4e0d\u518d\u5782\u76f4\uff0c\u80fd\u5426\u6839\u636e\u8fd0\u52a8\u7684\u77e2\u91cf\u8fdb\u884c\u5408\u6210\uff1f
\u4e0d\u80fd\u3002\u8ba1\u7b97\u7684\u4e24\u4e2a\u5206\u901f\u5ea6\uff0c\u662f\u5b9e\u9645\u8fd0\u52a8\u5728\u4e24\u4e2a\u6746\u4e0a\u7684\u6295\u5f71\uff0c\u5e94\u8be5\u505a\u4e24\u4e2a\u901f\u5ea6\u7684\u5782\u7ebf<\/strong>\uff0c\u4ea4\u70b9\u5373\u4e3a\u5b9e\u9645\u901f\u5ea6\u672b\u7aef\u70b9\uff08\u8096\u8001\u5e08\u8865\u5145\uff0c\u5f88\u5e05\uff09\u3002
\u8fd9\u91ccqiusir\u8865\u5145\u4e86\u4e00\u4e2a\u573a\u529b\u4e0b\uff0c\u5df2\u77e5\u6cbf\u4e24\u4e2a\u659c\u9762\u8fd0\u52a8\u5c0f\u7403\u7684\u52a0\u901f\u5ea6\uff08\u4e5f\u53ef\u4ee5\u7406\u89e3\u4e3a\u4e24\u6b21\u6295\u5f71\u7684\u52a0\u901f\u5ea6\uff09\uff0c\u540c\u6837\u7684\u4e0d\u80fd\u76f4\u63a5\u628a\u52a0\u901f\u5ea6\u8fdb\u884c\u77e2\u91cf\u5408\u6210\uff0c\u53ef\u4ee5\u505a\u5782\u7ebf\u5408\u6210\u3002
\u6cd52\uff1a\u4ee5C\u4e3a\u53c2\u8003\u7cfb
\u4ee5C\u4e3a\u53c2\u8003\u7cfb\uff0c\u5219B\u7ed5C\u505a\u5706\u5468\u8fd0\u52a8\uff0c\u65b9\u6cd5\u4e0e\u6c42A\u901f\u5ea6\u76f8\u540c\u3002\u6700\u540e\u8981\u8bb0\u5f97\u628a\u6362\u7cfb\u7684\u901f\u5ea6\u52a0\u56de\u3002<\/p>\n
\u8fd9\u9053\u9898\u6765\u6e90\u4e8e2025-2026\u5b66\u5e74\u5ea612\u6708\u4efdT8\u8003\u8bd5
\u5982\u56fe\uff0c\u5149\u6ed1\u7684\u7ad6\u76f4\u5899\u9762\u4e0aA\u5904\u548cB\u5904\u5404\u6709\u4e00\u4e2a\u9489\u5b50\uff0c\u4e8c\u8005\u5904\u4e8e\u540c\u4e00\u6c34\u5e73\u9ad8\u5ea6\uff0c\u95f4\u8ddd\u4e3a$l$\uff0c\u6709\u4e00\u8f7b\u8d28\u5f39\u6027\u7ef3\uff0c\u539f\u957f\u4e3a$l$\uff0c\u52b2\u5ea6\u7cfb\u6570\u4e3a$k$\uff0c\u4e00\u7aef\u7531A\u5904\u9489\u56fa\u5b9a\uff0c\u53e6\u4e00\u7aef\u7cfb\u6709\u4e00\u8d28\u91cf\u4e3a$m$\u7684\u5c0f\u7403\uff0c\u5176\u4e2d$g$\u4e3a\u91cd\u529b\u52a0\u901f\u5ea6\uff0cB\u5904\u9489\u6070\u597d\u5904\u4e8e\u5f39\u6027\u7ef3\u4e0b\u9762\uff0c\u9489\u5b50\u548c\u5c0f\u7403\u90fd\u53ef\u89c6\u4e3a\u8d28\u70b9\uff0c\u73b0\u5c06\u5c0f\u7403\u6c34\u5e73\u5411\u53f3\u62c9\u4f38\u5230\u4e0eA\u5904\u9489\u8ddd\u79bb\u4e3a$2l$\u7684C\u70b9\uff0c\u5c06\u5c0f\u7403\u7531\u9759\u6b62\u91ca\u653e\uff0c\u5219\u4e0b\u5217\u8bf4\u6cd5\u6b63\u786e\u7684\u662f\uff08\u3000\u3000\uff09
\n![\"\"](\"https:\/\/www.qiusir.com\/wp-content\/gallery\/physics\/jqx28-5.jpeg\")
\nA\uff0e\u5c0f\u7403\u5728\u6c34\u5e73\u548c\u7ad6\u76f4\u4e24\u4e2a\u65b9\u5411\u7684\u5206\u8fd0\u52a8\u5747\u4e3a\u7b80\u8c10\u8fd0\u52a8
B\uff0e\u5c0f\u7403\u5c06\u4e0eB\u5904\u9489\u53d1\u751f\u78b0\u649e
C\uff0e\u5c0f\u7403\u7684\u8fd0\u52a8\u8f68\u8ff9\u4e3a\u4e00\u6761\u76f4\u7ebf
D\uff0e\u5f53\u5c0f\u7403\u7b2c\u4e00\u6b21\u8fd0\u52a8\u81f3B\u5904\u9489\u7684\u6b63\u4e0b\u65b9\u65f6\uff0c\u5176\u901f\u5ea6\u65b9\u5411\u6c34\u5e73\u5411\u5de6<\/p>\n
\u4e24\u4e2a\u529b\u5747\u6ee1\u8db3\u7b80\u8c10\u8fd0\u52a8\u7684\u8868\u8fbe\u5f0f\uff0c\u6c34\u5e73\u7b80\u8c10\u5206\u8fd0\u52a8\u7684\u5e73\u8861\u4f4d\u7f6e\u5728$x = -\\frac{l}{2}$\u5904\uff0c\u7ad6\u76f4\u7b80\u8c10\u5206\u8fd0\u52a8\u7684\u5e73\u8861\u4f4d\u7f6e\u5728$y = \\frac{mg}{k}$\u5904\u3002
C\u9009\u9879\uff1a\u6839\u636e\u7b80\u8c10\u8fd0\u52a8\uff0c\u53ef\u77e5\u5c0f\u7403\u7684\u6c34\u5e73\u4f4d\u7f6e\u5750\u6807\u53ef\u8868\u793a\u4e3a$x = \\frac{3l}{2}\\cos(\\omega t) – \\frac{l}{2}$\uff0c\u7ad6\u76f4\u4f4d\u7f6e\u5750\u6807\u53ef\u8868\u793a\u4e3a$y = -\\frac{mg}{k}\\cos(\\omega t) + \\frac{mg}{k}$
\u8fd0\u52a8\u8f68\u8ff9\u6240\u6ee1\u8db3\u7684\u65b9\u7a0b\u4e3a$y = -\\frac{mg}{k} \\cdot \\frac{x + \\frac{l}{2}}{\\frac{3l}{2}} + \\frac{mg}{k} = -\\frac{2mg}{3kl}(x + \\frac{l}{2}) + \\frac{mg}{k}$\uff0c\u662f\u4e00\u6b21\u51fd\u6570\uff0c\u56fe\u50cf\u4e3a\u76f4\u7ebf\u3002
\u8fd9\u4e2a\u5c0f\u7403\u7684\u8fd0\u52a8\uff0c\u662f\u4ee5$(0, \\frac{mg}{k})$\u5750\u6807\u4e3a\u5e73\u8861\u4f4d\u7f6e\u7684\u7b80\u8c10\u8fd0\u52a8\uff0c\u51fa\u53d1\u70b9\u5c31\u662f\u6700\u8fdc\u70b9\u3002
\u8fd9\u91cc\u53d1\u73b0\u4e00\u4e2a\u6709\u8da3\u7684\u7ed3\u8bba\uff1a\u4e00\u4e2a\u7b80\u8c10\u8fd0\u52a8\u6cbf\u6b63\u4ea4\u5206\u89e3\uff0c\u4e24\u4e2a\u5206\u8fd0\u52a8\u4f9d\u7136\u662f\u7b80\u8c10\u8fd0\u52a8\u3002
\u4e00\u4e2a\u7b80\u8c10\u8fd0\u52a8\u6cbf\u659c\u4ea4\u5206\u89e3\uff0c\u4e24\u4e2a\u5206\u8fd0\u52a8\u4f9d\u7136\u662f\u7b80\u8c10\u8fd0\u52a8\u3002<\/p>\n