{"id":2826,"date":"2022-08-23T21:24:14","date_gmt":"2022-08-23T13:24:14","guid":{"rendered":"http:\/\/www.7mgh.com\/?p=2826"},"modified":"2022-08-24T07:47:07","modified_gmt":"2022-08-23T23:47:07","slug":"%e4%b8%80%e4%b8%aa%e9%ab%98%e8%80%83%e9%a2%98","status":"publish","type":"post","link":"https:\/\/www.7mgh.com\/?p=2826","title":{"rendered":"\u4e00\u4e2a\u9ad8\u8003\u9898"},"content":{"rendered":"\n

\u5982\u56fe\u6240\u793a\uff0c\u4e00\u4e2a\u8d28\u91cf\u4e3aM\u957f\u4e3aL\u7684\u5706\u7ba1\u7ad6\u76f4\u653e\u7f6e\uff0c\u9876\u7aef\u585e\u6709\u4e00\u4e2a\u8d28\u91cf\u4e3am\u7684\u5f39\u6027\u5c0f\u7403\uff0cM=4m\uff0c\u7403\u548c\u7ba1\u95f4\u7684\u6ed1\u52a8\u6469\u64e6\u529b\u548c\u6700\u5927\u9759\u6469\u64e6\u529b\u5927\u5c0f\u5747\u4e3a4mg\uff0e\u7ba1\u4ece\u4e0b\u7aef\u79bb\u5730\u9762\u8ddd\u79bb\u4e3aH\u5904\u81ea\u7531\u843d\u4e0b\uff0c\u8fd0\u52a8\u8fc7\u7a0b\u4e2d\uff0c\u7ba1\u59cb\u7ec8\u4fdd\u6301\u7ad6\u76f4\uff0c\u6bcf\u6b21\u843d\u5730\u540e\u5411\u4e0a\u5f39\u8d77\u7684\u901f\u5ea6\u4e0e\u843d\u5730\u65f6\u901f\u5ea6\u5927\u5c0f\u76f8\u7b49\uff0c\u4e0d\u8ba1\u7a7a\u6c14\u963b\u529b\uff0c\u91cd\u529b\u52a0\u901f\u5ea6\u4e3ag\uff0e\u6c42\uff1a<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\uff081\uff09\u7ba1\u7b2c\u4e00\u6b21\u843d\u5730\u5f39\u8d77\u65f6\u7ba1\u548c\u7403\u7684\u52a0\u901f\u5ea6\uff1b<\/p>\n\n\n\n

\uff082\uff09\u7ba1\u7b2c\u4e00\u6b21\u843d\u5730\u5f39\u8d77\u540e\uff0c\u82e5\u7403\u6ca1\u6709\u4ece\u7ba1\u4e2d\u6ed1\u51fa\uff0c\u5219\u7403\u4e0e\u7ba1\u8fbe\u5230\u76f8\u540c\u901f\u5ea6\u65f6\uff0c\u7ba1\u4e0a\u5347\u7684\u6700\u5927\u9ad8\u5ea6\u3002<\/p>\n\n\n\n

\uff083\uff09\u7ba1\u7b2c\u4e8c\u6b21\u5f39\u8d77\u540e\u7403\u4e0d\u81f4\u6ed1\u843d\uff0cL\u5e94\u6ee1\u8db3\u4ec0\u4e48\u6761\u4ef6\uff0e<\/p>\n\n\n\n

\n
\u89e3\u6790<\/a><\/div>\n<\/div>\n\n\n\n
\n\n\n\n

\uff081\uff09\u7ba1\u7b2c\u4e00\u6b21\u843d\u5730\u5f39\u8d77\u65f6\uff0c\u7ba1\u77ac\u95f4\u5411\u4e0a\u8fd0\u52a8\uff0c\u53d7\u5230\u81ea\u8eab\u91cd\u529b\u4ee5\u53ca\u6469\u64e6\u529b\uff0c\u6240\u4ee5\u7ba1\u7684\u52a0\u901f\u5ea6$a_1=\\frac{4mg+4mg}{4m}=2g$\u65b9\u5411\u5411\u4e0b\u3002\u7403\u53d7\u5230\u5411\u4e0a\u7684\u6469\u64e6\u529b\u548c\u5411\u4e0b\u7684\u91cd\u529b\uff0c\u7403\u52a0\u901f\u5ea6$a_2=\\frac{f-mg}{m}=\\frac{4mg-mg}{m}=3g$\u65b9\u5411\u5411\u4e0a\u3002<\/p>\n\n\n\n

\uff082\uff09\u53d6\u7ad6\u76f4\u5411\u4e0b\u4e3a\u6b63\u65b9\u5411\uff0e\u7403\u4e0e\u7ba1\u7b2c\u4e00\u6b21\u78b0\u5730\u65f6\u901f\u5ea6$v_0=\\sqrt{2gH}$ \uff0c\u65b9\u5411\u5411\u4e0b\uff0e\u78b0\u5730\u540e\u7ba1\u7684\u901f\u5ea6$v_1=- \\sqrt{2gH}$\uff0c\u65b9\u5411\u5411\u4e0a\uff1b\u7403\u7684\u901f\u5ea6$v_2=\\sqrt{2gH}$\uff0c\u65b9\u5411\u5411\u4e0b\u82e5\u7403\u521a\u597d\u6ca1\u6709\u4ece\u7ba1\u4e2d\u6ed1\u51fa\uff0c\u8bbe\u7ecf\u8fc7\u65f6\u95f4$t_1$\uff0c\u7403\u7ba1\u901f\u5ea6v\u76f8\u540c\uff0c\u5219\u6709<\/p>\n\n\n\n

$$-v_1+a_1t_1=v_2-a_2 {t_1}^2$$<\/p>\n\n\n\n

$$-\\sqrt{2gH}-2gt_1=\\sqrt{2gH}+3mgt_1$$<\/p>\n\n\n\n

$$2\\sqrt{2gH}=5mgt_1$$<\/p>\n\n\n\n

$$t_1=\\frac{2}{5}\\sqrt{\\frac{2H}{g}}$$<\/p>\n\n\n\n

\u6b64\u65f6\u7ba1\u4e0b\u7aef\u7684\u9ad8\u5ea6\u4e3a$h_1=v_0 t_1-\\frac{1}{2} {a_1} {t_1}^2$ \u5e26\u5165\u6570\u636e<\/p>\n\n\n\n

$$h_1=\\frac{12}{25}H$$<\/p>\n\n\n\n

\u6b64\u540e\u7ba1\u548c\u7403\u5171\u901f\u4e0a\u5347$v_g=v_0-a_2 t_1=\\frac{1}{5} \\sqrt{2gH}$<\/p>\n\n\n\n

\u5171\u901f\u4e0a\u5347\u7684\u9ad8\u5ea6 $$h_2=\\frac{v_g ^2}{2g}=\\frac{1}{25}H$$<\/p>\n\n\n\n

\u7ba1\u4e0a\u5347\u7684\u6700\u5927\u9ad8\u5ea6$H_1$$$H_1=h_1+h_2=\\frac{13}{25}H $$<\/p>\n\n\n\n

\uff083\uff09\u8bbe\u7b2c\u4e00\u6b21\u5f39\u8d77\u8fc7\u7a0b\u4e2d\u7403\u76f8\u5bf9\u4e8e\u7ba1\u7684\u4f4d\u79fb$x_1$\uff0c\u5728\u7ba1\u5f00\u59cb\u4e0b\u843d\u5230\u4e0a\u5347\u5230$H_1$\u7684\u8fc7\u7a0b\u4e2d\uff0c\u7531\u52a8\u80fd\u51cf\u5c11\u91cf\u7b49\u4e8e\u6469\u64e6\u529b\u505a\u529f<\/p>\n\n\n\n

$$Mg(H-H_1+mg(H-h_1 + x_1)-4mg x_1=0$$ <\/p>\n\n\n\n

$$x_1= \\frac{4}{5}H_1$$
\u5373L\u5e94\u6ee1\u8db3\u6761\u4ef6$x_1 +x_2 \\leq L$<\/p>\n\n\n\n

$$\\frac{4}{5}H +\\frac{4}{5}H_1\\leq L$$<\/p>\n\n\n\n

$$\\frac{4}{5}H +\\frac{4}{5} \\frac{13}{25}H\\leq L$$<\/p>\n\n\n\n

$$\\frac{152}{125}H\\leq L$$<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5982\u56fe\u6240\u793a\uff0c\u4e00\u4e2a\u8d28\u91cf\u4e3aM\u957f\u4e3aL\u7684\u5706\u7ba1\u7ad6\u76f4\u653e\u7f6e\uff0c\u9876\u7aef\u585e\u6709\u4e00\u4e2a\u8d28\u91cf\u4e3am\u7684\u5f39\u6027\u5c0f\u7403\uff0cM=4m\uff0c\u7403\u548c\u7ba1\u95f4\u7684\u6ed1\u52a8\u6469\u64e6\u529b\u548c\u6700\u5927\u9759\u6469\u64e6\u529b\u5927\u5c0f\u5747\u4e3a4mg\uff0e\u7ba1\u4ece\u4e0b\u7aef\u79bb\u5730\u9762\u8ddd\u79bb\u4e3aH\u5904\u81ea\u7531\u843d\u4e0b\uff0c\u8fd0\u52a8\u8fc7\u7a0b\u4e2d\uff0c\u7ba1\u59cb\u7ec8\u4fdd\u6301\u7ad6\u76f4\uff0c\u6bcf\u6b21\u843d\u5730\u540e\u5411\u4e0a\u5f39\u8d77\u7684\u901f\u5ea6\u4e0e\u843d\u5730\u65f6\u901f\u5ea6\u5927\u5c0f\u76f8\u7b49\uff0c\u4e0d\u8ba1\u7a7a\u6c14\u963b\u529b\uff0c\u91cd\u529b\u52a0\u901f\u5ea6\u4e3ag\uff0e\u6c42\uff1a \uff081\uff09\u7ba1\u7b2c\u4e00\u6b21\u843d\u5730\u5f39\u8d77\u65f6\u7ba1\u548c\u7403\u7684\u52a0\u901f\u5ea6\uff1b \uff082\uff09\u7ba1\u7b2c\u4e00\u6b21\u843d\u5730\u5f39\u8d77\u540e\uff0c\u82e5\u7403\u6ca1\u6709\u4ece\u7ba1\u4e2d\u6ed1\u51fa\uff0c\u5219\u7403\u4e0e\u7ba1\u8fbe\u5230\u76f8\u540c\u901f\u5ea6\u65f6\uff0c\u7ba1\u4e0a\u5347\u7684\u6700\u5927\u9ad8\u5ea6\u3002 \uff083\uff09\u7ba1\u7b2c\u4e8c\u6b21\u5f39\u8d77\u540e\u7403\u4e0d\u81f4\u6ed1\u843d\uff0cL\u5e94\u6ee1\u8db3\u4ec0\u4e48\u6761\u4ef6\uff0e \uff081\uff09\u7ba1\u7b2c\u4e00\u6b21\u843d\u5730\u5f39\u8d77\u65f6\uff0c\u7ba1\u77ac\u95f4\u5411\u4e0a\u8fd0\u52a8\uff0c\u53d7\u5230\u81ea\u8eab\u91cd\u529b\u4ee5\u53ca\u6469\u64e6\u529b\uff0c\u6240\u4ee5\u7ba1\u7684\u52a0\u901f\u5ea6$a_1=\\frac{4mg+4mg}{4m}=2g$\u65b9\u5411\u5411\u4e0b\u3002\u7403\u53d7\u5230\u5411\u4e0a\u7684\u6469\u64e6\u529b\u548c\u5411\u4e0b\u7684\u91cd\u529b\uff0c\u7403\u52a0\u901f\u5ea6$a_2=\\frac{f-mg}{m}=\\frac{4mg-mg}{m}=3g$\u65b9\u5411\u5411\u4e0a\u3002 \uff082\uff09\u53d6\u7ad6\u76f4\u5411\u4e0b\u4e3a\u6b63\u65b9\u5411\uff0e\u7403\u4e0e\u7ba1\u7b2c\u4e00\u6b21\u78b0\u5730\u65f6\u901f\u5ea6$v_0=\\sqrt{2gH}$ \uff0c\u65b9\u5411\u5411\u4e0b\uff0e\u78b0\u5730\u540e\u7ba1\u7684\u901f\u5ea6$v_1=- \\sqrt{2gH}$\uff0c\u65b9\u5411\u5411\u4e0a\uff1b\u7403\u7684\u901f\u5ea6$v_2=\\sqrt{2gH}$\uff0c\u65b9\u5411\u5411\u4e0b\u82e5\u7403\u521a\u597d\u6ca1\u6709\u4ece\u7ba1\u4e2d\u6ed1\u51fa\uff0c\u8bbe\u7ecf\u8fc7\u65f6\u95f4$t_1$\uff0c\u7403\u7ba1\u901f\u5ea6v\u76f8\u540c\uff0c\u5219\u6709 $$-v_1+a_1t_1=v_2-a_2 {t_1}^2$$ $$-\\sqrt{2gH}-2gt_1=\\sqrt{2gH}+3mgt_1$$ $$2\\sqrt{2gH}=5mgt_1$$ $$t_1=\\frac{2}{5}\\sqrt{\\frac{2H}{g}}$$ \u6b64\u65f6\u7ba1\u4e0b\u7aef\u7684\u9ad8\u5ea6\u4e3a$h_1=v_0 t_1-\\frac{1}{2} {a_1} {t_1}^2$ \u5e26\u5165\u6570\u636e $$h_1=\\frac{12}{25}H$$ \u6b64\u540e\u7ba1\u548c\u7403\u5171\u901f\u4e0a\u5347$v_g=v_0-a_2 t_1=\\frac{1}{5} […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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