{"id":923,"date":"2025-07-29T10:52:59","date_gmt":"2025-07-29T02:52:59","guid":{"rendered":"https:\/\/tilearn.space\/?p=923"},"modified":"2026-03-18T19:08:58","modified_gmt":"2026-03-18T11:08:58","slug":"2024%e5%b1%8a%e5%b4%87%e6%98%8e%e5%8c%ba%e5%88%9d%e4%b8%89%e4%b8%80%e6%a8%a1%e7%89%a9%e7%90%86%e7%ac%ac18%e9%a2%98","status":"publish","type":"post","link":"https:\/\/tilearn.space\/?p=923","title":{"rendered":"2024\u5c4a\u5d07\u660e\u533a\u521d\u4e09\u4e00\u6a21\u7269\u7406\u7b2c18\u9898"},"content":{"rendered":"<style><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><br \/>\n        body {<br \/>            font-family: -apple-system, BlinkMacSystemFont, \"Segoe UI\", Roboto, \"Helvetica Neue\", Arial, \"Noto Sans\", sans-serif, \"Apple Color Emoji\", \"Segoe UI Emoji\", \"Segoe UI Symbol\", \"Noto Color Emoji\";<br \/>            line-height: 1.8;<br \/>            color: #333;<br \/>            background-color: #f9f9f9;<br \/>            padding: 20px;<br \/>        }<br \/>        .container {<br \/>            max-width: 800px;<br \/>            margin: 0 auto;<br \/>            background-color: #fff;<br \/>            padding: 25px 40px;<br \/>            border-radius: 10px;<br \/>            box-shadow: 0 4px 12px rgba(0,0,0,0.08);<br \/>        }<br \/>        .problem-statement, .solution {<br \/>            margin-bottom: 30px;<br \/>        }<br \/>        h1, h2, h3 {<br \/>            color: #0056b3;<br \/>            border-bottom: 2px solid #eef;<br \/>            padding-bottom: 10px;<br \/>        }<br \/>        h1 {<br \/>            text-align: center;<br \/>        }<br \/>        .question-image {<br \/>            display: block;<br \/>            margin: 20px auto;<br \/>            max-width: 100%;<br \/>            border: 1px solid #ddd;<br \/>            border-radius: 5px;<br \/>        }<br \/>        .answer-box {<br \/>            background-color: #e6f7ff;<br \/>            border-left: 5px solid #1890ff;<br \/>            padding: 15px;<br \/>            margin: 15px 0;<br \/>            border-radius: 5px;<br \/>        }<br \/>        .step {<br \/>            font-weight: bold;<br \/>            color: #d9534f;<br \/>        }<br \/>        .conclusion {<br \/>            font-style: italic;<br \/>            text-align: right;<br \/>            color: #555;<br \/>            margin-top: 40px;<br \/>        }<br \/>        code {<br \/>            background-color: #eee;<br \/>            padding: 2px 4px;<br \/>            border-radius: 3px;<br \/>        }<br \/>    <\/style>\n<div class=\"container\">\n<h1><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-924\" title=\"0ad8b8f364fb4850c25dad3d3238bc7d\" src=\"http:\/\/tilearn.space\/wp-content\/uploads\/2025\/07\/0ad8b8f364fb4850c25dad3d3238bc7d.png\" alt=\"0ad8b8f364fb4850c25dad3d3238bc7d\" width=\"1091\" height=\"507\" srcset=\"https:\/\/tilearn.space\/wp-content\/uploads\/2025\/07\/0ad8b8f364fb4850c25dad3d3238bc7d.png 1091w, https:\/\/tilearn.space\/wp-content\/uploads\/2025\/07\/0ad8b8f364fb4850c25dad3d3238bc7d-300x139.png 300w, https:\/\/tilearn.space\/wp-content\/uploads\/2025\/07\/0ad8b8f364fb4850c25dad3d3238bc7d-1024x476.png 1024w, https:\/\/tilearn.space\/wp-content\/uploads\/2025\/07\/0ad8b8f364fb4850c25dad3d3238bc7d-768x357.png 768w\" sizes=\"auto, (max-width: 1091px) 100vw, 1091px\" \/><\/h1>\n<div class=\"conclusion\">\n<p><!-- \u7b80\u5355\u7684 CSS \u6837\u5f0f --><\/p>\n<style>\nbody {<br \/>\nfont-family: -apple-system, BlinkMacSystemFont, \"Segoe UI\", Roboto, \"Helvetica Neue\", Arial, \"Noto Sans\", sans-serif, \"Apple Color Emoji\", \"Segoe UI Emoji\", \"Segoe UI Symbol\", \"Noto Color Emoji\";<br \/>\nline-height: 1.8;<br \/>\ncolor: #333;<br \/>\nbackground-color: #f9f9f9;<br \/>\npadding: 20px;<br \/>\n}<br \/>\n.container {<br \/>\nmax-width: 800px;<br \/>\nmargin: 0 auto;<br \/>\nbackground-color: #fff;<br \/>\npadding: 25px 40px;<br \/>\nborder-radius: 10px;<br \/>\nbox-shadow: 0 4px 12px rgba(0,0,0,0.08);<br \/>\n}<br \/>\n.problem-statement, .solution {<br \/>\nmargin-bottom: 30px;<br \/>\n}<br \/>\nh1, h2, h3 {<br \/>\ncolor: #0056b3;<br \/>\nborder-bottom: 2px solid #eef;<br \/>\npadding-bottom: 10px;<br \/>\n}<br \/>\nh1 {<br \/>\ntext-align: center;<br \/>\n}<br \/>\n.question-image {<br \/>\ndisplay: block;<br \/>\nmargin: 20px auto;<br \/>\nmax-width: 100%;<br \/>\nborder: 1px solid #ddd;<br \/>\nborder-radius: 5px;<br \/>\n}<br \/>\n.answer-box {<br \/>\nbackground-color: #e6f7ff;<br \/>\nborder-left: 5px solid #1890ff;<br \/>\npadding: 15px;<br \/>\nmargin: 15px 0;<br \/>\nborder-radius: 5px;<br \/>\n}<br \/>\n.step {<br \/>\nfont-weight: bold;<br \/>\ncolor: #d9534f;<br \/>\n}<br \/>\n.conclusion {<br \/>\nfont-style: italic;<br \/>\ntext-align: right;<br \/>\ncolor: #555;<br \/>\nmargin-top: 40px;<br \/>\n}<br \/>\ncode {<br \/>\nbackground-color: #eee;<br \/>\npadding: 2px 4px;<br \/>\nborder-radius: 3px;<br \/>\n}<br \/>\n<\/style>\n<div class=\"container\">\n<div class=\"solution\">\n<h2><\/h2>\n<p>\u54c8\u55bd\u8001\u5e08\/\u540c\u5b66\uff01\u8fd9\u9053\u7269\u7406\u9898\u6709\u70b9\u610f\u601d\u54e6\uff0c\u7279\u522b\u662f\u6700\u540e\u4e00\u95ee\uff0c\u8981\u52a8\u52a8\u8111\u7b4b\u3002\u6211\u6765\u8bd5\u8bd5\u770b\uff01<\/p>\n<h3>(1) A \u5bb9\u5668\u4e2d\u6c34\u7684\u8d28\u91cf<\/h3>\n<p>\u8fd9\u4e00\u95ee\u5f88\u7b80\u5355\u5566\uff0c\u5c31\u662f\u7528\u5bc6\u5ea6\u516c\u5f0f\u3002\u6211\u4eec\u77e5\u9053\u6c34\u7684\u5bc6\u5ea6\u662f \\(\\rho_{\\text{\u6c34}} = 1.0 \\times 10^3 \\, \\text{kg\/m}^3\\)\u3002<\/p>\n<p>\u5df2\u77e5\uff1aA \u5bb9\u5668\u4e2d\u6c34\u7684\u4f53\u79ef \\(V_{\\text{\u6c34}} = 1 \\times 10^{-3} \\, \\text{m}^3\\)<\/p>\n<p>\u6839\u636e\u5bc6\u5ea6\u516c\u5f0f \\(\\rho = \\frac{m}{V}\\)\uff0c\u53ef\u4ee5\u5f97\u5230\u8d28\u91cf\u7684\u8ba1\u7b97\u516c\u5f0f \\(m = \\rho V\\)\u3002<\/p>\n<p>\u6240\u4ee5\uff0cA \u5bb9\u5668\u4e2d\u6c34\u7684\u8d28\u91cf\uff1a<br \/>\n$$ m_{\\text{\u6c34}} = \\rho_{\\text{\u6c34}} \\times V_{\\text{\u6c34}} = (1.0 \\times 10^3 \\, \\text{kg\/m}^3) \\times (1 \\times 10^{-3} \\, \\text{m}^3) = 1 \\, \\text{kg} $$<\/p>\n<div class=\"answer-box\"><strong>\u7b54\uff1aA \u5bb9\u5668\u4e2d\u6c34\u7684\u8d28\u91cf\u4e3a 1 \u5343\u514b\u3002<\/strong><\/div>\n<h3>(2) A \u5bb9\u5668\u5bf9\u5730\u9762\u7684\u538b\u5f3a<\/h3>\n<p>\u8981\u6c42\u5bf9\u5730\u9762\u7684\u538b\u5f3a\uff0c\u5148\u8981\u6c42\u51fa\u5bf9\u5730\u9762\u7684\u603b\u538b\u529b\uff0c\u518d\u7528\u538b\u5f3a\u516c\u5f0f \\(P = \\frac{F}{S}\\)\u3002<\/p>\n<p><span class=\"step\">\u7b2c\u4e00\u6b65\uff1a\u6c42\u6c34\u7684\u91cd\u529b \\(G_{\\text{\u6c34}}\\)<\/span><br \/>\n\u6211\u4eec\u521a\u7b97\u51fa\u6c34\u7684\u8d28\u91cf \\(m_{\\text{\u6c34}} = 1 \\, \\text{kg}\\)\u3002\u53d6 \\(g = 10 \\, \\text{N\/kg}\\)\u3002<br \/>\n$$ G_{\\text{\u6c34}} = m_{\\text{\u6c34}} \\times g = 1 \\, \\text{kg} \\times 10 \\, \\text{N\/kg} = 10 \\, \\text{N} $$<\/p>\n<p><span class=\"step\">\u7b2c\u4e8c\u6b65\uff1a\u6c42\u603b\u538b\u529b F<\/span><br \/>\n\u5bb9\u5668\u653e\u5728\u6c34\u5e73\u5730\u9762\u4e0a\uff0c\u6240\u4ee5\u5bf9\u5730\u9762\u7684\u538b\u529b \\(F\\) \u7b49\u4e8e\u5bb9\u5668\u548c\u6c34\u7684\u603b\u91cd\u529b \\(G_{\\text{\u603b}}\\)\u3002<br \/>\n\u5df2\u77e5\u5bb9\u5668\u7684\u91cd\u529b \\(G_{\\text{\u5bb9}} = 2 \\, \\text{N}\\)\u3002<br \/>\n$$ F = G_{\\text{\u603b}} = G_{\\text{\u5bb9}} + G_{\\text{\u6c34}} = 2 \\, \\text{N} + 10 \\, \\text{N} = 12 \\, \\text{N} $$<\/p>\n<p><span class=\"step\">\u7b2c\u4e09\u6b65\uff1a\u6c42\u538b\u5f3a P<\/span><br \/>\n\u5df2\u77e5\u5bb9\u5668\u4e0e\u6c34\u5e73\u5730\u9762\u7684\u63a5\u89e6\u9762\u79ef \\(S = 1.18 \\times 10^{-4} \\, \\text{m}^2\\)\u3002<br \/>\n$$ P = \\frac{F}{S} = \\frac{12 \\, \\text{N}}{1.18 \\times 10^{-4} \\, \\text{m}^2} \\approx 101695 \\, \\text{Pa} \\approx 1.02 \\times 10^5 \\, \\text{Pa} $$<\/p>\n<div class=\"answer-box\"><strong>\u7b54\uff1aA \u5bb9\u5668\u5bf9\u5730\u9762\u7684\u538b\u5f3a\u7ea6\u4e3a \\(1.02 \\times 10^5\\) \u5e15\u3002<\/strong><\/div>\n<h3>(3) \u6bd4\u8f83 \\(p_A\\) \u4e0e \\(p_B\\) \u7684\u5927\u5c0f\u5173\u7cfb\u53ca\u5bf9\u5e94\u7684 \\(\\Delta h\\) \u53d6\u503c\u8303\u56f4<\/h3>\n<p>\u8fd9\u4e00\u95ee\u662f\u538b\u8f74\u9898\u5427\uff01\u6709\u70b9\u6311\u6218\u6027\u3002\u6211\u4eec\u8981\u7528\u4ee3\u6570\u7684\u65b9\u6cd5\u6765\u89e3\u3002<\/p>\n<p>\u9996\u5148\uff0c\u5217\u51fa\u5df2\u77e5\u6761\u4ef6\uff1a<\/p>\n<ul>\n<li>A \u4e2d\u6db2\u4f53\uff08\u6c34\uff09\uff1a\\(\\rho_A = 1.0 \\times 10^3 \\, \\text{kg\/m}^3\\)\uff0c\u521d\u59cb\u6df1\u5ea6 \\(h_A = 7h\\)<\/li>\n<li>B \u4e2d\u6db2\u4f53\uff1a\\(\\rho_B = 0.8 \\times 10^3 \\, \\text{kg\/m}^3\\)\uff0c\u521d\u59cb\u6df1\u5ea6 \\(h_B = 8h\\)<\/li>\n<\/ul>\n<p>\u4ece A\u3001B \u4e24\u5bb9\u5668\u4e2d\u5206\u522b\u62bd\u51fa\u9ad8\u5747\u4e3a \\(\\Delta h\\) \u7684\u6db2\u4f53\u540e\uff0c\u5269\u4f59\u6db2\u4f53\u6df1\u5ea6\u5206\u522b\u4e3a\uff1a<\/p>\n<ul>\n<li>A \u4e2d\u5269\u4f59\u6df1\u5ea6\uff1a\\(h&#8217;_A = 7h &#8211; \\Delta h\\)<\/li>\n<li>B \u4e2d\u5269\u4f59\u6df1\u5ea6\uff1a\\(h&#8217;_B = 8h &#8211; \\Delta h\\)<\/li>\n<\/ul>\n<p>\u6839\u636e\u6db2\u4f53\u538b\u5f3a\u516c\u5f0f \\(p = \\rho g h\\)\uff0c\u6b64\u65f6 A\u3001B \u5bb9\u5668\u5e95\u90e8\u7684\u538b\u5f3a\u5206\u522b\u4e3a\uff1a<br \/>\n$$ p_A = \\rho_A g (7h &#8211; \\Delta h) $$<br \/>\n$$ p_B = \\rho_B g (8h &#8211; \\Delta h) $$<\/p>\n<p>\u6ce8\u610f\uff0c\u62bd\u51fa\u7684\u9ad8\u5ea6 \\(\\Delta h\\) \u4e0d\u80fd\u8d85\u8fc7 A \u4e2d\u539f\u6765\u7684\u6db2\u4f53\u9ad8\u5ea6\uff0c\u6240\u4ee5 \\(\\Delta h\\) \u6709\u4e00\u4e2a\u57fa\u672c\u8303\u56f4\uff1a\\(0 &lt; \\Delta h \\le 7h\\)\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u5206\u4e09\u79cd\u60c5\u51b5\u6765\u8ba8\u8bba\uff1a<\/p>\n<p><span class=\"step\">\u60c5\u51b5\u4e00\uff1a\\(p_A = p_B\\)<\/span><br \/>\n$$ \\rho_A g (7h &#8211; \\Delta h) = \\rho_B g (8h &#8211; \\Delta h) $$<br \/>\n\u4e24\u8fb9\u7ea6\u53bb \\(g\\) \u548c \\(10^3\\)\uff1a<br \/>\n$$ 1.0 \\times (7h &#8211; \\Delta h) = 0.8 \\times (8h &#8211; \\Delta h) $$<br \/>\n$$ 7h &#8211; \\Delta h = 6.4h &#8211; 0.8\\Delta h $$<br \/>\n\u79fb\u9879\u5408\u5e76\u540c\u7c7b\u9879\uff1a<br \/>\n$$ 7h &#8211; 6.4h = \\Delta h &#8211; 0.8\\Delta h $$<br \/>\n$$ 0.6h = 0.2\\Delta h $$<br \/>\n$$ \\Delta h = 3h $$<br \/>\n\u8fd9\u4e2a\u503c\u5728 \\(0 &lt; \\Delta h \\le 7h\\) \u7684\u8303\u56f4\u5185\uff0c\u662f\u6709\u6548\u7684\u3002<\/p>\n<p><span class=\"step\">\u60c5\u51b5\u4e8c\uff1a\\(p_A &gt; p_B\\)<\/span><br \/>\n$$ \\rho_A g (7h &#8211; \\Delta h) &gt; \\rho_B g (8h &#8211; \\Delta h) $$<br \/>\n\u6839\u636e\u4e0a\u9762\u7684\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u4e0d\u7b49\u5f0f\u53d8\u4e3a\uff1a<br \/>\n$$ 0.6h &gt; 0.2\\Delta h $$<br \/>\n$$ \\Delta h &lt; 3h $$<br \/>\n\u7ed3\u5408\u57fa\u672c\u8303\u56f4 \\(0 &lt; \\Delta h \\le 7h\\)\uff0c\u5f97\u5230\u6b64\u60c5\u51b5\u4e0b\u7684\u53d6\u503c\u8303\u56f4\u662f \\(0 &lt; \\Delta h &lt; 3h\\)\u3002<\/p>\n<p><span class=\"step\">\u60c5\u51b5\u4e09\uff1a\\(p_A &lt; p_B\\)<\/span><br \/>\n$$ \\rho_A g (7h &#8211; \\Delta h) &lt; \\rho_B g (8h &#8211; \\Delta h) $$<br \/>\n\u540c\u6837\uff0c\u4e0d\u7b49\u5f0f\u53d8\u4e3a\uff1a<br \/>\n$$ 0.6h &lt; 0.2\\Delta h $$ $$ \\Delta h &gt; 3h $$<br \/>\n\u7ed3\u5408\u57fa\u672c\u8303\u56f4 \\(0 &lt; \\Delta h \\le 7h\\)\uff0c\u5f97\u5230\u6b64\u60c5\u51b5\u4e0b\u7684\u53d6\u503c\u8303\u56f4\u662f \\(3h &lt; \\Delta h \\le 7h\\)\u3002<\/p>\n<div class=\"answer-box\"><strong>\u7b54\uff1a\u7efc\u4e0a\u6240\u8ff0\uff0c\u6bd4\u8f83\u7ed3\u679c\u5982\u4e0b\uff1a<\/strong><\/p>\n<ul>\n<li>\u5f53 <strong>\\(0 &lt; \\Delta h &lt; 3h\\)<\/strong> \u65f6\uff0c<strong>\\(p_A &gt; p_B\\)<\/strong>\u3002<\/li>\n<li>\u5f53 <strong>\\(\\Delta h = 3h\\)<\/strong> \u65f6\uff0c<strong>\\(p_A = p_B\\)<\/strong>\u3002<\/li>\n<li>\u5f53 <strong>\\(3h &lt; \\Delta h \\le 7h\\)<\/strong> \u65f6\uff0c<strong>\\(p_A &lt; p_B\\)<\/strong>\u3002<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"conclusion\">\n<p>\u505a\u5b8c\u5566\uff01\u611f\u89c9\u81ea\u5df1\u68d2\u68d2\u54d2\uff01( \u2022\u0300 \u03c9 \u2022\u0301 )\u2727<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u54c8\u55bd\u8001\u5e08\/\u540c\u5b66\uff01\u8fd9\u9053\u7269\u7406\u9898\u6709\u70b9\u610f\u601d\u54e6\uff0c\u7279\u522b\u662f\u6700\u540e\u4e00\u95ee\uff0c\u8981\u52a8\u52a8\u8111\u7b4b\u3002\u6211\u6765\u8bd5\u8bd5\u770b\uff01 (1) A \u5bb9\u5668\u4e2d\u6c34\u7684\u8d28\u91cf \u8fd9 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[34],"tags":[],"class_list":["post-923","post","type-post","status-publish","format-standard","hentry","category-wlfnj"],"_links":{"self":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/923","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=923"}],"version-history":[{"count":4,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/923\/revisions"}],"predecessor-version":[{"id":928,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/923\/revisions\/928"}],"wp:attachment":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=923"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=923"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=923"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}