{"id":233616,"date":"2025-06-13T09:04:37","date_gmt":"2025-06-13T09:04:37","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233616"},"modified":"2025-06-13T09:04:40","modified_gmt":"2025-06-13T09:04:40","slug":"liquid-displaced-fb-plvg-where-fb-is-the-buoyant-force-pl-is-the-density-of-the-liquid-not-the-density-of-the-submerged-object-and-v-is-the-volume-of-the-liquid-displaced","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/liquid-displaced-fb-plvg-where-fb-is-the-buoyant-force-pl-is-the-density-of-the-liquid-not-the-density-of-the-submerged-object-and-v-is-the-volume-of-the-liquid-displaced\/","title":{"rendered":"liquid displaced: FB = PLVg, where FB is the buoyant force, PL is the density of the liquid (not the density of the submerged object!), and V is the volume of the liquid displaced"},"content":{"rendered":"\n<p>liquid displaced: FB = PLVg, where FB is the buoyant force, PL is the density of the liquid (not the density of the submerged object!), and V is the volume of the liquid displaced. Since (PLV) is the mass of the displaced liquid, then (PLVg) is the weight of the displaced liquid. A wooden cube with a side of 10 cm is floating on the surface of the water. The density of wood is 0.75 g\/cm3 and the density of water is 1 g\/cm3. Is the cube floating completely submerged in water or only partially? If only partially, what percentage of the volume is submerged? (Draw a free body diagram of the block) If a cube of unknown material sinks completely and falls to the bottom of the water, draw a free body diagram. Can we find out the density of the block from only knowing that it sinks?<br>Archimedes&#8217; Principle: The buoyant force on a submerged object is equal to the weight of the volume of the liquid displaced: FB = PLVg, where FB is the buoyant force, PL is the density of the liquid (not the density of the submerged object!), and V is the volume of the liquid displaced. Since (PLV) is the mass of the displaced liquid, then (PLVg) is the weight of the displaced liquid. A wooden cube with a side of 10 cm is floating on the surface of the water. The density of wood is 0.75 g\/cm3 and the density of water is 1 g\/cm3. Is the cube floating completely submerged in water or only partially? If only partially, what percentage of the volume is submerged? (Draw a free body diagram of the block) If a cube of unknown material sinks completely and falls to the bottom of the water, draw a free body diagram. Can we find out the density of the block from only knowing that it sinks?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer:<\/h3>\n\n\n\n<p><strong>1. Wooden Cube:<\/strong><\/p>\n\n\n\n<p>The cube is <strong>only partially submerged<\/strong> in water.<\/p>\n\n\n\n<p>To find the <strong>percentage of volume submerged<\/strong>, use Archimedes\u2019 Principle:Fraction&nbsp;Submerged=Density&nbsp;of&nbsp;ObjectDensity&nbsp;of&nbsp;Liquid=0.751=0.75\\text{Fraction Submerged} = \\frac{\\text{Density of Object}}{\\text{Density of Liquid}} = \\frac{0.75}{1} = 0.75Fraction&nbsp;Submerged=Density&nbsp;of&nbsp;LiquidDensity&nbsp;of&nbsp;Object\u200b=10.75\u200b=0.75<\/p>\n\n\n\n<p>So, <strong>75% of the cube\u2019s volume is submerged<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>2. Free Body Diagram (Floating Cube):<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Upward Force (Buoyant Force, FB)<\/strong>: Acts upward and equals the weight of the displaced water.<\/li>\n\n\n\n<li><strong>Downward Force (Weight of the Cube, W)<\/strong>: Acts downward due to the mass of the cube.<\/li>\n<\/ul>\n\n\n\n<p>Since the cube is floating at equilibrium:FB=WFB = WFB=W<\/p>\n\n\n\n<p>This means the buoyant force balances the weight of the cube. Only part of the cube\u2019s volume displaces water to create that force.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>3. Cube of Unknown Material That Sinks:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Free Body Diagram:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Upward Force (Buoyant Force, FB)<\/strong>: Due to the displaced water, but <strong>less than the weight<\/strong> of the object.<\/li>\n\n\n\n<li><strong>Downward Force (Weight, W)<\/strong>: Greater than FB, causing the cube to sink.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>4. Can We Determine the Density of the Sunken Cube?<\/strong><\/p>\n\n\n\n<p>No, <strong>we cannot determine the exact density<\/strong> of the cube just by knowing that it sinks.<\/p>\n\n\n\n<p>We only know:Density&nbsp;of&nbsp;Object&gt;Density&nbsp;of&nbsp;Water(1\u2009g\/cm3)\\text{Density of Object} &gt; \\text{Density of Water} (1 \\, \\text{g\/cm}^3)Density&nbsp;of&nbsp;Object&gt;Density&nbsp;of&nbsp;Water(1g\/cm3)<\/p>\n\n\n\n<p>To find the exact density, more information is needed, such as the weight of the object or the volume of water displaced <strong>before<\/strong> it touches the bottom (if it reaches equilibrium while sinking slowly).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>wooden cube floats partially<\/strong>, with <strong>75% submerged<\/strong>.<\/li>\n\n\n\n<li>The <strong>sinking cube<\/strong> has a <strong>density greater than 1 g\/cm\u00b3<\/strong>, but the exact density cannot be determined without additional data.<\/li>\n\n\n\n<li>These conclusions follow from <strong>Archimedes&#8217; Principle<\/strong>, which relates buoyant force to the weight of the displaced fluid.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-284.jpeg\" alt=\"\" class=\"wp-image-233617\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>liquid displaced: FB = PLVg, where FB is the buoyant force, PL is the density of the liquid (not the density of the submerged object!), and V is the volume of the liquid displaced. Since (PLV) is the mass of the displaced liquid, then (PLVg) is the weight of the displaced liquid. A wooden cube [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233616","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233616","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233616"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233616\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233616"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233616"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}