{"id":34608,"date":"2021-03-31T13:00:46","date_gmt":"2021-03-31T13:00:46","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34608"},"modified":"2025-09-19T10:24:13","modified_gmt":"2025-09-19T10:24:13","slug":"de-flotabilitate-et-principio-archimedis","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/de-flotabilitate-et-principio-archimedis\/","title":{"rendered":"De Flotabilitate et Principio Archimedis"},"content":{"rendered":"<p><center><\/p>\n<h1>De Flotabilitate et Principio Archimedis<\/h1>\n<p><em><strong>Summarium:<\/strong><br \/>\nHaec lectio explanabit phaenomenon Flotabilitatis et Principium Archimedis, ostendens quomodo corpora in fluido immersa experiantur vim sustinentem aequalem ponderi fluidi expulsi. Hoc principio utimur ad portionem obiecti supra fluidum eminentem computandam, exemplis practicis illustratis.<br \/>\n    <\/em><\/p>\n<p>    <strong>Proposita Discendi<\/strong><br \/>\n    Post hanc lectionem discipulus poterit<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>Intelligere<\/strong> principium Archimedis eiusque relationem cum flotabilitate.<\/li>\n<li><strong>Computare<\/strong> vim sustinentem in corporibus in fluido immersis.<\/li>\n<li><strong>Determinare<\/strong> quam portionem obiecti flottantis supra fluidum emergat, secundum densitatem relativam.<\/li>\n<\/ol>\n<p><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/nikSJceTxJ0\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<h2>Vis Sustinentis<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=nikSJceTxJ0&amp;t=126s\" target=\"_blank\" rel=\"noopener\"><strong>Cum de flotabilitate loquimur,<\/strong><\/a> primum cogitamus corpora levius ponderare cum in fluido immersa sunt. Exempli gratia, saxum quod sub aqua cum difficultate attolli posset, extra eam fere impossibile moveri esset. Hoc phaenomenon explicatur per apparentiam vis quae vocatur vis sustinens.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=nikSJceTxJ0&amp;t=207s\" target=\"_blank\" rel=\"noopener\"><strong>Cum obiectum in fluido immergitur,<\/strong><\/a> apparet vis sustinens sursum directa, aequalis ponderi liquidi a corpore immerso expulsi. Propter hoc, omnia corpora in fluido immersa partem ponderis sui amittere videntur, cum sit differentia virium inter diversas regiones corporis secundum altitudinem. Ita vis sustinens erit:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F_{emp} = F_2 - F_1<\/span>\n<p>    <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/fuerza-de-empuje.jpg\" alt=\"fuerza de empuje\" width=\"293\" height=\"502\" class=\"aligncenter size-full wp-image-29232 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/fuerza-de-empuje.jpg\" alt=\"fuerza de empuje\" width=\"293\" height=\"502\" class=\"aligncenter size-full wp-image-29232 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/fuerza-de-empuje.jpg 293w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/fuerza-de-empuje-175x300.jpg 175w\" sizes=\"(max-width: 293px) 100vw, 293px\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">Cum <span class=\"katex-eq\" data-katex-display=\"false\">P=F\/A<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">P=\\rho g h<\/span>, possumus inferre <span class=\"katex-eq\" data-katex-display=\"false\">F=\\rho g A h<\/span>, ubi <span class=\"katex-eq\" data-katex-display=\"false\">\\rho<\/span> est densitas fluidi, <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> profunditas, <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> area superficiei ubi pressio applicatur, et <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> acceleratio gravitatis. His positis, vires in facies superiorem et inferiorem exercitae sunt:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F_1 = \\rho g A h_1<\/span>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F_2 = \\rho g A h_2<\/span>\n<p style=\"text-align: justify;\">Quare habetur:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n    \\begin{array}{rl}\n\n     F_{\\text{empuje}} &amp;= \\rho g A h_2 - \\rho g A h_1 \\\\ \\\\\n\n    &amp;=\\rho g A \\underbrace{h_2 - h_1}_{\\Delta h} \\\\ \\\\\n\n    &amp;= \\rho gV \\\\ \\\\\n\n    &amp; = Pondus voluminis liquidi expulsi\n\n    \\end{array}\n\n    <\/span>\n<p style=\"text-align: justify;\">Hoc est quod vocatur principium Archimedis.<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #008000;\">EXEMPLUM:<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=nikSJceTxJ0&amp;t=482s\" target=\"_blank\" rel=\"noopener\"><strong>Saxum 70[kg] in fundo lacus iacet.<\/strong><\/a> Si volumen eius est <span class=\"katex-eq\" data-katex-display=\"false\">3\\cdot 10^4 [cm^3]<\/span>, quanta vis requiritur ut levetur?<\/p>\n<p style=\"text-align: justify;\">SOLUTIO:<\/p>\n<p style=\"text-align: justify;\">Vis sustinens super saxum dabitur per:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n    \\begin{array}{rl}\n\n    F_{\\text{empuje}} &amp;= \\rho_{\\text{agua}} g V_{roca} \\\\ \\\\\n\n    &amp;= 10^3 \\left[\\dfrac{kg}{m^3}\\right] \\cdot 9,81\\left[\\dfrac{m}{s^2}\\right] \\cdot 3 \\cdot 10^4 [cm^3] \\\\ \\\\\n\n    &amp;= 10^3 \\left[\\dfrac{kg}{m^3}\\right] \\cdot 9,81\\left[\\dfrac{m}{s^2}\\right] \\cdot 3 \\cdot 10^4 \\left[\\dfrac{m}{100}\\right]^3 = 294[N]\n    \\end{array}\n\n    <\/span>\n<p style=\"text-align: justify;\">Dum vis ponderis saxi est:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">F_{\\text{peso}} = m_{\\text{roca}}g = 70[kg] \\cdot 9.81 \\left[\\dfrac{m}{s^2}\\right]=686[N]<\/span>\n<p style=\"text-align: justify;\">Itaque, ut saxum sub aqua levetur, sufficiet vi <span class=\"katex-eq\" data-katex-display=\"false\">F = 686[N] - 294[N] = 392[N]<\/span>. Sub aqua, hoc saxum fere dimidia vi levare potes quam extra eam opus esset.<\/p>\n<h2>De Flotabilitate et Principio Archimedis<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=nikSJceTxJ0&amp;t=858s\" target=\"_blank\" rel=\"noopener\"><strong>Principium Archimedis nos adiuvat intellegere cur quaedam corpora fluitent<\/strong><\/a> cum in quibusdam fluidis immerguntur. Exempli gratia, lignum in aqua. Generaliter, obiectum in fluido fluitabit si densitas medii maior est quam illa obiecti, et fluitabit donec supra superficiem emineat. Corpus se attollet donec ad statum aequilibrii perveniat. Quomodo computare possumus portionem corporis quae supra fluidum emergit? Facile est computare.<\/p>\n<p>    <img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/flotabilidad.jpg\" alt=\"La Flotabilidad y el Principio de Arqu\u00edmides\" width=\"543\" height=\"341\" class=\"aligncenter size-full wp-image-29234 lazyload\" \/><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/flotabilidad.jpg\" alt=\"La Flotabilidad y el Principio de Arqu\u00edmides\" width=\"543\" height=\"341\" class=\"aligncenter size-full wp-image-29234 lazyload\" srcset=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/flotabilidad.jpg 543w, http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/flotabilidad-300x188.jpg 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">Si aequamus vim ponderis cum vi sustinente, possumus computare quam portionem corporis supra superficiem exiet. Ratio talis est:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n     &amp; F_{\\text{peso}} = F_{\\text{empuje}}\\\\ \\\\\n\n    \\equiv &amp; m_{\\text{objeto}} g = m_{\\text{sumergido}} g \\\\ \\\\\n\n    \\equiv &amp; \\rho_{\\text{objeto}}V_{\\text{objeto}} g = \\rho_{\\text{sumergido}} V_{\\text{sumergido}}  g \\\\ \\\\\n\n    \\equiv &amp; \\dfrac{\\rho_{\\text{objeto}}}{\\rho_{\\text{sumergido}}} = \\dfrac{V_{\\text{sumergido}}}{V_{\\text{objeto}} } = Procentatio corporis immersi\n\n    \\end{array}<\/span>\n<p style=\"text-align: justify;\"><span style=\"color: #008000;\">EXEMPLUM:<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=nikSJceTxJ0&amp;t=1023s\" target=\"_blank\" rel=\"noopener\"><strong>Modellum simplex continens tamquam massa solida saxi supponit<\/strong><\/a> (cum densitate <span class=\"katex-eq\" data-katex-display=\"false\">=2800[kg\/m^3]<\/span>) quae super mantum terrae circumiectum fluitat (cum densitate <span class=\"katex-eq\" data-katex-display=\"false\">=3300[kg\/m^3]<\/span>). Supponentes continentem habere crassitudinem mediocris 35[km], calcula altitudinem mediam quae supra mantum eminere potest.<\/p>\n<p style=\"text-align: justify;\">SOLUTIO:<\/p>\n<p style=\"text-align: justify;\">Procentatio corporis immersi erit:<\/p>\n<p style=\"text-align: justify;\">Procentatio immersi <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle = \\frac{\\rho_{cuerpo}}{\\rho_{fluido}}<\/span>\n<p style=\"text-align: justify;\">Itaque, procentatio corporis quae non est immersa et quae supra mantum eminet erit:<\/p>\n<p style=\"text-align: justify;\">Procentatio quae eminet <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle = 1 - \\frac{\\rho_{cuerpo}}{\\rho_{fluido}} = 1 - \\frac{2800}{3300} \\approx 0,15 = 15\\%<\/span>\n<p style=\"text-align: justify;\">Cum crassitudo mediocris sit <span class=\"katex-eq\" data-katex-display=\"false\">35[km]<\/span>, quod eminere in mediocris erit <span class=\"katex-eq\" data-katex-display=\"false\">15\\% 35[km]\\approx 5,3 [km].<\/span>\n","protected":false},"excerpt":{"rendered":"<p>De Flotabilitate et Principio Archimedis Summarium: Haec lectio explanabit phaenomenon Flotabilitatis et Principium Archimedis, ostendens quomodo corpora in fluido immersa experiantur vim sustinentem aequalem ponderi fluidi expulsi. Hoc principio utimur ad portionem obiecti supra fluidum eminentem computandam, exemplis practicis illustratis. Proposita Discendi Post hanc lectionem discipulus poterit Intelligere principium Archimedis eiusque relationem cum flotabilitate. Computare [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29250,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":9,"footnotes":""},"categories":[1274,1250],"tags":[],"class_list":["post-34608","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanica-fluidorum","category-physica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>De Flotabilitate et Principio Archimedis - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Disce quomodo Flotabilitas et Principium Archimedis explicent cur corpora fluitent aut demergant. Disce vim sustinentem computare exemplis practicis quae te mirari facient. 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