{"id":14838,"date":"2018-04-24T09:01:35","date_gmt":"2018-04-24T08:01:35","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14838"},"modified":"2022-01-10T00:27:43","modified_gmt":"2022-01-10T00:27:43","slug":"um-tijolo-sobre-a-areia","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14838","title":{"rendered":"Um tijolo sobre a areia"},"content":{"rendered":"<p><ul id='GTTabs_ul_14838' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14838' class='GTTabs_curr'><a  id=\"14838_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14838' ><a  id=\"14838_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_14838'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Quando se coloca um objeto sobre a areia, esta fica marcada devido \u00e0 press\u00e3o exercida por esse objeto.<br \/>\nA tabela seguinte relaciona a press\u00e3o, exercida por um tijolo sobre a areia, com a \u00e1rea da face do tijolo que est\u00e1 assente na areia.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14840\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14840\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1.png\" data-orig-size=\"814,117\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1.png\" class=\"aligncenter wp-image-14840\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1-300x43.png\" alt=\"\" width=\"470\" height=\"68\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1-300x43.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1-768x110.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1.png 814w\" sizes=\"auto, (max-width: 470px) 100vw, 470px\" \/><\/a><\/p>\n<p>A press\u00e3o est\u00e1 expressa em newton por metro quadrado (N\/m<sup>2<\/sup>) e a \u00e1rea em metro quadrado (m<sup>2<\/sup>).<\/p>\n<ol>\n<li>A press\u00e3o exercida pelo tijolo \u00e9 inversamente proporcional \u00e0 \u00e1rea da face que est\u00e1 assente na areia.<br \/>\nQual \u00e9 o valor da constante de proporcionalidade inversa?<br \/>\nMostra como obtiveste a tua resposta.<\/li>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14843\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14843\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1b.png\" data-orig-size=\"201,275\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Tijolo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1b.png\" class=\"alignright wp-image-14843\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1b.png\" alt=\"\" width=\"180\" height=\"246\" \/><\/a>Na figura ao lado, podes ver um tijolo. Na posi\u00e7\u00e3o em que o tijolo se encontra, a press\u00e3o que ele exerce sobre a areia \u00e9 4000 N\/m<sup>2<\/sup>.<br \/>\nA face do tijolo que est\u00e1 assente na areia \u00e9 um ret\u00e2ngulo, em que o comprimento \u00e9 igual ao dobro da largura, tal como est\u00e1 assinalado na figura.<br \/>\nDe acordo com os dados da tabela, determina a largura,\u00a0\\(l\\), desse ret\u00e2ngulo.<br \/>\nApresenta todos os c\u00e1lculos que efetuares e, na tua resposta, indica a unidade de comprimento.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14838' onClick='GTTabs_show(1,14838)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14838'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14840\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14840\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1.png\" data-orig-size=\"814,117\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Tabela\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1.png\" class=\"aligncenter wp-image-14840\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1-300x43.png\" alt=\"\" width=\"470\" height=\"68\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1-300x43.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1-768x110.png 768w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1.png 814w\" sizes=\"auto, (max-width: 470px) 100vw, 470px\" \/><\/a><\/p>\n<ol>\n<li>A constante de proporcionalidade \u00e9 \\(k = 0,005 \\times 4000 = 0,01 \\times 2000 = 0,02 \\times 1000 = 20\\) (N).<br \/>\n\u00ad<\/li>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14843\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14843\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1b.png\" data-orig-size=\"201,275\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Tijolo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1b.png\" class=\"alignright wp-image-14843\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1b.png\" alt=\"\" width=\"180\" height=\"246\" \/><\/a>Comecemos por determinar\u00a0a \u00e1rea (<em>a<\/em>) da face do tijolo que est\u00e1 assente na areia:\\[\\begin{array}{*{20}{l}}{0,02 \\times 1000 = a \\times 4000}&amp; \\Leftrightarrow &amp;{a = \\frac{{0,02 \\times 1000}}{{4000}}}\\\\{}&amp; \\Leftrightarrow &amp;{a = 0,005}\\end{array}\\]Determinemos, agora, o valor de \\(l\\):\\[\\begin{array}{*{20}{l}}{a = 0,005}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{l \\times 2l = 0,005}&amp; \\wedge &amp;{l &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{\\begin{array}{*{20}{c}}{{l^2} = 0,0025}&amp; \\wedge &amp;{l &gt; 0}\\end{array}}\\\\{}&amp; \\Leftrightarrow &amp;{l = \\sqrt {0,0025} }\\\\{}&amp; \\Leftrightarrow &amp;{l = 0,05}\\end{array}\\]Portanto, a largura desse ret\u00e2ngulo \u00e9 0,05 metros.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14838' onClick='GTTabs_show(0,14838)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Quando se coloca um objeto sobre a areia, esta fica marcada devido \u00e0 press\u00e3o exercida por esse objeto. A tabela seguinte relaciona a press\u00e3o, exercida por um tijolo sobre a areia,&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14845,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[213,97,249],"tags":[426,250],"series":[],"class_list":["post-14838","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-proporcionalidade-inversa-e-funcoes-algebricas","tag-9-o-ano","tag-proporcionalidade-inversa-2"],"views":3566,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag124-1a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14838","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14838"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14838\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14845"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14838"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14838"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14838"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}