{"id":7344,"date":"2012-01-19T21:48:39","date_gmt":"2012-01-19T21:48:39","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7344"},"modified":"2022-01-30T16:23:14","modified_gmt":"2022-01-30T16:23:14","slug":"a-magnitude-de-um-sismo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7344","title":{"rendered":"A magnitude de um sismo"},"content":{"rendered":"<p><ul id='GTTabs_ul_7344' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7344' class='GTTabs_curr'><a  id=\"7344_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7344' ><a  id=\"7344_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_7344'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A magnitude $M$ de um sismo registada na escala de Richter est\u00e1 relacionada com a energia total $E$, em Joule, libertada por esse sismo pela f\u00f3rmula: $$M=0,694\\log E-3,64$$<\/p>\n<ol>\n<li>Exprima $E$ em fun\u00e7\u00e3o de $M$.<\/li>\n<li>Verifique se \u00e9 verdadeira a afirma\u00e7\u00e3o:<br \/>\n&#8220;<em>Um sismo de magnitude 6 liberta, aproximadamente, 28 vezes mais energia do que um sismo de magnitude 5<\/em>.&#8221;<\/li>\n<li>Por volta das 8 horas do dia 26 de Dezembro de 2004, um sismo de magnitude 9 graus foi registado na ilha de Sumatra, na costa da Indon\u00e9sia. Provocou uma calamidade natural de grandes propor\u00e7\u00f5es e causou a morte de mais de 150 mil pessoas.<br \/>\nQual a quantidade de energia que libertou?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7344' onClick='GTTabs_show(1,7344)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7344'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote><p>A magnitude $M$ de um sismo registada na escala de Richter est\u00e1 relacionada com a energia total $E$, em Joule, libertada por esse sismo pela f\u00f3rmula: $$M=0,694\\log E-3,64$$<\/p><\/blockquote>\n<p>\u00ad<\/p>\n<ol>\n<li>Ora, \\[\\begin{array}{*{35}{l}}<br \/>\nM=0,694\\log E-3,64 &amp; \\Leftrightarrow\u00a0 &amp; 0,694\\log E=M+3,64\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\log E=\\frac{M+3,64}{0,694}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; E={{10}^{\\frac{M+3,64}{0,694}}}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nLogo, $E={{10}^{\\frac{M+3,64}{0,694}}}$.<br \/>\n\u00ad<\/li>\n<li>Ora, $$\\begin{array}{*{35}{l}}<br \/>\n\\frac{E(6)}{E(5)} &amp; = &amp; \\frac{{{10}^{\\frac{6+3,64}{0,694}}}}{{{10}^{\\frac{5+3,64}{0,694}}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; {{10}^{\\frac{6+3,64}{0,694}-\\frac{5+3,64}{0,694}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; {{10}^{\\frac{1}{0,694}}}\u00a0 \\\\<br \/>\n{} &amp; \\approx\u00a0 &amp; 27,6\u00a0 \\\\<br \/>\n\\end{array}$$<br \/>\nPortanto, a afirma\u00e7\u00e3o \u00e9 verdadeira.<br \/>\n\u00ad<\/li>\n<li>A energia libertada por esse sismo foi de $E(9)={{10}^{\\frac{9+3,64}{0,694}}}\\approx 1,6\\times {{10}^{18}}$ Joule, aproximadamente.<br \/>\n\u00ad<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/p39OcNltTog\" width=\"640\" height=\"360\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7344' onClick='GTTabs_show(0,7344)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A magnitude $M$ de um sismo registada na escala de Richter est\u00e1 relacionada com a energia total $E$, em Joule, libertada por esse sismo pela f\u00f3rmula: $$M=0,694\\log E-3,64$$ Exprima $E$ em&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21123,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,267],"tags":[427,275],"series":[],"class_list":["post-7344","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-funcoes-exponenciais-e-logaritmicas","tag-12-o-ano","tag-funcao-logaritmica"],"views":2697,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2012\/01\/12V2Pag203-11_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7344","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=7344"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7344\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21123"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7344"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7344"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7344"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}