{"id":3540,"date":"2012-09-12T16:00:30","date_gmt":"2012-09-12T19:00:30","guid":{"rendered":"http:\/\/scienceblogs.com.br\/hypercubic\/?p=3540"},"modified":"2012-09-12T16:00:30","modified_gmt":"2012-09-12T19:00:30","slug":"verme-elstico","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/09\/verme-elstico\/","title":{"rendered":"O Verme no El\u00e1stico"},"content":{"rendered":"<p align=\"justify\"><img decoding=\"async\" src=\"http:\/\/scienceblogs.com.br\/hypercubic\/files\/2012\/09\/rubber-bands-021.jpg\" alt=\"\" \/><\/p>\n<p align=\"justify\">Um verme rasteja lentamente sobre um el\u00e1stico cujo comprimento aumenta, pois \u00e9 constantemente esticado (<a title=\"[Enigma] O Verme no El\u00e1stico\" href=\"http:\/\/scienceblogs.com.br\/hypercubic\/2012\/09\/enigma-verme-elstico\/\">vide as condi\u00e7\u00f5es<\/a>). Ser\u00e1 que, mesmo assim, ele consegue chegar ao fim do el\u00e1stico?<\/p>\n<p align=\"justify\">Foi um dos enigmas mais populares por aqui \u2014 15 coment\u00e1rios no momento em que escrevo \u2014 e tamb\u00e9m um dos mais ~pol\u00eamicos~.<!--more--><\/p>\n<p align=\"justify\">Inicialmente, tive que intervir e esclarecer algumas d\u00favidas: O verme \u00e9 um <em>highlander<\/em>? Sim, \u00e9. Mas o <strong>rafinha.bianchin<\/strong> me lembrou que uma M\u00e1quina de Carnot seria mais apropriada como mecanismo esticador. Tanto o rafinha quanto o <a href=\"http:\/\/scienceblogs.com.br\/uoleo\"><strong>Igor Santos<\/strong><\/a> apresentaram quest\u00f5es interessantes: e se o el\u00e1stico fosse uma fita de Mo\u00ebbius? E seria esse um experimento mental para imaginar a infla\u00e7\u00e3o c\u00f3smica?<\/p>\n<p align=\"justify\">Apesar dos pesares, esperto mesmo foi o <strong>girino<\/strong>. Mesmo que tenha apelado para o <a href=\"http:\/\/www.wolframalpha.com\/\"><em>Wolfram Alpha<\/em><\/a> e s\u00f3 tenha achado a equa\u00e7\u00e3o certa na terceira tentativa, quem acertou foi ele! Agora, vamos \u00e0 nossa solu\u00e7\u00e3o:<\/p>\n<p align=\"justify\"><em>Yes, he can!<\/em><\/p>\n<p align=\"justify\">\u00c9 preciso ter paci\u00eancia, por\u00e9m. Ao fim do primeiro minuto nosso vermezinho arrastou-se por <span style=\"font-family: Georgia\"><strong>1\/100<\/strong><\/span> do comprimento do el\u00e1stico. Ao t\u00e9rmino do segundo minuto, a dist\u00e2ncia que percorreu \u00e9 igual a <strong><span style=\"font-family: Georgia\">(1\/100 + 1\/200)<\/span><\/strong> do comprimento. Assim, ele alcan\u00e7ar\u00e1 a outra extremidade em <strong><em><span style=\"font-family: Georgia\">t<\/span><\/em><\/strong> minutos, quando <span style=\"font-family: Georgia\"><strong>1\/100 (1\/1 + 1\/2 + 1\/3 + \u2026 + 1\/<em>t<\/em>)<\/strong><\/span> for igual ou maior que <span style=\"font-family: Georgia\"><strong>1<\/strong>.<\/span><\/p>\n<p align=\"justify\">A express\u00e3o entre par\u00eanteses \u00e9 uma s\u00e9rie harm\u00f4nica e, como nosso el\u00e1stico ideal, pode ser t\u00e3o longa quanto desejarmos. No nosso exemplo, o verme alcan\u00e7ar\u00e1 sua meta em<\/p>\n<p align=\"center\"><span style=\"font-family: Georgia\"><strong><span style=\"font-size: large\"><em>t<\/em> = 1.509269 \u00d7 10^<span style=\"font-family: Georgia\"><strong><span style=\"font-size: large\">43<\/span><\/strong><\/span> minutos<\/span><\/strong><\/span><\/p>\n<p align=\"justify\">Ou cerca de <span style=\"font-family: Georgia;font-size: medium\"><strong>286.961.000.000.000.000.000.000.000.000.000.000<\/strong><\/span> de s\u00e9culos!<\/p>\n<p align=\"justify\">Eu disse que seria necess\u00e1rio ter paci\u00eancia.<\/p>\n<p align=\"justify\">Como bem notou o <a href=\"http:\/\/scienceblogs.com.br\/cognando\/\"><strong>Andr\u00e9 Souza<\/strong><\/a>: &#8220;Se seu c\u00e1lculo estiver correto, a solu\u00e7\u00e3o seria o verme colapsar em si mesmo, formando uma singularidade e contrabalan\u00e7ando o esticamento enquanto se move\u2026&#8221; E, sim, isso s\u00f3 \u00e9 poss\u00edvel por se tratar de um experimento mental.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Um verme rasteja lentamente sobre um el\u00e1stico cujo comprimento aumenta, pois \u00e9 constantemente esticado (vide as condi\u00e7\u00f5es). Ser\u00e1 que, mesmo assim, ele consegue chegar ao fim do el\u00e1stico? Foi um dos enigmas mais populares por aqui \u2014 15 coment\u00e1rios no momento em que escrevo \u2014 e tamb\u00e9m um dos mais ~pol\u00eamicos~.<\/p>\n","protected":false},"author":486,"featured_media":3542,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"material-hide-sections":[],"pgc_sgb_lightbox_settings":"","_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"categories":[152],"tags":[],"class_list":["post-3540","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-geral"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>O Verme no El\u00e1stico - hypercubic<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.blogs.unicamp.br\/hypercubic\/2012\/09\/verme-elstico\/\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Renato Pincelli\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/09\\\/verme-elstico\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/09\\\/verme-elstico\\\/\"},\"author\":{\"name\":\"Renato Pincelli\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/person\\\/c7be1e2811d061a75d3b4f4960eb53bd\"},\"headline\":\"O Verme no El\u00e1stico\",\"datePublished\":\"2012-09-12T19:00:30+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/09\\\/verme-elstico\\\/\"},\"wordCount\":313,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/09\\\/verme-elstico\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/wp-content\\\/uploads\\\/sites\\\/249\\\/2012\\\/09\\\/rubber-bands-021.jpg\",\"articleSection\":[\"Geral\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/09\\\/verme-elstico\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/09\\\/verme-elstico\\\/\",\"url\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2012\\\/09\\\/verme-elstico\\\/\",\"name\":\"O Verme no El\u00e1stico - 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