{"id":4799,"date":"2013-01-11T22:00:35","date_gmt":"2013-01-12T01:00:35","guid":{"rendered":"http:\/\/scienceblogs.com.br\/hypercubic\/?p=4799"},"modified":"2013-01-11T22:00:35","modified_gmt":"2013-01-12T01:00:35","slug":"estudo-noturno","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/hypercubic\/2013\/01\/estudo-noturno\/","title":{"rendered":"Estudo Noturno"},"content":{"rendered":"

\"Late_Night_Study____by_Pagina7Lipsa\"<\/a>O problema das l\u00e2mpadas dos dois estudantes<\/a> deve ter confundido bastante nossos leitores. Dos 11 coment\u00e1rios, poucos se aventuraram a tentar resolver o enigma. Ser\u00e1 que houve uma m\u00e1 adapta\u00e7\u00e3o do enunciado da minha parte ou falta de aten\u00e7\u00e3o dos leitores? Provavelmente, as duas coisas. Por isso, desta vez, vamos come\u00e7ar pela solu\u00e7\u00e3o “oficial”.<\/p>\n

Solu\u00e7\u00e3o oficial<\/h3>\n
\n

Para fins quantitativos, podemos supor que a resist\u00eancia das l\u00e2mpadas n\u00e3o depende das voltagens usadas. Isso est\u00e1 longe de ser preciso, mas d\u00e1 uma conclus\u00e3o qualitativamente correta. Se a voltagem da fonte \u00e9 V<\/strong>, a resist\u00eancia ri<\/sub><\/strong> de uma l\u00e2mpada \u00e9 V\u00b2\/wi<\/sub><\/strong>, onde wi<\/sub><\/strong> \u00e9 o valor nominal da l\u00e2mpada (sendo o \u00edndice i = A ou B<\/strong>). Quando as duas l\u00e2mpadas s\u00e3o conectadas em s\u00e9rie ao longo da fonte, a corrente usada ser\u00e1 V\/(rA<\/sub> + rB<\/sub>)<\/strong> e a pot\u00eancia dissipada na l\u00e2mpada i<\/strong>\u00a0 \u00e9<\/p>\n

\"image\"<\/a><\/p>\n

Assim, segundo o acordo original (wA = wB = 100 W<\/strong>), tanto PA<\/sub><\/strong> quanto PB<\/sub><\/strong> deveria ser igual a 25 W<\/strong>. Na realidade, por\u00e9m \u2014 como A<\/strong> usou uma l\u00e2mpada de 200 W<\/strong> e B<\/strong>, uma de 50 W<\/strong> \u2014, temos que PA<\/sub> = 8 W<\/strong> e PB<\/sub> = 32 W<\/strong>.<\/p>\n

Claramente, foi A,<\/strong> com seus 8 W<\/strong> de luz, quem falhou nos exames por falta de luz para estudar. Por compara\u00e7\u00e3o, B<\/strong> deveria ser considerado duplamente vencedor: ele recebe 32 W<\/strong>, mas paga por apenas (8 + 32)\/2 = 20 W<\/strong>. Por outro lado, uma ilumina\u00e7\u00e3o de 32 W<\/strong> d\u00e1 uma luz bastante pobre, de modo que B<\/strong> tamb\u00e9m pode ter falhado em seus exames.<\/p>\n<\/blockquote>\n

Na pr\u00e1tica, portanto, ningu\u00e9m se deu bem. Tanto o problema quanto a solu\u00e7\u00e3o foram extraidos do livro 200 Puzzling Physics Problems<\/em> (Peter Gn\u00e4dig et. al., Cambridge University Press, 2001).<\/p>\n

Agora, a discuss\u00e3o dos coment\u00e1rios.<\/p>\n

Solu\u00e7\u00f5es dos Leitores<\/h3>\n

O Felipe<\/a> lan\u00e7ou uma quest\u00e3o interessante, mas que aparentemente n\u00e3o deve ter sido considerada relevante pelos autores do problema:<\/p>\n

Ligaram as lampadas em s\u00e9rie? E o interruptor?<\/p>\n

Aquele que controla o interruptor se deu bem pois determina o hor\u00e1rio de ligar e desligar a luz.<\/p><\/blockquote>\n

O rafinha.bianchin<\/a> tentou pedir mais tempo e arriscou um bom racioc\u00ednio, ainda que n\u00e3o seja inteiramente correto:<\/p>\n

Presumo que as l\u00e2mpadas tenham sido dispostas em s\u00e9rie com a de 200W primeiro e depois a de 50W. N\u00e3o sei se isso faz muita diferen\u00e7a, mas vou deixar isso fixado.
\nAcredito que, ap\u00f3s uma consider\u00e1vel queda de potencial ap\u00f3s a corrente passar pela primeira l\u00e2mpada (resist\u00eancia proporcional a 1\/200), a segunda l\u00e2mpada (resist\u00eancia proporcional a 1\/50) ter\u00e1 menos \u201cluminisc\u00eancia\u201d.
\nPor outro lado, como a segunda l\u00e2mpada tem resist\u00eancia menor, por ela passar\u00e1 mais corrente.
\nMas, j\u00e1 que est\u00e3o ligadas em s\u00e9rie (que dois idiotas!), as duas hip\u00f3teses s\u00e3o teoricamente poss\u00edveis, sem falar em valores.
\nLogicamente, por\u00e9m, prefiro a primeira.<\/p><\/blockquote>\n

Por fim, embora sem acertar, o Nilton<\/a> foi o comentarista mais simples e direto:<\/p>\n

O estudante B, pois por sua l\u00e2mpada possuir menor pot\u00eancia, a do outro consume [sic] mais energia do circuito em s\u00e9rie a ponto de enfraquecer a luminesc\u00eancia de B.<\/p><\/blockquote>\n

A s\u00e9rie de enigmas retorna dentro de dez dias. Quem quiser contribuir com um problema pode entrar em contato conosco via inbox no Facebook<\/a> ou por coment\u00e1rio privado nesta postagem. As \u00fanica condi\u00e7\u00f5es que exijo \u00e9 que (1) o problema sugerido venha acompanhado da respectiva solu\u00e7\u00e3o e que (2) o colaborador n\u00e3o participe do desafio.<\/p>\n","protected":false},"excerpt":{"rendered":"

O problema das l\u00e2mpadas dos dois estudantes deve ter confundido bastante nossos leitores. Dos 11 coment\u00e1rios, poucos se aventuraram a tentar resolver o enigma. Ser\u00e1 que houve uma m\u00e1 adapta\u00e7\u00e3o do enunciado da minha parte ou falta de aten\u00e7\u00e3o dos leitores? Provavelmente, as duas coisas. Por isso, desta vez, vamos come\u00e7ar pela solu\u00e7\u00e3o “oficial”.<\/p>\n","protected":false},"author":486,"featured_media":4788,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_monsterinsights_skip_tracking":false,"material-hide-sections":[],"pgc_sgb_lightbox_settings":"","_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"categories":[152],"tags":[],"class_list":["post-4799","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-geral"],"yoast_head":"\nEstudo Noturno - 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\/2013\/01\/estudo-noturno\/\" \/>\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=\"3 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\\\/2013\\\/01\\\/estudo-noturno\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2013\\\/01\\\/estudo-noturno\\\/\"},\"author\":{\"name\":\"Renato Pincelli\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#\\\/schema\\\/person\\\/c7be1e2811d061a75d3b4f4960eb53bd\"},\"headline\":\"Estudo Noturno\",\"datePublished\":\"2013-01-12T01:00:35+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2013\\\/01\\\/estudo-noturno\\\/\"},\"wordCount\":592,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2013\\\/01\\\/estudo-noturno\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/wp-content\\\/uploads\\\/sites\\\/249\\\/2013\\\/01\\\/Late_Night_Study____by_Pagina7Lipsa.jpg\",\"articleSection\":[\"Geral\"],\"inLanguage\":\"pt-BR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2013\\\/01\\\/estudo-noturno\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2013\\\/01\\\/estudo-noturno\\\/\",\"url\":\"https:\\\/\\\/www.blogs.unicamp.br\\\/hypercubic\\\/2013\\\/01\\\/estudo-noturno\\\/\",\"name\":\"Estudo Noturno - 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