{"id":4716,"date":"2021-11-11T09:00:00","date_gmt":"2021-11-11T12:00:00","guid":{"rendered":"https:\/\/professorpinguim.com.br\/blog\/?p=4716"},"modified":"2023-08-06T21:16:46","modified_gmt":"2023-08-07T00:16:46","slug":"exercicios-de-analise-dimensional","status":"publish","type":"post","link":"https:\/\/professorpinguim.com.br\/blog\/exercicios-de-analise-dimensional\/","title":{"rendered":"Exerc\u00edcios de An\u00e1lise Dimensional"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Nesta aula, vamos resolver juntos alguns exerc\u00edcios sobre An\u00e1lise Dimensional. Acompanhe e bons estudos!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Exerc\u00edcios de An\u00e1lise Dimensional<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A grandeza f\u00edsica energia pode ser representada de v\u00e1rias formas e com a utiliza\u00e7\u00e3o de outras diferentes grandezas f\u00edsicas. A composi\u00e7\u00e3o destas outras grandezas f\u00edsicas nos define o que alguns chamam de formula\u00e7\u00e3o matem\u00e1tica.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Dentre elas, destacamos tr\u00eas:<\/strong><\/p>\n\n\n\n<!--more-->\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/N-JzKrVn6bK5zJKnDhMmeTsl4sBtnTlZwsMxN98SXpcgHYDRz-u1bcLrDHUrX9IrDsaCEfvrY6YoHysitIJ32znujopl24E77R69P--yNscRHMoNQ0x6pFwDF62QjGm-_XJFYlTf=s0\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Considerando o Sistema Internacional de Unidades, podemos representar energia como<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) kg . m . s<strong><sup>&#8211;<\/sup><\/strong><sup>1<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) kg . m\u00b2 . s<sup>1<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) kg . m<sup>&#8211;<\/sup>\u00b2 . s<sup>&#8211;<\/sup>\u00b2&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) kg . m\u00b2 . s\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e) kg . m\u00b2 . s<sup>&#8211;<\/sup>\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Da esquerda para a direita, temos as f\u00f3rmulas para medir, respectivamente, energia gravitacional, energia potencial el\u00e1stica e energia cin\u00e9tica.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N\u00e3o importa qual dessas f\u00f3rmulas voc\u00ea vai utilizar; qualquer uma delas vai nos ajudar a encontrar a dimens\u00e3o que essa energia tem.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o, vamos pegar a primeira f\u00f3rmula (E = m . g . h) e escrever a dimens\u00e3o no Sistema Internacional para cada uma das variantes. Acompanhe:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[m] = massa (kg)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[g] = gravidade (m\/s\u00b2 ou m.s<sup>&#8211;<\/sup>\u00b2)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[h] = altura (m)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Portanto, basta substituirmos a f\u00f3rmula para:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[E] = kg . m.s<sup>&#8211;<\/sup>\u00b2 . m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[E] = kg . m\u00b2 . s<sup>&#8211;<\/sup>\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESPOSTA: E<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 2<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Em um g\u00e1s ideal, o produto da press\u00e3o pelo volume dividido pela temperatura tem, no Sistema Internacional, unidade de medida de:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) Pa\/K<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) Nm\/K<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) m\u00b3\/K<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) Pa\/m\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver essa quest\u00e3o, temos que nos lembrar de alguma f\u00f3rmula que tenha todas as vari\u00e1veis: press\u00e3o, volume e temperatura. Obviamente, isso est\u00e1 relacionado com gases.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o, a quest\u00e3o nos pede:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[P] . [V] \/ [T]<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>press\u00e3o (P) \u00e9 a divis\u00e3o da for\u00e7a (F) sobre a \u00e1rea (A). Portanto: [P] = N \/ m\u00b2 ou N . m<sup>&#8211;<\/sup>\u00b2<\/li><li>temperatura (T) no Sistema Internacional \u00e9 medida em Kelvin (K).<\/li><li>volume (V) \u00e9 medido em metros c\u00fabicos (m\u00b3)<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Assim, teremos que:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[P] . [V] \/ [T]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N . m<sup>&#8211;<\/sup>\u00b2 . m\u00b3 \/ K<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">N . m \/ K<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESPOSTA: B<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Considere um tanque cil\u00edndrico contendo \u00e1gua at\u00e9 uma altura h, em metros. No fundo do tanque h\u00e1 uma torneira, atrav\u00e9s da qual passa um determinado volume (em m<\/strong><strong><sup>3<\/sup><\/strong><strong>) de \u00e1gua a cada segundo, resultando em uma vaz\u00e3o q (em m<\/strong><strong><sup>3<\/sup><\/strong><strong>\/s). \u00c9 poss\u00edvel escrever a altura em fun\u00e7\u00e3o da vaz\u00e3o q atrav\u00e9s da equa\u00e7\u00e3o h = Rq, onde a constante de proporcionalidade R pode ser entendida como uma resist\u00eancia mec\u00e2nica \u00e0 passagem do fluido pela torneira. Assim, a unidade de medida dessa resist\u00eancia \u00e9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) s\/m<sup>2<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) s\/m<sup>3<\/sup>.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) m<sup>3<\/sup>\/s.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) m\/s<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A quest\u00e3o quer que descubramos a unidade de R. Por isso, \u00e9 interessante o isolarmos na f\u00f3rmula. Assim:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">h = R . q<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">R = h \/ q<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pelo enunciado, j\u00e1 sabemos que:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[q] = m\u00b3 \/ s<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[R] = [h] \/ [q]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[R] =&nbsp; m \/ m\u00b3\/s<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[R] = s \/ m\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESPOSTA: A<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 4<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Considere um dado movimento oscilat\u00f3rio em que uma part\u00edcula seja sujeita a uma for\u00e7a proporcional a cos (\u03c9t<\/strong><strong><sup>2<\/sup><\/strong><strong>), onde t \u00e9 o tempo. \u00c9 correto afirmar que, neste caso, a unidade de medida de \u03c9 no SI \u00e9<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) s.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) s<sup>-1<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) s<sup>-2<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) s<sup>2<\/sup>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">O desafio nesta quest\u00e3o \u00e9 saber por onde come\u00e7ar, uma vez que n\u00e3o estamos trabalhando com grandezas muito conhecidas. Por\u00e9m, repare que o enunciado nos forneceu um cosseno, ou seja, temos em m\u00e3os um \u00e2ngulo.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lembre-se de que todo \u00e2ngulo \u00e9 adimensional. Isso porque, da Matem\u00e1tica, tiramos que um \u00e2ngulo qualquer (\u03b8) \u00e9 o arco (S) dividido pelo raio (R), ou seja:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b8 = S \/ R<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[\u03b8] = [S] \/ [R]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[\u03b8] = m \/ m = 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o, para a F\u00edsica, \u00e2ngulo adimensional, o que nos leva a:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[\u03c9t\u00b2] = [\u03c9] . [t\u00b2]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1 = [\u03c9] . s\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[\u03c9]&nbsp; = 1 \/ s\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">[\u03c9] = s<sup>&#8211;<\/sup>\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESPOSTA: C<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 5<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Em um sistema massa-mola, a energia potencial \u00e9 fun\u00e7\u00e3o do coeficiente el\u00e1stico K e da deforma\u00e7\u00e3o da mola. Em termos de unidade de energia e comprimento, a unidade de medida de K \u00e9?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) J\/m\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) J\/m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) J.m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) J.m\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sabemos que a energia tratada no enunciado \u00e9 a energia potencial el\u00e1stica, que tem a seguinte f\u00f3rmula:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/txCfGsU0GgvBTOV8EsMBGZxjB6w2R1weGzRLwM34hbMdAmzgZU1FwFle8dQBGj8NyqPWFvQyEbxaqx-Ae95W_aXo94hfjTUbXFVS0v4Kg-NcGG8LH_VberD5Em0tIeGvsagv0iKm=s0\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Novamente, para descobrirmos a unidade de K, precisamos isol\u00e1-lo na equa\u00e7\u00e3o. Teremos:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;K = 2. Ex\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Importante: quando estamos falando de An\u00e1lise DImensional, os numerais ficam fora dos nossos c\u00e1lculos, pois eles s\u00e3o adimensionais. Assim:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;[K] = [E][x]\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;[K] = Jm\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RESPOSTA: A<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Espero que voc\u00ea tenha entendido um pouco melhor como resolver exerc\u00edcios de An\u00e1lise Dimensional. Para conferir a resolu\u00e7\u00e3o dessas e de outras quest\u00f5es sobre essa mat\u00e9ria, assista \u00e0 minha live:<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"An\u00e1lise Dimensional | Resolu\u00e7\u00e3o Lista 1 | A05  [Professor Pinguim]\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/YglP0rbECLs?start=2&amp;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">E se quiser ajuda para melhorar seu n\u00edvel de F\u00edsica em outras mat\u00e9rias,<a href=\"https:\/\/professorpinguim.com.br\/\"> entre em contato comigo e escolha o curso de F\u00edsica mais adequado para voc\u00ea<\/a>!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>SAIBA MAIS<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a1\ufe0f <a href=\"https:\/\/professorpinguim.com.br\/blog\/o-fluxo-representa-o-volume-de-sangue-unesp-2014-1a-fase-questao-de-analise-dimensional\/\" target=\"_blank\" rel=\"noreferrer noopener\">Quest\u00e3o de An\u00e1lise Dimensional<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a1\ufe0f <a href=\"https:\/\/professorpinguim.com.br\/blog\/como-estudar-mecanica-para-vestibulares-paulistas\/\" target=\"_blank\" rel=\"noreferrer noopener\">Como estudar mec\u00e2nica para Vestibulares Paulistas<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u27a1\ufe0f <a href=\"https:\/\/professorpinguim.com.br\/blog\/exercicios-de-termologia\/\" target=\"_blank\" rel=\"noreferrer noopener\">Exerc\u00edcios de Termologia<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Me acompanhe nas redes sociais: curta a minha&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/www.facebook.com\/professorpinguim\/\" target=\"_blank\"><strong>p\u00e1gina no Facebook<\/strong><\/a><strong>,<\/strong>&nbsp;me&nbsp;siga no&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/www.instagram.com\/professorpinguim\/\" target=\"_blank\"><strong>Instagram<\/strong><\/a><strong>,<\/strong>&nbsp;se inscreva no&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/www.youtube.com\/c\/PinguimV%C3%ADdeoF%C3%ADsica\/?sub_confirmation=1\" target=\"_blank\"><strong>Youtube<\/strong><\/a>&nbsp;e participe do meu canal oficial no&nbsp;<strong><a href=\"https:\/\/professorpinguim.com.br\/telegram\">Telegram<\/a><\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nesta aula, vamos resolver juntos alguns exerc\u00edcios sobre An\u00e1lise Dimensional. Acompanhe e bons estudos! Exerc\u00edcios de An\u00e1lise Dimensional Quest\u00e3o 1 A grandeza f\u00edsica energia pode ser representada de v\u00e1rias formas e com a utiliza\u00e7\u00e3o de outras diferentes grandezas f\u00edsicas. A composi\u00e7\u00e3o destas outras grandezas f\u00edsicas nos define o que alguns chamam de formula\u00e7\u00e3o matem\u00e1tica. Dentre [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":4717,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[732],"tags":[696,381,560,653],"class_list":["post-4716","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-analise-dimensional","tag-exercicios-de-analise-dimensional","tag-exercicios-de-fisica","tag-fisica-basica","tag-fisica-vestibulares"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exerc\u00edcios de An\u00e1lise Dimensional - Professor Pinguim | F\u00edsica<\/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:\/\/professorpinguim.com.br\/blog\/exercicios-de-analise-dimensional\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Exerc\u00edcios de An\u00e1lise Dimensional - Professor Pinguim | F\u00edsica\" \/>\n<meta property=\"og:description\" content=\"Nesta aula, vamos resolver juntos alguns exerc\u00edcios sobre An\u00e1lise Dimensional. Acompanhe e bons estudos! Exerc\u00edcios de An\u00e1lise Dimensional Quest\u00e3o 1 A grandeza f\u00edsica energia pode ser representada de v\u00e1rias formas e com a utiliza\u00e7\u00e3o de outras diferentes grandezas f\u00edsicas. A composi\u00e7\u00e3o destas outras grandezas f\u00edsicas nos define o que alguns chamam de formula\u00e7\u00e3o matem\u00e1tica. 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