{"id":600,"date":"2020-10-02T09:40:05","date_gmt":"2020-10-02T13:40:05","guid":{"rendered":"http:\/\/fiziko.net\/?page_id=600"},"modified":"2020-10-02T11:06:12","modified_gmt":"2020-10-02T15:06:12","slug":"simulacao-energia","status":"publish","type":"page","link":"https:\/\/fiziko.net\/?page_id=600","title":{"rendered":"Simula\u00e7\u00e3o Energia"},"content":{"rendered":"\n<p class=\"has-text-align-left\">Um carro, com 1300 kg de massa, em um parque de divers\u00f5es se desloca sem atrito ao longo da pista indicada na figura 1.<\/p>\n\n\n\n<p class=\"has-text-align-left\">No diagrama esquem\u00e1tico da figura 2, o carro parte do repouso no ponto <em>A<\/em> situado a uma altura <em>h<\/em> acima da base do c\u00edrculo com raio igual a <em>R<\/em>. Considera o carro como uma part\u00edcula.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img fetchpriority=\"high\" decoding=\"async\" src=\"http:\/\/fiziko.net\/wp-content\/uploads\/2020\/10\/xgames-hot-wheels.jpg\" alt=\"\" class=\"wp-image-604\" width=\"468\" height=\"370\" srcset=\"https:\/\/fiziko.net\/wp-content\/uploads\/2020\/10\/xgames-hot-wheels.jpg 384w, https:\/\/fiziko.net\/wp-content\/uploads\/2020\/10\/xgames-hot-wheels-300x237.jpg 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><figcaption>Figura 1: Carro em looping; Fonte:https:\/\/onomeister.files.wordpress.com\/2012\/06\/xgames-hot-wheels.jpg<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" src=\"http:\/\/fiziko.net\/wp-content\/uploads\/2020\/10\/Loop.png\" alt=\"\" class=\"wp-image-603\" width=\"471\" height=\"269\" srcset=\"https:\/\/fiziko.net\/wp-content\/uploads\/2020\/10\/Loop.png 607w, https:\/\/fiziko.net\/wp-content\/uploads\/2020\/10\/Loop-300x171.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><figcaption>Figura 2: Diagrama esquem\u00e1tico<\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-left\">I \u2013 Considere o caso em que <img decoding=\"async\" title=\"h\\leq R\" src=\"https:\/\/latex.codecogs.com\/gif.latex?h\\leq&amp;space;R\">&nbsp;e que <img decoding=\"async\" title=\"0^o \\leq \\theta \\leq 90^o\" src=\"https:\/\/latex.codecogs.com\/gif.latex?0^o&amp;space;\\leq&amp;space;\\theta&amp;space;\\leq&amp;space;90^o\">, a velocidade da part\u00edcula se anula para qualquer valor de <em>\u03b8<\/em> no intervalo informado, quando a for\u00e7a normal que a pista exerce sobre o carro \u00e9 dada por:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">N=mgcos \\theta<\/div>\n\n\n\n<p class=\"has-text-align-left\">e o \u00e2ngulo em que ocorre isto for dado por:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\\theta = \\arccos \\left( 1 &#8211; \\frac{h}{R} \\right)<\/div>\n\n\n\n<p class=\"has-text-align-left\">II \u2013 Considere o caso em que <img decoding=\"async\" title=\"R \\leq h \\leq 2,5R\" src=\"https:\/\/latex.codecogs.com\/gif.latex?R&amp;space;\\leq&amp;space;h&amp;space;\\leq&amp;space;2,5R\"> e que <img decoding=\"async\" title=\"90^o \\leq \\theta \\leq 180^o\" src=\"https:\/\/latex.codecogs.com\/gif.latex?90^o&amp;space;\\leq&amp;space;\\theta&amp;space;\\leq&amp;space;180^o\">, a for\u00e7a normal se anula, para qualquer valor de <em>\u03b8<\/em> no intervalo informado, quando a velocidade do carro for dada por:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">v= \\sqrt{\\frac{2}{3}g\\left ( h-R \\right )}<\/div>\n\n\n\n<p class=\"has-text-align-left\">e o \u00e2ngulo em que ocorre isto for dado por:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\\theta = \\arccos \\left [ \\frac{2}{3}\\left ( 1-\\frac{h}{R} \\right ) \\right ]<\/div>\n\n\n\n<p class=\"has-text-align-left\">III \u2013 Mostre que se o carro executar o looping <img decoding=\"async\" title=\"h \\geq 2,5R\" src=\"https:\/\/latex.codecogs.com\/gif.latex?h&amp;space;\\geq&amp;space;2,5R\">, a for\u00e7a normal que a pista exerce sobre o carro nos pontos <em>B<\/em> e <em>C<\/em> \u00e9:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\\begin{cases}\nN_{B}=mg \\left(\\frac{2h}{R}-5 \\right)\n\\\\\nN_{C}=2mg \\left(\\frac{h}{R}-1 \\right)\n\\end{cases}<\/div>\n\n\n\n<p class=\"has-text-align-left\">e que as acelera\u00e7\u00f5es radial, tangencial e resultante s\u00e3o dadas por:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\\begin{cases}\na_{r}=2g \\left(\\frac{h}{R}-1 \\right)\n\\\\\na_{t}=g\n\\\\\na= \\sqrt{a_{t}^{2}+a_{r}^{2}}\n\\end{cases}<\/div>\n\n\n\n<p class=\"has-text-align-left\">com as velocidades em <em>B <\/em>e<em> C<\/em> dada por:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\\begin{cases}\nv_{B}=\\sqrt{2g(h-2R)}\n\\\\\nv_{C}=\\sqrt{2g(h-R)}\n\\end{cases}<\/div>\n\n\n\n<p class=\"has-text-align-left\"><strong>Constru\u00e7\u00e3o  do Simulador<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left\">1 \u2013 O usu\u00e1rio deve ser informar o valor do raio de curvatura da pista, que deve pertencer ao intervalo <img decoding=\"async\" title=\"10m \\leq R \\leq 20m\" src=\"https:\/\/latex.codecogs.com\/gif.latex?10m&amp;space;\\leq&amp;space;R&amp;space;\\leq&amp;space;20m\">;<\/p>\n\n\n\n<p class=\"has-text-align-left\">2 \u2013 O usu\u00e1rio deve ser informar o valor da altura acima da base do looping ao ponto <em>A<\/em>, que deve pertencer ao intervalo <img decoding=\"async\" title=\"0 < h \\leq 5R\" src=\"https:\/\/latex.codecogs.com\/gif.latex?0&amp;space;<&amp;space;h&amp;space;\\leq&amp;space;5R\">;<\/p>\n\n\n\n<p class=\"has-text-align-left\">3 \u2013 O programa deve informar a velocidade <img decoding=\"async\" title=\"v\" src=\"https:\/\/latex.codecogs.com\/gif.latex?v\">, a for\u00e7a normal exercida pela pista sobre o carro <em>N<\/em>, o \u00e2ngulo em que ocorre um dos eventos listado no desenvolvimento do modelo <em>\u03b8<\/em>, e as acelera\u00e7\u00f5es radial, tangencial e resultante se o carro chegar a executar o looping;<\/p>\n\n\n\n<p class=\"has-text-align-left\">4 \u2013 O autor do projeto deve considerar as condi\u00e7\u00f5es desenvolvidas acima.<\/p>\n\n\n\n<p class=\"has-text-align-left\"><strong>Exemplos de retorno de dados<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left\">Caso 1 &#8211; Se R = 20 m e <em>h<\/em> = 0,5R<\/p>\n\n\n\n<p class=\"has-text-align-left\">Retorno do modelo:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\\begin{cases}\nO\\quad carro\\quad n\u00e3o\\quad executa\\quad o\\quad looping;\n\\\\O\\quad carro\\quad para\\quad em\\quad \\theta = 60\u00b0;\n\\\\A\\quad for\u00e7a\\quad normal\\quad nessa\\quad posi\u00e7\u00e3o\\quad \u00e9\\quad N=6370 N;\n\\end{cases}<\/div>\n\n\n\n<p class=\"has-text-align-left\">Caso 2 &#8211; Se R = 20m e <em>h<\/em> = 2R<\/p>\n\n\n\n<p class=\"has-text-align-left\">Resultado do modelo:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\\begin{cases}\nO\\quad carro\\quad n\u00e3o\\quad executa\\quad o\\quad looping;\n\\\\A\\quad for\u00e7a\\quad normal\\quad se\\quad anula\\quad em\\quad \\theta = 131,8\u00b0;\n\\\\A\\quad velocidade\\quad do\\quad carro\\quad nesta\\quad posi\u00e7\u00e3o\\quad \u00e9\\quad v=11,4m\/s;\n\\end{cases}<\/div>\n\n\n\n<p class=\"has-text-align-left\">Caso 3 &#8211; Se R = 20m e <em>h<\/em> = 2,5R<\/p>\n\n\n\n<p>Resultado do modelo:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\">\\begin{cases}\nO\\quad carro\\quad executa\\quad o\\quad looping;\n\\\\A\\quad velocidade\\quad em\\quad B\\quad \u00e9\\quad v_{B}=14m\/s;\n\\\\A\\quad velocidade\\quad em\\quad C\\quad \u00e9\\quad v_{C}=24,25m\/s;\n\\\\A\\quad for\u00e7a\\quad normal\\quad em\\quad B\\quad \u00e9\\quad N_{B}=0;\n\\\\A\\quad for\u00e7a\\quad normal\\quad em\\quad C\\quad \u00e9\\quad N_{C}=38220N;\n\\\\A\\quad acelera\u00e7\u00e3o\\quad tangencial\\quad em\\quad C\\quad \u00e9\\quad a_{t}=g;\n\\\\A\\quad acelera\u00e7\u00e3o\\quad radial\\quad em\\quad C\\quad \u00e9\\quad a_{r}=3g;\n\\\\A\\quad acelera\u00e7\u00e3o\\quad resultante\\quad em\\quad C\\quad \u00e9\\quad a=3,16g;\n\\end{cases}<\/div>\n\n\n\n<p class=\"has-text-align-left\">Bom trabalho!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Um carro, com 1300 kg de massa, em um parque de divers\u00f5es se desloca sem atrito ao longo da pista indicada na figura 1. No diagrama esquem\u00e1tico da figura 2, o carro parte do repouso no ponto A situado a uma altura h acima da base do c\u00edrculo com raio igual a R. Considera o&hellip; <br \/> <a class=\"read-more\" href=\"https:\/\/fiziko.net\/?page_id=600\">Leia mais<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-600","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/pages\/600","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fiziko.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=600"}],"version-history":[{"count":9,"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/pages\/600\/revisions"}],"predecessor-version":[{"id":619,"href":"https:\/\/fiziko.net\/index.php?rest_route=\/wp\/v2\/pages\/600\/revisions\/619"}],"wp:attachment":[{"href":"https:\/\/fiziko.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}