{"id":3884,"date":"2010-10-09T03:21:35","date_gmt":"2010-10-09T02:21:35","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3884"},"modified":"2022-01-21T01:54:04","modified_gmt":"2022-01-21T01:54:04","slug":"rascunho-6","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3884","title":{"rendered":"Um plano inclinado"},"content":{"rendered":"<p><ul id='GTTabs_ul_3884' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3884' class='GTTabs_curr'><a  id=\"3884_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3884' ><a  id=\"3884_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o v1'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o v1<\/a><\/li>\n<li id='GTTabs_li_2_3884' ><a  id=\"3884_2\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o v2'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o v2<\/a><\/li>\n<li id='GTTabs_li_3_3884' ><a  id=\"3884_3\" onMouseOver=\"GTTabsShowLinks('Conclus\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Conclus\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_3884'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/45.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3890\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3890\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/45.jpg\" data-orig-size=\"368,242\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Plano inclinado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/45.jpg\" class=\"alignright wp-image-3890\" title=\"Plano inclinado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/45-300x197.jpg\" alt=\"\" width=\"240\" height=\"158\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/45-300x197.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/45-150x98.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/45.jpg 368w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><\/a>Observe a figura.<\/p>\n<p>Ignorando o atrito, o tempo <strong>t<\/strong> (em segundos) necess\u00e1rio para um bloco deslizar por um plano inclinado \u00e9 dado pela f\u00f3rmula <span style=\"color: #0000ff;\">\\[t=\\sqrt{\\frac{2a}{g\\times sen\\,\\theta \\times \\cos \\theta }}\\]<\/span>\u00a0 <span style=\"color: #008000;\">\\[t=\\sqrt{\\frac{2a}{g\\times sen\\,\\theta }}\\]<\/span> onde <strong>a<\/strong> \u00e9 a medida do comprimento da rampa, em metros, e <strong>g<\/strong> \u00e9 a acelera\u00e7\u00e3o da gravidade, aproximadamente 9,8 m\/s<sup>2<\/sup>.<\/p>\n<p>Quanto tempo demora a deslizar um bloco se $a=3,3$ m, quando:<\/p>\n<ul>\n<li>$\\theta =30{}^\\text{o}$<\/li>\n<li>$\\theta =45{}^\\text{o}$<\/li>\n<li>$\\theta =60{}^\\text{o}$<\/li>\n<\/ul>\n<p>(Aproxime o resultado \u00e0s cent\u00e9simas de segundo.)<\/p>\n<p><span style=\"color: #000000;\"><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3884' onClick='GTTabs_show(1,3884)'>Resolu\u00e7\u00e3o v1 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3884'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o v1<\/b><\/span><\/span><!--more--><\/p>\n<p>Para $a=3,3$ m e $g=9,8$ m\/s<sup>2<\/sup>, vem:<\/p>\n<ul>\n<li>$\\theta =30{}^\\text{o}$:<br \/>\n<span style=\"color: #0000ff;\">\\[\\begin{array}{*{35}{l}}<br \/>\nt(\\theta =30{}^\\text{o}) &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times sen\\,30{}^\\text{o}\\times \\cos 30{}^\\text{o}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times \\frac{1}{2}\\times \\frac{\\sqrt{3}}{2}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{8\\times 3,3\\times \\sqrt{3}}{9,8\\times 3}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{8,8\\times \\sqrt{3}}{9,8}}\u00a0 \\\\<br \/>\n{} &amp; \\simeq\u00a0 &amp; 1,25\\,\\,(s)\u00a0 \\\\<br \/>\n\\end{array}\\]<\/span><\/li>\n<li>$\\theta =45{}^\\text{o}$:<br \/>\n<span style=\"color: #0000ff;\">\\[\\begin{array}{*{35}{l}}<br \/>\nt(\\theta =45{}^\\text{o}) &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times sen\\,45{}^\\text{o}\\times \\cos 45{}^\\text{o}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times \\frac{\\sqrt{2}}{2}\\times \\frac{\\sqrt{2}}{2}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{4\\times 3,3}{9,8}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{6,6}{4,9}}\u00a0 \\\\<br \/>\n{} &amp; \\simeq\u00a0 &amp; 1,16\\,\\,(s)\u00a0 \\\\<br \/>\n\\end{array}\\]<\/span><\/li>\n<li>$\\theta =60{}^\\text{o}$:<br \/>\n<span style=\"color: #0000ff;\">\\[\\begin{array}{*{35}{l}}<br \/>\nt(\\theta =60{}^\\text{o}) &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times sen\\,60{}^\\text{o}\\times \\cos 60{}^\\text{o}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times \\frac{\\sqrt{3}}{2}\\times \\frac{1}{2}}}\u00a0 \\\\<br \/>\n{} &amp; \\simeq\u00a0 &amp; 1,25\\,\\,(s)\u00a0 \\\\<br \/>\n\\end{array}\\]<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center;\"><script src=\"https:\/\/cdn.geogebra.org\/apps\/deployggb.js\"><\/script>\r\n<div id=\"ggbApplet\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":635,\r\n\"height\":302,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from 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is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/p>\n<p><span style=\"color: #000000;\"><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3884' onClick='GTTabs_show(0,3884)'>&lt;&lt; Enunciado<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3884' onClick='GTTabs_show(2,3884)'>Resolu\u00e7\u00e3o v2 &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_2_3884'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o v2<\/b><\/span><\/span><\/p>\n<p>Para $a=3,3$ m e $g=9,8$ m\/s<sup>2<\/sup>, vem:<\/p>\n<ul>\n<li>$\\theta =30{}^\\text{o}$:<br \/>\n<span style=\"color: #008000;\">\\[\\begin{array}{*{35}{l}}<br \/>\nt(\\theta =30{}^\\text{o}) &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times sen\\,30{}^\\text{o}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times \\frac{1}{2}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{6,6}{4,9}}\u00a0 \\\\<br \/>\n{} &amp; \\simeq\u00a0 &amp; 1,16\\,\\,(s)\u00a0 \\\\<br \/>\n\\end{array}\\]<\/span><\/li>\n<li>$\\theta =45{}^\\text{o}$:<br \/>\n<span style=\"color: #008000;\">\\[\\begin{array}{*{35}{l}}<br \/>\nt(\\theta =45{}^\\text{o}) &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times sen\\,45{}^\\text{o}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times \\frac{\\sqrt{2}}{2}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{4\\times 3,3\\times \\sqrt{2}}{9,8\\times 2}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{3,3\\times \\sqrt{2}}{4,9}}\u00a0 \\\\<br \/>\n{} &amp; \\simeq\u00a0 &amp; 0,98\\,\\,(s)\u00a0 \\\\<br \/>\n\\end{array}\\]<\/span><\/li>\n<li>$\\theta =60{}^\\text{o}$:<br \/>\n<span style=\"color: #008000;\">\\[\\begin{array}{*{35}{l}}<br \/>\nt(\\theta =60{}^\\text{o}) &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times sen\\,60{}^\\text{o}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{2\\times 3,3}{9,8\\times \\frac{\\sqrt{3}}{2}}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{4\\times 3,3\\times \\sqrt{3}}{9,8\\times 3}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; \\sqrt{\\frac{2,2\\times \\sqrt{3}}{4,9}}\u00a0 \\\\<br \/>\n{} &amp; \\simeq\u00a0 &amp; 0,88\\,\\,(s)\u00a0 \\\\<br \/>\n\\end{array}\\]<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center;\"><div id=\"ggbApplet2\" style=\"margin: 0 auto;\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":635,\r\n\"height\":303,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6\",\r\n\"showToolBarHelp\":false,\r\n\"showResetIcon\":true,\r\n\"enableLabelDrags\":false,\r\n\"enableShiftDragZoom\":false,\r\n\"enableRightClick\":false,\r\n\"errorDialogsActive\":false,\r\n\"useBrowserForJS\":false,\r\n\"preventFocus\":false,\r\n\"language\":\"pt\",\r\n\/\/ use this instead of ggbBase64 to load a material from GeoGebraTube\r\n\/\/ \"material_id\":12345,\r\n\"ggbBase64\":\"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\"};\r\n\/\/ is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet2 = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet'); applet2.inject('ggbApplet2')};\r\n<\/script><\/p>\n<p style=\"text-align: left;\"><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3884' onClick='GTTabs_show(1,3884)'>&lt;&lt; Resolu\u00e7\u00e3o v1<\/a><\/span><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3884' onClick='GTTabs_show(3,3884)'>Conclus\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_3_3884'>\n<span class='GTTabs_titles'><b>Conclus\u00e3o<\/b><\/span><\/p>\n<p style=\"text-align: left;\"><span style=\"color: #0000ff;\">\\[t=\\sqrt{\\frac{2a}{g\\times sen\\,\\theta \\times \\cos \\theta }}\\]<\/span>\u00a0 <span style=\"color: #008000;\">\\[t=\\sqrt{\\frac{2a}{g\\times sen\\,\\theta }}\\]<\/span><\/p>\n<p style=\"text-align: left;\">Comente os resultados obtidos em cada uma das modela\u00e7\u00f5es.<\/p>\n<p style=\"text-align: left;\">A situa\u00e7\u00e3o apresentada pode ser modelada por ambas as fun\u00e7\u00f5es?<br \/>\nJustifique a sua resposta.<\/p>\n<ul>\n<li>\n<div style=\"text-align: left;\">\u00a0Simulador: <a href=\"http:\/\/www.mhhe.com\/physsci\/physical\/giambattista\/iplane\/iplane.html\" target=\"_blank\" rel=\"noopener\">http:\/\/www.mhhe.com\/physsci\/physical\/giambattista\/iplane\/iplane.html<\/a><\/div>\n<\/li>\n<\/ul>\n<p style=\"text-align: left;\">\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3884' onClick='GTTabs_show(2,3884)'>&lt;&lt; Resolu\u00e7\u00e3o v2<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o v1 Enunciado Observe a figura. Ignorando o atrito, o tempo t (em segundos) necess\u00e1rio para um bloco deslizar por um plano inclinado \u00e9 dado pela f\u00f3rmula \\[t=\\sqrt{\\frac{2a}{g\\times sen\\,\\theta \\times \\cos \\theta }}\\]\u00a0&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20800,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,99],"tags":[422,423],"series":[],"class_list":["post-3884","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-trigonometria","tag-11-o-ano","tag-trigonometria"],"views":2291,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/11V1Pag094-45_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3884","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=3884"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3884\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20800"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3884"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3884"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3884"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}