{"id":34486,"date":"2024-09-16T13:00:55","date_gmt":"2024-09-16T13:00:55","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34486"},"modified":"2025-09-08T04:10:39","modified_gmt":"2025-09-08T04:10:39","slug":"labor-et-energia-mechanica","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/","title":{"rendered":"Labor et Energia Mechanica"},"content":{"rendered":"<p><center><\/p>\n<h1>Labor et Energia Mechanica<\/h1>\n<p><em><strong>Summarium:<\/strong><br \/>\n    Huic seriei lectionum incumbemus ad investigandam rationem quae inter laborem, energiam et nonnullas eius formas exsistit: kineticam et potentialem. Ex his analysibus computabimus spatium inhibitionis mobilis, quod, cum celeritate initiali profectum, usque ad stationem progreditur, atque etiam simpliciabimus studium casus liberi.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Proposita Discendi<\/strong><br \/>\nPost hanc lectionem discipulus poterit:<\/p>\n<ol style=\"text-align:left;\">\n<li><strong>Intellegere<\/strong> rationem inter laborem et energiam kineticam.<\/li>\n<li><strong>Applicare<\/strong> Theorema Virium Vivarum ad intellegendam variationem energiae kineticae.<\/li>\n<li><strong>Explicare<\/strong> notionem energiae potentialis eiusque relationem cum positione obiecti in campo gravitatorio.<\/li>\n<\/ol>\n<p><strong>INDEX<\/strong><br \/>\n    <a href=\"#1\">Labor et Energia kinetica<\/a><br \/>\n    <a href=\"#11\">Relatio inter laborem et energiam kineticam<\/a><br \/>\n    <a href=\"#12\">Energia kinetica et spatium inhibitionis<\/a><br \/>\n    <a href=\"#2\">Labor et Energia potentialis<\/a><br \/>\n    <a href=\"#21\">Energia potentialis et casus liber<\/a><\/p>\n<p>    <\/center><\/p>\n<p>    <center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/_q-5C4FQOaU\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>Labor et Energia Kinetica<\/h2>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_q-5C4FQOaU&amp;t=130s\" target=\"_blank\" rel=\"noopener\"><strong>Cum vim in massam applicamus,<\/strong><\/a> sentimus nos aliquid systemati addere; intuitive dicimus nos \u00abenergiam addere\u00bb, quamquam hoc non necessario verum est. Si vis non sufficit ad frangendum attritum staticum, tum non licet dicere utrum massa mutata sit necne. Certe aliquid systemati addimus, \u00abconatum\u00bb ut ita dicamus, sed etiam verum est quod attritus staticus hunc \u00abconatum\u00bb in sensu opposito et complementario reddit. Attamen, cum attritus staticus rumpitur, tunc fieri potest mutationem in systemate discernere: nunc in statu motus diverso versatur. Ad producendum illum novum statum motus, necesse est \u00abaliquid novum\u00bb systemati addere: hoc \u00abaliquid\u00bb est quod vocamus energiam kineticam.<\/p>\n<p style=\"text-align:justify;\">Iam duas magnitudines physicas habemus quae statum obiecti physici, vel systematis, describunt: momentum lineare quod bene novimus, quod statum motus repraesentat, et energiam kineticam quam incipiemus investigare et quae, ad praesens, <em>repraesentabit quid nos addere debuerimus ut corpus vel systema ex quiete ad illum statum motus perduceremus.<\/em><\/p>\n<p><a name=\"11\"><\/a><\/p>\n<h3>Relatio inter laborem et energiam kineticam<\/h3>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=_q-5C4FQOaU&amp;t=865s\" target=\"_blank\" rel=\"noopener\"><strong>Redeamus ad massam et vim<\/strong><\/a> quae eam in motum ponit. Si vis motum non producit, dicimus nihil systemati additum esse, dum si producit, dicimus energiam kineticam addi. Cum motus producitur, corpus necessario certam trajectoriam percurrit et dum id facit, vis energiam addet. Hanc actionem addendi vel detrahendi energiam kineticam \u00ablaborem mechanicum efficere\u00bb appellabimus, ita <strong>definimus elementum laboris mechanici <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dW<\/span><\/span> per aequationem<\/strong><\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{lr}\n\n    dW =\\vec{F} \\cdot d\\vec{r} &amp; (1)\n\n    \\end{array}<\/span>\n<\/p>\n<p style=\"text-align:justify;\">ubi <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}<\/span> est vis applicata et <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d\\vec{r}<\/span><\/span> est elementum translationis super quod vis egit. Cum haec vis applicetur corpori massae <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span>, utens <a href=\"https:\/\/toposuranos.com\/las-leyes-de-newton\/\" target=\"_blank\" rel=\"noopener\">secunda lege Newtoni<\/a> scribere possumus<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{lr}\n\n    \\displaystyle\\vec{F} =\\frac{d\\vec{p}}{dt} = m\\frac{d\\vec{v}}{dt} &amp; (2)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">Itaque, ex aequationibus (1) et (2) habebitur<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{llr}\n\n    dW &amp; \\displaystyle =m\\frac{d\\vec{v}}{dt} \\cdot d\\vec{r} = m\\frac{d\\vec{r}}{dt} \\cdot d\\vec{v} = m\\vec{v} \\cdot d\\vec{v} &amp; (3)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">Integrando hanc ultimam expressionem ad obtinendum laborem totum effectum habebitur:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{llr}\n\n    W &amp; = \\displaystyle {\\int_{i}^{f}} m\\vec{v} \\cdot d\\vec{v} = \\left.\\frac{1}{2}m \\|\\vec{v}\\|^2 \\right|_i^f &amp; \\\\ \\\\\n\n    &amp; \\displaystyle = \\frac{1}{2}m \\|\\vec{v}_f\\|^2 - \\frac{1}{2}m\\|\\vec{v}_i\\|^2 &amp; (4)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">Ex hoc ratiocinio videre possumus laborem mechanicum aequivalere differentiae eiusdem magnitudinis in duobus statibus diversis, alteri correspondentis statui finali et alteri initiali. Talis magnitudo respondet ei quod addendum (vel detrahendum) fuit ad statum motus mutandum et est quod vocamus <strong>Energiam Kineticam,<\/strong> atque proinde definitur per aequationem:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{llr}\n\n    E_{cin} &amp; \\displaystyle = \\frac{1}{2}m\\|\\vec{v}\\|^2 &amp; (5)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">Itaque habetur<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{llr}\n\n    W &amp; = \\Delta E_{cin} &amp;  (6)\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">Hoc ultimum est quod notum est ut <strong>Theorema Virium Vivarum.<\/strong><\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ddddff;\">\n<h4 style=\"color: #800000;\">Exercitium<\/h4>\n<p style=\"text-align:justify;\"><strong>a) <a href=\"https:\/\/www.youtube.com\/watch?v=_q-5C4FQOaU&amp;t=1148s\" target=\"_blank\" rel=\"noopener\">Vehiculum sicut KIA Rio 5 pondus habet<\/a><\/strong> circiter 1.580 kg. Finge te hoc vehiculo in urbe moderata celeritate 50 km\/h vehi et ad semaphorum rubrum occurrere. Ut consistat, vehiculum hanc energiam per systema frenorum dissipare debet. Deinde, ut celeritatem recipiat, energiam ex combustibili per motorem obtinere debet. Si semaphorum viride fuisset, frena non necessaria fuissent, ita energia servata esset. Computa quantitatem energiae servatae si semaphorum viride est.<\/p>\n<p>    <strong>b)<\/strong> Repete computationes partis prioris, sed nunc suppone te celeritate minus moderata 70 km\/h vehere. Expone impensum extra energiae in forma centesimorum.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/dGK-y2Pqu74\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"12\"><\/a><\/p>\n<h3>Energia Kinetica et Spatium Inhibitionis<\/h3>\n<p style=\"text-align:justify;\">Error valde communis a gubernatoribus committitur est putare spatium inhibitionis directe proportionale esse celeritati: si duplicamus celeritatem, etiam duplicatur spatium inhibitionis. In hac sectione recognoscemus errorem post talem intuitionem et demonstrabimus spatium inhibitionis re vera proportionale esse quadrato celeritatis.<\/p>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=dGK-y2Pqu74&amp;t=113s\" target=\"_blank\" rel=\"noopener\"><strong>Supponamus nos habere massam<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> super plano horizontali moventem cum celeritate initiali <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_i\\hat{x}<\/span><\/span> ubi est coefficiens attritus kinetici <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu_c<\/span>.<\/span> Ex hoc videmus esse vim attritus motui oppositam <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{F}_{roce}=-\\mu_c mg\\hat{x}<\/span><\/span> quae aget donec corpus quiescat postquam spatium inhibitionis <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_{fre}<\/span><\/span> percucurrerit. Labor ab hac vi effectus datur per:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n    \\displaystyle W_{roce}= \\int_{0}^{x_{fre}} \\vec{F}_{roce} \\cdot d\\vec{l} = \\int_{0}^{x_{fre}} -\\mu_c mg dx = -\\mu_cmgx_{fre}\n\n    <\/span>\n<p style=\"text-align:justify;\">Ex altera parte, variatio energiae kineticae corporis quod incipit cum celeritate initiali <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_i<\/span><\/span> et ad quietem pervenit relicta velocitate finali <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">v_f=0<\/span><\/span> est:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\Delta E_{cin}= \\frac{1}{2}m (\\underbrace{\\color{red}{v_f^2}}_{= 0} - v_i^2) = - \\frac{1}{2}mv_i^2\n\n    <\/span>\n<p style=\"text-align:justify;\">Ita, si tota energia kinetica ab attritu dissipatur donec corpus ad quietem perducatur, habebitur:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\begin{array}{rrl}\n\n    &amp; W_{roce} &amp; \\displaystyle = \\Delta E_{cin} \\\\ \\\\\n\n \\equiv   &amp; -\\mu_cmg x_{fre} &amp; \\displaystyle = - \\frac{1}{2}mv_i^2 \\\\ \\\\\n\n \\equiv   &amp; x_{fre} &amp; = \\frac{1}{2} \\frac{v_i^2}{\\mu_c g}\n\n    \\end{array}<\/span>\n<p style=\"text-align:justify;\">Ex hoc habetur quod demonstrandum erat, spatium inhibitionis esse proportionale celeritati in quadratum.<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ddddff;\">\n<h4 style=\"color: #800000;\">Exercitium<\/h4>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=dGK-y2Pqu74&amp;t=510s\" target=\"_blank\" rel=\"noopener\"><strong>Massula 300[kg] movetur cum celeritate<\/strong><\/a> 15[km\/h] super plano horizontali. Si inter planum horizontale et massam est attritus kineticus <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mu_c=0,67<\/span><\/span>. Computa spatium quod massa percurrit donec omnino consistat.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/GXxkhk00quw\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Labor et Energia Potentialis<\/h2>\n<p><P style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=GXxkhk00quw&amp;t=6s\" target=\"_blank\" rel=\"noopener\"><strong>Imaginemos nos habere corpus<\/strong><\/a> massae <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> quod cadit ex altitudine <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h_i<\/span><\/span> ad altitudinem finalem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h_f<\/span><\/span> ( cum <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h_f \\leq h_i<\/span><\/span> ). Tunc habebimus laborem a vi gravitatis effectum esse huiusmodi:<\/P><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle W_g = \\int_{h_i}^{h_f} \\vec{F}_g \\cdot d\\vec{l} = \\int_{h_i}^{h_f} -mgdz = -mg(h_f - h_i)<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">Ex hoc habemus quod, si altitudo initialis est <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h_i = h<\/span><\/span> et altitudo finalis est in plano terrae <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">h_f = 0<\/span><\/span>, tunc habebitur:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle W_g = -mg(0 - h) = mgh<\/span><\/span><\/p>\n<p style=\"text-align:justify;\">Ex hoc habemus quod, cum corpus cadit ex altitudine <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span>, dimittitur energia cum eius positione relativa in spatio coniuncta. Hanc energiam appellamus <strong>Energia Potentialis.<\/strong><\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\begin{array}{rr}{E_{pot} = mgh} &amp; (7)\\end{array}<\/span><\/span><\/p>\n<p><a name=\"21\"><\/a><\/p>\n<h3>Energia Potentialis et Casus Liber<\/h3>\n<p style=\"text-align:justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=GXxkhk00quw&amp;t=329s\" target=\"_blank\" rel=\"noopener\"><strong>Reminiscamur problema<\/strong><\/a> <a href=\"https:\/\/toposuranos.com\/movimiento-rectilineo-uniformemente-acelerado-mrua\/\" rel=\"noopener\" target=\"_blank\">casus liberi<\/a>. Utendo nunc energia potentiali et kinetica quam investigavimus, possumus celeritatem casus reperire multo simpliciori modo. Energia est alia ex illis magnitudinibus physicis quae naturam conservativam habent; id est, non creatur nec destruitur, sed tantum transformatur. Cum corpus ad altitudinem <span class=\"katex-eq\" data-katex-display=\"false\">h<\/span> supra terram positum est, cum hoc cadit per actionem gravitatis usque ad terram, energia eius potentialis non evanescit, sed in aliam formam energiae mutatur: in energiam motus, ita ut habeatur:<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n    E_{pot,inicial} &amp; = E_{cin, final} \\\\ \\\\ mgh &amp;\\displaystyle = \\frac{1}{2}mv^2 \\\\ \\\\ v^2 &amp; = 2gh \\\\ \\\\ v&amp; =\\sqrt{2gh}\\end{array}<\/span>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #ddddff;\">\n<h4 style=\"color: #800000;\">Exercitium<\/h4>\n<p>    <a href=\"https:\/\/www.youtube.com\/watch?v=GXxkhk00quw&amp;t=443s\" target=\"_blank\" rel=\"noopener\"><strong>Montanae russica initium habet<\/strong><\/a> ad altitudinem 150[m] a terra. Si currus sine attritu per binarios montanae russicae movetur et ex quiete incipit, computa celeritatem cum in altitudine invenitur:<\/p>\n<p>    <strong>a)<\/strong> 90[m] a terra.<\/p>\n<p>    <strong>b)<\/strong> 50[m] a terra.<\/p>\n<p>    <strong>c)<\/strong> 10[m] a terra.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Labor et Energia Mechanica Summarium: Huic seriei lectionum incumbemus ad investigandam rationem quae inter laborem, energiam et nonnullas eius formas exsistit: kineticam et potentialem. Ex his analysibus computabimus spatium inhibitionis mobilis, quod, cum celeritate initiali profectum, usque ad stationem progreditur, atque etiam simpliciabimus studium casus liberi. Proposita Discendi Post hanc lectionem discipulus poterit: Intellegere rationem [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28589,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":4,"footnotes":""},"categories":[1262,1250],"tags":[],"class_list":["post-34486","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fundamenta-mechanicae","category-physica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Labor et Energia Mechanica - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Labor et energia inter se coniuncta sunt: labor est cum vis aliquid movet atque ei energiam tribuit. Energia est quae permittit res moveri aut mutari, sicut cum aliquid in motu est (energia kinetica) aut in positione alta est (energia potentialis). Breviter, labor energiam utitur ad res movendas aut mutandas.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Labor et Energia Mechanica\" \/>\n<meta property=\"og:description\" content=\"Labor et energia inter se coniuncta sunt: labor est cum vis aliquid movet atque ei energiam tribuit. Energia est quae permittit res moveri aut mutari, sicut cum aliquid in motu est (energia kinetica) aut in positione alta est (energia potentialis). Breviter, labor energiam utitur ad res movendas aut mutandas.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2024-09-16T13:00:55+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-08T04:10:39+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/energia-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Labor et Energia Mechanica\" \/>\n<meta name=\"twitter:description\" content=\"Labor et energia inter se coniuncta sunt: labor est cum vis aliquid movet atque ei energiam tribuit. Energia est quae permittit res moveri aut mutari, sicut cum aliquid in motu est (energia kinetica) aut in positione alta est (energia potentialis). Breviter, labor energiam utitur ad res movendas aut mutandas.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/energia.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"Labor et Energia Mechanica\",\"datePublished\":\"2024-09-16T13:00:55+00:00\",\"dateModified\":\"2025-09-08T04:10:39+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/\"},\"wordCount\":1231,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/09\\\/energia.jpg\",\"articleSection\":[\"Fundamenta Mechanicae\",\"Physica\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/\",\"name\":\"Labor et Energia Mechanica - toposuranos.com\\\/material\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/#primaryimage\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/09\\\/energia.jpg\",\"datePublished\":\"2024-09-16T13:00:55+00:00\",\"dateModified\":\"2025-09-08T04:10:39+00:00\",\"description\":\"Labor et energia inter se coniuncta sunt: labor est cum vis aliquid movet atque ei energiam tribuit. Energia est quae permittit res moveri aut mutari, sicut cum aliquid in motu est (energia kinetica) aut in positione alta est (energia potentialis). Breviter, labor energiam utitur ad res movendas aut mutandas.\",\"breadcrumb\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/#breadcrumb\"},\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/#primaryimage\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/09\\\/energia.jpg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2024\\\/09\\\/energia.jpg\",\"width\":1792,\"height\":1024},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/la\\\/labor-et-energia-mechanica\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/es\\\/cursos-de-matematica-y-fisica\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Labor et Energia Mechanica\"}]},{\"@type\":\"WebSite\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#website\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"name\":\"toposuranos.com\\\/material\",\"description\":\"\",\"publisher\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"es\"},{\"@type\":\"Organization\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#organization\",\"name\":\"toposuranos.com\\\/material\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/logo.png\",\"width\":2400,\"height\":2059,\"caption\":\"toposuranos.com\\\/material\"},\"image\":{\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/groups\\\/toposuranos\",\"https:\\\/\\\/x.com\\\/topuranos\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UC16yDm12cPcrwsE0fAM7X1g\",\"https:\\\/\\\/www.linkedin.com\\\/company\\\/69429190\"]},{\"@type\":\"Person\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/#\\\/schema\\\/person\\\/e15164361c3f9a2a02cf6c234cf7fdc1\",\"name\":\"giorgio.reveco\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"es\",\"@id\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"contentUrl\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/wp-content\\\/uploads\\\/2023\\\/10\\\/1694478625378-96x96.jpeg\",\"caption\":\"giorgio.reveco\"},\"description\":\"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.\",\"sameAs\":[\"http:\\\/\\\/toposuranos.com\\\/material\"],\"url\":\"http:\\\/\\\/toposuranos.com\\\/material\\\/author\\\/giorgio-reveco\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Labor et Energia Mechanica - toposuranos.com\/material","description":"Labor et energia inter se coniuncta sunt: labor est cum vis aliquid movet atque ei energiam tribuit. Energia est quae permittit res moveri aut mutari, sicut cum aliquid in motu est (energia kinetica) aut in positione alta est (energia potentialis). Breviter, labor energiam utitur ad res movendas aut mutandas.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/","og_locale":"es_ES","og_type":"article","og_title":"Labor et Energia Mechanica","og_description":"Labor et energia inter se coniuncta sunt: labor est cum vis aliquid movet atque ei energiam tribuit. Energia est quae permittit res moveri aut mutari, sicut cum aliquid in motu est (energia kinetica) aut in positione alta est (energia potentialis). Breviter, labor energiam utitur ad res movendas aut mutandas.","og_url":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/","og_site_name":"toposuranos.com\/material","article_publisher":"https:\/\/www.facebook.com\/groups\/toposuranos","article_published_time":"2024-09-16T13:00:55+00:00","article_modified_time":"2025-09-08T04:10:39+00:00","og_image":[{"url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/energia-1024x585.jpg","type":"","width":"","height":""}],"author":"giorgio.reveco","twitter_card":"summary_large_image","twitter_title":"Labor et Energia Mechanica","twitter_description":"Labor et energia inter se coniuncta sunt: labor est cum vis aliquid movet atque ei energiam tribuit. Energia est quae permittit res moveri aut mutari, sicut cum aliquid in motu est (energia kinetica) aut in positione alta est (energia potentialis). Breviter, labor energiam utitur ad res movendas aut mutandas.","twitter_image":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/energia.jpg","twitter_creator":"@topuranos","twitter_site":"@topuranos","twitter_misc":{"Escrito por":"giorgio.reveco","Tiempo de lectura":"1 minuto"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/#article","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/"},"author":{"name":"giorgio.reveco","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1"},"headline":"Labor et Energia Mechanica","datePublished":"2024-09-16T13:00:55+00:00","dateModified":"2025-09-08T04:10:39+00:00","mainEntityOfPage":{"@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/"},"wordCount":1231,"commentCount":0,"publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"image":{"@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/energia.jpg","articleSection":["Fundamenta Mechanicae","Physica"],"inLanguage":"es","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/#respond"]}]},{"@type":"WebPage","@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/","url":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/","name":"Labor et Energia Mechanica - toposuranos.com\/material","isPartOf":{"@id":"http:\/\/toposuranos.com\/material\/#website"},"primaryImageOfPage":{"@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/#primaryimage"},"image":{"@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/#primaryimage"},"thumbnailUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/energia.jpg","datePublished":"2024-09-16T13:00:55+00:00","dateModified":"2025-09-08T04:10:39+00:00","description":"Labor et energia inter se coniuncta sunt: labor est cum vis aliquid movet atque ei energiam tribuit. Energia est quae permittit res moveri aut mutari, sicut cum aliquid in motu est (energia kinetica) aut in positione alta est (energia potentialis). Breviter, labor energiam utitur ad res movendas aut mutandas.","breadcrumb":{"@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/#breadcrumb"},"inLanguage":"es","potentialAction":[{"@type":"ReadAction","target":["http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/"]}]},{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/#primaryimage","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/energia.jpg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2024\/09\/energia.jpg","width":1792,"height":1024},{"@type":"BreadcrumbList","@id":"http:\/\/toposuranos.com\/material\/la\/labor-et-energia-mechanica\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"http:\/\/toposuranos.com\/material\/es\/cursos-de-matematica-y-fisica\/"},{"@type":"ListItem","position":2,"name":"Labor et Energia Mechanica"}]},{"@type":"WebSite","@id":"http:\/\/toposuranos.com\/material\/#website","url":"http:\/\/toposuranos.com\/material\/","name":"toposuranos.com\/material","description":"","publisher":{"@id":"http:\/\/toposuranos.com\/material\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"http:\/\/toposuranos.com\/material\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"es"},{"@type":"Organization","@id":"http:\/\/toposuranos.com\/material\/#organization","name":"toposuranos.com\/material","url":"http:\/\/toposuranos.com\/material\/","logo":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/logo.png","width":2400,"height":2059,"caption":"toposuranos.com\/material"},"image":{"@id":"http:\/\/toposuranos.com\/material\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/groups\/toposuranos","https:\/\/x.com\/topuranos","https:\/\/www.youtube.com\/channel\/UC16yDm12cPcrwsE0fAM7X1g","https:\/\/www.linkedin.com\/company\/69429190"]},{"@type":"Person","@id":"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1","name":"giorgio.reveco","image":{"@type":"ImageObject","inLanguage":"es","@id":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","url":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","contentUrl":"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2023\/10\/1694478625378-96x96.jpeg","caption":"giorgio.reveco"},"description":"Soy Licenciado en F\u00edsica, Magister en Ingenier\u00eda Industrial y Docente Universitario. Me dedico a desmitificar la f\u00edsica y las matem\u00e1ticas. Mi objetivo es hacer que estos campos sean f\u00e1cilmente comprensibles para todos, proporcionando las herramientas para explorar no solo el mundo que nos rodea, sino tambi\u00e9n las profundidades de nuestra propia existencia y el orden natural que nos conecta con el cosmos.","sameAs":["http:\/\/toposuranos.com\/material"],"url":"http:\/\/toposuranos.com\/material\/author\/giorgio-reveco\/"}]}},"_links":{"self":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/34486","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/comments?post=34486"}],"version-history":[{"count":0,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/posts\/34486\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media\/28589"}],"wp:attachment":[{"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/media?parent=34486"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/categories?post=34486"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/toposuranos.com\/material\/wp-json\/wp\/v2\/tags?post=34486"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}