{"id":486,"date":"2020-11-28T17:08:10","date_gmt":"2020-11-28T17:08:10","guid":{"rendered":"https:\/\/pickedshares.com\/?p=486"},"modified":"2021-05-31T18:14:26","modified_gmt":"2021-05-31T18:14:26","slug":"engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/","title":{"rendered":"Calculation of the resultant force"},"content":{"rendered":"\n<p>This exercise is about the calculation of the resultant force in a <a href=\"https:\/\/mypages.iit.edu\/~krawczyk\/phdsza\/02conc.htm\" target=\"_blank\" rel=\"noreferrer noopener\">concurrent force system<\/a> and addresses the following questions:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>How to calculate the components of a force?<\/li><li>When do I use sine or cosine for angle calculation?<\/li><li>How to determine the angle of a resulting force?<\/li><li>How to determine the resulting force the graphical way?<\/li><\/ul>\n\n\n\n<p>Here is an <a href=\"https:\/\/pickedshares.com\/en\/online-calculator-resulting-force\/\">online calculation tool<\/a> for your assistance.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>There are four forces acting on a power line pole in the horizontal plane. Calculate the resultant force for the following parameters:<\/p>\n\n\n\nF1 = 1.000 N, \u03b1 = 45\u00b0 <br>\nF2 = 800 N, \u03b2 = 20\u00b0 <br>\nF3 = 1.500 N, \u03b3 = 30\u00b0 <br>\nF4 = 900 N, \u03b4 = 15\u00b0\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1.png\" alt=\"Four forces acting on a power line pole\" class=\"wp-image-2069\" width=\"604\" height=\"415\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1.png 805w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1-300x206.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1-768x528.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1-400x275.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1-800x550.png 800w\" sizes=\"auto, (max-width: 604px) 100vw, 604px\" \/><figcaption>Four forces acting on a power line pole<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p>The following video is in German language. Please scroll down for the written version.<\/p>\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=\"lyte-wrapper\" title=\"Resultierende Kraft berechnen (neue Version) - Technische Mechanik 1, &Uuml;bung 1\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_IURojyB2ihA\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\"><div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FIURojyB2ihA%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/IURojyB2ihA\" \/><meta itemprop=\"duration\" content=\"PT5M5S\" \/><meta itemprop=\"uploadDate\" content=\"2021-01-20T12:18:25Z\" \/><\/div><div id=\"lyte_IURojyB2ihA\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FIURojyB2ihA%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Resultierende Kraft berechnen (neue Version) - Technische Mechanik 1, \u00dcbung 1<\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/IURojyB2ihA\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FIURojyB2ihA%2F0.jpg\" alt=\"Resultierende Kraft berechnen (neue Version) - Technische Mechanik 1, &Uuml;bung 1\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Aufgabe: An einem Leitungsmast greifen 4 Kr\u00e4fte in der horizontalen Ebene an. Wie gro\u00df ist die resultierende Kraft? Ich zeige &quot;2,5&quot; L\u00f6sungen: 1. Rechnerisch 2. Zeichnerisch 3. mit einem Onlinerechner :) Im Video zeige ich, wie man die resultierende Kraft berechnet, indem man die einzelnen Kr\u00e4fte in ihre Komponenten zerlegt und dann in x- und y-Rechnung zusammenrechnet. Dann wird der Winkel der Resultierenden berechnet und der Betrag der resultierenden Kraft mit dem Satz des Pythagoras bestimmt. Anschlie\u00dfend zeige ich, wie man grafisch zur selben L\u00f6sung kommt, und ganz zum Schluss zeige ich noch den passenden Onlinerechner, mit dem man die resultierende Kraft von 2 oder 3 oder 4 Kr\u00e4ften bestimmen kann. Hier der Link zum Onlinerechner: https:\/\/pickedshares.com\/onlinerechner-resultierende-kraft\/ Und hier die \u00dcbung zum Nachlesen: https:\/\/pickedshares.com\/technische-mechanik-1-uebung-1-resultierende-kraft-berechnen\/\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<h3 class=\"wp-block-heading\">Calculation of the resultant force<\/h3>\n\n\n\n<p>The resultant force is called F<sub>R<\/sub> in this calculation. So the component of the resultant force in x-direction is F<sub>Rx<\/sub> and the component in y-direction is F<sub>Ry<\/sub>. The components of the resultant force are equal to the sum of the concurrent forces in each direction.<\/p>\n\n\n\n<meta http-equiv=\"Content-Type\" content=\"text\/html; charset=utf-8\">\n    <script type=\"text\/x-mathjax-config\">  MathJax.Hub.Config({\n    displayAlign: \"left\",\n    context: \"MathJax\",\n    TeX: {TagSide: \"left\"}\n  })\n<\/script>\n    <script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n      \n  \n    <!-- ****************************************************** -->\n    <!-- *        Created with wxMaxima version 20.06.6       * -->\n    <!-- ****************************************************** -->\n    <noscript>\n      <div class=\"error message\">\n        <p>Please enable JavaScript in order to get a 2d display of the equations embedded in this web page.<\/p>\n      <\/div>\n    <\/noscript>\n    <p hidden=\"hidden\">\\(      \\DeclareMathOperator{\\abs}{abs}\n      \\newcommand{\\ensuremath}[1]{\\mbox{$#1$}}\n\\)<\/p>\n    \n    <!-- Text cell -->\n    <div class=\"comment\">Sum of forces in direction x:\n<\/div>\n<div style=\"overflow:auto;\">\n    <!-- Code cell -->\n    <p class=\"line25\">\\[\\tag{1} {F_{\\mathit{Rx}}}={F_4} \\sin{\\left( \\delta \\right) }-{F_3} \\cos{\\left( \\gamma \\right) }-{F_2} \\cos{\\left( \\beta \\right) }+{F_1} \\cos{\\left( \\alpha \\right) }\\]\n<\/p>\n<\/div>\n    <!-- Text cell -->\n    <div class=\"comment\">Sum of forces in direction y:\n<\/div>\n<div style=\"overflow:auto;\">\n    <!-- Code cell -->\n    <p class=\"line25\">\\[\\tag{2} {F_{\\mathit{Ry}}}=-{F_4} \\cos{\\left( \\delta \\right) }-{F_3} \\sin{\\left( \\gamma \\right) }+{F_2} \\sin{\\left( \\beta \\right) }+{F_1} \\sin{\\left( \\alpha \\right) }\\]\n<\/p>\n<\/div>\n<!-- Text cell -->\n    <div class=\"comment\">The resulting force is calculated from the Pythagorean theorem.\n<\/div>\n    <!-- Code cell -->\n    <p class=\"line50\">\\[\\tag{3} {F_R}=\\sqrt{{{{F_{\\mathit{Ry}}}}^{2}}+{{{F_{\\mathit{Rx}}}}^{2}}}\\]\n<\/p>\n<!-- Text cell -->\n    <div class=\"comment\">The angle between the x-axis and the resulting force is\n<\/div>\n    <!-- Code cell -->\n    <p class=\"line75\">\\[\\tag{4} \\epsilon =\\operatorname{atan}\\left( \\frac{{F_{\\mathit{Ry}}}}{{F_{\\mathit{Rx}}}}\\right) \\]\n<\/p>\n   <!-- Text cell -->\n    <div class=\"comment\">But now to the real numbers. So the x-component of the resulting force is\n<\/div>\n    <!-- Code cell -->\n    <p class=\"line25\">\\[\\tag{5} {F_{\\mathit{Rx}}}=-1110.7 N\\]\n<\/p>\n<!-- Text cell -->\n    <div class=\"comment\">The y-component of the resulting force is\n<\/div>\n    <!-- Code cell -->\n    <p class=\"line25\">\\[\\tag{6} {F_{\\mathit{Ry}}}=-638.6 N\\]\n<\/p>\n<!-- Text cell -->\n    <div class=\"comment\">And the resulting force is\n<\/div>\n<!-- Code cell -->\n    <p class=\"line25\">\\[\\tag{7} {F_{\\mathit{R}}}=1.281 N\\]\n<\/p>\n<!-- Text cell -->\n    <div class=\"comment\">With an angle of\n<\/div>\n    <!-- Code cell -->\n    <p class=\"line25\">\\[\\tag{8} \\epsilon =29.9\u00b0\\]\n<\/p>\n\n\n\n<p>There is another way how to determine the resultant force for two or more forces. It is the<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Graphical determination of the resultant force<\/h3>\n\n\n\n<p>The individual forces have to be drawn to scale (!). The easiest way is to draw the forces as shown here, starting from the origin of the coordinate system and then move them in parallel. The order of the shift does not matter, it is only important that in the end a \"chain\" of all forces is created. The resulting force is obtained by connecting the origin of the coordinate system to the end of the chain.<\/p>\n\n\n\n<p>The following picture corresponds to the above 4 forces F<sub>1<\/sub> to F<sub>4<\/sub>, this time shown precisely and to scale. The black arrows are the force vectors displaced in parallel, the blue vector is the resulting force.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"751\" height=\"626\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1_2.png\" alt=\"Graphical determination of the resulting force\" class=\"wp-image-1299\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1_2.png 751w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1_2-300x250.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1_2-400x333.png 400w\" sizes=\"auto, (max-width: 751px) 100vw, 751px\" \/><figcaption>Graphical determination of the resultant force<\/figcaption><\/figure>\n\n\n\n<p>We have some more <a href=\"https:\/\/pickedshares.com\/en\/tag\/resulting-force\/\">exercises about resultant forces<\/a> here.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">General facts about resultant forces<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Can resulting forces be zero?<\/h3>\n\n\n\n<p>Yes, they can. If the concurrent forces are perfectly acting against each other, the resulting force can be zero. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Can resulting forces be negative?<\/h3>\n\n\n\n<p>Only their components can be negative. The algebraic sign of the x- or y-component of the resulting force shows in which direction the component points (this can be seen in the exercise above).<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Calculation of the resultant force\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/\" aria-label=\"Read more about Calculation of the resultant force\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":2071,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[47,29],"class_list":["post-486","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-resultant-force","tag-statics","infinite-scroll-item","masonry-post","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-33"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Calculation of the resultant force &#8226; Mechanics Exercise and Solution<\/title>\n<meta name=\"description\" content=\"This exercise shows how to calculate the resultant force from 4 forces and how to determine the resultant force graphically.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Calculation of the resultant force &#8226; Mechanics Exercise and Solution\" \/>\n<meta property=\"og:description\" content=\"This exercise shows how to calculate the resultant force from 4 forces and how to determine the resultant force graphically.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/\" \/>\n<meta property=\"og:site_name\" content=\"pickedshares\" \/>\n<meta property=\"article:published_time\" content=\"2020-11-28T17:08:10+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-05-31T18:14:26+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1-twit.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1108\" \/>\n\t<meta property=\"og:image:height\" content=\"822\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:image\" content=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1-twit.png\" \/>\n<meta name=\"twitter:creator\" content=\"@pickedshares\" \/>\n<meta name=\"twitter:site\" content=\"@pickedshares\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#\\\/schema\\\/person\\\/6c617a6a61de9623da53f74a56810033\"},\"headline\":\"Calculation of the resultant force\",\"datePublished\":\"2020-11-28T17:08:10+00:00\",\"dateModified\":\"2021-05-31T18:14:26+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/\"},\"wordCount\":575,\"publisher\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/pickedshares.com\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/tm1-1mini.png\",\"keywords\":[\"Resultant force\",\"Statics\"],\"articleSection\":[\"Engineering Mechanics I\",\"Exercises\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/\",\"url\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/\",\"name\":\"Calculation of the resultant force &#8226; Mechanics Exercise and Solution\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/pickedshares.com\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/tm1-1mini.png\",\"datePublished\":\"2020-11-28T17:08:10+00:00\",\"dateModified\":\"2021-05-31T18:14:26+00:00\",\"description\":\"This exercise shows how to calculate the resultant force from 4 forces and how to determine the resultant force graphically.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/#primaryimage\",\"url\":\"https:\\\/\\\/pickedshares.com\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/tm1-1mini.png\",\"contentUrl\":\"https:\\\/\\\/pickedshares.com\\\/wp-content\\\/uploads\\\/2021\\\/01\\\/tm1-1mini.png\",\"width\":483,\"height\":332,\"caption\":\"Four forces acting on a power line pole.\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Start\",\"item\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Exercises\",\"item\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/category\\\/exercises\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Engineering Mechanics I\",\"item\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/category\\\/exercises\\\/engineering-mechanics-i\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Calculation of the resultant force\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#website\",\"url\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/\",\"name\":\"pickedshares\",\"description\":\"Engineering Design, Project Management, Tools and Exercises\",\"publisher\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#organization\",\"name\":\"pickedshares.com\",\"url\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"\",\"contentUrl\":\"\",\"caption\":\"pickedshares.com\"},\"image\":{\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/x.com\\\/pickedshares\",\"https:\\\/\\\/www.instagram.com\\\/pickedshares\\\/\",\"https:\\\/\\\/www.youtube.com\\\/channel\\\/UCSh8qo2-6dhtbZqSLStt3Rg\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/pickedshares.com\\\/en\\\/#\\\/schema\\\/person\\\/6c617a6a61de9623da53f74a56810033\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g\",\"caption\":\"admin\"},\"sameAs\":[\"https:\\\/\\\/pickedshares.com\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Calculation of the resultant force &#8226; Mechanics Exercise and Solution","description":"This exercise shows how to calculate the resultant force from 4 forces and how to determine the resultant force graphically.","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":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/","og_locale":"en_US","og_type":"article","og_title":"Calculation of the resultant force &#8226; Mechanics Exercise and Solution","og_description":"This exercise shows how to calculate the resultant force from 4 forces and how to determine the resultant force graphically.","og_url":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/","og_site_name":"pickedshares","article_published_time":"2020-11-28T17:08:10+00:00","article_modified_time":"2021-05-31T18:14:26+00:00","og_image":[{"width":1108,"height":822,"url":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1-twit.png","type":"image\/png"}],"author":"admin","twitter_card":"summary_large_image","twitter_image":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1-twit.png","twitter_creator":"@pickedshares","twitter_site":"@pickedshares","twitter_misc":{"Written by":"admin","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/#article","isPartOf":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/"},"author":{"name":"admin","@id":"https:\/\/pickedshares.com\/en\/#\/schema\/person\/6c617a6a61de9623da53f74a56810033"},"headline":"Calculation of the resultant force","datePublished":"2020-11-28T17:08:10+00:00","dateModified":"2021-05-31T18:14:26+00:00","mainEntityOfPage":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/"},"wordCount":575,"publisher":{"@id":"https:\/\/pickedshares.com\/en\/#organization"},"image":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/#primaryimage"},"thumbnailUrl":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1mini.png","keywords":["Resultant force","Statics"],"articleSection":["Engineering Mechanics I","Exercises"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/","url":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/","name":"Calculation of the resultant force &#8226; Mechanics Exercise and Solution","isPartOf":{"@id":"https:\/\/pickedshares.com\/en\/#website"},"primaryImageOfPage":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/#primaryimage"},"image":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/#primaryimage"},"thumbnailUrl":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1mini.png","datePublished":"2020-11-28T17:08:10+00:00","dateModified":"2021-05-31T18:14:26+00:00","description":"This exercise shows how to calculate the resultant force from 4 forces and how to determine the resultant force graphically.","breadcrumb":{"@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/#primaryimage","url":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1mini.png","contentUrl":"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-1mini.png","width":483,"height":332,"caption":"Four forces acting on a power line pole."},{"@type":"BreadcrumbList","@id":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-1-calculation-of-the-resulting-force\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Start","item":"https:\/\/pickedshares.com\/en\/"},{"@type":"ListItem","position":2,"name":"Exercises","item":"https:\/\/pickedshares.com\/en\/category\/exercises\/"},{"@type":"ListItem","position":3,"name":"Engineering Mechanics I","item":"https:\/\/pickedshares.com\/en\/category\/exercises\/engineering-mechanics-i\/"},{"@type":"ListItem","position":4,"name":"Calculation of the resultant force"}]},{"@type":"WebSite","@id":"https:\/\/pickedshares.com\/en\/#website","url":"https:\/\/pickedshares.com\/en\/","name":"pickedshares","description":"Engineering Design, Project Management, Tools and Exercises","publisher":{"@id":"https:\/\/pickedshares.com\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/pickedshares.com\/en\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/pickedshares.com\/en\/#organization","name":"pickedshares.com","url":"https:\/\/pickedshares.com\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/pickedshares.com\/en\/#\/schema\/logo\/image\/","url":"","contentUrl":"","caption":"pickedshares.com"},"image":{"@id":"https:\/\/pickedshares.com\/en\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/x.com\/pickedshares","https:\/\/www.instagram.com\/pickedshares\/","https:\/\/www.youtube.com\/channel\/UCSh8qo2-6dhtbZqSLStt3Rg"]},{"@type":"Person","@id":"https:\/\/pickedshares.com\/en\/#\/schema\/person\/6c617a6a61de9623da53f74a56810033","name":"admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/948d17e3c131a29d2f00c792d96bb1899342a69d8ccda0673ef9089a0988b3bd?s=96&d=mm&r=g","caption":"admin"},"sameAs":["https:\/\/pickedshares.com"]}]}},"_links":{"self":[{"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/posts\/486","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/comments?post=486"}],"version-history":[{"count":22,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/posts\/486\/revisions"}],"predecessor-version":[{"id":5632,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/posts\/486\/revisions\/5632"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/media\/2071"}],"wp:attachment":[{"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/media?parent=486"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/categories?post=486"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pickedshares.com\/en\/wp-json\/wp\/v2\/tags?post=486"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}