{"id":516,"date":"2020-11-30T11:25:44","date_gmt":"2020-11-30T11:25:44","guid":{"rendered":"https:\/\/pickedshares.com\/?p=516"},"modified":"2021-05-08T11:27:48","modified_gmt":"2021-05-08T11:27:48","slug":"engineering-mechanics-1-exercise-6-calculate-the-resulting-moment","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-6-calculate-the-resulting-moment\/","title":{"rendered":"Calculate the resulting moment"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>The forces F<sub>1<\/sub> and F<sub>2<\/sub> are located in the x-y plane. Calculate the resulting moment for both forces combined at the origin.<\/p>\n\n\n\n<p>F<sub>1<\/sub> = 20 N, F<sub>2<\/sub> = 30 N<\/p>\n\n\n\n<p>x<sub>1<\/sub> = 1 m, x<sub>2<\/sub> = 2 m, y<sub>1<\/sub> = 1 m, y<sub>2<\/sub> = 2 m<\/p>\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\/02\/tm1-6-1.png\" alt=\"Two forces in the coordinate system\" class=\"wp-image-3262\" width=\"589\" height=\"563\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-6-1.png 785w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-6-1-300x287.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-6-1-768x735.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-6-1-400x383.png 400w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><figcaption>Two forces in the coordinate system<\/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.<\/p>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"Technische Mechanik 1, &Uuml;bung 6 - Resultierendes Moment berechnen\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_YjHIEo1zt38\" 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%2FYjHIEo1zt38%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/YjHIEo1zt38\" \/><meta itemprop=\"duration\" content=\"PT2M44S\" \/><meta itemprop=\"uploadDate\" content=\"2020-09-16T18:51:35Z\" \/><\/div><div id=\"lyte_YjHIEo1zt38\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FYjHIEo1zt38%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Technische Mechanik 1, \u00dcbung 6 - Resultierendes Moment berechnen<\/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\/YjHIEo1zt38\" 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%2FYjHIEo1zt38%2F0.jpg\" alt=\"Technische Mechanik 1, &Uuml;bung 6 - Resultierendes Moment berechnen\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Die Kr\u00e4fte F1 und F2 liegen in der x-y-Ebene. Berechnen Sie das resultierende Moment, wenn die beiden Kr\u00e4fte F1 und F2 im Ursprung zusammengefasst werden. Diese \u00dcbung findet man auch auf https:\/\/pickedshares.com\/technische-mechanik-1-uebung-6-resultierendes-moment-berechnen\/ This exercise can also be found at https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-6-calculate-the-resulting-moment\/\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<p>We assume <a href=\"https:\/\/pickedshares.com\/en\/right-hand-rules\/\" target=\"_blank\" rel=\"noreferrer noopener\">left-turning moments to be positive<\/a>. The resulting moment is given by:<\/p>\n\n\n\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\\[ \\require{cancel} \\]\n\\[ \\newcommand{\\myvec}[1]{{\\begin{pmatrix}#1\\end{pmatrix}}} \\]\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{1} M_0 = F_1 \\cdot x_1 - F_2 \\cdot y_1 \\]<\/p>\n\n<p>\\[\\tag{2} M_0 = 20 N \\cdot 1 m - 30 N \\cdot 1 m \\]<\/p>\n\n<p>\\[\\tag{3} M_0 = -10 N m \\]<\/p>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Annotations<\/h2>\n\n\n\n<p>The assumption of the left-turning positive moments results from the <a href=\"https:\/\/pickedshares.com\/en\/right-hand-rules\/\">right-hand-rules<\/a>. The z-axis of the coordinate system points to the viewer, this leads to left-oriented positive moments.<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Calculate the resulting moment\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-6-calculate-the-resulting-moment\/\" aria-label=\"Read more about Calculate the resulting moment\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":3264,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[48,29],"class_list":["post-516","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-resulting-moments","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>Calculate the resulting moment &#8226; pickedshares<\/title>\n<meta name=\"description\" content=\"Two forces are located in the horizontal plane. 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