{"id":503,"date":"2020-11-29T17:02:44","date_gmt":"2020-11-29T17:02:44","guid":{"rendered":"https:\/\/pickedshares.com\/?p=503"},"modified":"2021-05-31T18:11:44","modified_gmt":"2021-05-31T18:11:44","slug":"engineering-mechanics-1-exercise-2-determine-missing-force-and-angle-with-a-given-resulting-force","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-2-determine-missing-force-and-angle-with-a-given-resulting-force\/","title":{"rendered":"Determine missing force and angle with a given resultant force"},"content":{"rendered":"\n<p>This exercise is about how to determine a missing force and adresses the following questions:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>How to calculate a missing force by a given resultant force?<\/li><li>How to determine the angle of a force?<\/li><li>How to change equations and solve unknown values (or how to solve a simple equation system)?<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Task<\/h3>\n\n\n\n<p>A ship is being pulled by three tugs. Tug 1 pulls with F<sub>1<\/sub> = 7 kN, tug 2 with F<sub>2<\/sub> = 6 kN. The force for tug 3 and its angle has to be calculated for a resultant force of 10 kN in x-direction.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"717\" height=\"648\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/TM1E2.png\" alt=\"tugs with pulling forces\" class=\"wp-image-392\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/TM1E2.png 717w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/TM1E2-300x271.png 300w\" sizes=\"auto, (max-width: 717px) 100vw, 717px\" \/><figcaption>Tugs with pulling forces<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\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-16-9 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"Technische Mechanik 1, &Uuml;bung 2 - Kraft und Winkel bei einer gegebenen Resultierenden ermitteln\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_B9iHrwSdan4\" 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%2FB9iHrwSdan4%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/B9iHrwSdan4\" \/><meta itemprop=\"duration\" content=\"PT9M41S\" \/><meta itemprop=\"uploadDate\" content=\"2020-02-15T17:10:44Z\" \/><\/div><meta itemprop=\"accessibilityFeature\" content=\"captions\" \/><div id=\"lyte_B9iHrwSdan4\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FB9iHrwSdan4%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Technische Mechanik 1, \u00dcbung 2 - Kraft und Winkel bei einer gegebenen Resultierenden ermitteln<\/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\/B9iHrwSdan4\" 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%2FB9iHrwSdan4%2F0.jpg\" alt=\"Technische Mechanik 1, &Uuml;bung 2 - Kraft und Winkel bei einer gegebenen Resultierenden ermitteln\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Ein Schiff wird von drei Schleppern gezogen. Schlepper 1 und 2 ziehen mit den jeweils gegebenen Kr\u00e4ften und Winkeln, f\u00fcr Schlepper 3 wird sowohl die Kraft als auch der Winkel f\u00fcr den Fall gesucht, dass die resultierende Kraft 10 kN in x-Richtung betr\u00e4gt. Diese \u00dcbung findet man auch auf https:\/\/pickedshares.com\/technische-mechanik-1-uebung-2-kraft-und-winkel-bei-einer-gegebenen-resultierenden-ermitteln\/ A ship is towed by 3 tugs. Tug 1 tows with the force F1 = 7 kN, tug 2 with F2 = 6 kN. With which force and at what angle must tug 3 tow so that a resulting force of 10 kN acts in the direction of the x-axis? This exercise can also be found at https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-2-determine-missing-force-and-angle-with-a-given-resulting-force\/\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<p>The boundary conditions for the solution are: the sum of all forces in the x direction is 10 kN, the sum of all forces in the y direction is zero.<\/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\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{1} \\sum F_x= 10 kN = F_1\\cos(60\u00b0)+F_2\\cos(45\u00b0)+F_3\\cos(\\alpha)\\]<\/p>\n<p>\\[\\tag{2} \\sum F_y= 0 = F_1\\sin(60\u00b0)-F_2\\sin(45\u00b0)+F_3\\sin(\\alpha)\\]<\/p>\n<\/div>\n\n\n\n<p>Equation 1 is solved for F<sub>3<\/sub> and inserted into equation 2.<\/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\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{3} F_3= \\frac{10 kN - F_1\\cos(60\u00b0) - F_2\\cos(45\u00b0)}{\\cos(\\alpha)}\\]<\/p>\n<p>\\[\\tag{4} 0 = F_1\\sin(60\u00b0)-F_2\\sin(45\u00b0)+\\frac{10 kN - F_1\\cos(60\u00b0) - F_2\\cos(45\u00b0)}{\\cos(\\alpha)}\\sin(\\alpha)  \\]<\/p>\n<\/div>\n\n\n\n<p>Equation 4 is solved to<\/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\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{5} \\alpha = \\arctan\\left(\\frac{F_2\\sin(45\u00b0)-F_1\\sin(60\u00b0)}{10 kN - F_1\\cos(60\u00b0) - F_2\\cos(45\u00b0)}\\right)  \\]<\/p>\n<\/div>\n<p>\\[\\tag{6} \\alpha = -38.9\u00b0  \\]<\/p>\n\n\n\n<p>and the missing force is<\/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<p>\\[\\tag{7} F_3 = 2.9 kN  \\]<\/p>\n\n\n\n<p>Here we have some more <a href=\"https:\/\/pickedshares.com\/en\/tag\/resulting-force\/\">exercises about resulting forces<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Determine missing force and angle with a given resultant force\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-2-determine-missing-force-and-angle-with-a-given-resulting-force\/\" aria-label=\"Read more about Determine missing force and angle with a given resultant force\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":393,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[47,29],"class_list":["post-503","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>Determine missing force and angle with a given resultant force<\/title>\n<meta name=\"description\" content=\"Three tugs are pulling a ship with a given resultant force. 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