{"id":513,"date":"2020-11-30T09:57:05","date_gmt":"2020-11-30T09:57:05","guid":{"rendered":"https:\/\/pickedshares.com\/?p=513"},"modified":"2021-05-08T11:24:44","modified_gmt":"2021-05-08T11:24:44","slug":"engineering-mechanics-1-exercise-5-determine-force-length-and-angle","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-5-determine-force-length-and-angle\/","title":{"rendered":"Asymmetrical load on two ropes"},"content":{"rendered":"\n<p>This exercise investigates an asymmetrical load on two ropes and is about how to determine geometrical conditions for a force in a <a href=\"http:\/\/mechanicsmap.psu.edu\/websites\/2_equilibrium_concurrent\/concurrent_forces\/concurrentforces.html\" target=\"_blank\" rel=\"noreferrer noopener\">concurrent force system<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A weight load of G = 100 N shall be suspended from two ropes 1 and 2 in such a way that the dimensions a = 2 m and h = 2 m are met and the force in rope 1 reach the value S<sub>1<\/sub> = 80 N. How long must the distance between the two supports, hereby referred as l, be?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"816\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-1-1024x816.png\" alt=\"A load hangs asymmetrically on two ropes\" class=\"wp-image-3355\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-1-1024x816.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-1-300x239.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-1-768x612.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-1-400x319.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-1-800x638.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-1.png 1489w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>A load hangs asymmetrically on two ropes<\/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 solution.<\/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=\"Kraft, L&auml;nge und Winkel ermitteln - Technische Mechanik 1, &Uuml;bung 5\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_4iGRCZc0wo8\" 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%2F4iGRCZc0wo8%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/4iGRCZc0wo8\" \/><meta itemprop=\"duration\" content=\"PT8M59S\" \/><meta itemprop=\"uploadDate\" content=\"2020-02-28T20:01:20Z\" \/><\/div><div id=\"lyte_4iGRCZc0wo8\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2F4iGRCZc0wo8%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Kraft, L\u00e4nge und Winkel ermitteln - Technische Mechanik 1, \u00dcbung 5<\/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\/4iGRCZc0wo8\" 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%2F4iGRCZc0wo8%2F0.jpg\" alt=\"Kraft, L&auml;nge und Winkel ermitteln - Technische Mechanik 1, &Uuml;bung 5\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"Eine Last mit der Eigengewichtskraft G = 100 N soll an zwei Seilen 1 und 2 so aufgeh\u00e4ngt werden, dass die Ma\u00dfe a und h eingehalten werden und die Kraft in Seil 1 den Wert S1 annimmt. Wie gro\u00df ist l? Diese \u00dcbung findet man auch auf https:\/\/pickedshares.com\/technische-mechanik-1-uebung-5-kraft-laenge-und-winkel-ermitteln\/ A load G shall be held from ropes 1 and 2 in such a way that dimensions a and b are maintained and the force in rope 1 assumes the specified value S1. Calculate the length l! This exercise can also be found at https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-5-determine-force-length-and-angle\/\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<p>The load G splits into the two rope forces S1 and S2. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"828\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-2-1024x828.png\" alt=\"The two rope forces\" class=\"wp-image-3359\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-2-1024x828.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-2-300x243.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-2-768x621.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-2-400x323.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-2-800x647.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-2.png 1483w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>The two rope forces<\/figcaption><\/figure>\n\n\n\n<p>At the connection point of the ropes a concurrent force system establishes. All forces act at the same central point. (The forces S<sub>1<\/sub> and S<sub>2<\/sub> are drawn side by side for readability, both are acting on the same point.)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-3.png\" alt=\"The forces at the node\" class=\"wp-image-3361\" width=\"405\" height=\"412\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-3.png 540w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-3-295x300.png 295w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/02\/tm1-5-3-400x407.png 400w\" sizes=\"auto, (max-width: 405px) 100vw, 405px\" \/><figcaption>The forces at the node<\/figcaption><\/figure><\/div>\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<p>The equilibria of forces for the x and y directions are established. For this purpose, the rope forces are broken down into their respective components.<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{1} \\sum F_x = 0 = -S_{1x} + S_{2x} \\] <\/p>\n<p>\\[\\tag{2} \\sum F_y = 0 = S_{1y} + S_{2y} - G \\] <\/p>\n<\/div>\n\n<p>The angle \u03b1 can be calculated from the given lengths h and a.<\/p>\n<p>\\[\\tag{3} \\alpha = arctan \\left( \\frac{h}{a} \\right) = 45\u00b0 \\]<\/p>\n\n<p>With this angle and the specified force for rope 1, the x-components of the force in rope 1 can be calculated.<\/p>\n\n<p>\\[\\tag{4} S_{1x} = S_1 cos \\alpha \\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{5} S_{1x} = 80 N \\cdot cos 45\u00b0 = 56.6 N \\]<\/p>\n<\/div>\n<p>\\[\\tag{6} S_{2x} = S_{1x} = 56.6 N \\]<\/p>\n\n<p>And also the y component.<\/p>\n\n<p>\\[\\tag{7} S_{1y} = S_1 sin \\alpha \\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{8} S_{1y} = 80 N \\cdot sin 45\u00b0 = 56.6 N \\]<\/p>\n<\/div>\n\n<p>From equation 2 follows<\/p>\n\n<p>\\[\\tag{9} S_{2y} = G - S_{1y} \\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{10} S_{2y} = 100 N - 56.6 N = 43.4 N \\]<\/p>\n<\/div>\n\n<p>The force in rope 2 is calculated using the Pythagorean theorem.<\/p>\n\n<p>\\[\\tag{11} S_2 = \\sqrt{S_{2x}^2 + S_{2y}^2} \\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{12} S_2 = \\sqrt{56.6^2 N^2 + 43.4^2 N^2} = 71.3 N \\]<\/p>\n<\/div>\n\n<p>The angle \u03b2 results from<\/p>\n<p>\\[\\tag{13} S_{2x} = S_2 cos \\beta \\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{14} \\beta = arccos \\left( \\frac{S_{2x}}{S_2} \\right) = 37.5\u00b0  \\]<\/p>\n<\/div>\n\n<p>The angle \u03b2 is related to h, l and a. The required length l can now be calculated from this.<\/p>\n<p>\\[\\tag{15} \\beta = arctan \\left( \\frac{h}{l-a} \\right) \\]<\/p>\n<p>\\[\\tag{16} tan \\beta = \\frac{h}{l-a}  \\]<\/p>\n<p>\\[\\tag{17} l = \\frac{h}{tan \\beta} + a = 4.6 m \\]<\/p>\n\n\n\n<p>So this was the way to determine geometrical conditions for an asymmetrical load on two ropes. Here we have a quite similar <a href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-4-calculate-the-permissible-angle\/\">exercise about a symmetrical suspended load on two ropes<\/a>.<\/p>\n\n\n\n<p>Don't miss the other <a href=\"https:\/\/pickedshares.com\/en\/category\/exercises\/engineering-mechanics-i\/\">exercises regarding Engineering Mechanics<\/a> 1!<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Asymmetrical load on two ropes\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-5-determine-force-length-and-angle\/\" aria-label=\"Read more about Asymmetrical load on two ropes\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":389,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[47,29],"class_list":["post-513","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>Asymmetrical load on two ropes &#8226; Engineering Mechanics<\/title>\n<meta name=\"description\" content=\"This exercise is about an asymmetrical load on two ropes. 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