{"id":709,"date":"2020-12-06T20:34:52","date_gmt":"2020-12-06T20:34:52","guid":{"rendered":"https:\/\/pickedshares.com\/?p=709"},"modified":"2021-05-08T11:42:37","modified_gmt":"2021-05-08T11:42:37","slug":"engineering-mechanics-1-exercise-15-reaction-forces-of-a-hook-wrench","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-15-reaction-forces-of-a-hook-wrench\/","title":{"rendered":"Reaction forces of a hook wrench"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A hook wrench is attached to a stationary shaft. Which reaction forces arise in A and B under the assumption that the contact in B is frictionless?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"531\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-134116_Sketch-1024x531.jpg\" alt=\"Hook wrench on shaft\" class=\"wp-image-418\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-134116_Sketch-1024x531.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-134116_Sketch-300x156.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-134116_Sketch-768x398.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201105-134116_Sketch.jpg 1418w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Hook wrench on the shaft<\/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=\"Reaktionskr&auml;fte bestimmen - Technische Mechanik 1, &Uuml;bung 15\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_cFDzqefUonY\" 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%2FcFDzqefUonY%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/cFDzqefUonY\" \/><meta itemprop=\"duration\" content=\"PT8M3S\" \/><meta itemprop=\"uploadDate\" content=\"2020-11-03T23:00:05Z\" \/><\/div><div id=\"lyte_cFDzqefUonY\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FcFDzqefUonY%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Reaktionskr\u00e4fte bestimmen - Technische Mechanik 1, \u00dcbung 15<\/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\/cFDzqefUonY\" 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%2FcFDzqefUonY%2F0.jpg\" alt=\"Reaktionskr&auml;fte bestimmen - Technische Mechanik 1, &Uuml;bung 15\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"An einer feststehenden Welle wird ein Hakenschl\u00fcssel angesetzt. Welche Reaktionskr\u00e4fte entstehen in A und B unter der Annahme, dass der Kontakt in B reibungsfrei ist?\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"676\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-093800_Sketch-1024x676.jpg\" alt=\"Reaction forces on the shaft\" class=\"wp-image-586\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-093800_Sketch-1024x676.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-093800_Sketch-300x198.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-093800_Sketch-768x507.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-093800_Sketch-400x264.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-093800_Sketch-800x528.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/Screenshot_20201202-093800_Sketch.jpg 1481w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Reaction forces on the shaft<\/figcaption><\/figure>\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<p>The reaction forces on the shaft are shown in the sketch of the solution. The hook wrench touches the shaft at points A and B. On a spatial shaft a line contact would occur.<\/p>\n\n<p>The equilibrium of forces in the x-direction is<\/p>\n<p>\\[\\tag{1} \\sum F_x = 0 = F_B - F_{Ax} \\]<\/p>\n<p>\\[\\tag{2} F_{Ax} = F_B \\]<\/p>\n\n<p>The equilibrium of forces in the y-direction is<\/p>\n<p>\\[\\tag{3} \\sum F_y = 0 = F_{Ay} - F \\]<\/p>\n<p>\\[\\tag{4} F_{Ay} = F \\]<\/p>\n\n<p>The equilibrium of moments is established around the axis of rotation of the shaft. The moment applied by the force F is referred to as M <sub> F <\/sub>, so that the moment equilibrium reads<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{5} \\sum M = 0 = - M_F + F_A \\cdot \\frac{d}{2} \\]<\/p>\n<\/div>\n<p>\\[\\tag{6}  F_A \\cdot \\frac{d}{2} = F \\cdot l \\]<\/p>\n<p>\\[\\tag{7}  F_A = \\frac{2 \\cdot F \\cdot l}{d} \\]<\/p>\n\n<p>The still unknown horizontal forces are calculated using the Pythagorean theorem:<\/p>\n<p>\\[\\tag{8}  F_A^2 = F_{Ax}^2 + F_{Ay}^2 \\]<\/p>\n<p>\\[\\tag{9}  \\left( \\frac{2 \\cdot F \\cdot l}{d} \\right)^2 = F_{Ax}^2 + F^2 \\]<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[\\tag{10}  F_{Ax} = \\sqrt{\\left( \\frac{2 \\cdot F \\cdot l}{d} \\right)^2 - F^2} \\]<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Reaction forces of a hook wrench\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-15-reaction-forces-of-a-hook-wrench\/\" aria-label=\"Read more about Reaction forces of a hook wrench\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":412,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[46,29],"class_list":["post-709","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-reaction-forces","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>Reaction forces of a hook wrench &#8226; pickedshares<\/title>\n<meta name=\"description\" content=\"A hook wrench is attached to a stationary shaft and loaded with a force. 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