{"id":775,"date":"2020-12-09T07:22:10","date_gmt":"2020-12-09T07:22:10","guid":{"rendered":"https:\/\/pickedshares.com\/?p=775"},"modified":"2021-05-08T12:08:57","modified_gmt":"2021-05-08T12:08:57","slug":"engineering-mechanics-1-exercise-27-rope-friction","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-27-rope-friction\/","title":{"rendered":"Belt friction"},"content":{"rendered":"\n<p>This is an exercise to introduce the capstan formula. Here you can find an <a href=\"https:\/\/pickedshares.com\/en\/belt-friction-calculator\/\">online calculation tool for belt friction<\/a>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A load of m = 100 kg is lowered with a rope wrapped around a pole. The wrap angle can be seen in the sketch below. The <a href=\"https:\/\/pickedshares.com\/en\/static-and-sliding-friction-values\/\">coefficient of sliding friction<\/a> is \u00b5 = 0,2. What value for the holding force F is needed to lower the load without acceleration (G = m * g)?<\/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\/2020\/11\/Screenshot_20201119-141730_Sketch-1024x899.jpg\" alt=\"Forces on a rope wrapped around a pole\" class=\"wp-image-468\" width=\"512\" height=\"450\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-141730_Sketch-1024x899.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-141730_Sketch-300x263.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-141730_Sketch-768x674.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-141730_Sketch-400x351.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-141730_Sketch-800x702.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-141730_Sketch.jpg 1192w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption>Forces on a rope wrapped around a pole<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p>A solution video will be published soon <a href=\"http:\/\/www.youtube.com\/channel\/UCSh8qo2-6dhtbZqSLStt3Rg\" target=\"_blank\" rel=\"noreferrer noopener\">on this channel<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1019\" height=\"795\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-142357_Sketch.jpg\" alt=\"Wrap angle alpha\" class=\"wp-image-469\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-142357_Sketch.jpg 1019w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-142357_Sketch-300x234.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-142357_Sketch-768x599.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-142357_Sketch-400x312.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/11\/Screenshot_20201119-142357_Sketch-800x624.jpg 800w\" sizes=\"auto, (max-width: 1019px) 100vw, 1019px\" \/><figcaption>Wrap angle alpha<\/figcaption><\/figure>\n\n\n\n<p>The holding force F is calculated using the Euler-Eytelwein formula (rope friction formula), which for this case 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{1} G = Fe^{\u00b5\\alpha}\\]<\/p>\n\n\n\n<p>With the given values \u200b\u200band the angle of wrap alpha measured from the sketch<\/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<p>\\[\\tag{2} G =mg\\]<\/p>\n<p>\\[\\tag{3} \u00b5 = 0.2\\]<\/p>\n<p>\\[\\tag{4} \\alpha = \\frac{3}{2}\\pi\\]<\/p>\n\n\n\n<p>this leads 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<p>\\[\\tag{5} mg = Fe^{\\frac{3}{10}\\pi}\\]<\/p>\n<p>\\[\\tag{6} F = \\frac{mg}{e^{\\frac{3}{10}\\pi}}\\]<\/p>\n\n\n\n<p>or in a different notation and with inserted values<\/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{7} F = 100 kg \\cdot 9.81 \\frac{m}{s^2} \\cdot e^{-\\frac{3}{10}\\pi}\\]<\/p>\n<\/div>\n<p>\\[\\tag{8} F = 382.26 N\\]<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Belt friction\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-27-rope-friction\/\" aria-label=\"Read more about Belt friction\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":467,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[27,29],"class_list":["post-775","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-friction","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>Belt friction &#8226; 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