{"id":981,"date":"2020-12-17T15:41:09","date_gmt":"2020-12-17T15:41:09","guid":{"rendered":"https:\/\/pickedshares.com\/?p=981"},"modified":"2021-05-08T12:26:48","modified_gmt":"2021-05-08T12:26:48","slug":"engineering-mechanics-1-exercise-35-calculate-center-of-gravity","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-35-calculate-center-of-gravity\/","title":{"rendered":"Center of gravity, combined bodies"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The center of gravity has to be calculated for the body shown. The body consists of two individual bodies of different materials.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Given values:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a = 30 mm, b = 25 mm, c = 60 mm, d = 30 mm, e = 50 mm<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Body 1 consists of steel with a density of \u03c1 = 7.850 kg\/m\u00b3,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Body 2 is made of aluminium with a density of \u03c1 = 2.660 kg\/m\u00b3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"499\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-35big-1024x499.jpg\" alt=\"Composite body with different materials\" class=\"wp-image-968\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-35big-1024x499.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-35big-300x146.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-35big-768x374.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-35big-1536x748.jpg 1536w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-35big-400x195.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-35big-800x389.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-35big.jpg 1709w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Composite body with different materials<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A note on the direction of projection: a circle with a center point indicates a coordinate axis that points at the viewer. A circle with a cross is a coordinate axis that points away from the viewer.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\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\n<p>The equation for calculating the center of gravity coordinate is, noted here as an example for x <sub> S <\/sub>:<\/p>\n<p>\\[ \\tag{1} x_S = \\frac{\\sum \\rho_i \\cdot V_i \\cdot x_i}{\\sum \\rho_i \\cdot V_i} \\]<\/p>\n\n<p>The values \u200b\u200bof the individual bodies are recorded in a table<\/p>\n\n<div style=\"width:100%;overflow:scroll;\">\n<table>\n<thead>\n<tr>\n<th>\\[ i \\]<\/th><th>\\[ V_i \\]<\/th><th>\\[ x_i \\]<\/th><th>\\[ y_i \\]<\/th><th>\\[ z_i \\]<\/th><th>\\[ \\rho_i \\]<\/th><th>\\[ \\rho_i \\cdot V_i \\]<\/th><th>\\[ \\rho_i \\cdot V_i \\cdot x_i \\]<\/th><th>\\[ \\rho_i \\cdot V_i \\cdot y_i \\]<\/th><th>\\[ \\rho_i \\cdot V_i \\cdot z_i \\]<\/th><\/tr>\n<tr>\n<th><\/th><th>\\[ {mm}^3 \\]<\/th><th>\\[ mm \\]<\/th><th>\\[ mm \\]<\/th><th>\\[ mm \\]<\/th><th>\\[ 10^{-6}kg\/{mm}^3 \\]<\/th><th>\\[ kg \\]<\/th><th>\\[ kgmm \\]<\/th><th>\\[ kgmm \\]<\/th><th>\\[ kgmm \\]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<\/tbody>\n<tbody><tr>\n<td>1<\/td><td>54.000<\/td><td>-15<\/td><td>-15<\/td><td>0<\/td><td>7,85<\/td><td>0,424<\/td><td>-6,359<\/td><td>-6,359<\/td><td>0<\/td>\n<\/tr>\n<tr>\n<td>2<\/td><td>75.000<\/td><td>12,5<\/td><td>-5<\/td><td>0<\/td><td>2,66<\/td><td>0,2<\/td><td>2,494<\/td><td>-0,998<\/td><td>0<\/td>\n<\/tr>\n<tr>\n<td><\/td><td><\/td><td><\/td><td><\/td><td><\/td><td>\\[ \\sum \\]<\/td><td>0,624<\/td><td>-3,865<\/td><td>-7,357<\/td><td>0<\/td>\n<\/tr>\n\n<\/tbody><\/table>\n<\/div>\n\n<p>This results in the following center of gravity coordinates:\n<\/p>\n\n<div style=\"overflow:auto;\">\n<p>\\[ \\tag{2} x_S = \\frac{-3.865 kg\\,mm}{0.624kg} = -6.2\\,mm \\]<\/p>\n<p>\\[ \\tag{3} y_S = \\frac{-7.357 kg\\,mm}{0.624kg} = -11.8\\,mm \\]<\/p>\n<p>\\[ \\tag{4} z_S = \\frac{0 kg\\,mm}{0.624kg} = 0\\,mm \\]<\/p>\n<\/div>\n\n<p>So the center of gravity of the combined body is determined.<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Center of gravity, combined bodies\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-35-calculate-center-of-gravity\/\" aria-label=\"Read more about Center of gravity, combined bodies\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":975,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[50],"class_list":["post-981","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-centre-points","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 v27.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Center of gravity, combined bodies &#8226; pickedshares<\/title>\n<meta name=\"description\" content=\"A body is combined of two sub-bodies with different materials. 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