{"id":8174,"date":"2020-07-05T13:45:28","date_gmt":"2020-07-05T17:45:28","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?page_id=8174"},"modified":"2024-10-05T18:09:20","modified_gmt":"2024-10-05T22:09:20","slug":"influence-of-speed-on-cable-tensions","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/influence-of-speed-on-cable-tensions\/","title":{"rendered":"Influence of speed on cable tensions"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7686 aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/07\/Untitled-300x201.jpg\" alt=\"\" width=\"357\" height=\"185\" \/><\/p>\n<div class=\"page\" title=\"Page 3\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>Two wires, OP and AP, connect particle P (having a mass of m) to fixed points O and A, respectively, where OA is a vertical line. The particle rotates about axis OA such that P has a constant speed of vP and with the two wires remaining taut as particle moves on a circular path of radius R<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>What do we know from the start about the influence of the speed and the weight of P on the tension in the two wires?<\/p>\n<ul>\n<li>If the speed of P is increased, P will want to swing outward. This will increase the tension in wire AP but decrease the tension in wire OP. For too large of a rotation rate, wire OP will go slack.<\/li>\n<li>If the weight of P is increased, P will want to swing downward. This will increase the tension in wire OP but decrease the tension in wire AP. If the weight of P is increased too much, wire AP will go slack.<\/li>\n<li>Summarizing above, if the speed of P is too large, wire OP will go slack. If the speed of P is too small, wire AP will go slack.<\/li>\n<\/ul>\n<p>Consider the animations below from three simulations for which both wires remain taut: a slow rotation rate, an intermediate rotation rate and a fast rotation rate.<\/p>\n<p><strong><em>Slow rotation rate<\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/06\/H4_A_18_slow.gif\" width=\"621\" height=\"313\" \/><\/p>\n<p><strong><em>Intermediate rotation rate<\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/06\/H4_A_18_intermediate.gif\" width=\"621\" height=\"313\" \/><\/p>\n<p><strong><em>Fast rotation rate<\/em><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2020\/06\/H4_A_18_fast.gif\" width=\"621\" height=\"313\" \/><\/p>\n<p><strong><em>Observations<\/em><\/strong>: These three animations confirm our original assessment that as the speed is increased, the tension in wire AP increases, and the tension in wire OP decreases.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Two wires, OP and AP, connect particle P (having a mass of m) to fixed points O and A, respectively, where OA is a vertical line. The particle rotates about axis OA such that P has a constant speed of vP and with the two wires remaining taut as particle moves on a circular path &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/influence-of-speed-on-cable-tensions\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Influence of speed on cable tensions<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":14,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-8174","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8174","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/comments?post=8174"}],"version-history":[{"count":6,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8174\/revisions"}],"predecessor-version":[{"id":8183,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8174\/revisions\/8183"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/14"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=8174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}