{"id":2364,"date":"2021-09-04T08:51:29","date_gmt":"2021-09-04T12:51:29","guid":{"rendered":"https:\/\/josmfs.net\/?p=2364"},"modified":"2024-04-07T14:47:23","modified_gmt":"2024-04-07T18:47:23","slug":"twisting-beam-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/09\/04\/twisting-beam-problem\/","title":{"rendered":"Twisting Beam Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2362\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/09\/Twisting-Beam-Fig2.jpg\" alt=\"\" width=\"200\" height=\"130\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/09\/Twisting-Beam-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/09\/Twisting-Beam-Fig2-300x195.jpg 300w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Here is a slightly different kind of problem from the Polish Mathematical Olympiads.<\/p>\n<p><strong>\u201c106<\/strong>. A beam of length <em>a<\/em> is suspended horizontally by its ends by means of two parallel ropes of lengths <em>b<\/em>.\u00a0 We twist the beam through an angle \u03c6 about the vertical axis passing through the centre of the beam.\u00a0 How far will the beam rise?\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Twisting-Beam-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/09\/Twisting-Beam-Problem-210813.pdf\">Twisting Beam Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a slightly different kind of problem from the Polish Mathematical Olympiads. \u201c106. A beam of length a is suspended horizontally by its ends by means of two parallel ropes of lengths b.\u00a0 We twist the beam through an angle \u03c6 about the vertical axis passing through the centre of the beam.\u00a0 How far [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[40,222],"class_list":["post-2364","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-analytic-geometry","tag-polish-math-olympiads"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2364","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2364"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2364\/revisions"}],"predecessor-version":[{"id":3668,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2364\/revisions\/3668"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}