{"id":332757,"date":"2016-12-07T03:00:00","date_gmt":"2016-12-07T00:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=6e3c3ef4fc5930e527d36eb6663fb3fd"},"modified":"2016-12-07T03:00:00","modified_gmt":"2016-12-07T00:00:00","slug":"approaching-the-brachistochrone-using-inclined-planes-striving-for-shortest-or-equal-travellingtimes","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=332757","title":{"rendered":"Approaching the brachistochrone using inclined planes\u2014striving for shortest or equal travelling\r\ntimes"},"content":{"rendered":"<p>The classical brachistochrone problem asks for the path on which a mobile point M just driven by its<br \/>\nown gravity will travel in the shortest possible time between two given points A and B . The<br \/>\nresulting curve, the cycloid, will also be the tautochrone curve, i.e. the travelling time of the<br \/>\nmobile point will not depend on its starting position. We discuss three similar problems of<br \/>\nincreasing complexity that restrict the motion to inclined planes. Without using calculus we derive<br \/>\nthe respective optimal geometry and compare the theoretical values to measured travelling times. The<br \/>\nobserved discrepancies are quantitatively modelled by including angular motion and friction. We also<br \/>\ninvestigate the correspondence between the original problem and our setups. The topic provides a<br \/>\nconceptually simple yet non-trivial problem setting inviting for problem based learning and complex<br \/>\nlearning activities such as planing suitable experiments or modelling the relevant &#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The classical brachistochrone problem asks for the path on which a mobile point M just driven by its<br \/>\nown gravity will travel in the shortest possible time between two given points A and B . The<br \/>\nresulting curve, the cycloid, will also be the tautochro&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-332757","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/332757","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=332757"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/332757\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=332757"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=332757"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=332757"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}