{"id":498,"date":"2016-11-03T19:53:44","date_gmt":"2016-11-04T02:53:44","guid":{"rendered":"https:\/\/sites.evergreen.edu\/psam1617\/?p=498"},"modified":"2016-11-03T19:57:57","modified_gmt":"2016-11-04T02:57:57","slug":"classical-mechanics-homework-assignment-11","status":"publish","type":"post","link":"https:\/\/sites.evergreen.edu\/psam1617\/classical-mechanics-homework-assignment-11\/","title":{"rendered":"Classical Mechanics Homework Assignment #11"},"content":{"rendered":"<p><strong>Classical Mechanics Homework Assignment #11, due <del><\/del><span style=\"color: #000000\">by 5 pm Monday November 7 to Krishna&#8217;s office Lab 2 3255<\/span>. All problems from Taylor except as indicated.<br \/> <\/strong><\/p>\n<ol>\n<li>Choose one of 7.20, 7.22, or 7.23 that you didn&#8217;t do for <strong><a href=\"https:\/\/sites.evergreen.edu\/psam1617\/classical-mechanics-homework-assignment-10\/\">Homework #10<\/a><\/strong><\/li>\n<li>Choose one of 7.29, 7.30, or 7.35 that you didn&#8217;t do for <strong><a href=\"https:\/\/sites.evergreen.edu\/psam1617\/classical-mechanics-homework-assignment-10\/\">Homework #10<\/a><\/strong><\/li>\n<li>7.50<\/li>\n<li>7.52 (see note)<\/li>\n<li>Consider a simple pendulum with mass <em>m<\/em> and (massless) string of length <em>b<\/em>, released from rest at an angle <em>\u03b8<\/em><sub>0<\/sub> with respect to vertical. Determine the tension in the string as a function of angle <em>\u03b8<\/em> and other given and known constants. Check that your answer makes sense in the limit cases when <em>\u03b8 <\/em>= <em>\u03b8<\/em><sub>0<\/sub> (i.e. at the top of the swing) and when <em>\u03b8<\/em> = 0 (the bottom of the swing). This is the problem we discussed in class; recall from that discussion that we could only get so for with the Lagrangian method, so don&#8217;t hesitate to use a Newtonian framework as needed. (see note)<\/li>\n<li>There are only five problems on this homework set.<\/li>\n<\/ol>\n<p>Notes:<\/p>\n<ul>\n<li>For 7.52, convince yourself that the geometry requires <em>x<\/em> = <em>R\u03a6<\/em>, so that the constraint is <em>f(x, \u03a6)<\/em> = <em>x &#8211; R\u03a6<\/em> = 0.<\/li>\n<li>For Problem 5, here&#8217;s a necessary intermediate step you can use to check your work: <em>v<\/em><sup>2<\/sup> = 2<em>gb<\/em>(cos <em>\u03b8<\/em> &#8211; cos <em>\u03b8<\/em><sub>0<\/sub>)<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Classical Mechanics Homework Assignment #11, due by 5 pm Monday November 7 to Krishna&#8217;s office Lab 2 3255. All problems from Taylor except as indicated. Choose one of 7.20, 7.22, or 7.23 that you didn&#8217;t do for Homework #10 Choose &hellip; <a href=\"https:\/\/sites.evergreen.edu\/psam1617\/classical-mechanics-homework-assignment-11\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":219,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/posts\/498"}],"collection":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/users\/219"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/comments?post=498"}],"version-history":[{"count":0,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/posts\/498\/revisions"}],"wp:attachment":[{"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/media?parent=498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/categories?post=498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.evergreen.edu\/psam1617\/wp-json\/wp\/v2\/tags?post=498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}