{"id":13433,"date":"2022-02-18T09:59:42","date_gmt":"2022-02-18T14:59:42","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?p=13433"},"modified":"2024-10-10T09:35:42","modified_gmt":"2024-10-10T13:35:42","slug":"homework-h4-b","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/xx\/homework-h4-b\/","title":{"rendered":"Homework H4.A.16"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-13434 aligncenter\" src=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2022\/01\/Screen-Shot-2022-01-17-at-12.22.57-PM-300x254.jpg\" alt=\"\" width=\"300\" height=\"254\" srcset=\"https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2022\/01\/Screen-Shot-2022-01-17-at-12.22.57-PM-300x254.jpg 300w, https:\/\/www.purdue.edu\/freeform\/me274\/wp-content\/uploads\/sites\/15\/2022\/01\/Screen-Shot-2022-01-17-at-12.22.57-PM.jpg 736w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><em><strong>Discussion and hints:<\/strong><\/em><\/p>\n<p>Let&#8217;s first take a look at the motion of the mechanism, as shown in the simulation results below.<\/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\/2022\/01\/H4A_16.gif\" width=\"606\" height=\"419\" \/><\/p>\n<p>The kinematics for this problem are a little complicated. Recall that we studied these types of &#8220;constrained motion&#8221; kinematics problems back in Section 1.D of the lecture book. Here, we will now get to use the skills developed there in solving this problem in kinetics.<\/p>\n<p>Recall the following <span style=\"text-decoration: underline\"><em>f<\/em><em>our-step plan<\/em><\/span> outline in the lecture book and discussed in lecture:<\/p>\n<p><em><strong>Step 1: FBDs<\/strong><\/em><br \/>\nDraw <span style=\"text-decoration: underline\"><em>individual<\/em><\/span> free body diagrams for bodies A and B.<\/p>\n<p><em><strong>Step 2: Kinetics (Newton&#8217;s 2nd Law)<\/strong><\/em><br \/>\nWrite down the appropriate Newton&#8217;s 2nd law equations for blocks A and B.<\/p>\n<p><em><strong>Step 3: Kinematics<\/strong><\/em><br \/>\nHere, we will use the assumption that the cable length, <em>L<\/em>, does not change as the system moves (the cable does not stretch, go slack or break). For this, write <em>L<\/em> in terms of the motion variables s<sub>A<\/sub> and s<sub>B<\/sub>. You might want to review the material and examples from Section 1.D of the lecture book in doing this. Differentiate this relation once to relate the speeds of A and B, and then, once again, to relate the accelerations of A and B. <em>NOTE<\/em>: Be sure to use the same sign conventions for forces as for accelerations. For example, if you choose positive x as being to the right, then a<sub>A<\/sub> = &#8211; s<sub>A<\/sub>_ddot.<\/p>\n<p><em><strong>Step 4: Solve<\/strong><\/em><br \/>\nAt this point you will have three equations involving the tension in the cable, the acceleration of A and the acceleration of B. Solve these three equations for those three unknowns.<\/p>\n<hr \/>\n<p>Any questions??<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Discussion and hints: Let&#8217;s first take a look at the motion of the mechanism, as shown in the simulation results below. The kinematics for this problem are a little complicated. Recall that we studied these types of &#8220;constrained motion&#8221; kinematics problems back in Section 1.D of the lecture book. Here, we will now get to &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/xx\/homework-h4-b\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Homework H4.A.16<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":14940,"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-13433","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/13433","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=13433"}],"version-history":[{"count":2,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/13433\/revisions"}],"predecessor-version":[{"id":15129,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/13433\/revisions\/15129"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/14940"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/media?parent=13433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}