{"id":8339,"date":"2020-07-09T12:53:53","date_gmt":"2020-07-09T16:53:53","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?page_id=8339"},"modified":"2022-07-10T10:29:28","modified_gmt":"2022-07-10T14:29:28","slug":"you-cant-push-with-a-string","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/you-cant-push-with-a-string\/","title":{"rendered":"You can&#8217;t push on a string"},"content":{"rendered":"<p>System I shown below is made up of a particle of mass P connected to a pin joint at O with a rigid bar having negligible mass. Particle P is given a velocity to the left with a speed of <em>v<\/em><sub>P1<\/sub> when at position 1. System II is identical to System I, except that the rigid bar is replaced by a string.<\/p>\n<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\/take_away_slides_part1-1-scaled.jpg\" alt=\"\" width=\"670\" height=\"379\" \/><\/p>\n<div>For each system, it is desired to determine the minimum value of speed for P at position 1, (<em>v<\/em><sub>P1<\/sub>)<sub>min\u00a0<\/sub>in order for P to reach the top position at 2. For an initial speed larger than these minimum values, the motions of the two systems are as shown below. As expected, the paths of P in both systems is circular, with the load carried by the bar\/string being in tension.<\/div>\n<div><\/div>\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\/07\/section_04B_02.gif\" width=\"621\" height=\"313\" \/><\/p>\n<div><\/div>\n<div><strong><em>System I<\/em><\/strong><\/div>\n<div>For System I, (<em>v<\/em><sub>P1<\/sub>)<sub>min<\/sub> will correspond to <strong><em>v<\/em><sub>P2<\/sub> = 0<\/strong>. Using <span style=\"text-decoration: underline\"><em>conservation of energy<\/em><\/span>, it can be shown that (<em>v<\/em><sub>P1<\/sub>)<sub>min<\/sub> = \u221a(4gL).<\/div>\n<div><\/div>\n<div>The motions for the two systems using this minimum value for the initial speed of P are shown below. As expected, System I with the rigid bar has P reaching the top position with nearly zero speed. Near this top position the bar is in compression. At this speed, System II with the string behaves differently: the string goes slack (since the string cannot sustain compression), and P never reaches the top position. Therefore a larger value for (<em>v<\/em><sub>P1<\/sub>)<sub>min<\/sub> \u00a0is needed for the string.<\/div>\n<div><\/div>\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\/07\/section_04B_02_slower.gif\" width=\"621\" height=\"313\" \/><\/p>\n<div><\/div>\n<div>\n<div><strong><em>System II<\/em><\/strong><\/div>\n<div>Based on the above observation, the value of (<em>v<\/em><sub>P1<\/sub>)<sub>min<\/sub>\u00a0for System II will need to be larger than that for System I. How do we determine this minimum speed? See the following.<\/div>\n<div><\/div>\n<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\/take_away_slides_part1-3-scaled-e1594317572484.jpg\" alt=\"\" width=\"670\" height=\"379\" \/><\/p>\n<\/div>\n<p>Here we used Newton&#8217;s 2nd law to determine the relationship required between the string tension and the speed of P. The minimum speed for P at the top occurs when the string goes slack, or <em>F<\/em> = 0. Then using the work\/energy equation, we find the minimum speed of P at the bottom.<\/p>\n<div><\/div>\n<div><\/div>\n<div><\/div>\n<div>\n<div><\/div>\n<\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>System I shown below is made up of a particle of mass P connected to a pin joint at O with a rigid bar having negligible mass. Particle P is given a velocity to the left with a speed of vP1 when at position 1. System II is identical to System I, except that the &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/you-cant-push-with-a-string\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">You can&#8217;t push on a string<\/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-8339","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8339","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=8339"}],"version-history":[{"count":9,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8339\/revisions"}],"predecessor-version":[{"id":12669,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/8339\/revisions\/12669"}],"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=8339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}