{"id":17912,"date":"2022-12-04T15:53:12","date_gmt":"2022-12-04T20:53:12","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me274\/?page_id=17912"},"modified":"2024-10-05T18:09:20","modified_gmt":"2024-10-05T22:09:20","slug":"friction-and-work","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/friction-and-work\/","title":{"rendered":"Friction and work"},"content":{"rendered":"<p><em><strong>Problem<br \/>\n<\/strong><\/em>Earlier, we saw that the work done by friction on a particle sliding on a rough surface is negative, causing a loss in total mechanical energy as the particle slides. Here, we will address the question: <em>Does this result also apply to rigid bodies that roll <span style=\"text-decoration: underline\">and<\/span> slip on a rough surface?<\/em><\/p>\n<p>Consider a homogeneous circular disk that is placed on a rough, horizontal surface with a velocity to the right and with zero angular speed.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-7787 aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2022\/12\/Screen-Shot-2022-12-04-at-3.35.09-PM.jpg\" alt=\"\" width=\"331\" height=\"115\" \/><\/p>\n<p>Since the initial rotation rate is zero, the disk will initially slip on the horizontal surface as the disk moves to the right. As the disk slips, there is a friction force acting to the left on the disk at the contact point. During slipping, the friction force opposes the direction of motion of the contact point &#8211; that is, the friction force acts to the left. As a result of the work done by this friction, the kinetic energy of the disk decreases. This is shown in the initial stage of the animation shown below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2022\/12\/work_slipping.gif\" width=\"569\" height=\"210\" \/><\/p>\n<p>As the disk continues to roll with slipping, the friction force also produces a clockwise rotation of the disk. Once disk picks up enough angular velocity to produce a no-slip condition at the contact point, the disk no longer slips, reducing the friction force to zero, and from that point on the disk does not see a loss in kinetic energy as it continues rolling without slipping. This is shown in the latter stage of the animation above.<\/p>\n<p>In summary for this problem, the friction resulting from rolling <span style=\"text-decoration: underline\"><em>with<\/em><\/span> slipping on a rough surface does negative work; however, the subsequent rolling <span style=\"text-decoration: underline\"><em>without<\/em><\/span> slipping sees the friction force going to zero, with the disk continuing to move with constant speed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problem Earlier, we saw that the work done by friction on a particle sliding on a rough surface is negative, causing a loss in total mechanical energy as the particle slides. Here, we will address the question: Does this result also apply to rigid bodies that roll and slip on a rough surface? Consider a &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me274\/course-material\/animations\/friction-and-work\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Friction and work<\/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-17912","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/17912","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=17912"}],"version-history":[{"count":4,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/17912\/revisions"}],"predecessor-version":[{"id":17917,"href":"https:\/\/www.purdue.edu\/freeform\/me274\/wp-json\/wp\/v2\/pages\/17912\/revisions\/17917"}],"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=17912"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}