{"id":5916,"date":"2011-12-04T10:06:03","date_gmt":"2011-12-04T10:06:03","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2011\/12\/04\/the-advent-calendar-of-physics-3\/"},"modified":"2011-12-04T10:06:03","modified_gmt":"2011-12-04T10:06:03","slug":"the-advent-calendar-of-physics-3","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2011\/12\/04\/the-advent-calendar-of-physics-3\/","title":{"rendered":"The Advent Calendar of Physics: The Spring&#8217;s the Thing"},"content":{"rendered":"<p>Continuing our countdown to Newton&#8217;s birthday, let&#8217;s acknowledge the contributions of one of his contemporaries and rivals with today&#8217;s equation:<\/p>\n<blockquote>\n<p><img decoding=\"async\" src=\"http:\/\/scienceblogs.com\/principles\/wp-content\/blogs.dir\/467\/files\/2012\/04\/i-edfebc70cd4099906bb6909a53544c8f-dec04_hooke.png\" alt=\"i-edfebc70cd4099906bb6909a53544c8f-dec04_hooke.png\" \/><\/p>\n<\/blockquote>\n<p>This is, of course, Hooke&#8217;s Law for a spring, which he famously published in 1660:<\/p>\n<blockquote>\n<p>ceiiinosssttuv<\/p>\n<\/blockquote>\n<p>Clears everything right up, doesn&#8217;t it? OK, maybe not. This one&#8217;s not only in Latin, it&#8217;s a cryptogram, unscrambling to &#8220;ut tensio sic vis,&#8221; which translates roughly to &#8220;as the extension, so the force,&#8221; giving the correct proportionality between the force exerted by a spring or other elastic material and the amount that material has been stretched.<\/p>\n<p>Why is this important? Well, because springs are incredibly important, as this video clearly demonstrates:<\/p>\n<p><!--more--><\/p>\n<p><iframe loading=\"lazy\" width=\"420\" height=\"315\" src=\"http:\/\/www.youtube.com\/embed\/ngBNklagsHQ\" frameborder=\"0\" allowfullscreen><\/iframe><\/p>\n<p>Deranged 1950&#8217;s educational shorts aside, springs really are very important in physics, not least because Hooke&#8217;s law is mathematically elegant. A mass hung from the end of a spring will bounce up and down in a regular way, making a simple harmonic oscillator. Plugging Hooke&#8217;s law into >a href=&#8221;http:\/\/scienceblogs.com\/principles\/2011\/12\/the_advent_calendar_of_physics.php&#8221;>Newton&#8217;s second law<\/a> gets you a differential equation for the position of the mass at the end of the spring that&#8217;s among the easiest differential equations to solve. For this reason, a huge part of model-making in physics consists of finding ways to approximate other interactions as being like a spring, so you can use the simple harmonic oscillator solution as a starting point to understand what&#8217;s going on.<\/p>\n<p>This approximation is essential for understanding the behavior of materials in both classical and quantum-mechanical contexts. It&#8217;s even the starting point for thinking about quantum electrodynamics, where light is treated as a collection of photons, not just a classical wave. So, Hooke&#8217;s law is a critical step in the development of physics, and while Newton didn&#8217;t much like him (some of Newton&#8217;s most famous quotes reputedly include bitchy little swipes at Hooke), it&#8217;s worth a moment to honor his accomplishment as part of our countdown to Newton&#8217;s birthday.<\/p>\n<p>Come back tomorrow for the next equation of the season.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Continuing our countdown to Newton&#8217;s birthday, let&#8217;s acknowledge the contributions of one of his contemporaries and rivals with today&#8217;s equation: This is, of course, Hooke&#8217;s Law for a spring, which he famously published in 1660: ceiiinosssttuv Clears everything right up, doesn&#8217;t it? OK, maybe not. This one&#8217;s not only in Latin, it&#8217;s a cryptogram, unscrambling&hellip; <a class=\"more-link\" href=\"http:\/\/chadorzel.com\/principles\/2011\/12\/04\/the-advent-calendar-of-physics-3\/\">Continue reading <span class=\"screen-reader-text\">The Advent Calendar of Physics: The Spring&#8217;s the Thing<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[666,80,11],"tags":[],"class_list":["post-5916","post","type-post","status-publish","format-standard","hentry","category-advent","category-history_of_science","category-science","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/5916","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=5916"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/5916\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=5916"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=5916"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=5916"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}