Enough blogging about personal stuff like our cats. Here is a neat little physics puzzle instead.<\/p>\n
Solving this question requires nothing more than elementary high school physics (assuming you were taught physics in high school; if not, shame on the educational system where you grew up). No tricks, no gimmicks, no relativity theory, no quantum mechanics, just a straightforward application of what you were taught about Newtonian physics.<\/p>\n
We have two parallel rail tracks. There is no friction, no air resistance, no dissipative forces.<\/p>\n
On the first track, let’s call it A<\/em>, there is a train. It weighs 10,000 kilograms. It is accelerated by an electric motor from 0 to 10 meters per second. Its kinetic energy, when it is moving at \\(v=10~{\\rm m\/s}\\), is of course \\(K=\\tfrac{1}{2}mv^2=500~{\\rm kJ}\\).<\/p>\n Next, we accelerate it from 10 to 20 meters per second. At \\(v=20~{\\rm m\/s}\\), its kinetic energy is \\(K=2000~{\\rm kJ}\\), so an additional \\(1500~{\\rm kJ}\\) was required to achieve this change in speed.<\/p>\n All this is dutifully recorded by a power meter that measures the train’s electricity consumption. So far, so good.<\/p>\n But now let’s look at the B<\/em> track, where there is a train moving at the constant speed of \\(10~{\\rm m\/s}\\). When the A<\/em> train is moving at the same speed, the two trains are motionless relative to each other; from B<\/em>‘s perspective, the kinetic energy of A<\/em> is zero. And when A<\/em> accelerates to \\(20~{\\rm m\/s}\\) relative to the ground, its speed relative to B<\/em> will be \\(10~{\\rm m\/s}\\); so from B<\/em>‘s perspective, the change in kinetic energy is \\(500~{\\rm kJ}\\).<\/p>\n But the power meter is not lying. It shows that the A<\/em> train used \\(1500~{\\rm kJ}\\) of electrical energy.<\/p>\n Question: Where did the missing \\(1000~{\\rm kJ}\\) go?<\/p>\n First one with the correct answer gets a virtual cookie.<\/p>\n Enough blogging about personal stuff like our cats. Here is a neat little physics puzzle instead. Solving this question requires nothing more than elementary high school physics (assuming you were taught physics in high school; if not, shame on the educational system where you grew up). No tricks, no gimmicks, no relativity theory, no quantum […]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-8782","post","type-post","status-publish","format-standard","hentry","category-physics","category-3-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/8782","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8782"}],"version-history":[{"count":5,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/8782\/revisions"}],"predecessor-version":[{"id":8788,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/8782\/revisions\/8788"}],"wp:attachment":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8782"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8782"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8782"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}