{"id":11655,"date":"2021-06-16T12:35:46","date_gmt":"2021-06-16T12:35:46","guid":{"rendered":"http:\/\/www.max-sperling.bplaced.net\/?p=11655"},"modified":"2024-04-19T11:15:32","modified_gmt":"2024-04-19T11:15:32","slug":"exercise-1-energy","status":"publish","type":"post","link":"http:\/\/www.max-sperling.bplaced.net\/?p=11655","title":{"rendered":"Physics &#8211; Exercise 1 (Energy)"},"content":{"rendered":"<p><strong>Given<\/strong><br \/>\nA ball is rolling down a hill on the earth without any friction and starts with a velocity of 0 m\/s at the peak and ends up with 30 m\/s at the valley.<\/p>\n<hr>\n<p><strong>Find<\/strong><br \/>\n<center>The height of the hill.<\/center><\/p>\n<hr>\n<p><strong>Solution<\/strong><br \/>\n<center><br \/>\n\\(<br \/>\n\\begin{array}{l}<br \/>\n  E_{pot} + E_{kin} = const \\\\<br \/>\n  E_{pot} = m \\cdot g \\cdot h \\\\<br \/>\n  E_{kin} = \\frac{m \\cdot v^2}{2} \\\\\\\\<br \/>\n\\end{array}<br \/>\n\\)<br \/>\n\\(<br \/>\n\\begin{align*}<br \/>\n  E_{peak} &#038;= E_{valley} \\\\<br \/>\n  E_{pot_{peak}} + E_{kin_{peak}} &#038;= E_{pot_{valley}} + E_{kin_{valley}} \\\\<br \/>\n  E_{pot}(h=h_{peak}) + E_{kin}(v=0\\frac{m}{s}) &#038;= E_{pot}(h=0m) + E_{kin}(v=30\\frac{m}{s}) \\\\<br \/>\n  E_{pot}(h=h_{peak}) &#038;= E_{kin}(v=30\\frac{m}{s}) \\\\<br \/>\n  m \\cdot g \\cdot h_{peak} &#038;= \\frac{m \\cdot (30\\frac{m}{s})^2}{2} \\\\<br \/>\n  h_{peak} &#038;= \\frac{(30\\frac{m}{s})^2}{2 \\cdot g} \\\\<br \/>\n  h_{peak} &#038;= \\frac{(30\\frac{m}{s})^2}{2 \\cdot 9,81\\frac{m}{s^2}} \\\\<br \/>\n  h_{peak} &#038;\\approx 45,87m<br \/>\n\\end{align*}<br \/>\n\\)<br \/>\n<\/center><\/p>\n<hr>\n<p><strong>Answer<\/strong><br \/>\n<center>h<sub>peak<\/sub> \u2248 45,87m<\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given A ball is rolling down a hill on the earth without any friction and starts with a velocity of<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[60],"tags":[],"_links":{"self":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/11655"}],"collection":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11655"}],"version-history":[{"count":2,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/11655\/revisions"}],"predecessor-version":[{"id":17477,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/11655\/revisions\/17477"}],"wp:attachment":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11655"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11655"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}