{"id":11296,"date":"2026-07-09T14:28:03","date_gmt":"2026-07-09T14:28:03","guid":{"rendered":"https:\/\/www.myengineeringbuddy.com\/blog\/the-law-of-conservation-of-mechanical-energy\/"},"modified":"2026-07-19T05:07:56","modified_gmt":"2026-07-19T05:07:56","slug":"the-law-of-conservation-of-mechanical-energy","status":"publish","type":"post","link":"https:\/\/www.myengineeringbuddy.com\/blog\/the-law-of-conservation-of-mechanical-energy\/","title":{"rendered":"The Law of Conservation of Mechanical Energy Explained"},"content":{"rendered":"\r\n\r\n<div style=\"background-color: #f8f8f8; border-left: 4px solid #d0d0d0; padding: 12px 16px; margin-bottom: 20px;\"><strong>Key Takeaways<\/strong>\r\n<ul>\r\n<li>Mechanical energy is conserved only when non-conservative and external forces do zero work.<\/li>\r\n<li>If non-conservative forces act, use the work-energy theorem instead.<\/li>\r\n<li>Total mechanical energy equals kinetic energy plus potential energy of the system.<\/li>\r\n<li>At maximum spring compression, all kinetic energy converts to elastic potential energy.<\/li>\r\n<li>Work done by external forces equals the change in total mechanical energy.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Statement of the Law of Conservation of Mechanical Energy<\/h2>\r\n<p>The law of Conservation of Mechanical Energy states that if no external forces act (or the work done by them is zero) and the internal forces are conservative, the mechanical energy of the system remains constant. Students working through classical mechanics often find that a <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/signals-and-systems\/\">signals and systems tutor<\/a> can help bridge the mathematical foundations shared across physics and engineering topics.<\/p>\r\n<h2>When Can and Cannot the Law of Conservation of Mechanical Energy Be Applied?<\/h2>\r\n<p>If non-conservative forces do work on the system or external forces do work on the system, we cannot use the conservation principle of total mechanical energy.<\/p>\r\n<p>Suppose work done by non-conservative forces equals zero. In that case, work done by external forces equals zero, and internal forces operating within the system are conservative; then and only can we use the principle of conservation of total mechanical energy.<\/p>\r\n<h2>Evidence Through Examples<\/h2>\r\n<h3>Example 1: Freely Falling Object Near the Earth&#8217;s Surface<\/h3>\r\n<p>Suppose a body of mass m is falling from rest near the earth&#8217;s surface. Initially (e = 0), it was at point A, at a height H above the earth&#8217;s surface. For engineers preparing for licensing exams, understanding energy methods is also central to <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/circuit-analysis\/\">circuit analysis tutoring<\/a>, where energy storage in capacitors and inductors follows analogous principles.<\/p>\r\n<p>Considering (earth + body) as a system and ground surface is considered a reference line. When the body is at point A, the total mechanical energy of the system is<\/p>\r\n<p style=\"text-align: center;\"><img class=\"lazyload\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-orig-src=\"https:\/\/myengineeringbuddy.com\/wp-content\/uploads\/2022\/07\/Figure-1-181x300.png\" alt=\"Diagram showing a freely falling object at height H above the earth's surface\" \/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27464%27%20height%3D%2721%27%20viewBox%3D%270%200%20464%2021%27%3E%3Crect%20width%3D%27464%27%20height%3D%2721%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-46f1e0ef772ca7bdf83d8baf670f81d0_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#84;&#77;&#123;&#69;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#65;&#125;&#32;&#61;&#32;&#75;&#123;&#69;&#95;&#65;&#125;&#32;&#43;&#32;&#80;&#123;&#69;&#95;&#65;&#125;&#32;&#61;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#123;&#40;&#48;&#41;&#94;&#50;&#125;&#32;&#43;&#32;&#109;&#103;&#72;&#32;&#61;&#32;&#109;&#103;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"464\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p>But at time t, the body reaches point B, the kinetic energy of the body increases, and the system&#8217;s potential energy decreases (because h &lt; H). So, we see that the gain in the body&#8217;s kinetic energy is equal to the loss in potential energy of the system.<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27260%27%20height%3D%2721%27%20viewBox%3D%270%200%20260%2021%27%3E%3Crect%20width%3D%27260%27%20height%3D%2721%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c0c7e291467d69979575385bd1a48437_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#84;&#77;&#123;&#69;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#66;&#125;&#32;&#61;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#66;&#94;&#50;&#32;&#43;&#32;&#109;&#103;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"260\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p>According to the principle of conservation of energy:<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27204%27%20height%3D%2720%27%20viewBox%3D%270%200%20204%2020%27%3E%3Crect%20width%3D%27204%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-12396f82d7c54cfa11f2988b16a4872f_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#84;&#77;&#123;&#69;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#66;&#125;&#32;&#61;&#32;&#123;&#40;&#84;&#77;&#123;&#69;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"204\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27369%27%20height%3D%2720%27%20viewBox%3D%270%200%20369%2020%27%3E%3Crect%20width%3D%27369%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7d5d127974758ccc3c753f65d9a0df2b_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#66;&#94;&#50;&#32;&#43;&#32;&#109;&#103;&#104;&#32;&#61;&#32;&#48;&#32;&#43;&#32;&#109;&#103;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"369\" style=\"vertical-align: -5px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27582%27%20height%3D%2741%27%20viewBox%3D%270%200%20582%2041%27%3E%3Crect%20width%3D%27582%27%20height%3D%2741%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-eee1414158af5ed8b30c7dc6d2717483_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#117;&#110;&#100;&#101;&#114;&#98;&#114;&#97;&#99;&#101;&#32;&#123;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#66;&#94;&#50;&#32;&#45;&#32;&#48;&#125;&#95;&#123;&#123;&#114;&#109;&#123;&#103;&#97;&#105;&#110;&#32;&#105;&#110;&#32;&#75;&#125;&#125;&#123;&#114;&#109;&#123;&#46;&#69;&#125;&#125;&#123;&#114;&#109;&#123;&#46;&#125;&#125;&#125;&#32;&#61;&#32;&#117;&#110;&#100;&#101;&#114;&#98;&#114;&#97;&#99;&#101;&#32;&#123;&#109;&#103;&#72;&#32;&#45;&#32;&#109;&#103;&#104;&#125;&#95;&#123;&#123;&#114;&#109;&#123;&#108;&#111;&#115;&#115;&#32;&#105;&#110;&#32;&#80;&#125;&#125;&#123;&#114;&#109;&#123;&#46;&#69;&#125;&#125;&#123;&#114;&#109;&#123;&#46;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"582\" style=\"vertical-align: -4px;\"\/><\/p>\r\n<h3>Example 2: A Mass Attached to a Spring Oscillating on a Smooth Surface<\/h3>\r\n<p>Consider a body moving with speed v<sub>0<\/sub> on a smooth horizontal surface. As the body of mass m moves further, spring compresses. We are inserted to calculate the maximum compression produced in the spring.<\/p>\r\n<p style=\"text-align: center;\"><img class=\"lazyload\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-orig-src=\"https:\/\/myengineeringbuddy.com\/wp-content\/uploads\/2022\/07\/Figure-2-300x223.png\" alt=\"Diagram of a block of mass m attached to a spring on a smooth horizontal surface\" \/><\/p>\r\n<p>Assuming block of mass m and spring as a system.<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27519%27%20height%3D%2721%27%20viewBox%3D%270%200%20519%2021%27%3E%3Crect%20width%3D%27519%27%20height%3D%2721%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-6db53c0e4ba343250e8b015fd025adbb_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#84;&#77;&#123;&#69;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#123;&#105;&#110;&#125;&#125;&#32;&#61;&#32;&#123;&#40;&#75;&#46;&#69;&#46;&#41;&#95;&#123;&#66;&#111;&#100;&#121;&#125;&#125;&#32;&#43;&#32;&#40;&#80;&#46;&#69;&#123;&#46;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#32;&#61;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#48;&#94;&#50;&#32;&#43;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#107;&#123;&#40;&#48;&#41;&#94;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"519\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p>At the moment of maximum compression, the body&#8217;s speed becomes zero. Hence we see that the K.E. of the body decreases and the P.E. of the system increases. So, loss in K.E. of the body is equal to gain in elastic potential energy.<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27535%27%20height%3D%2721%27%20viewBox%3D%270%200%20535%2021%27%3E%3Crect%20width%3D%27535%27%20height%3D%2721%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-154fd38c2fc937ae862b1e8ca5ed29de_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#84;&#77;&#123;&#69;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#102;&#125;&#32;&#61;&#32;&#123;&#40;&#75;&#46;&#69;&#46;&#41;&#95;&#123;&#66;&#111;&#100;&#121;&#125;&#125;&#32;&#43;&#32;&#40;&#80;&#46;&#69;&#123;&#46;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#32;&#61;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#123;&#40;&#48;&#41;&#94;&#50;&#125;&#32;&#43;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#107;&#120;&#95;&#123;&#109;&#97;&#120;&#32;&#125;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"535\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p>According to the principle of conservation of TME:<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27196%27%20height%3D%2720%27%20viewBox%3D%270%200%20196%2020%27%3E%3Crect%20width%3D%27196%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-73837e1c2037fa2df8a998fdad5241e3_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#84;&#77;&#123;&#69;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#102;&#125;&#32;&#61;&#32;&#123;&#40;&#84;&#77;&#123;&#69;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"196\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27576%27%20height%3D%2720%27%20viewBox%3D%270%200%20576%2020%27%3E%3Crect%20width%3D%27576%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-0258fc621c7e0fecd719468270616284_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#123;&#40;&#48;&#41;&#94;&#50;&#125;&#32;&#43;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#107;&#120;&#95;&#123;&#109;&#97;&#120;&#32;&#125;&#94;&#50;&#32;&#61;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#48;&#94;&#50;&#32;&#43;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#107;&#123;&#40;&#48;&#41;&#94;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"576\" style=\"vertical-align: -5px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27582%27%20height%3D%2749%27%20viewBox%3D%270%200%20582%2049%27%3E%3Crect%20width%3D%27582%27%20height%3D%2749%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-3e29705f9d48ebd0a6d9dc56329dab63_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#117;&#110;&#100;&#101;&#114;&#98;&#114;&#97;&#99;&#101;&#32;&#123;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#107;&#120;&#95;&#123;&#109;&#97;&#120;&#32;&#125;&#94;&#50;&#32;&#45;&#32;&#48;&#125;&#95;&#123;&#123;&#114;&#109;&#123;&#103;&#97;&#105;&#110;&#32;&#105;&#110;&#32;&#80;&#125;&#125;&#123;&#114;&#109;&#123;&#46;&#69;&#125;&#125;&#123;&#114;&#109;&#123;&#46;&#32;&#111;&#102;&#32;&#115;&#121;&#115;&#116;&#101;&#109;&#125;&#125;&#125;&#32;&#61;&#32;&#117;&#110;&#100;&#101;&#114;&#98;&#114;&#97;&#99;&#101;&#32;&#123;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#48;&#94;&#50;&#32;&#45;&#32;&#48;&#125;&#95;&#123;&#123;&#114;&#109;&#123;&#108;&#111;&#115;&#115;&#32;&#105;&#110;&#32;&#75;&#125;&#125;&#123;&#114;&#109;&#123;&#46;&#69;&#125;&#125;&#123;&#114;&#109;&#123;&#46;&#32;&#111;&#102;&#32;&#98;&#111;&#100;&#121;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"582\" style=\"vertical-align: -9px;\"\/><\/p>\r\n<h2>The Equation of Conservation of Mechanical Energy<\/h2>\r\n<p>According to the work-energy theorem, as we know, the work done by all the forces equals the change in the kinetic energy. Hence we can write,<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27485%27%20height%3D%2718%27%20viewBox%3D%270%200%20485%2018%27%3E%3Crect%20width%3D%27485%27%20height%3D%2718%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d6a17731df9753d0fac0098b231abb62_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#99;&#111;&#110;&#115;&#101;&#114;&#118;&#97;&#116;&#105;&#118;&#101;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#110;&#111;&#110;&#32;&#45;&#32;&#99;&#111;&#110;&#115;&#101;&#114;&#118;&#97;&#116;&#105;&#118;&#101;&#125;&#125;&#125;&#125;&#32;&#43;&#32;&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#101;&#120;&#116;&#101;&#114;&#110;&#97;&#108;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#123;&#75;&#95;&#102;&#125;&#32;&#45;&#32;&#123;&#75;&#95;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"485\" style=\"vertical-align: -6px;\"\/> \u00a0\u00a0\u00a0\u2026(1)<\/p>\r\n<p>Here, the three terms on the left denote the work done by the conservative internal forces, non-conservative internal forces, and external forces.<\/p>\r\n<p>As we know, <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27153%27%20height%3D%2720%27%20viewBox%3D%270%200%20153%2020%27%3E%3Crect%20width%3D%27153%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-8c9c18e71f3989ed006f75e283d11aab_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#114;&#109;&#123;&#99;&#125;&#125;&#125;&#32;&#61;&#32;&#45;&#32;&#40;&#123;&#85;&#95;&#102;&#125;&#32;&#45;&#32;&#123;&#85;&#95;&#105;&#125;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"153\" style=\"vertical-align: -6px;\"\/> \u00a0\u00a0\u00a0\u2026(2)<\/p>\r\n<p>Here, U stands for the potential energy of the system. Now from (1) &amp; (2),<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27330%27%20height%3D%2720%27%20viewBox%3D%270%200%20330%2020%27%3E%3Crect%20width%3D%27330%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-09f879737cada13d13d9c75a3f8d8aa2_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#105;&#110;&#116;&#125;&#125;&#125;&#125;&#32;&#43;&#32;&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#101;&#120;&#116;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#40;&#123;&#75;&#95;&#102;&#125;&#32;&#45;&#32;&#123;&#85;&#95;&#102;&#125;&#41;&#32;&#45;&#32;&#40;&#123;&#75;&#95;&#105;&#125;&#32;&#45;&#32;&#123;&#85;&#95;&#105;&#125;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"330\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27336%27%20height%3D%2720%27%20viewBox%3D%270%200%20336%2020%27%3E%3Crect%20width%3D%27336%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-6060c88cf7e6d5528a9c61191b64fbbc_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#105;&#110;&#116;&#125;&#125;&#125;&#125;&#32;&#43;&#32;&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#101;&#120;&#116;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#123;&#40;&#84;&#46;&#77;&#46;&#69;&#46;&#41;&#95;&#102;&#125;&#32;&#45;&#32;&#123;&#40;&#84;&#46;&#77;&#46;&#69;&#46;&#41;&#95;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"336\" style=\"vertical-align: -6px;\"\/> \u00a0\u00a0\u00a0\u2026(3)<\/p>\r\n<p>Where T.M.E. = K + U is the total mechanical energy.<\/p>\r\n<p>If the internal forces are conservative but external forces act on the system and they do work, <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%2787%27%20height%3D%2715%27%20viewBox%3D%270%200%2087%2015%27%3E%3Crect%20width%3D%2787%27%20height%3D%2715%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-a999b34dc350667d8942e51d119f1114_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#105;&#110;&#116;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: -3px;\"\/> then from equation (3) we can write,<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27260%27%20height%3D%2720%27%20viewBox%3D%270%200%20260%2020%27%3E%3Crect%20width%3D%27260%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bd26ff68791908269ce69041175a4076_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#101;&#120;&#116;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#123;&#40;&#84;&#46;&#77;&#46;&#69;&#46;&#41;&#95;&#102;&#125;&#32;&#45;&#32;&#123;&#40;&#84;&#46;&#77;&#46;&#69;&#46;&#41;&#95;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"260\" style=\"vertical-align: -6px;\"\/> \u00a0\u00a0\u00a0\u2026(4)<\/p>\r\n<p>Therefore, we can write that the work done by external forces equals the change in the total mechanical energy of the system. Here equation (4) is a mathematical form of energy conservation. Simulation-based tools used in <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/python\/\">Python tutoring<\/a> are increasingly applied to model energy conservation problems numerically, complementing the analytical approach shown here.<\/p>\r\n<h2>Solved Problems<\/h2>\r\n<h3>Example 1: Finding Work Done by Air Friction<\/h3>\r\n<p>A body dropped from height h reaches the ground with speed <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%2772%27%20height%3D%2716%27%20viewBox%3D%270%200%2072%2016%27%3E%3Crect%20width%3D%2772%27%20height%3D%2716%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bcecfa2199c2c2c6b88217550339ff5c_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#49;&#46;&#50;&#115;&#113;&#114;&#116;&#32;&#123;&#103;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"\/>. Calculate the work done by air friction.<\/p>\r\n<p>In the above question <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27128%27%20height%3D%2718%27%20viewBox%3D%270%200%20128%2018%27%3E%3Crect%20width%3D%27128%27%20height%3D%2718%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-889792e6347a1fd38a9befeddd9cb038_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#123;&#109;&#97;&#116;&#104;&#111;&#112;&#123;&#114;&#109;&#32;&#105;&#110;&#116;&#125;&#125;&#125;&#125;&#32;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -6px;\"\/>. Air friction is a non-conservative force. So, we cannot use the principle of conservation of total mechanical energy. In this condition, we should use the work-energy theorem,<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27255%27%20height%3D%2720%27%20viewBox%3D%270%200%20255%2020%27%3E%3Crect%20width%3D%27255%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-e07bdf197aa21e8e40a139ff6b6c4b10_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#75;&#46;&#69;&#46;&#41;&#95;&#102;&#125;&#32;&#45;&#32;&#123;&#40;&#75;&#46;&#69;&#46;&#41;&#95;&#105;&#125;&#32;&#61;&#32;&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#97;&#108;&#108;&#32;&#102;&#111;&#114;&#99;&#101;&#115;&#125;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"255\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<h3>Example 2: Finding Spring Constant<\/h3>\r\n<p>A block of mass m moving at a speed v compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring.<\/p>\r\n<p style=\"text-align: center;\"><img class=\"lazyload\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-orig-src=\"https:\/\/myengineeringbuddy.com\/wp-content\/uploads\/2022\/07\/Figure-3-300x251.png\" alt=\"Diagram of a block of mass m compressing a spring on a horizontal surface\" \/><\/p>\r\n<p>Let the system be (spring + block).<\/p>\r\n<p>Here, <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27309%27%20height%3D%2720%27%20viewBox%3D%270%200%20309%2020%27%3E%3Crect%20width%3D%27309%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-6bb981b58434359cc0d5a75a8702c787_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#110;&#111;&#110;&#32;&#45;&#32;&#99;&#111;&#110;&#115;&#101;&#114;&#118;&#97;&#116;&#105;&#118;&#101;&#32;&#102;&#111;&#114;&#99;&#101;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#48;&#44;&#59;&#44;&#40;&#123;&#87;&#95;&#102;&#125;&#32;&#61;&#32;&#48;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"309\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27338%27%20height%3D%2720%27%20viewBox%3D%270%200%20338%2020%27%3E%3Crect%20width%3D%27338%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-2da2e07f976c325c860aa313d9d08037_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#123;&#114;&#109;&#123;&#101;&#120;&#116;&#101;&#114;&#110;&#97;&#108;&#32;&#102;&#111;&#114;&#99;&#101;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#48;&#44;&#59;&#44;&#40;&#123;&#87;&#95;&#123;&#109;&#103;&#125;&#125;&#32;&#61;&#32;&#48;&#44;&#44;&#123;&#87;&#95;&#78;&#125;&#32;&#61;&#32;&#48;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"338\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p>Internal force (spring force) is conservative. So, we must use the principle of conservation of total mechanical energy.<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27403%27%20height%3D%2720%27%20viewBox%3D%270%200%20403%2020%27%3E%3Crect%20width%3D%27403%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-5bec93e35ed1c8ae5c29b451c1646c35_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#84;&#46;&#77;&#46;&#69;&#123;&#46;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#102;&#125;&#32;&#45;&#32;&#123;&#40;&#84;&#46;&#77;&#46;&#69;&#123;&#46;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#105;&#125;&#32;&#61;&#32;&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;&#32;&#43;&#32;&#123;&#87;&#95;&#123;&#123;&#109;&#97;&#116;&#104;&#111;&#112;&#123;&#114;&#109;&#32;&#105;&#110;&#116;&#125;&#125;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"403\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27224%27%20height%3D%2720%27%20viewBox%3D%270%200%20224%2020%27%3E%3Crect%20width%3D%27224%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-0d5f229b3de5256f56bd49bab1273fea_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#40;&#84;&#46;&#77;&#46;&#69;&#123;&#46;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#102;&#125;&#32;&#61;&#32;&#123;&#40;&#84;&#46;&#77;&#46;&#69;&#123;&#46;&#95;&#123;&#115;&#121;&#115;&#125;&#125;&#41;&#95;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"224\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p>Because, <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27234%27%20height%3D%2718%27%20viewBox%3D%270%200%20234%2018%27%3E%3Crect%20width%3D%27234%27%20height%3D%2718%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-98f3fc83b871932a73f982f8b9731764_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;&#32;&#61;&#32;&#48;&#44;&#59;&#44;&#44;&#123;&#87;&#95;&#123;&#123;&#109;&#97;&#116;&#104;&#111;&#112;&#123;&#114;&#109;&#32;&#105;&#110;&#116;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"234\" style=\"vertical-align: -6px;\"\/> in the above example.<\/p>\r\n<p>Mechanical energy conservation also appears in FE exam problems; students preparing for that exam can benefit from working with a <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/fe-mechanical\/\">FE Mechanical tutor<\/a> to practise these problem types systematically.<\/p>\r\n<h3>Example 3: Speed and Height Calculations for a Freely Falling Particle<\/h3>\r\n<p>A particle is released from height H. At a certain height from the ground, its kinetic energy is twice its gravitational potential energy. Find the speed of particles and height at that moment.<\/p>\r\n<p>Ans: Considering particles and earth as a system; here <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27234%27%20height%3D%2718%27%20viewBox%3D%270%200%20234%2018%27%3E%3Crect%20width%3D%27234%27%20height%3D%2718%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-98f3fc83b871932a73f982f8b9731764_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;&#32;&#61;&#32;&#48;&#44;&#59;&#44;&#44;&#123;&#87;&#95;&#123;&#123;&#109;&#97;&#116;&#104;&#111;&#112;&#123;&#114;&#109;&#32;&#105;&#110;&#116;&#125;&#125;&#125;&#125;&#32;&#61;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"234\" style=\"vertical-align: -6px;\"\/> and internal forces operating within the system are conservative in nature.<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27245%27%20height%3D%2718%27%20viewBox%3D%270%200%20245%2018%27%3E%3Crect%20width%3D%27245%27%20height%3D%2718%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-839d59e2cbeeee900e89c0dddd03a8ec_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#75;&#46;&#69;&#123;&#46;&#95;&#105;&#125;&#32;&#43;&#32;&#80;&#46;&#69;&#123;&#46;&#95;&#105;&#125;&#32;&#61;&#32;&#75;&#46;&#69;&#123;&#46;&#95;&#102;&#125;&#32;&#43;&#32;&#80;&#46;&#69;&#123;&#46;&#95;&#102;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"245\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27418%27%20height%3D%2721%27%20viewBox%3D%270%200%20418%2021%27%3E%3Crect%20width%3D%27418%27%20height%3D%2721%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-0fb91b2b93cfbccbc2ff289e23db618b_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#123;&#40;&#48;&#41;&#94;&#50;&#125;&#32;&#43;&#32;&#109;&#103;&#72;&#32;&#61;&#32;&#75;&#46;&#69;&#123;&#46;&#95;&#102;&#125;&#32;&#43;&#32;&#109;&#103;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"418\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27324%27%20height%3D%2723%27%20viewBox%3D%270%200%20324%2023%27%3E%3Crect%20width%3D%27324%27%20height%3D%2723%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-0f3fc2024bfeeb48d580a5f3788d82ee_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#102;&#94;&#50;&#32;&#61;&#32;&#109;&#103;&#40;&#72;&#32;&#45;&#32;&#104;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"324\" style=\"vertical-align: -8px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27445%27%20height%3D%2723%27%20viewBox%3D%270%200%20445%2023%27%3E%3Crect%20width%3D%27445%27%20height%3D%2723%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-135fd4aa2854ceb108e97e1cfbc013ea_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#102;&#94;&#50;&#32;&#61;&#32;&#109;&#103;&#108;&#101;&#102;&#116;&#40;&#32;&#123;&#72;&#32;&#45;&#32;&#102;&#114;&#97;&#99;&#123;&#72;&#125;&#123;&#51;&#125;&#125;&#32;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"445\" style=\"vertical-align: -8px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27395%27%20height%3D%2723%27%20viewBox%3D%270%200%20395%2023%27%3E%3Crect%20width%3D%27395%27%20height%3D%2723%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-2ebfc471e5f91a2da6dd7cf4c4967ab5_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#118;&#95;&#102;&#94;&#50;&#32;&#61;&#32;&#50;&#103;&#32;&#99;&#100;&#111;&#116;&#32;&#102;&#114;&#97;&#99;&#123;&#123;&#50;&#72;&#125;&#125;&#123;&#51;&#125;&#32;&#61;&#32;&#102;&#114;&#97;&#99;&#123;&#123;&#52;&#103;&#72;&#125;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"395\" style=\"vertical-align: -8px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27283%27%20height%3D%2718%27%20viewBox%3D%270%200%20283%2018%27%3E%3Crect%20width%3D%27283%27%20height%3D%2718%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-77246363b8bbfc2226e518249114f804_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#123;&#118;&#95;&#102;&#125;&#32;&#61;&#32;&#50;&#115;&#113;&#114;&#116;&#32;&#123;&#102;&#114;&#97;&#99;&#123;&#123;&#103;&#72;&#125;&#125;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"283\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p>Also, <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27138%27%20height%3D%2720%27%20viewBox%3D%270%200%20138%2020%27%3E%3Crect%20width%3D%27138%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c091d6c4cce9ef7ada48ed7ff2f4a1e8_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#75;&#46;&#69;&#123;&#46;&#95;&#102;&#125;&#32;&#61;&#32;&#50;&#123;&#40;&#80;&#46;&#69;&#46;&#41;&#95;&#102;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27282%27%20height%3D%2723%27%20viewBox%3D%270%200%20282%2023%27%3E%3Crect%20width%3D%27282%27%20height%3D%2723%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-67f2a2686914873bb1fe8905342fcda7_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#102;&#94;&#50;&#32;&#61;&#32;&#50;&#109;&#103;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"282\" style=\"vertical-align: -8px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27284%27%20height%3D%2719%27%20viewBox%3D%270%200%20284%2019%27%3E%3Crect%20width%3D%27284%27%20height%3D%2719%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-edd50c67dcb9fc73af9f4ef1136192d8_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#50;&#109;&#103;&#104;&#32;&#61;&#32;&#109;&#103;&#40;&#72;&#32;&#45;&#32;&#104;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"284\" style=\"vertical-align: -5px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27239%27%20height%3D%2716%27%20viewBox%3D%270%200%20239%2016%27%3E%3Crect%20width%3D%27239%27%20height%3D%2716%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-8672054c7f48f1aeaeb9c7dfc8fcd361_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#51;&#109;&#103;&#104;&#32;&#61;&#32;&#109;&#103;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"239\" style=\"vertical-align: -4px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27226%27%20height%3D%2716%27%20viewBox%3D%270%200%20226%2016%27%3E%3Crect%20width%3D%27226%27%20height%3D%2716%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-35a7bc34a31181873ab06cb80e0c9c83_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#104;&#32;&#61;&#32;&#102;&#114;&#97;&#99;&#123;&#72;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"226\" style=\"vertical-align: -4px;\"\/><\/p>\r\n<h3>Example 4: Finding Work Done Using the Conservation of Energy Approach<\/h3>\r\n<p>Under the action of force, 2 kg body moves such that its position x varies as a function of time given by <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%2793%27%20height%3D%2719%27%20viewBox%3D%270%200%2093%2019%27%3E%3Crect%20width%3D%2793%27%20height%3D%2719%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-633fe40498b90411f40ddae4dcd82b91_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#120;&#32;&#61;&#32;&#102;&#114;&#97;&#99;&#123;&#123;&#123;&#116;&#94;&#51;&#125;&#125;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -4px;\"\/>; x is in meter, t is in second. Calculate the work done by the force in the first two seconds.<\/p>\r\n<p>Ans: Considering 2 kg body and earth as a system. Here, external force does work on the system, <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%2765%27%20height%3D%2715%27%20viewBox%3D%270%200%2065%2015%27%3E%3Crect%20width%3D%2765%27%20height%3D%2715%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-3bcaaea32f6ae247a19f5afebfe0649f_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;&#32;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"65\" style=\"vertical-align: -3px;\"\/>. Hence, we cannot use the energy conservation principle for this numerical.<\/p>\r\n<p>So, here we will use the work energy theorem,<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27174%27%20height%3D%2718%27%20viewBox%3D%270%200%20174%2018%27%3E%3Crect%20width%3D%27174%27%20height%3D%2718%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d13919a6bee1c9178e69bc2391cf8adf_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#75;&#46;&#69;&#123;&#46;&#95;&#102;&#125;&#32;&#45;&#32;&#75;&#46;&#69;&#123;&#46;&#95;&#105;&#125;&#32;&#61;&#32;&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"174\" style=\"vertical-align: -6px;\"\/> \u00a0\u00a0\u00a0<img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27167%27%20height%3D%2720%27%20viewBox%3D%270%200%20167%2020%27%3E%3Crect%20width%3D%27167%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f0a55d4452fa17b63746578ea234f5d6_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#40;&#123;&#87;&#95;&#123;&#109;&#103;&#125;&#125;&#32;&#61;&#32;&#48;&#44;&#59;&#44;&#123;&#87;&#95;&#78;&#125;&#32;&#61;&#32;&#48;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"167\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27254%27%20height%3D%2723%27%20viewBox%3D%270%200%20254%2023%27%3E%3Crect%20width%3D%27254%27%20height%3D%2723%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-223fd54368263130df5146bec7cfad20_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#102;&#94;&#50;&#32;&#45;&#32;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#109;&#118;&#95;&#105;&#94;&#50;&#32;&#61;&#32;&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"254\" style=\"vertical-align: -8px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27190%27%20height%3D%2723%27%20viewBox%3D%270%200%20190%2023%27%3E%3Crect%20width%3D%27190%27%20height%3D%2723%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-6740eda6565973edda97f334181b0ada_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#102;&#114;&#97;&#99;&#123;&#109;&#125;&#123;&#50;&#125;&#40;&#118;&#95;&#102;&#94;&#50;&#32;&#45;&#32;&#118;&#95;&#105;&#94;&#50;&#41;&#32;&#61;&#32;&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"190\" style=\"vertical-align: -8px;\"\/> \u00a0\u00a0\u00a0\u2026(1)<\/p>\r\n<p>Here, <img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27190%27%20height%3D%2723%27%20viewBox%3D%270%200%20190%2023%27%3E%3Crect%20width%3D%27190%27%20height%3D%2723%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-6740eda6565973edda97f334181b0ada_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#102;&#114;&#97;&#99;&#123;&#109;&#125;&#123;&#50;&#125;&#40;&#118;&#95;&#102;&#94;&#50;&#32;&#45;&#32;&#118;&#95;&#105;&#94;&#50;&#41;&#32;&#61;&#32;&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"190\" style=\"vertical-align: -8px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27177%27%20height%3D%2719%27%20viewBox%3D%270%200%20177%2019%27%3E%3Crect%20width%3D%27177%27%20height%3D%2719%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bd7bc114536fe59825f97dd3e51993ff_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#118;&#32;&#61;&#32;&#123;&#116;&#94;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"177\" style=\"vertical-align: -4px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27169%27%20height%3D%2721%27%20viewBox%3D%270%200%20169%2021%27%3E%3Crect%20width%3D%27169%27%20height%3D%2721%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-a805a12ff2c540e9c74c43f4f4672b92_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#118;&#95;&#102;&#125;&#32;&#61;&#32;&#123;&#40;&#50;&#41;&#94;&#50;&#125;&#32;&#61;&#32;&#52;&#44;&#123;&#114;&#109;&#123;&#109;&#47;&#115;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"169\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27166%27%20height%3D%2720%27%20viewBox%3D%270%200%20166%2020%27%3E%3Crect%20width%3D%27166%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-4bacadb0bbe0dc947f2c97389b83c437_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#123;&#118;&#95;&#105;&#125;&#32;&#61;&#32;&#123;&#40;&#48;&#41;&#94;&#50;&#125;&#32;&#61;&#32;&#48;&#44;&#123;&#114;&#109;&#123;&#109;&#47;&#115;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"166\" style=\"vertical-align: -5px;\"\/><\/p>\r\n<p>Now, from (1),<\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27253%27%20height%3D%2720%27%20viewBox%3D%270%200%20253%2020%27%3E%3Crect%20width%3D%27253%27%20height%3D%2720%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-4ea652d3c3cdd61fb94fdd24d9608c07_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#50;&#125;&#108;&#101;&#102;&#116;&#40;&#32;&#123;&#123;&#52;&#94;&#50;&#125;&#32;&#45;&#32;&#123;&#48;&#94;&#50;&#125;&#125;&#32;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#61;&#32;&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"253\" style=\"vertical-align: -5px;\"\/><\/p>\r\n<p><img decoding=\"async\" src=\"data:image\/svg+xml,%3Csvg%20xmlns%3D%27http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%27%20width%3D%27229%27%20height%3D%2716%27%20viewBox%3D%270%200%20229%2016%27%3E%3Crect%20width%3D%27229%27%20height%3D%2716%27%20fill-opacity%3D%220%22%2F%3E%3C%2Fsvg%3E\" data-orig-src=\"https:\/\/www.myengineeringbuddy.com\/blog\/wp-content\/ql-cache\/quicklatex.com-0aac4c464e3ce4679971d9dc6c803796_l3.svg\" class=\"lazyload ql-img-inline-formula \" alt=\"&#82;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#113;&#117;&#97;&#100;&#32;&#123;&#87;&#95;&#123;&#101;&#120;&#116;&#125;&#125;&#32;&#61;&#32;&#49;&#54;&#44;&#74;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"229\" style=\"vertical-align: -4px;\"\/><\/p>\r\n<p>Still not sure about the law of conservation of mechanical energy? My Engineering Buddy provides top physics tutors who can help you learn and master it in a private 1:1 session. Contact us at <a href=\"mailto:meb@myengineeringbuddy.com\">meb@myengineeringbuddy.com<\/a> or WhatsApp +91 8971 383660 to get started.<\/p>\r\n<p>Students exploring related STEM disciplines may also find these resources useful: <a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/transform-learning-with-stem-tutoring-boost-grades-and-build-21st-century-skills\/\">how STEM tutoring boosts grades and builds 21st-century skills<\/a>, <a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/the-complete-guide-to-life-sciences-tutoring-how-online-tutors-transform-student-success\/\">a complete guide to life sciences tutoring<\/a>, <a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/complete-guide-to-geology-tutoring-how-online-help-transforms-student-success\/\">how online geology tutoring transforms student success<\/a>, and <a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/expert-dentistry-tutoring-services-academic-support-for-aspiring-dental-professionals\/\">expert dentistry tutoring for aspiring dental professionals<\/a>.<\/p>\r\n<p>Related: <a href=\"https:\/\/www.myengineeringbuddy.com\/the-law-of-conservation-of-linear-momentum\/\">The law of conservation of linear momentum<\/a> | <a href=\"https:\/\/www.myengineeringbuddy.com\/how-does-a-fuse-work\/\">How does a fuse work<\/a> | <a href=\"https:\/\/www.myengineeringbuddy.com\/homework-help\/physics-homework-help\/\">Physics Homework Help<\/a> | <a href=\"https:\/\/www.myengineeringbuddy.com\/online-tutoring\/online-physics-tutor\/\">Physics Tutor Online<\/a><\/p>\r\n<p>Digital logic design students working with hardware description languages can find structured support through a <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/vhdl\/\">VHDL tutor<\/a> to complement their physics and engineering coursework.<\/p>\r\n<h2>Related Reading<\/h2>\r\n<ul>\r\n<li><a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/architectural-education-on-space-saving-toilet-layouts-and-fixtures-for-small-bathrooms\/\">Architectural education on space-saving toilet layouts and fixtures for small bathrooms<\/a><\/li>\r\n<li><a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/environmental-science-tutoring-your-complete-guide-to-academic-success\/\">Environmental science tutoring: your complete guide to academic success<\/a><\/li>\r\n<li><a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/hubspot-reviews-alternatives-pricing-offerings\/\">HubSpot reviews, alternatives, pricing and offerings<\/a><\/li>\r\n<li><a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/master-fashion-studies-with-expert-online-tutoring\/\">Master fashion studies with expert online tutoring<\/a><\/li>\r\n<\/ul>\r\n","protected":false},"excerpt":{"rendered":"<p>Key Takeaways Mechanical energy is conserved only when non-conservative and  [&#8230;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-11296","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/posts\/11296","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/comments?post=11296"}],"version-history":[{"count":3,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/posts\/11296\/revisions"}],"predecessor-version":[{"id":12233,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/posts\/11296\/revisions\/12233"}],"wp:attachment":[{"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/media?parent=11296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/categories?post=11296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/tags?post=11296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}