{"id":437,"date":"2024-02-02T20:42:15","date_gmt":"2024-02-02T15:12:15","guid":{"rendered":"http:\/\/physicscatalyst.com\/article\/?p=437"},"modified":"2024-02-02T20:42:20","modified_gmt":"2024-02-02T15:12:20","slug":"how-to-apply-law-of-conservation-of-energy-in-mechanics","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/how-to-apply-law-of-conservation-of-energy-in-mechanics\/","title":{"rendered":"How to apply law of conservation of energy in mechanics"},"content":{"rendered":"\n

We often comes across the problems in mechanics where we need to apply the law of conservation of energy where gravitational potential energy or gravity is involved . For solving such problems you can consider the following problem solving strategy,<\/p>\n\n\n\n

    \n
  1. First of all define the system which includes all the interacting bodies . Now choose a zero point for gravitational potential energy according to your convenience.<\/li>\n\n\n\n
  2. Select the body of interest and identify the point about which information is given in the question. Also identify the point where you want to find out asked quantity about the body of interest.<\/li>\n\n\n\n
  3. Check for the possibility of the presence of non-conservative forces. If there are no non-conservative forces present then write down the energy conservation equation for the system and identify the unknown quantity asked in the question.<\/li>\n\n\n\n
  4. Solve the equation for the unknown quantities asked in the question by substituting the given quantities in the equation obtained.<\/li>\n<\/ol>\n\n\n\n

    If only conservative forces involved like Gravity<\/strong><\/p>\n\n\n\n

    Total Energy at point A = Total Energy at point B<\/p>\n\n\n\n

    If non-conservative forces like Friction are involved, we need to write the energy loss in overcoming Friction<\/strong><\/p>\n\n\n\n

    Total Energy at Point A – Total Energy at point B = Workdone to overcome friction forces<\/p>\n\n\n\n

    or<\/p>\n\n\n\n

    $\\Delta U + $\\Delta K.E$ = work done by friction<\/p>\n\n\n\n

    Solved Examples<\/strong><\/h2>\n\n\n\n

    Question<\/strong><\/p>\n\n\n\n

    An object of mass M slides downward along a plane inclined at angle $\\theta$.
    The coefficient of friction is k
    Find d(U + KE)\/dt
    (a) $kmg^2cos \\theta (sin \\theta – kcos \\theta)$
    (b) $kmg^2sin \\theta (sin \\theta – kcos \\theta)$
    (c) $kmg^2 (sin \\theta – kcos \\theta)$
    (d) none of the above
    Solution<\/strong>
    $ma = mgsin \\theta – kmgcos \\theta$
    $a = gsin \\theta – kgcos \\theta$
    So v = u + at
    $v = g (sin \\theta – kcos \\theta)t$
    now $\\Delta U + \\Delta K.E$ = work done by friction
    d(U + E)\/dt = friction force. velocity
    $= kmg cos \\theta \\times g (sin \\theta – kcos \\theta)$
    $=kmg^2cos \\theta (sin \\theta – kcos \\theta)$<\/p>\n\n\n\n

    Related Articles<\/strong><\/p>\n\n\n\n

    How to Solve Equilibrium and Potential energy Questions Effectively for JEE Examination<\/a>
    Energy facts<\/a>
    How to find the force if you know the potential energy<\/a>
    How to solve Work And Energy\/kinetic energy problems<\/a>
    Download Class 10 Physics formulas and summary pdf<\/a>
    How to find workdone by several forces acting on a object<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    We often comes across the problems in mechanics where we need to apply the law of conservation of energy where gravitational potential energy or gravity is involved . For solving such problems you can consider the following problem solving strategy,<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[14,37],"tags":[],"class_list":["post-437","post","type-post","status-publish","format-standard","hentry","category-physics","category-tips-and-tricks"],"yoast_head":"\nHow to apply law of conservation of energy in mechanics - physicscatalyst's Blog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/physicscatalyst.com\/article\/how-to-apply-law-of-conservation-of-energy-in-mechanics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to apply law of conservation of energy in mechanics - physicscatalyst's Blog\" \/>\n<meta property=\"og:description\" content=\"We often comes across the problems in mechanics where we need to apply the law of conservation of energy where gravitational potential energy or gravity is involved . 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