{"id":608,"date":"2018-04-29T11:49:22","date_gmt":"2018-04-29T06:19:22","guid":{"rendered":"http:\/\/physicscatalyst.com\/article\/?p=608"},"modified":"2022-11-04T12:06:30","modified_gmt":"2022-11-04T06:36:30","slug":"conservative-and-non-conservative-forces","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/conservative-and-non-conservative-forces\/","title":{"rendered":"Conservative and Non conservative forces"},"content":{"rendered":"

What are\u00a0Conservative and Non conservative forces?<\/strong><\/p>\n

If the work done on particle by a force is independent of how particle moves and depends only on initial and final position of the objects then such a force is called conservative force . Similarly if the word done is not independent of the path then that force is non-conservative force<\/p>\n

This can also be states as if the work done by the force in closed loop is zero then it is a conservative force ,otherwise it is a non-conservative force.Non-conservative forces are called\u00a0dissipative force<\/p>\n

For conservative Force<\/p>\n

$W_{closed \\; loop} =\\oint \\mathbf{F}.d\\mathbf{r} =0$<\/p>\n

For non-conservative Force<\/p>\n

$W_{closed \\; loop} =\\oint \\mathbf{F}.d\\mathbf{r}\u00a0 \\neq\u00a0 0$<\/p>\n

Examples of\u00a0Conservative and Non conservative forces<\/strong><\/p>\n

Here is the list of Conservative and Non-conservative forces<\/p>\n\n\n\n\n\n\n\n\n
Conservative Forces<\/strong><\/td>\nNon conservative Forces<\/strong><\/td>\n<\/tr>\n
Gravitation $(mg)$<\/td>\nFriction$(\\mu N)$<\/td>\n<\/tr>\n
Elastic Forces $(kx)$<\/td>\nViscosity<\/td>\n<\/tr>\n
Electric Forces $(\\frac{kq}{r^{2}})$<\/td>\nAir resistance<\/td>\n<\/tr>\n
<\/td>\nMotor or rocket propulsion<\/td>\n<\/tr>\n
<\/td>\nThe tension in the cord $(T)$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Some Points about Conservative forces and Non-conservative forces<\/strong><\/p>\n

1) Potential energy is defined for Conservative forces<\/p>\n

2) An object that starts at a given point and returns to the same point, then\u00a0network done by the conservative force is zero\u00a0while in case of non-conservative force, it will not be zero<\/p>\n

3) When several conservative forces act on a particle, the potential energy\u00a0is the sum of the potential energies for each force<\/p>\n

4) Potential energy belongs to the system not to single particle as it is\u00a0associated with Force and force on one object is always exerted by other particles<\/p>\n

5) If only conservative forces are acting, the mechanical energy(K.E+P.E) of\u00a0the system remains constant<\/p>\n

How to find if the force is conservative<\/strong><\/p>\n

we can use two ways<\/p>\n

    \n
  1. \n
      \n
    1. we can calculate the work done between two points across two paths and compare if the work done is same.If it is same, it is conservative force<\/li>\n
    2. We can use below equation
      \n$\\frac{\\partial F_x}{\\partial y}=\\frac{\\partial F_y}{\\partial x}$<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n

      Example-1<\/strong><\/p>\n

      A force $\\mathbf{F}=xy \\mathbf{i} + xy\\mathbf{j}$ acts on a particle moving a XY plan.Find out if the force is conservative<\/p>\n

      Solution<\/strong><\/p>\n

      $\\frac{\\partial F_x}{\\partial y} = x$<\/p>\n

      $\\frac{\\partial F_y}{\\partial x} = y$<\/p>\n

      Now\u00a0$\\frac{\\partial F_x}{\\partial y} \\neq\u00a0\\frac{\\partial F_y}{\\partial x} $, So it is not conservative force<\/p>\n

      Example -2<\/strong><\/p>\n

      Find out if the below force is conservative<\/p>\n

      $\\mathbf{F}=xy^3 \\mathbf{i} + x^3y\\mathbf{j}$<\/p>\n

      Solution<\/strong><\/p>\n

      $\\frac{\\partial F_x}{\\partial y} = 3xy^2$<\/p>\n

      $\\frac{\\partial F_y}{\\partial x} = 3yx^2$<\/p>\n

      Now\u00a0$\\frac{\\partial F_x}{\\partial y} \\neq\u00a0\\frac{\\partial F_y}{\\partial x} $, So it is not conservative force<\/p>\n

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

      Different type of Forces and their origin<\/a><\/p>\n

      How to find the conservative force if you know the potential energy<\/a><\/p>\n

      How to solve electric force and field problems<\/a><\/p>\n

      How to Solve Equilibrium and Potential energy Questions Effectively for JEE Examination<\/a><\/p>\n

      How to apply the law of conservation of energy in mechanics<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

      Some Points about Conservative forces and Non conservative forces
      \n1) Potential energy are defined for Conservative forces
      \n2) An object that starts at a given point and return to the same point,then
      \nnet workdone by the conservative force is zero while in case of non conservative force ,it will not be zero<\/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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","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-608","post","type-post","status-publish","format-standard","hentry","category-physics","category-tips-and-tricks"],"yoast_head":"\nConservative and Non conservative forces - 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