{"id":862,"date":"2024-02-04T23:47:46","date_gmt":"2024-02-04T18:17:46","guid":{"rendered":"http:\/\/physicscatalyst.com\/article\/?p=862"},"modified":"2024-02-04T23:47:49","modified_gmt":"2024-02-04T18:17:49","slug":"find-force-potential-energy","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/","title":{"rendered":"How to Calculate the force given potential energy"},"content":{"rendered":"\n
\"force<\/a>
force from potential energy<\/figcaption><\/figure><\/div>\n\n\n\n

Any conservative force<\/a> acting on an object within a system equals the negative derivative of the potential energy of the system with respect to x.<\/p>\n\n\n\n

For one dimensional motion, the force can be found from Potential energy<\/a> using following formula<\/p>\n\n\n\n

$F_{x}=-\\frac{\\partial U}{\\partial x}$<\/p>\n\n\n\n

The generalized equation in three dimension is<\/p>\n\n\n\n

$F_{x}=-\\frac{\\partial U}{\\partial x}$
$F_{y}=-\\frac{\\partial U}{\\partial y}$
$F_{z}=-\\frac{\\partial U}{\\partial z}$<\/p>\n\n\n\n

In vector form<\/p>\n\n\n\n

$\\boldsymbol{\\mathbf{F}}=F_{x}\\mathbf{i}+F_{y}\\mathbf{j}+F_{z}\\mathbf{k}$<\/p>\n\n\n\n

Few examples to check on these<\/strong>
(1) Spring :<\/strong>
In the case of the deformed spring
$U=\\frac{1}{2}Kx^{2}$
Now
$F_{x}=-\\frac{\\partial U}{\\partial x}$
or
$F_{x}=-kx$<\/p>\n\n\n\n

Which we already know is the restoring force in Spring mass system<\/p>\n\n\n\n

(2)  Gravity<\/strong><\/p>\n\n\n\n

$U=mgH$
Now
$F_{x}=-\\frac{\\partial U}{\\partial x}$
or
$F_{x}=-mg$
Which we already know is the gravitational force in gravity<\/p>\n\n\n\n

(3) Potential Energy of a certain object is given by
$U= 10x^2 + 25z^3$
Now
$F_{x}=-\\frac{\\partial U}{\\partial x}$
or
$F_{x}=-20x$
Also
$ F_{y}=-\\frac{\\partial U}{\\partial y} =0$
Also
$ F_{z}=-\\frac{\\partial U}{\\partial z} =-75z^2$
Hence the Force will be given
$\\boldsymbol{F}=-20x \\mathbf{i} -75z^2 \\mathbf{k}$<\/p>\n\n\n\n

(4) Potential Energy of a certain object is given by
$U= \\frac {2yz}{x}$
Now
$F_{x}=-\\frac{\\partial U}{\\partial x}$
or
$F_{x}= \\frac {2yz}{x^2} $
Also
$ F_{y}=-\\frac{\\partial U}{\\partial y} =-\\frac {2z}{x}$
Also
$ F_{z}=-\\frac{\\partial U}{\\partial z} = -\\frac {2y}{x}$
Hence the Force will be given
$\\boldsymbol{F}= \\frac {2yz}{x^2} \\mathbf{i} – \\frac {2z}{x} \\mathbf{j} – \\frac {2y}{x} \\mathbf{k}$ <\/p>\n\n\n\n

Related articles on energy problems<\/strong><\/span><\/p>\n\n\n\n

stable unstable and neutral equilibrium<\/a>
how to solve kinetic and potential energy problems<\/a>
apply the law of conservation of energy<\/a>
http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/pegrav.html<\/a> <\/p>\n","protected":false},"excerpt":{"rendered":"

For one dimensional motion, the force can be found from Potential energy using following formula<\/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":"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],"tags":[],"class_list":["post-862","post","type-post","status-publish","format-standard","hentry","category-physics"],"yoast_head":"\nHow to Calculate the force given potential energy - physicscatalyst's Blog<\/title>\n<meta name=\"description\" content=\"check out this page for How to find the force if you know the potential energy\" \/>\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\/find-force-potential-energy\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Calculate the force given potential energy - physicscatalyst's Blog\" \/>\n<meta property=\"og:description\" content=\"check out this page for How to find the force if you know the potential energy\" \/>\n<meta property=\"og:url\" content=\"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/\" \/>\n<meta property=\"og:site_name\" content=\"physicscatalyst's Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:published_time\" content=\"2024-02-04T18:17:46+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-02-04T18:17:49+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2012\/06\/pe_force.png\" \/>\n<meta name=\"author\" content=\"physicscatalyst\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"physicscatalyst\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"How to Calculate the force given potential energy - physicscatalyst's Blog","description":"check out this page for How to find the force if you know the potential energy","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/","og_locale":"en_US","og_type":"article","og_title":"How to Calculate the force given potential energy - physicscatalyst's Blog","og_description":"check out this page for How to find the force if you know the potential energy","og_url":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/","og_site_name":"physicscatalyst's Blog","article_publisher":"https:\/\/www.facebook.com\/PhysicsCatalyst","article_author":"https:\/\/www.facebook.com\/PhysicsCatalyst","article_published_time":"2024-02-04T18:17:46+00:00","article_modified_time":"2024-02-04T18:17:49+00:00","og_image":[{"url":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2012\/06\/pe_force.png","type":"","width":"","height":""}],"author":"physicscatalyst","twitter_misc":{"Written by":"physicscatalyst","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/#article","isPartOf":{"@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/"},"author":{"name":"physicscatalyst","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/person\/9b302efdc9b32e459cb1e61ab7506d3f"},"headline":"How to Calculate the force given potential energy","datePublished":"2024-02-04T18:17:46+00:00","dateModified":"2024-02-04T18:17:49+00:00","mainEntityOfPage":{"@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/"},"wordCount":353,"commentCount":0,"publisher":{"@id":"https:\/\/physicscatalyst.com\/article\/#organization"},"image":{"@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/#primaryimage"},"thumbnailUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2012\/06\/pe_force.png","articleSection":["Physics"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/","url":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/","name":"How to Calculate the force given potential energy - physicscatalyst's Blog","isPartOf":{"@id":"https:\/\/physicscatalyst.com\/article\/#website"},"primaryImageOfPage":{"@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/#primaryimage"},"image":{"@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/#primaryimage"},"thumbnailUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2012\/06\/pe_force.png","datePublished":"2024-02-04T18:17:46+00:00","dateModified":"2024-02-04T18:17:49+00:00","description":"check out this page for How to find the force if you know the potential energy","breadcrumb":{"@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/#primaryimage","url":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2012\/06\/pe_force.png","contentUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2012\/06\/pe_force.png","width":535,"height":243},{"@type":"BreadcrumbList","@id":"https:\/\/physicscatalyst.com\/article\/find-force-potential-energy\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/physicscatalyst.com\/article\/"},{"@type":"ListItem","position":2,"name":"Physics","item":"https:\/\/physicscatalyst.com\/article\/physics\/"},{"@type":"ListItem","position":3,"name":"How to Calculate the force given potential energy"}]},{"@type":"WebSite","@id":"https:\/\/physicscatalyst.com\/article\/#website","url":"https:\/\/physicscatalyst.com\/article\/","name":"physicscatalyst's Blog","description":"Learn free for class 9th, 10th science\/maths , 12th and IIT-JEE Physics and maths.","publisher":{"@id":"https:\/\/physicscatalyst.com\/article\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/physicscatalyst.com\/article\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/physicscatalyst.com\/article\/#organization","name":"physicscatalyst","url":"https:\/\/physicscatalyst.com\/article\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/logo\/image\/","url":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2024\/08\/cropped-logo-1.jpg","contentUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2024\/08\/cropped-logo-1.jpg","width":96,"height":96,"caption":"physicscatalyst"},"image":{"@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/PhysicsCatalyst","https:\/\/x.com\/physicscatalyst","https:\/\/www.youtube.com\/user\/thephysicscatalyst","https:\/\/www.instagram.com\/physicscatalyst\/"]},{"@type":"Person","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/person\/9b302efdc9b32e459cb1e61ab7506d3f","name":"physicscatalyst","sameAs":["https:\/\/physicscatalyst.com","https:\/\/www.facebook.com\/PhysicsCatalyst","https:\/\/x.com\/physicscatalyst"]}]}},"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"shareaholic-thumbnail":false},"uagb_author_info":{"display_name":"physicscatalyst","author_link":"https:\/\/physicscatalyst.com\/article\/author\/physicscatalyst\/"},"uagb_comment_info":0,"uagb_excerpt":"For one dimensional motion, the force can be found from Potential energy using following formula","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/862","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=862"}],"version-history":[{"count":2,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/862\/revisions"}],"predecessor-version":[{"id":9012,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/862\/revisions\/9012"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}