{"id":1506,"date":"2024-01-18T17:46:12","date_gmt":"2024-01-18T12:16:12","guid":{"rendered":"http:\/\/physicscatalyst.com\/article\/?p=1506"},"modified":"2024-01-18T17:46:17","modified_gmt":"2024-01-18T12:16:17","slug":"effectively-solve-momentum-collisions","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/effectively-solve-momentum-collisions\/","title":{"rendered":"How to effectively solve the Momentum and Collisions problems"},"content":{"rendered":"\n<p><span style=\"text-decoration: underline;\"><strong>Things to remember for&nbsp;momentum problems<\/strong><\/span><br>1) Law of conservation of Momentum. The total momentum for the isolated remains constant<br>2) Elastic collision: In this collison, Momentum and Kinetic energy of the system remains conserved<br>3) Inelastic collision: In this collision ,Momentum is conserved only<\/p>\n\n\n\n<p><span style=\"text-decoration: underline;\"><strong>General approach to solve the momentum problems<\/strong><\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Choose your frame of&nbsp;reference<\/li>\n\n\n\n<li>Set up a coordinate system and define your velocities with respect to that system.It is usually convenient to have the x axis coincide with one of the initial velocities.<\/li>\n\n\n\n<li>In your sketch of the coordinate system, draw and label all velocity vectors and include all the given information.<\/li>\n\n\n\n<li>Write expressions for the x and y components of the momentum of each object before and after the collision. Remember to include the appropriate signs for the components of the velocity vectors.<\/li>\n\n\n\n<li>Write expressions for the total momentum in the x direction before and after the collision and equate the two. Repeat this procedure for the total momentum in the y direction. These steps follow from the fact that, because the momentum of the system is conserved in any collision(law on conservation of linear momentum), the total momentum along any direction must also be constant. Remember, it is the momentum of the system that is constant, not the momentan of the individual objects.<\/li>\n\n\n\n<li>If the collision is inelastic, kinetic energy is not conserved, and additional information is probably required. If the collision is perfectly inelastic, the final velocities of the two objects are equal. Solve the momentum equations for the unknown quantities.<\/li>\n\n\n\n<li>If the collision is elastic, kinetic energy is conserved, and you can equate the total kinetic energy before the collision to the total kinetic energy after the collision to get an additional relationship between the velocities.And you can solve the energy and momentum equation to find out the find velocities.<\/li>\n\n\n\n<li>Centre of mass can be useful feature in solving the momentum problems<\/li>\n\n\n\n<li>Remember we need to get as many equation as the number of unknown<\/li>\n<\/ul>\n\n\n\n<p><span style=\"text-decoration: underline;\"><strong>Type of momentum problems<\/strong><\/span><br>1) Two free-moving objects colliding<br>2) An object exploding into two or more pieces<br>3) Problems having elastic or inelastic collision<\/p>\n\n\n\n<p><span style=\"text-decoration: underline;\"><strong>Some Quick Formula for standard momentum problems<\/strong><\/span><br>a) One dimensional perfectly elastic collision<\/p>\n\n\n\n<p>Law of conservation of momentum<br>P<sub>f<\/sub> = P<sub>i<\/sub><br>Since the motion is One dimensional, Conservation of Energy becomes<br>v<sub>1f<\/sub> \u2013 v<sub>2f<\/sub> = \u2013(v<sub>1i<\/sub> \u2013 v<sub>2i<\/sub>)<\/p>\n\n\n\n<p>b) One dimensional totally inelastic collision<br>Law of conservation of momentum<br>P<sub>f<\/sub> = P<sub>i<\/sub><br>Imp point v<sub>f<\/sub> is same for both the object<\/p>\n\n\n\n<p>c) Two dimensional totally inelastic collision<br>Law of conservation of momentum in x and y axis<br>P<sub>fx<\/sub> = P<sub>ix<\/sub><br>P<sub>fy<\/sub> = P<sub>iy<\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula.png\"><img loading=\"lazy\" decoding=\"async\" width=\"1160\" height=\"566\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula.png\" alt=\"momentum problems\" class=\"wp-image-4120\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula.png 1160w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula-300x146.png 300w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula-768x375.png 768w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula-1024x500.png 1024w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula-800x390.png 800w\" sizes=\"auto, (max-width: 1160px) 100vw, 1160px\" \/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula_1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"706\" height=\"256\" src=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula_1.png\" alt=\"momentum problems\" class=\"wp-image-4121\" srcset=\"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula_1.png 706w, https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2013\/10\/momentum_formula_1-300x109.png 300w\" sizes=\"auto, (max-width: 706px) 100vw, 706px\" \/><\/a><\/figure>\n\n\n\n<p><span style=\"text-decoration: underline;\"><strong>Detailed Notes for Momentum and Collision can be found at<\/strong><\/span><br><a href=\"https:\/\/physicscatalyst.com\/chapter.php\"> Click Here<\/a><\/p>\n\n\n\n<p><strong>Videos to help you in Problem Solving<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-embed-handler wp-block-embed-embed-handler wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"how to solve conservation of momentum problems\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/UERvKx-cqJs?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-embed-handler wp-block-embed-embed-handler wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"how to solve momentum problems\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/HkaQb9nQCik?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>&lt;iframe width=&#8221;560&#8243; height=&#8221;315&#8243; src=&#8221;https:\/\/www.youtube.com\/embed\/HkaQb9nQCik&#8221; frameborder=&#8221;0&#8243; allowfullscreen>&lt;\/iframe><\/p>\n\n\n\n<p><strong>Must Read Articles<\/strong><\/p>\n\n\n\n<p><a href=\"https:\/\/physicscatalyst.com\/article\/how-to-do-the-physics-problems\/\">how to study physics problems<\/a><br><a href=\"https:\/\/physicscatalyst.com\/article\/how_solve_shm_problems\/\">how to solve Simple Harmonic Motion(SHM) problems effectively<\/a><br><a href=\"https:\/\/physicscatalyst.com\/article\/conservative-conservative-forces\/\">Conservative and Non conservative forces<\/a><br><a href=\"https:\/\/physicscatalyst.com\/article\/effectively-memorize-physics-formula\/\">Effectively Memorize Physics Formula<\/a><br><a href=\"https:\/\/physicscatalyst.com\/article\/newtons-third-law-of-motion\/\">Newton\u2019s Third Law of motion (action-reaction and examples)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Things to remember<br \/>\n1) Law of conservation of Momentum. The total momentum for the isolated remains constant<br \/>\n2) Elastic collision: In this collison, Momentum and Kinetic energy of the system remains conserved<br \/>\n3) Inelastic collision: In this collision ,Momentum is conserved only<\/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":[42,40,48,14],"tags":[],"class_list":["post-1506","post","type-post","status-publish","format-standard","hentry","category-competitive-exams","category-jeeadvanced","category-jeemain","category-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>How to effectively solve the Momentum and Collisions problems - physicscatalyst&#039;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\/effectively-solve-momentum-collisions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to effectively solve the Momentum and Collisions problems - physicscatalyst&#039;s Blog\" \/>\n<meta property=\"og:description\" content=\"Things to remember 1) Law of conservation of Momentum. 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The total momentum for the isolated remains constant 2) Elastic collision: In this collison, Momentum and Kinetic energy of the system remains conserved 3) Inelastic collision: In this collision ,Momentum is conserved only","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/1506","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=1506"}],"version-history":[{"count":3,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/1506\/revisions"}],"predecessor-version":[{"id":8831,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/1506\/revisions\/8831"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=1506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=1506"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=1506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}