{"id":183646,"date":"2025-01-16T19:00:13","date_gmt":"2025-01-16T19:00:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=183646"},"modified":"2025-01-16T19:00:17","modified_gmt":"2025-01-16T19:00:17","slug":"a-2000-kg-car-moving-north-at-25-m-s-collides-head-on-with-a-5000-kg-truck-moving-south-at-35-m-s","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/16\/a-2000-kg-car-moving-north-at-25-m-s-collides-head-on-with-a-5000-kg-truck-moving-south-at-35-m-s\/","title":{"rendered":"A 2000 kg car moving north at 25 m\/s collides head-on with a 5000 kg truck moving south at 35 m\/s"},"content":{"rendered":"\n<p>A 2000 kg car moving north at 25 m\/s collides head-on with a 5000 kg truck moving south at 35 m\/s. The car and truck stick together after the collision. How much mechanical energy is lost in the collision (find KE;-KE)? 1.25 * 10 ^ 6 * J 5.57 * 10 ^ 6 * J 2.57 * 10 ^ 6 * J 3.56 * 10 ^ 6 * J<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To solve for the mechanical energy lost in the collision, we can first determine the initial and final kinetic energy of the system and then compute the energy lost as the difference between them.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the Initial Kinetic Energy (KE_initial)<\/h3>\n\n\n\n<p>We need to calculate the kinetic energy of both the car and the truck before the collision.<\/p>\n\n\n\n<p>The formula for kinetic energy is: KE=12mv2KE = \\frac{1}{2} m v^2<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>mm is the mass of the object,<\/li>\n\n\n\n<li>vv is the velocity of the object.<\/li>\n<\/ul>\n\n\n\n<p>For the car: KEcar&nbsp;initial=12\u00d72000\u2009kg\u00d7(25\u2009m\/s)2=0.5\u00d72000\u00d7625=625000\u2009JKE_{\\text{car initial}} = \\frac{1}{2} \\times 2000 \\, \\text{kg} \\times (25 \\, \\text{m\/s})^2 = 0.5 \\times 2000 \\times 625 = 625000 \\, \\text{J}<\/p>\n\n\n\n<p>For the truck: KEtruck&nbsp;initial=12\u00d75000\u2009kg\u00d7(35\u2009m\/s)2=0.5\u00d75000\u00d71225=3062500\u2009JKE_{\\text{truck initial}} = \\frac{1}{2} \\times 5000 \\, \\text{kg} \\times (35 \\, \\text{m\/s})^2 = 0.5 \\times 5000 \\times 1225 = 3062500 \\, \\text{J}<\/p>\n\n\n\n<p>Total initial kinetic energy: KEinitial=KEcar&nbsp;initial+KEtruck&nbsp;initial=625000\u2009J+3062500\u2009J=3687500\u2009JKE_{\\text{initial}} = KE_{\\text{car initial}} + KE_{\\text{truck initial}} = 625000 \\, \\text{J} + 3062500 \\, \\text{J} = 3687500 \\, \\text{J}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the Final Kinetic Energy (KE_final)<\/h3>\n\n\n\n<p>After the collision, the car and truck stick together, so their combined mass is: mtotal=2000\u2009kg+5000\u2009kg=7000\u2009kgm_{\\text{total}} = 2000 \\, \\text{kg} + 5000 \\, \\text{kg} = 7000 \\, \\text{kg}<\/p>\n\n\n\n<p>The velocity of the combined mass can be determined using the principle of conservation of momentum. The initial momentum of the system is: pinitial=mcar\u00d7vcar&nbsp;initial+mtruck\u00d7vtruck&nbsp;initialp_{\\text{initial}} = m_{\\text{car}} \\times v_{\\text{car initial}} + m_{\\text{truck}} \\times v_{\\text{truck initial}} pinitial=(2000\u2009kg\u00d725\u2009m\/s)+(5000\u2009kg\u00d7(\u221235\u2009m\/s))=50000\u2212175000=\u2212125000\u2009kg\u22c5m\/sp_{\\text{initial}} = (2000 \\, \\text{kg} \\times 25 \\, \\text{m\/s}) + (5000 \\, \\text{kg} \\times (-35 \\, \\text{m\/s})) = 50000 &#8211; 175000 = -125000 \\, \\text{kg} \\cdot \\text{m\/s}<\/p>\n\n\n\n<p>Since momentum is conserved, the final momentum pfinalp_{\\text{final}} is the same: pfinal=mtotal\u00d7vfinalp_{\\text{final}} = m_{\\text{total}} \\times v_{\\text{final}} vfinal=pinitialmtotal=\u2212125000\u2009kg\u22c5m\/s7000\u2009kg=\u221217.86\u2009m\/sv_{\\text{final}} = \\frac{p_{\\text{initial}}}{m_{\\text{total}}} = \\frac{-125000 \\, \\text{kg} \\cdot \\text{m\/s}}{7000 \\, \\text{kg}} = -17.86 \\, \\text{m\/s}<\/p>\n\n\n\n<p>Now, we calculate the final kinetic energy: KEfinal=12\u00d77000\u2009kg\u00d7(\u221217.86\u2009m\/s)2=0.5\u00d77000\u00d7318.7=1115450\u2009JKE_{\\text{final}} = \\frac{1}{2} \\times 7000 \\, \\text{kg} \\times (-17.86 \\, \\text{m\/s})^2 = 0.5 \\times 7000 \\times 318.7 = 1115450 \\, \\text{J}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Calculate the Mechanical Energy Lost<\/h3>\n\n\n\n<p>Finally, the mechanical energy lost is the difference between the initial and final kinetic energies: Energy&nbsp;lost=KEinitial\u2212KEfinal=3687500\u2009J\u22121115450\u2009J=2572050\u2009J\\text{Energy lost} = KE_{\\text{initial}} &#8211; KE_{\\text{final}} = 3687500 \\, \\text{J} &#8211; 1115450 \\, \\text{J} = 2572050 \\, \\text{J}<\/p>\n\n\n\n<p>So, the mechanical energy lost in the collision is approximately: 2.57\u00d7106\u2009J2.57 \\times 10^6 \\, \\text{J}<\/p>\n\n\n\n<p>Thus, the correct answer is <strong>2.57 \u00d7 10^6 J<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>In this inelastic collision, where the car and truck stick together after the impact, kinetic energy is not conserved. This is because some of the initial kinetic energy is transformed into other forms of energy, such as heat, sound, or deformation of the vehicles. The total momentum is conserved, which allows us to calculate the final velocity of the combined mass. The energy lost is the difference between the total initial kinetic energy and the total final kinetic energy.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A 2000 kg car moving north at 25 m\/s collides head-on with a 5000 kg truck moving south at 35 m\/s. The car and truck stick together after the collision. How much mechanical energy is lost in the collision (find KE;-KE)? 1.25 * 10 ^ 6 * J 5.57 * 10 ^ 6 * J [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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":"","ast-disable-related-posts":"","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":[25],"tags":[],"class_list":["post-183646","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183646","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=183646"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183646\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}