{"id":25731,"date":"2025-06-19T06:29:35","date_gmt":"2025-06-19T06:29:35","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25731"},"modified":"2025-06-19T06:29:43","modified_gmt":"2025-06-19T06:29:43","slug":"2000-kg-car-moving-at-an-initial-speed-of-25-m-s-along-a-horizontal-road-skids-to-a-stop-in-60-m","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/2000-kg-car-moving-at-an-initial-speed-of-25-m-s-along-a-horizontal-road-skids-to-a-stop-in-60-m\/","title":{"rendered":"2000-kg car moving at an initial speed of 25 m\/s along a horizontal road skids to a stop in 60 m"},"content":{"rendered":"\n<p>2000-kg car moving at an initial speed of 25 m\/s along a horizontal road skids to a stop in 60 m. (a) Find the energy dissipated by friction (b) Find the coefficient of kinetic friction between the tires and the road_ (Note: When stopping without skidding and using conventional brakes; 100 percent of the kinetie energy is dissipated by friction within the brakes:<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-light-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mass of car, m=2000\u2009kgm = 2000 \\, \\text{kg}m=2000kg<\/li>\n\n\n\n<li>Initial speed, vi=25\u2009m\/sv_i = 25 \\, \\text{m\/s}vi\u200b=25m\/s<\/li>\n\n\n\n<li>Final speed, vf=0\u2009m\/sv_f = 0 \\, \\text{m\/s}vf\u200b=0m\/s<\/li>\n\n\n\n<li>Skid distance, d=60\u2009md = 60 \\, \\text{m}d=60m<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(a) <strong>Energy dissipated by friction<\/strong><\/h3>\n\n\n\n<p>Since the car comes to a stop, all its initial kinetic energy is lost due to friction.<\/p>\n\n\n\n<p>The <strong>initial kinetic energy (KE)<\/strong> is: KE=12mv2=12(2000)(25)2=1000\u00d7625=625,000\u2009JKE = \\frac{1}{2}mv^2 = \\frac{1}{2}(2000)(25)^2 = 1000 \\times 625 = 625{,}000 \\, \\text{J}KE=21\u200bmv2=21\u200b(2000)(25)2=1000\u00d7625=625,000J<\/p>\n\n\n\n<p>So, the <strong>energy dissipated by friction<\/strong> is: 625,000\u2009J\\boxed{625{,}000 \\, \\text{J}}625,000J\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">(b) <strong>Coefficient of kinetic friction, \u03bck\\mu_k\u03bck\u200b<\/strong><\/h3>\n\n\n\n<p>To find the coefficient of kinetic friction, we use the <strong>work-energy principle<\/strong>. The work done by friction is equal to the loss of kinetic energy: W=fk\u22c5d=\u03bck\u22c5N\u22c5d=\u03bck\u22c5mg\u22c5dW = f_k \\cdot d = \\mu_k \\cdot N \\cdot d = \\mu_k \\cdot mg \\cdot dW=fk\u200b\u22c5d=\u03bck\u200b\u22c5N\u22c5d=\u03bck\u200b\u22c5mg\u22c5d<\/p>\n\n\n\n<p>Set this equal to the energy dissipated: \u03bck\u22c5mg\u22c5d=12mv2\\mu_k \\cdot mg \\cdot d = \\frac{1}{2}mv^2\u03bck\u200b\u22c5mg\u22c5d=21\u200bmv2<\/p>\n\n\n\n<p>Cancel out mmm from both sides: \u03bck\u22c5g\u22c5d=12v2\\mu_k \\cdot g \\cdot d = \\frac{1}{2}v^2\u03bck\u200b\u22c5g\u22c5d=21\u200bv2<\/p>\n\n\n\n<p>Solve for \u03bck\\mu_k\u03bck\u200b: \u03bck=v22gd=2522\u22c59.8\u22c560=6251176\u22480.531\\mu_k = \\frac{v^2}{2gd} = \\frac{25^2}{2 \\cdot 9.8 \\cdot 60} = \\frac{625}{1176} \\approx 0.531\u03bck\u200b=2gdv2\u200b=2\u22c59.8\u22c560252\u200b=1176625\u200b\u22480.531<\/p>\n\n\n\n<p>So, the <strong>coefficient of kinetic friction<\/strong> is: 0.531\\boxed{0.531}0.531\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation <\/h3>\n\n\n\n<p>When a car moves and then stops due to skidding, its kinetic energy is converted entirely into heat and sound through friction. This means that the energy the car had while moving is used up to overcome the force of friction between the tires and the road.<\/p>\n\n\n\n<p>To calculate the energy lost, we use the formula for kinetic energy. This energy depends on the mass of the car and the square of its speed. Since the final speed is zero, the entire kinetic energy is lost during braking. Plugging in the values, we find that 625,000 joules of energy were dissipated as the car skidded to a stop.<\/p>\n\n\n\n<p>Next, to find the coefficient of kinetic friction, we consider how much force was needed to stop the car over a given distance. The friction force is what slows the car down. This force is the product of the normal force and the coefficient of friction. Since the car is on a horizontal road, the normal force equals the weight of the car. Using the work-energy principle, we equate the work done by this friction force to the car\u2019s lost kinetic energy. This allows us to solve for the coefficient.<\/p>\n\n\n\n<p>The result, approximately 0.531, is reasonable for rubber tires on dry pavement. A higher value would suggest a more abrupt stop, and a lower value would indicate less effective friction. This coefficient is crucial in real-world applications such as designing road surfaces and braking systems to ensure vehicles can stop safely.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-85.jpeg\" alt=\"\" class=\"wp-image-25735\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-85.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-85-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-85-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>2000-kg car moving at an initial speed of 25 m\/s along a horizontal road skids to a stop in 60 m. (a) Find the energy dissipated by friction (b) Find the coefficient of kinetic friction between the tires and the road_ (Note: When stopping without skidding and using conventional brakes; 100 percent of the kinetie [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-25731","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25731","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=25731"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25731\/revisions"}],"predecessor-version":[{"id":25736,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25731\/revisions\/25736"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}