{"id":224731,"date":"2025-06-03T12:07:32","date_gmt":"2025-06-03T12:07:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224731"},"modified":"2025-06-03T12:07:34","modified_gmt":"2025-06-03T12:07:34","slug":"a-1-83-kg-book-is-placed-on-a-flat-desk","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/a-1-83-kg-book-is-placed-on-a-flat-desk\/","title":{"rendered":"A 1.83 kg book is placed on a flat desk."},"content":{"rendered":"\n

A 1.83 kg book is placed on a flat desk. Suppose the coefficient of static friction between the book and the desk is 0.562 and the coefficient of kinetic friction is 0.305. How much force is needed to begin moving the book? How much force is needed to keep the book moving at constant speed once it begins moving?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong><\/h3>\n\n\n\n
    \n
  • Force needed to begin moving the book (static friction):<\/strong>
    Fstatic\u00a0max=\u03bcs\u22c5N=0.562\u22c5(1.83\u22c59.8)=10.07\u2009NF_{\\text{static max}} = \\mu_s \\cdot N = 0.562 \\cdot (1.83 \\cdot 9.8) = 10.07 \\, \\text{N}<\/li>\n\n\n\n
  • Force needed to keep the book moving at constant speed (kinetic friction):<\/strong>
    Fkinetic=\u03bck\u22c5N=0.305\u22c5(1.83\u22c59.8)=5.47\u2009NF_{\\text{kinetic}} = \\mu_k \\cdot N = 0.305 \\cdot (1.83 \\cdot 9.8) = 5.47 \\, \\text{N}<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    Explanation<\/strong><\/h3>\n\n\n\n

    When a book is placed on a flat desk, it experiences a downward gravitational force due to its weight. This force is given by Fg=m\u22c5gF_g = m \\cdot g, where mm is the mass of the book (1.83 kg), and gg is the acceleration due to gravity (approximately 9.8 m\/s\u00b2). Thus, the gravitational force on the book is: Fg=1.83\u22c59.8=17.93\u2009NF_g = 1.83 \\cdot 9.8 = 17.93 \\, \\text{N}<\/p>\n\n\n\n

    This force is balanced by the normal force exerted upward by the desk, also 17.93 N. When trying to move the book, we must overcome the static friction<\/strong> that resists motion. The maximum static friction force is given by: Fstatic max=\u03bcs\u22c5N=0.562\u22c517.93\u224810.07\u2009NF_{\\text{static max}} = \\mu_s \\cdot N = 0.562 \\cdot 17.93 \\approx 10.07 \\, \\text{N}<\/p>\n\n\n\n

    This means a horizontal force of at least 10.07 N is required to start moving the book.<\/p>\n\n\n\n

    Once the book starts moving, kinetic friction<\/strong> takes over, which is generally lower than static friction. The kinetic friction force is: Fkinetic=\u03bck\u22c5N=0.305\u22c517.93\u22485.47\u2009NF_{\\text{kinetic}} = \\mu_k \\cdot N = 0.305 \\cdot 17.93 \\approx 5.47 \\, \\text{N}<\/p>\n\n\n\n

    To keep the book moving at a constant velocity, the applied force must match this kinetic friction force, 5.47 N. If the applied force is greater, the book will accelerate; if it\u2019s less, the book will slow down and stop.<\/p>\n\n\n\n

    In summary, it takes more force to start<\/em> the motion due to static friction (10.07 N), but less force to maintain<\/em> the motion due to kinetic friction (5.47 N). This difference illustrates how friction acts to resist changes in motion and how surfaces interact differently depending on whether they are at rest or sliding.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    A 1.83 kg book is placed on a flat desk. Suppose the coefficient of static friction between the book and the desk is 0.562 and the coefficient of kinetic friction is 0.305. How much force is needed to begin moving the book? How much force is needed to keep the book moving at constant speed […]<\/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-224731","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224731","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=224731"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224731\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224731"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224731"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}