{"id":199534,"date":"2025-03-12T04:58:03","date_gmt":"2025-03-12T04:58:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199534"},"modified":"2025-03-12T04:58:06","modified_gmt":"2025-03-12T04:58:06","slug":"an-object-of-mass-4-00-kg-is-held-motionless-at-the-top-of-a-ramp-that-is-inclined-at-an-angle-of-35-degrees-relative-to-horizontal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/12\/an-object-of-mass-4-00-kg-is-held-motionless-at-the-top-of-a-ramp-that-is-inclined-at-an-angle-of-35-degrees-relative-to-horizontal\/","title":{"rendered":"An object of mass 4.00 kg is held motionless at the top of a ramp that is inclined at an angle of 35 degrees relative to horizontal"},"content":{"rendered":"\n

An object of mass 4.00 kg is held motionless at the top of a ramp that is inclined at an angle of 35 degrees relative to horizontal. The object is given a gentle shove giving it an initial velocity of 4.00 m\/s down the ramp. Exactly 0.443 seconds after being released, the object is 2.00 m away from its release point.
Draw a free body diagram showing all forces on the object.
Determine the acceleration of the object.
Determine the force of friction.<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To analyze the motion of the object on the inclined plane, let’s break it down step by step.<\/p>\n\n\n\n

Step 1: Free Body Diagram<\/strong><\/h3>\n\n\n\n

A free-body diagram (FBD) shows all the forces acting on the object. In this case, the object experiences:<\/p>\n\n\n\n

    \n
  1. Gravity (Fg = mg)<\/strong> acting downward.<\/li>\n\n\n\n
  2. Normal Force (Fn)<\/strong> exerted by the surface, perpendicular to the ramp.<\/li>\n\n\n\n
  3. Friction Force (Ff)<\/strong> opposing motion, acting up the ramp.<\/li>\n<\/ol>\n\n\n\n

    We’ll generate a free-body diagram image<\/strong> to illustrate these forces.<\/p>\n\n\n\n

    \n\n\n\n

    Step 2: Determine the Acceleration<\/strong><\/h3>\n\n\n\n

    Using the kinematic equation:<\/p>\n\n\n\n

    [
    s = v_0t + \\frac{1}{2} a t^2
    ]<\/p>\n\n\n\n

    where:<\/p>\n\n\n\n

      \n
    • ( s = 2.00 ) m (displacement),<\/li>\n\n\n\n
    • ( v_0 = 4.00 ) m\/s (initial velocity),<\/li>\n\n\n\n
    • ( t = 0.443 ) s (time),<\/li>\n\n\n\n
    • ( a ) = unknown.<\/li>\n<\/ul>\n\n\n\n

      Substituting the values:<\/p>\n\n\n\n

      [
      2.00 = (4.00)(0.443) + \\frac{1}{2} a (0.443)^2
      ]<\/p>\n\n\n\n

      [
      2.00 = 1.772 + \\frac{1}{2} a (0.196)
      ]<\/p>\n\n\n\n

      [
      2.00 – 1.772 = 0.098a
      ]<\/p>\n\n\n\n

      [
      0.228 = 0.098a
      ]<\/p>\n\n\n\n

      [
      a = 2.33 \\text{ m\/s}^2
      ]<\/p>\n\n\n\n

      \n\n\n\n

      Step 3: Determine the Force of Friction<\/strong><\/h3>\n\n\n\n

      The forces along the ramp:<\/p>\n\n\n\n

      [
      F_{\\text{net}} = m a
      ]<\/p>\n\n\n\n

      [
      F_{\\text{gravity}} = mg \\sin \\theta = (4.00)(9.81) \\sin 35^\\circ
      ]<\/p>\n\n\n\n

      [
      F_{\\text{gravity}} = 22.46 \\text{ N}
      ]<\/p>\n\n\n\n

      Since ( F_{\\text{net}} = F_{\\text{gravity}} – F_{\\text{friction}} ),<\/p>\n\n\n\n

      [
      (4.00)(2.33) = 22.46 – F_{\\text{friction}}
      ]<\/p>\n\n\n\n

      [
      9.32 = 22.46 – F_{\\text{friction}}
      ]<\/p>\n\n\n\n

      [
      F_{\\text{friction}} = 13.14 \\text{ N}
      ]<\/p>\n\n\n\n

      \n\n\n\n

      Conclusion<\/strong><\/h3>\n\n\n\n
        \n
      • Acceleration<\/strong>: ( 2.33 ) m\/s\u00b2 down the ramp.<\/li>\n\n\n\n
      • Friction Force<\/strong>: ( 13.14 ) N opposing motion.<\/li>\n<\/ul>\n\n\n\n

        free-body diagram<\/strong> <\/p>\n\n\n\n

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

        An object of mass 4.00 kg is held motionless at the top of a ramp that is inclined at an angle of 35 degrees relative to horizontal. The object is given a gentle shove giving it an initial velocity of 4.00 m\/s down the ramp. Exactly 0.443 seconds after being released, the object is 2.00 […]<\/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-199534","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199534","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=199534"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199534\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199534"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199534"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199534"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}