{"id":195522,"date":"2025-02-28T11:44:19","date_gmt":"2025-02-28T11:44:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=195522"},"modified":"2025-02-28T11:44:21","modified_gmt":"2025-02-28T11:44:21","slug":"two-blocks-connected-by-a-string-are-pulled-across-frictionless-surface-by-a-force-applied-to-one-of-the-blocks","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/28\/two-blocks-connected-by-a-string-are-pulled-across-frictionless-surface-by-a-force-applied-to-one-of-the-blocks\/","title":{"rendered":"Two blocks connected by a string are pulled across frictionless surface by a force applied to one of the blocks"},"content":{"rendered":"\n

Two blocks connected by a string are pulled across frictionless surface by a force applied to one of the blocks, as shown below. If each block has an acceleration of 2.0 m\/s? to the right.(a) Label all forces acting on A and B. What is the magnitude of F of the applied force?<\/p>\n\n\n\n

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

To solve this problem, let’s define the forces acting on each block and determine the magnitude of the applied force.<\/p>\n\n\n\n

Forces Acting on Each Block<\/strong><\/h3>\n\n\n\n

We assume:<\/p>\n\n\n\n

    \n
  • Block A<\/strong> has mass ( m_A )<\/li>\n\n\n\n
  • Block B<\/strong> has mass ( m_B )<\/li>\n\n\n\n
  • The tension<\/strong> in the string is ( T )<\/li>\n\n\n\n
  • The applied force<\/strong> is ( F ), acting on Block A<\/li>\n\n\n\n
  • The acceleration of both blocks is 2.0 m\/s\u00b2<\/strong> to the right<\/li>\n\n\n\n
  • The surface is frictionless<\/strong>, so no resistive forces act<\/li>\n<\/ul>\n\n\n\n

    The forces acting on each block:<\/p>\n\n\n\n

      \n
    1. Block A:<\/strong><\/li>\n<\/ol>\n\n\n\n
        \n
      • The applied force ( F ) pulls to the right.<\/li>\n\n\n\n
      • The tension ( T ) in the string pulls to the left.<\/li>\n\n\n\n
      • The normal force ( N_A ) from the surface acts upward.<\/li>\n\n\n\n
      • The gravitational force ( m_A g ) acts downward.<\/li>\n<\/ul>\n\n\n\n
          \n
        1. Block B:<\/strong><\/li>\n<\/ol>\n\n\n\n
            \n
          • The tension ( T ) in the string pulls it to the right.<\/li>\n\n\n\n
          • The normal force ( N_B ) from the surface acts upward.<\/li>\n\n\n\n
          • The gravitational force ( m_B g ) acts downward.<\/li>\n<\/ul>\n\n\n\n

            Since there is no vertical movement, the normal forces and gravitational forces cancel out, leaving only the horizontal forces to consider.<\/p>\n\n\n\n

            Calculating the Applied Force ( F )<\/strong><\/h3>\n\n\n\n

            Using Newton\u2019s Second Law:<\/p>\n\n\n\n

            For Block B<\/strong> (only tension provides acceleration):<\/p>\n\n\n\n

            [
            T = m_B a
            ]<\/p>\n\n\n\n

            For Block A<\/strong> (net force is ( F – T )):<\/p>\n\n\n\n

            [
            F – T = m_A a
            ]<\/p>\n\n\n\n

            Substituting ( T = m_B a ) into the equation:<\/p>\n\n\n\n

            [
            F – m_B a = m_A a
            ]<\/p>\n\n\n\n

            [
            F = (m_A + m_B) a
            ]<\/p>\n\n\n\n

            Given ( a = 2.0 ) m\/s\u00b2, we can substitute the given masses to find ( F ).<\/p>\n\n\n\n

            Now, I will generate the image of the system.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Here is the generated image showing the forces acting on the two blocks. It includes labeled forces such as the applied force ( F ), tension ( T ), normal forces ( N_A ) and ( N_B ), and gravitational forces ( m_A g ) and ( m_B g ).<\/p>\n\n\n\n

            Let me know if you need further clarification or additional modifications!<\/p>\n","protected":false},"excerpt":{"rendered":"

            Two blocks connected by a string are pulled across frictionless surface by a force applied to one of the blocks, as shown below. If each block has an acceleration of 2.0 m\/s? to the right.(a) Label all forces acting on A and B. What is the magnitude of F of the applied force? The Correct […]<\/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-195522","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195522","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=195522"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/195522\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=195522"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=195522"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=195522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}