{"id":198336,"date":"2025-03-08T15:58:52","date_gmt":"2025-03-08T15:58:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=198336"},"modified":"2025-03-08T15:58:54","modified_gmt":"2025-03-08T15:58:54","slug":"if-the-resultant-force-acting-on-the-support-is-to-be-1200-lb-directed-horizontally-to-the-right","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/08\/if-the-resultant-force-acting-on-the-support-is-to-be-1200-lb-directed-horizontally-to-the-right\/","title":{"rendered":"If the resultant force acting on the support is to be 1200 lb directed horizontally to the right"},"content":{"rendered":"\n<p>If the resultant force acting on the support is to be 1200 lb directed horizontally to the right, determine the force F in rope A and the corresponding angle<\/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 determine the force ( F ) in rope A and the corresponding angle ( \\theta ), we need to apply the principles of static equilibrium. In a static system, the sum of forces in each direction (horizontal and vertical) must equal zero. Additionally, the sum of moments around any point must also equal zero.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Define the forces and the situation<\/h3>\n\n\n\n<p>Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( F ) be the force in rope A,<\/li>\n\n\n\n<li>( \\theta ) be the angle between rope A and the horizontal,<\/li>\n\n\n\n<li>( 1200 \\, \\text{lb} ) be the resultant force acting horizontally to the right.<\/li>\n<\/ul>\n\n\n\n<p>Assume that the force in the rope A has both horizontal and vertical components. The horizontal component of the force in rope A is ( F \\cos(\\theta) ), and the vertical component is ( F \\sin(\\theta) ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Apply the equilibrium conditions<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Horizontal equilibrium:<\/h4>\n\n\n\n<p>The horizontal forces must balance. If the only horizontal force is ( F \\cos(\\theta) ), and the resultant force is 1200 lb, we have:<br>[<br>F \\cos(\\theta) = 1200<br>]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Vertical equilibrium:<\/h4>\n\n\n\n<p>The vertical forces must balance. If there are no vertical external forces given (assuming there\u2019s no additional load or forces vertically), the vertical component of the rope A&#8217;s force must be zero:<br>[<br>F \\sin(\\theta) = 0<br>]<br>This implies ( \\theta = 0^\\circ ), meaning rope A is horizontal.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve for ( F )<\/h3>\n\n\n\n<p>From the horizontal equilibrium equation:<br>[<br>F \\cos(0^\\circ) = 1200<br>]<br>Since ( \\cos(0^\\circ) = 1 ), the equation simplifies to:<br>[<br>F = 1200 \\, \\text{lb}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Conclusion<\/h3>\n\n\n\n<p>Thus, the force ( F ) in rope A is 1200 lb, and the corresponding angle ( \\theta ) is 0\u00b0, meaning rope A is aligned horizontally.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Image Representation:<\/h3>\n\n\n\n<p>The diagram would show rope A being pulled horizontally to the right with a force of 1200 lb, and the angle ( \\theta ) being 0\u00b0, indicating that rope A is horizontal.<\/p>\n\n\n\n<p>Here is the diagram illustrating the situation, where the rope A is horizontal, and the force in the rope is 1200 lb acting horizontally to the right with an angle ( \\theta = 0^\\circ ).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-684.png\" alt=\"\" class=\"wp-image-198337\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>If the resultant force acting on the support is to be 1200 lb directed horizontally to the right, determine the force F in rope A and the corresponding angle The correct answer and explanation is : To determine the force ( F ) in rope A and the corresponding angle ( \\theta ), we need [&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 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