{"id":163808,"date":"2024-11-09T06:57:23","date_gmt":"2024-11-09T06:57:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=163808"},"modified":"2024-11-09T06:57:25","modified_gmt":"2024-11-09T06:57:25","slug":"three-horizontal-forces-are-pulling-on-a-ring-at-rest","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/09\/three-horizontal-forces-are-pulling-on-a-ring-at-rest\/","title":{"rendered":"Three horizontal forces are pulling on a ring, at rest"},"content":{"rendered":"\n<p>Three horizontal forces are pulling on a<br>ring, at rest. F1 is 12.0 N at a 0\u00b0 angle, and<br>F2 is 18.0 N at a 90\u00b0 direction. What is the<br>x-component of F3?\u200b<\/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<h3 class=\"wp-block-heading\">Problem Understanding:<\/h3>\n\n\n\n<p>We are dealing with three horizontal forces acting on a ring. Two of them, (F_1) and (F_2), are already known, and the third force, (F_3), is the unknown force. We are asked to determine the <strong>x-component<\/strong> of (F_3).<\/p>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(F_1 = 12.0 \\, \\text{N}) at a (0^\\circ) angle (along the positive x-axis).<\/li>\n\n\n\n<li>(F_2 = 18.0 \\, \\text{N}) at a (90^\\circ) angle (along the positive y-axis).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Approach:<\/h3>\n\n\n\n<p>The ring is at rest, which implies that the <strong>net force<\/strong> acting on it must be <strong>zero<\/strong>. According to Newton\u2019s first law of motion, if the object is not accelerating, the sum of the forces in both the <strong>x-direction<\/strong> and the <strong>y-direction<\/strong> must be zero. This means that the sum of the x-components of the forces and the sum of the y-components of the forces must each equal zero.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Force components in the x-direction<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(F_1) has an x-component of 12.0 N (since it&#8217;s along the positive x-axis).<\/li>\n\n\n\n<li>(F_2) has no x-component because it acts in the y-direction.<\/li>\n\n\n\n<li>Let (F_3) have components (F_{3x}) in the x-direction and (F_{3y}) in the y-direction. For the ring to remain at rest, the sum of the x-components must be zero:<br>[<br>F_1 + F_{3x} = 0<br>]<br>Substituting (F_1 = 12.0 \\, \\text{N}), we get:<br>[<br>12.0 + F_{3x} = 0<br>]<br>Solving for (F_{3x}):<br>[<br>F_{3x} = -12.0 \\, \\text{N}<br>]<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The <strong>x-component<\/strong> of (F_3) is <strong>-12.0 N<\/strong>. This negative value indicates that (F_3) is acting in the negative x-direction, which is required to balance out the 12.0 N force in the positive x-direction from (F_1).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>The net force on the ring must be zero for the ring to remain at rest, meaning that the forces in both the x and y directions must cancel each other out. Since (F_1) is directed along the positive x-axis, and (F_2) along the positive y-axis, the third force, (F_3), must counteract these forces. To balance the forces in the x-direction, (F_3) must have an equal and opposite component in the x-direction. Thus, the x-component of (F_3) must be (-12.0 \\, \\text{N}).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Three horizontal forces are pulling on aring, at rest. F1 is 12.0 N at a 0\u00b0 angle, andF2 is 18.0 N at a 90\u00b0 direction. What is thex-component of F3?\u200b The Correct Answer and Explanation is : Problem Understanding: We are dealing with three horizontal forces acting on a ring. Two of them, (F_1) and [&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 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-163808","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163808","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=163808"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163808\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=163808"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=163808"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=163808"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}