{"id":168333,"date":"2024-11-17T09:15:28","date_gmt":"2024-11-17T09:15:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=168333"},"modified":"2024-11-17T09:15:31","modified_gmt":"2024-11-17T09:15:31","slug":"at-an-instant-when-a-4-0-kg-object-has-an-acceleration-equal-to-5i-3j-m-s2-one-of-the-two-forces-acting-on-the-object-is-known-to-be-12i-22j-n","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/17\/at-an-instant-when-a-4-0-kg-object-has-an-acceleration-equal-to-5i-3j-m-s2-one-of-the-two-forces-acting-on-the-object-is-known-to-be-12i-22j-n\/","title":{"rendered":"At an instant when a 4.0-kg object has an acceleration equal to (5i + 3j) m\/s2, one of the two forces acting on the object is known to be (12i + 22j) N."},"content":{"rendered":"\n<p>At an instant when a 4.0-kg object has an acceleration equal to (5i + 3j) m\/s2, one of the two forces acting on the object is known to be (12i + 22j) N. Determine the magnitude of the other force acting on the object.<br>1) 2.0 N<br>2) 13 N<br>3) 18 N<br>4) 1.7 N<br>5) 20 N<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to apply <strong>Newton&#8217;s Second Law of Motion<\/strong>, which states:<\/p>\n\n\n\n<p>[<br>\\mathbf{F}_{\\text{net}} = m \\cdot \\mathbf{a}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(\\mathbf{F}_{\\text{net}}) is the net force acting on the object.<\/li>\n\n\n\n<li>(m) is the mass of the object.<\/li>\n\n\n\n<li>(\\mathbf{a}) is the acceleration vector of the object.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the net force vector<\/h3>\n\n\n\n<p>Given that the mass of the object is ( m = 4.0 \\, \\text{kg} ) and the acceleration is (\\mathbf{a} = (5i + 3j) \\, \\text{m\/s}^2), we can use Newton\u2019s second law to find the net force:<\/p>\n\n\n\n<p>[<br>\\mathbf{F}_{\\text{net}} = m \\cdot \\mathbf{a} = (4.0 \\, \\text{kg}) \\cdot (5i + 3j) \\, \\text{m\/s}^2<br>]<\/p>\n\n\n\n<p>[<br>\\mathbf{F}_{\\text{net}} = (20i + 12j) \\, \\text{N}<br>]<\/p>\n\n\n\n<p>So, the net force acting on the object is:<\/p>\n\n\n\n<p>[<br>\\mathbf{F}_{\\text{net}} = 20 \\hat{i} + 12 \\hat{j} \\, \\text{N}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Break the problem into two forces<\/h3>\n\n\n\n<p>We know that there are two forces acting on the object. One of them is (\\mathbf{F}<em>1 = (12i + 22j) \\, \\text{N}), and the net force is (\\mathbf{F}<\/em>{\\text{net}} = 20i + 12j \\, \\text{N}).<\/p>\n\n\n\n<p>Using the principle of superposition, the net force is the vector sum of the two forces:<\/p>\n\n\n\n<p>[<br>\\mathbf{F}_{\\text{net}} = \\mathbf{F}_1 + \\mathbf{F}_2<br>]<\/p>\n\n\n\n<p>We can solve for the second force (\\mathbf{F}_2):<\/p>\n\n\n\n<p>[<br>\\mathbf{F}<em>2 = \\mathbf{F}<\/em>{\\text{net}} &#8211; \\mathbf{F}_1<br>]<\/p>\n\n\n\n<p>Substitute the values of (\\mathbf{F}_{\\text{net}}) and (\\mathbf{F}_1):<\/p>\n\n\n\n<p>[<br>\\mathbf{F}_2 = (20i + 12j) &#8211; (12i + 22j)<br>]<\/p>\n\n\n\n<p>[<br>\\mathbf{F}_2 = (20i &#8211; 12i) + (12j &#8211; 22j)<br>]<\/p>\n\n\n\n<p>[<br>\\mathbf{F}_2 = 8i &#8211; 10j \\, \\text{N}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find the magnitude of (\\mathbf{F}_2)<\/h3>\n\n\n\n<p>To find the magnitude of (\\mathbf{F}_2), we use the Pythagorean theorem:<\/p>\n\n\n\n<p>[<br>|\\mathbf{F}_2| = \\sqrt{(8)^2 + (-10)^2}<br>]<\/p>\n\n\n\n<p>[<br>|\\mathbf{F}_2| = \\sqrt{64 + 100} = \\sqrt{164}<br>]<\/p>\n\n\n\n<p>[<br>|\\mathbf{F}_2| \\approx 12.8 \\, \\text{N}<br>]<\/p>\n\n\n\n<p>The closest answer choice is <strong>13 N<\/strong>, so the magnitude of the other force is approximately <strong>13 N<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The correct answer is <strong>2) 13 N<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>At an instant when a 4.0-kg object has an acceleration equal to (5i + 3j) m\/s2, one of the two forces acting on the object is known to be (12i + 22j) N. Determine the magnitude of the other force acting on the object.1) 2.0 N2) 13 N3) 18 N4) 1.7 N5) 20 N The [&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-168333","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168333","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=168333"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/168333\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=168333"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=168333"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=168333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}