{"id":255911,"date":"2025-07-13T11:19:04","date_gmt":"2025-07-13T11:19:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=255911"},"modified":"2025-07-13T11:19:06","modified_gmt":"2025-07-13T11:19:06","slug":"three-forces-of-magnitudes-and-are-applied-to-a-block-of-mass-initially-at-rest-at-angles-shown-on-the-diagram","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/13\/three-forces-of-magnitudes-and-are-applied-to-a-block-of-mass-initially-at-rest-at-angles-shown-on-the-diagram\/","title":{"rendered":"Three forces of magnitudes\u00a0,\u00a0, and\u00a0\u00a0are applied to a block of mass\u00a0, initially at rest, at angles shown on the diagram."},"content":{"rendered":"\n
Three forces of magnitudes , , and  are applied to a block of mass , initially at rest, at angles shown on the diagram.<\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Correct Answer:<\/strong> 1.8<\/p>\n\n\n\n
Explanation<\/h3>\n\n\n\n
To find the magnitude of the resultant force, we must first determine the x and y components of each individual force vector and then sum them to find the components of the resultant force. The magnitude can then be calculated using the Pythagorean theorem. All angles are measured counterclockwise from the positive x axis.<\/p>\n\n\n\n
1. Decompose each force into its x and y components:<\/strong><\/p>\n\n\n\n
    \n
  • Force F\u2081:<\/strong>
    The magnitude is |F\u2081| = 4.0 N, and the angle is \u03b8\u2081 = 25\u00b0.
    F\u2081x = |F\u2081| cos(\u03b8\u2081) = 4.0 N * cos(25\u00b0) \u2248 3.63 N
    F\u2081y = |F\u2081| sin(\u03b8\u2081) = 4.0 N * sin(25\u00b0) \u2248 1.69 N<\/li>\n\n\n\n
  • Force F\u2082:<\/strong>
    The magnitude is |F\u2082| = 6.0 N, and the angle is \u03b8\u2082 = 325\u00b0. This angle is in the fourth quadrant.
    F\u2082x = |F\u2082| cos(\u03b8\u2082) = 6.0 N * cos(325\u00b0) \u2248 4.91 N
    F\u2082y = |F\u2082| sin(\u03b8\u2082) = 6.0 N * sin(325\u00b0) \u2248 -3.44 N<\/li>\n\n\n\n
  • Force F\u2083:<\/strong>
    The magnitude is |F\u2083| = 8.0 N, and it points directly along the negative x axis, so its angle is \u03b8\u2083 = 180\u00b0.
    F\u2083x = |F\u2083| cos(\u03b8\u2083) = 8.0 N * cos(180\u00b0) = -8.0 N
    F\u2083y = |F\u2083| sin(\u03b8\u2083) = 8.0 N * sin(180\u00b0) = 0 N<\/li>\n<\/ul>\n\n\n\n
    2. Sum the components to find the resultant force components (F_rx and F_ry):<\/strong><\/p>\n\n\n\n
      \n
    • Sum of x components:
      F_rx = F\u2081x + F\u2082x + F\u2083x = 3.63 N + 4.91 N + (-8.0 N) = 0.54 N<\/li>\n\n\n\n
    • Sum of y components:
      F_ry = F\u2081y + F\u2082y + F\u2083y = 1.69 N + (-3.44 N) + 0 N = -1.75 N<\/li>\n<\/ul>\n\n\n\n
      3. Calculate the magnitude of the resultant force |F_r|:<\/strong><\/p>\n\n\n\n
      Using the Pythagorean theorem, |F_r| = \u221a(F_rx\u00b2 + F_ry\u00b2).
      |F_r| = \u221a((0.54 N)\u00b2 + (-1.75 N)\u00b2)
      |F_r| = \u221a(0.2916 N\u00b2 + 3.0625 N\u00b2)
      |F_r| = \u221a(3.3541 N\u00b2)
      |F_r| \u2248 1.831 N<\/p>\n\n\n\n
      The problem requires the answer to be expressed in newtons to two significant figures. Rounding 1.831 N gives 1.8 N.<\/p>\n\n\n\n
      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
      Three forces of magnitudes , , and  are applied to a block of mass , initially at rest, at angles shown on the diagram. The Correct Answer and Explanation is: Correct Answer: 1.8 Explanation To find the magnitude of the resultant force, we must first determine the x and y components of each individual force vector and then sum them […]<\/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-255911","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255911","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=255911"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/255911\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=255911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=255911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=255911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}