{"id":113,"date":"2018-01-14T13:43:21","date_gmt":"2018-01-14T05:43:21","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=113"},"modified":"2018-01-14T13:43:21","modified_gmt":"2018-01-14T05:43:21","slug":"solving-vectors-problems-determine-resultant-of-two-vectors-using-components-of-vector","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/solving-vectors-problems-determine-resultant-of-two-vectors-using-components-of-vector.htm","title":{"rendered":"Determine resultant of two vectors using components of vector","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Solved problems in vectors<\/a> – determine resultant of two vectors using components of the vector<\/a><\/p>\n

1. F<\/span><\/span>1<\/span><\/sub> = 6 N, F<\/span><\/span>2<\/span><\/sub> = 10 N. Determine resultant vector.<\/span><\/span><\/p>\n

\"SolvingSolution<\/span><\/span><\/p>\n

F<\/span><\/span>1x<\/span><\/sub> = F<\/span><\/span>1<\/span><\/sub> cos 60<\/span><\/span>o<\/span><\/span><\/sup> = (6)(0.5) = 3 N (<\/span><\/span>positive because it has same direction with x axis<\/span><\/span>)<\/span><\/span><\/p>\n

F<\/span><\/span>2x <\/span><\/sub>= F<\/span><\/span>2<\/span><\/sub> cos 30<\/span><\/span>o<\/span><\/span><\/sup> = (10)(0.5<\/span><\/span>\u221a<\/span><\/span>3) <\/span><\/span>= 5<\/span><\/span>\u221a<\/span><\/span>3 <\/span><\/span>= (5)(1.372) = -8.66 N (negative because it has same direction with -x axis)<\/span><\/span><\/p>\n

F<\/span><\/span>1y<\/span><\/sub> = F<\/span><\/span>1<\/span><\/sub> sin 60<\/span><\/span>o<\/span><\/span><\/sup> = (6)(0.5<\/span><\/span>\u221a<\/span><\/span>3) = 3<\/span><\/span>\u221a<\/span><\/span>3 = (3)(1.372) = 4.116 N (<\/span><\/span>positive because it has same direction with y axis<\/span><\/span>)<\/span><\/span><\/p>\n

F<\/span><\/span>2y<\/span><\/sub> = F<\/span><\/span>2<\/span><\/sub> sin 30<\/span><\/span>o<\/span><\/span><\/sup> = (10)(0.5<\/span><\/span>) = -5 N (negative because it has same direction with -y axis)<\/span><\/span><\/p>\n

F<\/span><\/span>x<\/span><\/sub> = F<\/span><\/span>1x <\/span><\/sub>– F<\/span><\/span>2x <\/span><\/sub>= 3 \u2013 8.66 = -5.66 N<\/span><\/span><\/p>\n

F<\/span><\/span>y<\/span><\/sub> = F<\/span><\/span>1y <\/span><\/sub>– F<\/span><\/span>2y <\/span><\/sub>= 4.116 \u2013 5 = -0.884 N<\/span><\/span><\/p>\n

\"Solving<\/p>\n

 <\/p>\n

Resultant of these two forces is 5.7 N.<\/span><\/span><\/p>\n\n

2. F<\/span><\/span>1<\/span><\/sub> = 4 N, F<\/span><\/span>2<\/span><\/sub> = 4 N, F<\/span><\/span>3<\/span><\/sub> = 8 N. Determine resultant vector.<\/span><\/span><\/p>\n

Solution<\/span><\/span><\/p>\n

\"SolvingF<\/span><\/span>1x<\/span><\/sub> = F<\/span><\/span>1<\/span><\/sub> cos 60<\/span><\/span>o<\/span><\/span><\/sup> = (4)(0.5) = 2 N (<\/span><\/span>positive because it has same direction with x axis<\/span><\/span>)<\/span><\/span><\/p>\n

F<\/span><\/span>2x <\/span><\/sub>= -4 <\/span><\/span>N (negative because it has same direction with -x axis)<\/span><\/span><\/p>\n

F<\/span><\/span>3x <\/span><\/sub>= F<\/span><\/span>3<\/span><\/sub> cos 60<\/span><\/span>o<\/span><\/span><\/sup> = (8)(0.5) = 4 N (<\/span><\/span>positive because it has same direction with x axis<\/span><\/span>)<\/span><\/span><\/p>\n

F<\/span><\/span>1y<\/span><\/sub> = F<\/span><\/span>1<\/span><\/sub> sin 60<\/span><\/span>o<\/span><\/span><\/sup> = (4)(0.5<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span>) <\/span><\/span> = 2<\/span><\/span>\u221a<\/span><\/span>3 N (<\/span><\/span>positive because it has same direction with y axis<\/span><\/span>)<\/span><\/span><\/p>\n

F<\/span><\/span>2y<\/span><\/sub> = 0<\/span><\/span><\/p>\n

F<\/span><\/span>3y<\/span><\/sub> = F<\/span><\/span>3<\/span><\/sub> sin 60<\/span><\/span>o<\/span><\/span><\/sup> = (8)(0.5<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span>) <\/span><\/span> = -4<\/span><\/span>\u221a<\/span><\/span>3 N (negative <\/span><\/span>because it has same direction with -y axis<\/span><\/span>)<\/span><\/span><\/p>\n

F<\/span><\/span>x<\/span><\/sub> = F<\/span><\/span>1x <\/span><\/sub>– F<\/span><\/span>2x <\/span><\/sub>+ F<\/span><\/span>3x<\/span><\/sub> = 2 \u2013 4 + 4 = 2 N<\/span><\/span><\/p>\n

F<\/span><\/span>y<\/span><\/sub> = F<\/span><\/span>1y <\/span><\/sub>+ F<\/span><\/span>2y <\/span><\/sub>– F<\/span><\/span>3y<\/span><\/sub> = 2<\/span><\/span>\u221a<\/span><\/span>3 + 0 – 4<\/span><\/span>\u221a<\/span><\/span>3 = -2<\/span><\/span>\u221a<\/span><\/span>3 N<\/span><\/span><\/p>\n

\"Solving<\/p>\n

Resultant of these three forces is 5.7 N.<\/span><\/span><\/p>\n\n

[wpdm_package id=’542′]<\/p>\n

[wpdm_package id=’554′]<\/p>\n

    \n
  1. Determine the resultant of in a line vector<\/a><\/li>\n
  2. Determine vector components<\/a><\/li>\n
  3. Determine the resultant of two vectors using the Pythagorean theorem<\/a><\/li>\n
  4. Determine the resultant of two vectors using cosines equation<\/a><\/li>\n
  5. Determine the resultant of two vectors using components of vectors<\/a><\/li>\n<\/ol>\n

    <\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

    Solved problems in vectors – determine resultant of two vectors using components of the vector 1. F1 = 6 N, F2 = 10 N. Determine resultant vector. Solution F1x = F1 cos 60o = (6)(0.5) = 3 N (positive because it has same direction with x axis) F2x = F2 cos 30o = (10)(0.5\u221a3) = … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Determine resultant of two vectors using components of vector","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-113","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/113","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=113"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/113\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=113"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}