{"id":96,"date":"2018-01-14T13:18:07","date_gmt":"2018-01-14T05:18:07","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=96"},"modified":"2018-01-14T13:18:07","modified_gmt":"2018-01-14T05:18:07","slug":"solving-vectors-problems-determine-vector-components","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/solving-vectors-problems-determine-vector-components.htm","title":{"rendered":"Determine vector components","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Solved problems in vectors<\/a> – determine vector components<\/a><\/p>\n

1. A force of 20 Newton makes an angle of 30<\/span><\/span>o<\/span><\/span><\/sup> with the x-axis. Find both the x and y component of the force.<\/span><\/span><\/p>\n

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

F<\/span><\/span>x<\/span><\/sub> = F cos <\/span><\/span>30<\/span><\/span>o<\/span><\/span><\/sup> = (20)(cos 30<\/span><\/span>o<\/span><\/span><\/sup>) = (20)(0.5<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span>) = 10<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span> Newton<\/span><\/span><\/p>\n

F<\/span><\/span>y<\/span><\/sub> = F sin <\/span><\/span>30<\/span><\/span>o<\/span><\/span><\/sup> = (20)(sin 30<\/span><\/span>o<\/span><\/span><\/sup>) = (20)(0.5) = 10 Newton<\/span><\/span><\/p>\n

<\/p>\n

2. F<\/span><\/span>1<\/span><\/sub> = 20 Newton makes an angle of 30<\/span><\/span>o<\/span><\/span><\/sup> with the y axis and F<\/span><\/span>2<\/span><\/sub> = 30 Newton makes an angle of 60o<\/sup> with the -x axis. Find both the x and y components of F<\/span><\/span>1<\/span><\/sub> and F<\/span><\/span>2<\/span><\/sub>.<\/span><\/span><\/p>\n

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

F<\/span><\/span>1x<\/span><\/sub> = F<\/span><\/span>1<\/span><\/sub> cos <\/span><\/span>60<\/span><\/span>o<\/span><\/span><\/sup> = (20)(cos 60<\/span><\/span>o<\/span><\/span><\/sup>) = (20)(0.5) = -10 Newton (negative because it has same direction with -x axis)<\/span><\/span><\/p>\n

F<\/span><\/span>2x<\/span><\/sub> = F<\/span><\/span>2<\/span><\/sub> cos <\/span><\/span>60<\/span><\/span>o<\/span><\/span><\/sup> = (30)(cos 60<\/span><\/span>o<\/span><\/span><\/sup>) = (30)(0.5) = -15 Newton (negative because it has same direction with -x axis)<\/span><\/span><\/p>\n

F<\/span><\/span>1y<\/span><\/sub> = F<\/span><\/span>1<\/span><\/span><\/sub> sin <\/span><\/span>60<\/span><\/span>o<\/span><\/span><\/sup> = (20)(sin 60<\/span><\/span>o<\/span><\/span><\/sup>) = (20)(0.5<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span>) = 10<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span> Newton (positive because it has same direction with y axis)<\/span><\/span><\/p>\n

F<\/span><\/span>2y<\/span><\/sub> = F<\/span><\/span>2<\/span><\/span><\/sub> sin <\/span><\/span>60<\/span><\/span>o<\/span><\/span><\/sup> = (30)(sin 60<\/span><\/span>o<\/span><\/span><\/sup>) = (30)(0.5<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span>) = -15<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span> Newton (negative because it has same direction with -y axis)<\/span><\/span><\/p>\n

<\/p>\n

3. F<\/span><\/span>1<\/span><\/sub> = 2 N, F<\/span><\/span>2<\/span><\/sub> = 4 N, F<\/span><\/span>3<\/span><\/sub> = 6 N. Find both the x and y components of F<\/span><\/span>1<\/span><\/sub>, F<\/span><\/span>2<\/span><\/sub> and F<\/span><\/span>3<\/span><\/sub>!<\/span><\/span><\/p>\n

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

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

F<\/span><\/span>2x<\/span><\/sub> = F<\/span><\/span>2<\/span><\/sub> cos <\/span><\/span>30<\/span><\/span>o<\/span><\/span><\/sup> = (4)(cos 30<\/span><\/span>o<\/span><\/span><\/sup>) = (4)(0.5<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span>) = -2<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span> Newton (negative because it has the same direction with -x axis)<\/span><\/span><\/p>\n

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

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

F<\/span><\/span>2<\/span>y<\/span><\/sub> = F<\/span><\/span>2<\/span><\/sub> sin 3<\/span><\/span>0<\/span><\/span>o<\/span><\/span><\/sup> = (4)(sin 30<\/span><\/span>o<\/span><\/span><\/sup>) = (4)(0.5) = 2 Newton (positive because it has the same direction with y axis)<\/span><\/span><\/p>\n

F<\/span><\/span>3y<\/span><\/sub> = F<\/span><\/span>3<\/span><\/sub> sin <\/span><\/span>60<\/span><\/span>o<\/span><\/span><\/sup> = (6)(sin 60<\/span><\/span>o<\/span><\/span><\/sup>) = (6)(0.5<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span>) = -3<\/span><\/span>\u221a<\/span><\/span>3<\/span><\/span> Newton (negative because it has the same direction with -y axis)<\/span><\/span><\/p>\n

<\/p>\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 resultant of two vectors using Pythagorean theorem<\/a><\/li>\n
  4. Determine resultant of two vectors using cosines equation<\/a><\/li>\n
  5. Determine 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 vector components 1. A force of 20 Newton makes an angle of 30o with the x-axis. Find both the x and y component of the force. Solution Fx = F cos 30o = (20)(cos 30o) = (20)(0.5\u221a3) = 10\u221a3 Newton Fy = F sin 30o = (20)(sin 30o) = … 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 vector components","_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-96","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\/96","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=96"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/96\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=96"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=96"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}