{"id":239,"date":"2018-01-24T09:17:59","date_gmt":"2018-01-24T01:17:59","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=239"},"modified":"2018-01-24T09:17:59","modified_gmt":"2018-01-24T01:17:59","slug":"particles-in-two-dimensional-equilibrium-application-of-newtons-first-law-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/particles-in-two-dimensional-equilibrium-application-of-newtons-first-law-problems-and-solutions.htm","title":{"rendered":"Particles in two-dimensional equilibrium \u2013 application of Newton’s first law problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. Find the tension force T1<\/sub>, T2<\/sub>, and T3<\/sub>. Ignore cord’s mass<\/a>.<\/p>\n

\"Particles<\/p>\n

Solution<\/p>\n

\"Particles<\/p>\n

(a) Free-body diagram for object (b) Free-body diagram for cord<\/span><\/span><\/p>\n

Apply the Newton’s first law<\/a> on the object :<\/span><\/span><\/p>\n

\u03a3F<\/span><\/span>y<\/sub> = 0<\/span><\/span><\/p>\n

T<\/span><\/span>1<\/span><\/sub> \u2013 w = 0<\/span><\/span><\/p>\n

T<\/span><\/span>1<\/span><\/sub> = w = m g <\/span><\/span><\/p>\n

T<\/span><\/span>1<\/span><\/sub> = (5 kg)(9.8 m\/s<\/span><\/span>2<\/span><\/span><\/sup>) <\/span><\/span><\/p>\n

T<\/span><\/span>1 <\/span><\/sub>= 49 kg m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

T<\/b><\/span><\/span>1<\/b><\/span><\/sub> = 49 N<\/b><\/span><\/span><\/p>\n

Apply Newton’s first law on the cord :<\/span><\/span><\/p>\n

\u2211Fx<\/sub> = 0<\/span><\/span><\/p>\n

T<\/span><\/span>3x<\/span><\/sub> \u2013 T <\/span><\/span>2x <\/span><\/sub>= 0<\/span><\/span><\/p>\n

T<\/span><\/span>3 <\/span><\/sub>cos 30<\/span><\/span>o<\/span><\/span><\/sup> \u2013 T<\/span><\/span>2<\/span><\/sub> cos 40<\/span><\/span>o <\/span><\/span><\/sup>= 0<\/span><\/span><\/p>\n

0.87 T<\/span><\/span>3 <\/span><\/sub>\u2013 0.77 T<\/span><\/span>2 <\/span><\/sub>= 0<\/span><\/span><\/p>\n

0.87 T<\/span><\/span>3<\/span><\/sub> = 0.77 T<\/span><\/span>2<\/span><\/sub><\/p>\n

T<\/span><\/span>2 <\/span><\/sub>= 0.87 T<\/span><\/span>3 <\/span><\/sub>\/ 0.77 = 1.1 T<\/span><\/span>3 <\/span><\/sub>———- Equation 1<\/span><\/span><\/p>\n

<\/p>\n

——<\/span><\/span><\/p>\n

\u2211F<\/span><\/span>y<\/span><\/sub> = 0<\/span><\/span><\/p>\n

T<\/span><\/span>3y<\/span><\/sub> + T<\/span><\/span>2y<\/span><\/sub> \u2013 T<\/span><\/span>1y<\/span><\/sub> = 0<\/span><\/span><\/p>\n

T<\/span><\/span>3 <\/span><\/span><\/sub>sin 30<\/span><\/span>o<\/sup> <\/span><\/span>+ T<\/span><\/span>2 <\/span><\/span><\/sub>sin 40<\/span><\/span>o<\/span><\/span><\/sup> \u2013 T<\/span><\/span>1<\/span><\/span><\/sub> = 0<\/span><\/span><\/p>\n

0.5 T<\/span><\/span>3 <\/span><\/sub>+ 0.64 T<\/span><\/span>2 <\/span><\/sub>\u2013 49 N = 0 ———- Equation 2<\/span><\/span><\/p>\n

Substituting T<\/span><\/span>2 <\/span><\/sub>in the equation 2 <\/span><\/span> into the equation 2 :<\/span><\/span><\/p>\n

0.5 T<\/span><\/span>3 <\/span><\/sub>+ 0.64 (1.1 T<\/span><\/span>3<\/span><\/sub>) \u2013 49 N = 0<\/span><\/span><\/p>\n

0.5 T<\/span><\/span>3<\/span><\/sub> + 0.70 T<\/span><\/span>3 <\/span><\/sub>\u2013 49 = 0<\/span><\/span><\/p>\n

1.2 T<\/span><\/span>3<\/span><\/sub> \u2013 49 = 0<\/span><\/span><\/p>\n

1.2 T<\/span><\/span>3 <\/span><\/sub>= 49<\/span><\/span><\/p>\n

T<\/span><\/span>3<\/span><\/sub> = 49 \/ 1.2 <\/span><\/span><\/p>\n

T<\/b><\/span><\/span>3<\/b><\/span><\/sub> = 41 N<\/b><\/span><\/span><\/p>\n

———<\/span><\/span><\/p>\n

T<\/span><\/span>2<\/span><\/sub> = 1.1 T<\/span><\/span>3<\/span><\/sub><\/p>\n

T<\/span><\/span>2<\/span><\/sub> = (1.1)(40.8 N) <\/span><\/span><\/p>\n

T<\/b><\/span><\/span>2<\/b><\/span><\/sub> = 45 N<\/b><\/span><\/span><\/p>\n

[wpdm_package id=’488′]<\/p>\n

    \n
  1. Particles in one-dimensional equilibrium<\/a><\/li>\n
  2. Particles in two-dimensional equilibrium<\/a><\/li>\n
  3. Equilibrium of bodies connected by cord and pulley<\/a><\/li>\n
  4. Equilibrium of bodies on inclined plane<\/a><\/li>\n<\/ol>\n

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

    1. Find the tension force T1, T2, and T3. Ignore cord’s mass. Solution (a) Free-body diagram for object (b) Free-body diagram for cord Apply the Newton’s first law on the object : \u03a3Fy = 0 T1 \u2013 w = 0 T1 = w = m g T1 = (5 kg)(9.8 m\/s2) T1 = 49 kg … 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":"Particles in two-dimensional equilibrium \u2013 application of Newton's first law problems and solutions","_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-239","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\/239","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=239"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/239\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}