{"id":230,"date":"2018-01-23T18:09:27","date_gmt":"2018-01-23T10:09:27","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=230"},"modified":"2018-01-23T18:09:27","modified_gmt":"2018-01-23T10:09:27","slug":"particles-in-one-dimensional-equilibrium-application-of-newtons-first-law-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/particles-in-one-dimensional-equilibrium-application-of-newtons-first-law-problems-and-solutions.htm","title":{"rendered":"Particles in the one-dimensional equilibrium \u2013 application of the Newton’s first law problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. Mass<\/a> of an object, m = 10 kg, supported by a cord. Find the tension in the cord! <\/span><\/span><\/sup>g = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

\"ParticlesKnown :<\/u><\/span><\/span><\/p>\n

Mass (m) = 10 kg<\/span><\/span><\/p>\n

Acceleration due to gravity<\/a> (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted :<\/u><\/span><\/span> The tension force (T)<\/span><\/span><\/p>\n

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

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

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

T = w<\/span><\/span><\/p>\n

T = m g<\/span><\/span><\/p>\n

T = (10 kg)(10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 100 kg m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

T = 100 Newton<\/span><\/span><\/p>\n

<\/p>\n

2. Mass of the object is 10 kg. Find the tension in the cord….. Acceleration due to gravity = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>.<\/span><\/span><\/p>\n

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

Known :<\/u><\/span><\/span><\/p>\n

Mass (m) = 10 kg<\/span><\/span><\/p>\n

Acceleration due to gravity (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>.<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The tension force (T)<\/span><\/span><\/p>\n

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

\"Particlesw = weight<\/a> = m g = (10 kg)(10 m\/s2<\/span><\/span><\/sup>) = 100 kg m\/s<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

T<\/span><\/span>1<\/span><\/sub> = the tension force 1<\/span><\/span><\/p>\n

T<\/span><\/span>1x<\/span><\/sub> = the x-component of the tension force 1 = T<\/span><\/span>1<\/span><\/sub> cos 45<\/span><\/span>o<\/span><\/span><\/sup> = 0.7 T<\/span><\/span>1<\/span><\/sub><\/p>\n

T<\/span><\/span>1y<\/span><\/sub> = the y-component of the tension force 2 = T<\/span><\/span>1<\/span><\/span><\/sub> sin 45<\/span><\/span>o<\/span><\/span><\/sup> = 0.7 T<\/span><\/span>1<\/span><\/sub><\/p>\n

T<\/span><\/span>2<\/span><\/sub> = the tension force 2<\/span><\/span><\/p>\n

T<\/span><\/span>2x<\/span><\/sub> = the x-component of the tension force 2 = T<\/span><\/span>2<\/span><\/sub> cos 45<\/span><\/span>o<\/span><\/span><\/sup> = 0.7 T<\/span><\/span>2<\/span><\/sub><\/p>\n

T<\/span><\/span>2y<\/span><\/sub> = the y-component of the tension force 2 = T<\/span><\/span>2<\/span><\/sub> sin 45<\/span><\/span>o<\/span><\/span><\/sup> = 0.7 T<\/span><\/span>2<\/span><\/sub><\/p>\n

The equilibrium condition <\/u><\/span><\/span>\u03a3F = 0.<\/u><\/span><\/span><\/p>\n

y axis :<\/span><\/span><\/p>\n

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

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

0.7T<\/span><\/span>1<\/span><\/sub> + 0.7T<\/span><\/span>2<\/span><\/sub> \u2013 100 = 0<\/span><\/span><\/p>\n

0.7T<\/span><\/span>1<\/span><\/sub> + 0.7T<\/span><\/span>2<\/span><\/sub> = 100 —– equation 1<\/span><\/span><\/p>\n

x axis :<\/span><\/span><\/p>\n

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

T<\/span><\/span>2x<\/span><\/sub> – T<\/span><\/span>1x<\/span><\/sub> = 0<\/span><\/span><\/p>\n

0.7T<\/span><\/span>2<\/span><\/sub> \u2013 0.7T<\/span><\/span>1<\/span><\/sub> = 0<\/span><\/span><\/p>\n

0.7T<\/span><\/span>2<\/span><\/sub> = 0.7T<\/span><\/span>1<\/span><\/sub><\/p>\n

T<\/span><\/span>2<\/span><\/sub> = T<\/span><\/span>1<\/span><\/sub> —– equation 2<\/span><\/span><\/p>\n

Determine magnitude of T<\/span><\/span>1<\/span><\/sub> :<\/span><\/span><\/p>\n

0.7T<\/span><\/span>1 <\/span><\/sub>+ 0.7T<\/span><\/span>1 <\/span><\/sub>= 100<\/span><\/span><\/p>\n

1.4T<\/span><\/span>1<\/span><\/sub> = 100<\/span><\/span><\/p>\n

T<\/span><\/span>1<\/span><\/sub> = 100 \/ 1.4<\/span><\/span><\/p>\n

T<\/span><\/span>1 <\/span><\/sub>= 71.4 Newton<\/span><\/span><\/p>\n

T<\/span><\/span>1<\/span><\/sub> = T<\/span><\/span>2<\/span><\/sub> so T<\/span><\/span>2<\/span><\/sub> = 71.4 Newton<\/span><\/span><\/p>\n

[wpdm_package id=’486′]<\/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. Mass of an object, m = 10 kg, supported by a cord. Find the tension in the cord! g = 10 m\/s2 Known : Mass (m) = 10 kg Acceleration due to gravity (g) = 10 m\/s2 Wanted : The tension force (T) Solution : \u03a3Fy = 0 T \u2013 w = 0 T … 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 the one-dimensional equilibrium \u2013 application of the 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-230","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\/230","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=230"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/230\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=230"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=230"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=230"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}