{"id":8172,"date":"2023-05-01T06:45:22","date_gmt":"2023-05-01T06:45:22","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=8172"},"modified":"2024-05-25T06:48:30","modified_gmt":"2024-05-25T06:48:30","slug":"gravity-equation","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/gravity-equation.htm","title":{"rendered":"Gravity equation","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

3 questions about Gravity equation<\/span><\/p>\n

1. Three particles each with a mass of 1 kg are at the vertices of an equilateral triangle whose sides are 1 m long. How large is the gravitational force experienced by each point particle (in G)?<\/span><\/p>\n

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

The magnitude of the gravitational force experienced by one of the particles. <\/span><\/p>\n

F12<\/sub> = G (m1<\/sub>)(m2<\/sub>) \/ r2 <\/sup>= G (1)(1) \/ 12 <\/sup>= G\/1 = G<\/span><\/p>\n

F13<\/sub> = G (m1<\/sub>)(m3<\/sub>) \/ r2 <\/sup>= G (1)(1) \/ 12 <\/sup>= G\/1 = G<\/span><\/p>\n

Resultant gravitational force at point 1:<\/span><\/p>\n

F1 <\/sub>= \u221a12<\/sup>+12<\/sup> = \u221a1+1 = \u221a2 Newton <\/span><\/p>\n

2. The figure below depicts three objects m1<\/sub> = 6 kg; m2<\/sub> = 3 kg and m3<\/sub> = 4 kg lie on a straight line. Determine the magnitude and direction of the resultant gravitational force experienced by m2! (state in G)<\/span><\/p>\n

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

m1 <\/sub>= 6 kg\"Gravity<\/span><\/p>\n

m2<\/sub> = 3 kg<\/span><\/p>\n

m3<\/sub> = 4 kg<\/span><\/p>\n

gravitational constant = G<\/span><\/p>\n

r21<\/sub> = 4 m<\/span><\/p>\n

r23<\/sub> = 2 m<\/span><\/p>\n

Wanted:<\/u> F resultant gravity experienced by m2<\/sub><\/span><\/p>\n

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

The gravitational force between m2<\/sub> and m3<\/sub>:<\/span><\/p>\n

F = G (3)(4) \/ 22<\/sup> = G 12 \/ 4 = 3G<\/span><\/p>\n

The gravitational force between m2<\/sub> and m1<\/sub>:<\/span><\/p>\n

F = G (3)(6) \/ 42<\/sup> = G 18 \/ 16 = 1,125G<\/span><\/p>\n

3. Object A with a mass of 1 kg and object B with a mass of 2 kg are separated by a distance of 2 m from one another. Point P is 2 m from object A and 2 m from object B. How strong is the gravitational field at point P?<\/span><\/p>\n

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

mA<\/sub> = 1 kg<\/span><\/p>\n

mB <\/sub>= 2 kg<\/span><\/p>\n

rPA<\/sub> = 2 m<\/span><\/p>\n

rPB <\/sub>= 2 m<\/span><\/p>\n

Gravity constant = G<\/span><\/p>\n

Wanted:<\/u> E gravity at point P<\/span><\/p>\n

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

EPA<\/sub> = G (mA<\/sub>) \/ r2 <\/sup>= G (1) \/ 22 <\/sup>= G\/4 = 0,25G<\/span><\/p>\n

EPB<\/sub> = G (mB<\/sub>) \/ r2 <\/sup>= G (2) \/ 22 <\/sup>= 2G\/4 = 0,5G<\/span><\/p>\n

Resultant gravitational field strength at point P:<\/span><\/p>\n

E = \u221a0,25G2<\/sup>+0,5G2<\/sup> = \u221a0,0625G2<\/sup>+0,25G2<\/sup> = \u221a0,3125G2<\/sup> = 0,56G N\/kg<\/span><\/p>\n

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

3 questions about Gravity equation 1. Three particles each with a mass of 1 kg are at the vertices of an equilateral triangle whose sides are 1 m long. How large is the gravitational force experienced by each point particle (in G)? Solution The magnitude of the gravitational force experienced by one of the particles. … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"closed","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":"3","_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":"Gravity equation","_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-8172","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\/8172","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=8172"}],"version-history":[{"count":7,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8172\/revisions"}],"predecessor-version":[{"id":8384,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/8172\/revisions\/8384"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=8172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=8172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=8172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}