{"id":925,"date":"2018-02-20T15:46:06","date_gmt":"2018-02-20T07:46:06","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=925"},"modified":"2018-02-20T15:46:06","modified_gmt":"2018-02-20T07:46:06","slug":"newtons-law-of-universal-gravitation-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/newtons-law-of-universal-gravitation-problems-and-solutions.htm","title":{"rendered":"Newton’s law of universal gravitation \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. The distance<\/a> between <\/span><\/span>a 40-kg person and a 30-kg person is 2 m. What is the magnitude of the gravitational force<\/a> each exerts on the other. Universal constant = <\/span><\/span>6.67 x 10<\/span><\/span>-11<\/span><\/span><\/sup> N m<\/span><\/span>2<\/span><\/span><\/sup> \/ kg<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

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

m<\/span><\/span>1<\/span><\/sub> = 40 kg, m<\/span><\/span>2<\/span><\/sub> = 30 kg, r = 2 m, G = 6.67 x 10<\/span><\/span>-11<\/span><\/span><\/sup> N m<\/span><\/span>2<\/span><\/span><\/sup> \/ kg<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted :<\/u><\/span><\/span> the magnitude of gravitational force <\/span><\/span>(F) ?<\/span><\/span><\/p>\n

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

\"Newton's<\/p>\n\n

2.\u00a0The distance between Earth and Moon (r) is 3.84 x 108<\/sup> m. <\/span><\/span>What is the magnitude of gravitational force each exerts on the other? <\/span><\/span><\/p>\n

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

Earth’s mass<\/a> <\/span><\/span>(m<\/span><\/span>E<\/span><\/sub>) = 5.97 x 10<\/span><\/span>24<\/span><\/span><\/sup> kg<\/span><\/span><\/p>\n

Moon’s mass <\/span><\/span>(m<\/span><\/span>M<\/span><\/sub>) = 7.35 x 10<\/span><\/span>22<\/span><\/span><\/sup> kg<\/span><\/span><\/p>\n

The distance between Earth’s center and the Moon’s center <\/span><\/span>(r) = 3.84 x 10<\/span><\/span>8<\/span><\/span><\/sup> m<\/span><\/span><\/p>\n

Universal constant <\/span><\/span>(G) = 6.67 x 10<\/span><\/span>-11<\/span><\/span><\/sup> N m<\/span><\/span>2<\/span><\/span><\/sup> \/ kg<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted:<\/u><\/span><\/span> The magnitude of gravitational force (F)<\/span><\/span><\/p>\n

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

\"Newton's<\/p>\n\n

3. <\/span><\/span>What is the distance from the Earth, <\/span><\/span><\/span>the magnitude of the gravitational force of the earth and the moon is zero?<\/span><\/span><\/span><\/p>\n

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

Earth’s mass <\/span><\/span>= 5.97 x 10<\/span><\/span>24<\/span><\/span><\/sup> kg<\/span><\/span><\/p>\n

Moon’s mass <\/span><\/span>= 7.35 x 10<\/span><\/span>22<\/span><\/span><\/sup> kg<\/span><\/span><\/p>\n

The distance between Earth’s center and Moon’s center<\/span><\/span> (r) = 3.84 x 10<\/span><\/span>8<\/span><\/span><\/sup> m.<\/span><\/span><\/p>\n

Universal constant (<\/span><\/span>G) = 6.67 x 10<\/span><\/span>-11<\/span><\/span><\/sup> N m<\/span><\/span>2<\/span><\/span><\/sup> \/ kg<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted:<\/u><\/span><\/span> distance from Earth<\/span><\/span><\/p>\n

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

\"Newton's<\/p>\n

Net gravitational force is zero.<\/span><\/span><\/p>\n

\"Newton's<\/p>\n

Use quadratic formula :<\/span><\/span><\/p>\n

A = – <\/span><\/span>6.35<\/span><\/span><\/p>\n

B = – <\/span><\/span>7.68 x 10<\/span><\/span>8<\/span><\/span><\/sup><\/p>\n

C = 87.76 x 10<\/span><\/span>-14<\/span><\/span><\/sup><\/p>\n

\"Newton's<\/span><\/span><\/p>\n

 <\/p>\n

[wpdm_package id=’955′]<\/p>\n

    \n
  1. Newton’s law of universal gravitation problems and solutions<\/a><\/li>\n
  2. Gravitational force, weight problems, and solutions<\/a><\/li>\n
  3. Acceleration due to gravity problems and solutions<\/a><\/li>\n
  4. Geosynchronous satellite problems and solutions<\/a><\/li>\n
  5. Kepler’s law problems and solutions problems and solutions<\/a><\/li>\n<\/ol>\n

     <\/p>\n

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

    1. The distance between a 40-kg person and a 30-kg person is 2 m. What is the magnitude of the gravitational force each exerts on the other. Universal constant = 6.67 x 10-11 N m2 \/ kg2 Known : m1 = 40 kg, m2 = 30 kg, r = 2 m, G = 6.67 x … 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":"Newton's law of universal gravitation \u2013 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-925","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\/925","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=925"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/925\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}