{"id":383,"date":"2018-01-30T15:29:29","date_gmt":"2018-01-30T07:29:29","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=383"},"modified":"2018-01-30T15:29:29","modified_gmt":"2018-01-30T07:29:29","slug":"centripetal-force-in-uniform-circular-motion-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/centripetal-force-in-uniform-circular-motion-problems-and-solutions.htm","title":{"rendered":"Centripetal force in uniform circular motion \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. A 0.<\/span><\/span>1<\/span><\/span>-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius <\/span><\/span>50 cm<\/span><\/span> and ball’s <\/span><\/span>angular speed<\/a> i<\/span><\/span>s <\/span><\/span>4 rad s<\/span><\/span>-1<\/span><\/span><\/sup>. What is the magnitude of the centripetal <\/span><\/span>force?<\/span><\/span><\/p>\n

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

Mass <\/span><\/span><\/a>(m) = 100 gram = 100\/1000 kg = 1\/10 kg = 0.1 kg<\/span><\/span><\/p>\n

Angular speed <\/span><\/span>(<\/span><\/span>\u03c9) = 4 radians\/se<\/span><\/span>cond<\/span><\/span><\/p>\n

Radius (r) <\/span><\/span>= 50 cm = 50\/100 m = 0.5 m<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Centripetal force<\/span><\/span><\/a><\/p>\n

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

Centripetal force is net force which produces centripetal acceleration<\/a> :<\/span><\/span><\/p>\n

\u2211F = m a<\/span><\/span>r<\/span><\/sub><\/p>\n

\u2211F = m v<\/span><\/span>2<\/span><\/span><\/sup>\/r = m <\/span><\/span>\u03c9<\/span><\/span>2<\/span><\/span><\/sup> r<\/span><\/span><\/p>\n

\u2211F = <\/i><\/span><\/span>net force = centripetal force<\/i><\/span><\/span>, m = <\/i><\/span><\/span>mass<\/i><\/span><\/span>, v = <\/i><\/span><\/span>speed<\/i><\/span><\/span>, <\/i><\/span><\/span>\u03c9 = <\/i><\/span><\/span>angular speed<\/i><\/span><\/span>, <\/i><\/span><\/span>r = <\/i><\/span><\/span>radius<\/i><\/span><\/span><\/p>\n

\u2211F = m <\/span><\/span>\u03c9<\/span><\/span>2<\/span><\/span><\/sup> r = (0.1)(4)<\/span><\/span>2 <\/span><\/span><\/sup>(0.5) = (0.1)(16)(0,5) = 0.8 Newton<\/span><\/span><\/p>\n

<\/p>\n

2. <\/span><\/span>A ball is revolving uniformly in a horizontal circle. If the speed changed to four times the initial value, what is the magnitude of centripetal force…..<\/span><\/span><\/p>\n

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

Mass <\/span><\/span>= m<\/span><\/span><\/p>\n

Speed <\/span><\/span>= v<\/span><\/span><\/p>\n

Initial speed = v<\/span><\/span>o<\/span><\/sub><\/p>\n

Radius (r) <\/span><\/span>= r<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> Magnitude of centripetal force<\/span><\/span><\/p>\n

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

\"Centripetal<\/p>\n

3. <\/span><\/span>A banked curve of radius R is designed so that a car traveling at speed 12 ms<\/span><\/span>\u20131 <\/span><\/span><\/sup>can negotiate the turn safely. The coefficient of static friction<\/a> between car and road = <\/span><\/span>0.4. What is radius <\/span><\/span>R. Acceleration due to gravity<\/a> (<\/span><\/span>g<\/span><\/span>) <\/span><\/span>= 10 ms<\/span><\/span>\u20132<\/span><\/span><\/sup>. <\/span><\/span><\/p>\n

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

Speed <\/span><\/span>(v) = 12 m\/s<\/span><\/span><\/p>\n

Coefficient of static friction <\/span><\/span>(<\/span><\/span>\u03bc<\/span><\/span>s<\/span><\/sub>) <\/span><\/span>= 0.4<\/span><\/span><\/p>\n

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

Wanted:<\/u><\/span><\/span> Radius (R)<\/span><\/span><\/p>\n

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

\"Centripetal<\/p>\n

<\/p>\n

[wpdm_package id=’501′]<\/p>\n

    \n
  1. Mass and weight<\/a><\/li>\n
  2. Normal force<\/a><\/li>\n
  3. Newton’s second law of motion<\/a><\/li>\n
  4. Friction force<\/a><\/li>\n
  5. Motion on a horizontal surface without friction force<\/a><\/li>\n
  6. The motion of two bodies with the same acceleration on the rough horizontal surface with the friction force<\/a><\/li>\n
  7. Motion on the inclined plane without friction force<\/a><\/li>\n
  8. Motion on the rough inclined plane with the friction force<\/a><\/li>\n
  9. Motion in an elevator<\/a><\/li>\n
  10. The motion of bodies connected by cord and pulley<\/a><\/li>\n
  11. Two bodies with the same magnitude of accelerations<\/a><\/li>\n
  12. Rounding a flat curve – dynamics of circular motion<\/a><\/li>\n
  13. Rounding a banked curve – dynamics of circular motion<\/a><\/li>\n
  14. Uniform motion in a horizontal circle<\/a><\/li>\n
  15. Centripetal force in uniform circular motion<\/a><\/li>\n<\/ol>\n

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

    1. A 0.1-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 50 cm and ball’s angular speed is 4 rad s-1. What is the magnitude of the centripetal force? Known : Mass (m) = 100 gram = 100\/1000 kg = 1\/10 kg = 0.1 kg Angular speed … 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":"Centripetal force in uniform circular motion \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-383","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\/383","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=383"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/383\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}