{"id":330,"date":"2018-01-27T12:56:43","date_gmt":"2018-01-27T04:56:43","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=330"},"modified":"2018-01-27T12:56:43","modified_gmt":"2018-01-27T04:56:43","slug":"rounding-a-banked-curve-dynamics-of-cicular-motion-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/rounding-a-banked-curve-dynamics-of-cicular-motion-problems-and-solutions.htm","title":{"rendered":"Rounding a banked curve \u2013 dynamics of circular motion problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. A car rounding a banked curve. What is an angle for the road which has a curve of radius 60 meters with a design speed of 20 m\/ s? Assume there is no friction<\/a> between car and road.
\n<\/span><\/span><\/p>\n

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

\"RoundingN = normal force<\/a><\/span><\/span><\/p>\n

N sin <\/span><\/span>\u03b8<\/span><\/span> = horizontal component of the normal force<\/span><\/span><\/p>\n

N cos <\/span><\/span>\u03b8<\/span><\/span> = vertical component of the normal force<\/span><\/span><\/p>\n

w = m g = the weight<\/a> of the car<\/span><\/span><\/p>\n

The road is designed to be banked to eliminate dependence on friction. <\/span><\/span><\/p>\n

The net horizontal force, the <\/span><\/span>horizontal component of the normal force (<\/span><\/span>N sin <\/span><\/span>\u03b8)<\/span><\/span>, <\/span><\/span>required to keep the car moving in a circle around the curve. <\/span><\/span><\/p>\n

We choose x-axis as horizontal and y-axis as vertical, so that centripetal acceleration, a<\/span><\/span>R<\/span><\/span><\/sub>, is along the horizontal direction. In the horizontal direction, the only force is the horizontal component of the normal force <\/span><\/span>(<\/span><\/span>N sin <\/span><\/span>\u03b8), needed to produce the centripetal acceleration<\/a>. N sin \u03b8 = centripetal force<\/a>.
\n<\/span><\/span><\/p>\n

Apply Newton’s law of motion in the vertical direction :<\/span><\/span><\/p>\n

\"Rounding<\/p>\n

<\/p>\n

Apply Newton’s law of motion in the horizontal direction :<\/span><\/span><\/p>\n

\"Rounding<\/p>\n

Substitu<\/span><\/span>ting N in equation 1 into N in equation 2 <\/span><\/span>:<\/span><\/span><\/p>\n

\"Rounding<\/p>\n

[wpdm_package id=’497′]<\/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 the 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

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

    1. A car rounding a banked curve. What is an angle for the road which has a curve of radius 60 meters with a design speed of 20 m\/ s? Assume there is no friction between car and road. Solution N = normal force N sin \u03b8 = horizontal component of the normal force N … 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":"Rounding a banked curve \u2013 dynamics of circular motion 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-330","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\/330","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=330"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/330\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}