{"id":1112,"date":"2018-02-25T06:27:15","date_gmt":"2018-02-24T22:27:15","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1112"},"modified":"2018-02-25T06:27:15","modified_gmt":"2018-02-24T22:27:15","slug":"momentum-and-impulse-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/momentum-and-impulse-problems-and-solutions.htm","title":{"rendered":"Momentum and impulse \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. A small ball is thrown horizontally with a constant speed of 10 m\/s. The ball hits the wall and reflected with the same speed. What is the change in linear momentum<\/a> of the ball? <\/span><\/span><\/p>\n

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

Mass<\/a> (m) = 0.2 kg<\/span><\/span><\/p>\n

Initial speed (vo<\/sub>) = -10 m\/s<\/span><\/span><\/p>\n

Final speed (vt<\/sub>) = 10 m\/s <\/span><\/span><\/p>\n

The plus and minus sign indicates that the objects moves in opposite direction.<\/i><\/p>\n

Wanted <\/u>:<\/u> the change in linear momentum (\u0394p)<\/span><\/span><\/p>\n

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

Formula of the change in linear momentum <\/b>:<\/span><\/span><\/p>\n

\u0394p = m vt<\/sub> \u2013 m vo <\/sub>= m (vt<\/sub> \u2013 vo<\/sub>)<\/span><\/span><\/p>\n

The change in linear momentum :<\/span><\/span><\/p>\n

\u0394p = 0.2 (10 \u2013 (-10)) = 0.2 (10 + 10) <\/span><\/span><\/p>\n

\u0394p = 0.2 (20) <\/span><\/span><\/p>\n

\u0394p <\/b>= 4 kg m\/s<\/b><\/span><\/span><\/p>\n

<\/p>\n

2. A 10-gram ball falls freely<\/a> from a height, hits the floor at 15 m\/s, then reflected upward at 10 m\/s. Determine the impulse!<\/span><\/span><\/p>\n

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

Mass (m) = 10 gram = 0.01 kg<\/span><\/span><\/p>\n

Initial velocity (vo<\/sub>) = -15 m\/s<\/span><\/span><\/p>\n

Final velocity (vt<\/sub>) = 10 m\/s<\/span><\/span><\/p>\n

Wanted :<\/span> Impulse<\/a> (I)<\/span><\/span><\/p>\n

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

The impulse (I) equals the change in momentum (\u0394p) <\/span><\/span><\/p>\n

I = m vt <\/sub>\u2013 m vo<\/sub> = m (vt<\/sub> \u2013 vo<\/sub>)<\/span><\/span><\/p>\n

Impulse :<\/span><\/span><\/p>\n

I = 0.01 (10 \u2013 (-15)) = 0.01 (10 + 15)<\/span><\/span><\/p>\n

I = 0.01 (25)<\/span><\/span><\/p>\n

I = 0.25 kg m\/s<\/b><\/span><\/span><\/p>\n

<\/p>\n

3. A 200-gram ball thrown horizontally with a speed of 4 m\/s, then the ball was hit in the same direction. The duration of the ball in contact with the bat is 2 mi<\/span>l<\/span>liseconds and the ball speed after leaving the bat is 12 m\/s. The <\/span>magnitude of <\/span>force <\/span>exerted <\/span>by the batter on the ball is …<\/span><\/span><\/span><\/p>\n

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

Mass (m) = 200 gram = 0.2 kg<\/span><\/span><\/p>\n

Initial velocity (vo<\/sub>) = 4 m\/s<\/span><\/span><\/p>\n

Final velocity (vt<\/sub>) = 12 m\/s<\/span><\/span><\/p>\n

Time interval (t) = 2 milliseconds = (2\/1000) seconds = 0.002 seconds <\/span><\/span><\/p>\n

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

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

Formula of impulse :<\/span><\/span><\/p>\n

I = F t<\/span><\/span><\/p>\n

Formula of the change in momentum :<\/span><\/span><\/p>\n

m vt<\/sub> \u2013 m vo<\/sub> = m (vt<\/sub> \u2013 vo<\/sub>)<\/span><\/span><\/p>\n

The impulse (I) equals the change in momentum (\u0394p) <\/span><\/span><\/p>\n

I = \u0394p<\/span><\/span><\/p>\n

F t = m (vt<\/sub> \u2013 vo<\/sub>)<\/span><\/span><\/p>\n

F (0.002) = (0.2)(12 \u2013 4)<\/span><\/span><\/p>\n

F (0.002) = (0.2)(8)<\/span><\/span><\/p>\n

F (0.002) = 1.6<\/span><\/span><\/p>\n

F = 1.6 \/ 0.002<\/span><\/span><\/p>\n

F = 800 Newton<\/span><\/span><\/p>\n

[wpdm_package id=’1155′]<\/p>\n

    \n
  1. Linear momentum problems and solutions<\/a><\/li>\n
  2. Momentum and impulse problems and solutions<\/a><\/li>\n
  3. Perfectly elastic collisions in one dimension problems and solutions<\/a><\/li>\n
  4. Perfectly inelastic collisions in one dimension problems and solutions<\/a><\/li>\n
  5. Inelastic collisions in one dimension problems and solutions<\/a><\/li>\n<\/ol>\n

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

    1. A small ball is thrown horizontally with a constant speed of 10 m\/s. The ball hits the wall and reflected with the same speed. What is the change in linear momentum of the ball? Known : Mass (m) = 0.2 kg Initial speed (vo) = -10 m\/s Final speed (vt) = 10 m\/s The … 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":"Momentum and impulse \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-1112","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\/1112","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=1112"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1112\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}