{"id":1124,"date":"2018-02-25T15:46:40","date_gmt":"2018-02-25T07:46:40","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1124"},"modified":"2018-02-25T15:46:40","modified_gmt":"2018-02-25T07:46:40","slug":"inelastic-collisions-in-one-dimension-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/inelastic-collisions-in-one-dimension-problems-and-solutions.htm","title":{"rendered":"Partially inelastic collisions in one dimension – problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>A <\/span><\/span>500-gr<\/span><\/span>am object, A, moving at <\/span><\/span>10 m\/s <\/span><\/span>and 200-gram object, B, moving at 12 m\/s. The objects approach each other and collide. If the speed of object A after the collision<\/a> is 6 m\/s, what is the speed of object B after the collision?<\/span><\/span><\/p>\n

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

Mass <\/span><\/span><\/a>of object 1 <\/span><\/span>(m<\/span><\/span>1<\/span><\/sub>) = 500 gram = 0.5 kg<\/span><\/span><\/p>\n

Mass <\/span><\/span>of object <\/span><\/span>2 (m<\/span><\/span>2<\/span><\/sub>) = 200 gram = 0.2 kg<\/span><\/span><\/p>\n

Initial velocity<\/a> of object 1 <\/span><\/span>(v<\/span><\/span>1<\/span><\/sub>) = -10 m\/s<\/span><\/span><\/p>\n

Initial velocity of object 2 <\/span><\/span>(v<\/span><\/span>2<\/span><\/sub>) = 12 m\/s<\/span><\/span><\/p>\n

The final velocity of object 1 <\/span><\/span>(v<\/span><\/span>1<\/span><\/sub>\u2019) = 6 m\/s<\/span><\/span><\/p>\n

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

Wanted<\/u><\/span><\/span> : <\/span><\/span>the final velocity of object 2 <\/span><\/span>(v<\/span><\/span>2<\/span><\/sub>\u2019)<\/span><\/span><\/p>\n

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

m<\/span><\/span>1<\/span><\/sub> v<\/span><\/span>1<\/span><\/sub> + m<\/span><\/span>2<\/span><\/sub> v<\/span><\/span>2<\/span><\/sub> = m<\/span><\/span>1<\/span><\/sub> v<\/span><\/span>1<\/span><\/sub>\u2019 + m<\/span><\/span>2<\/span><\/sub> v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

(0.5)(-10) + (0.2)(12) = (0.5)(6) + (0.2)(v<\/span><\/span>2<\/span><\/sub>\u2019)<\/span><\/span><\/p>\n

-5 + 2.4 = 3 + 0.2 v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

-2.6 = 3 + 0.2 v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

-2.6 \u2013 3 = 0.2 v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

-5.6 = 0.2 v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

v<\/span><\/span>2<\/span><\/sub>\u2019 = -5.6 \/ 0.2<\/span><\/span><\/p>\n

v<\/span><\/span>2<\/span><\/sub>\u2019 = -28 m\/s<\/span><\/span><\/p>\n

The speed of object 2 after collision is 28 m\/s.<\/span><\/span><\/p>\n

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

<\/p>\n

2. Two equal-mass objects approach each other and collide. The speed of object 1 is 6 m\/s and the speed of object 2 is 8 m\/s. After the collision, object 2 moves leftward with speed of 5 m\/s. What is the magnitude and direction of the velocity of object 1 after the collision<\/a>?<\/span><\/span><\/p>\n

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

Mass <\/span><\/span>of object <\/span><\/span>1 (m<\/span><\/span>1<\/span><\/sub>) = m<\/span><\/span><\/p>\n

Mass <\/span><\/span>of object 2 <\/span><\/span>(m<\/span><\/span>2<\/span><\/sub>) = m<\/span><\/span><\/p>\n

Initial speed of object 1 <\/span><\/span>(v<\/span><\/span>1<\/span><\/sub>) = -6 m\/s<\/span><\/span><\/p>\n

initial speed of object 2 <\/span><\/span>(v<\/span><\/span>2<\/span><\/sub>) = 8 m\/s<\/span><\/span><\/p>\n

The final speed of object 2 <\/span><\/span>(v<\/span><\/span>2<\/span><\/sub>\u2019) = -5 m\/s<\/span><\/span><\/p>\n

Wanted<\/u><\/span><\/span> : <\/span><\/span>the magnitude and direction of object 1 after collision<\/span><\/span><\/p>\n

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

Formula of conservation of linear momentum<\/a> :<\/span><\/span><\/p>\n

m<\/span><\/span>1<\/span><\/sub> v<\/span><\/span>1<\/span><\/sub> + m<\/span><\/span>2<\/span><\/sub> v<\/span><\/span>2<\/span><\/sub> = m<\/span><\/span>1<\/span><\/sub> v<\/span><\/span>1<\/span><\/sub>\u2019 + m<\/span><\/span>2<\/span><\/sub> v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

m v<\/span><\/span>1<\/span><\/sub> + m<\/span><\/span> v<\/span><\/span>2<\/span><\/sub> = m<\/span><\/span> v<\/span><\/span>1<\/span><\/sub>\u2019 + m<\/span><\/span> v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

m (v<\/span><\/span>1<\/span><\/sub> + v<\/span><\/span>2<\/span><\/sub>) = m (v<\/span><\/span>1<\/span><\/sub>\u2019 + v<\/span><\/span>2<\/span><\/sub>\u2019) <\/span><\/span><\/p>\n

v<\/span><\/span>1<\/span><\/sub> + v<\/span><\/span>2<\/span><\/sub> = v<\/span><\/span>1<\/span><\/sub>\u2019 + v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

-6 + 8 = v<\/span><\/span>1<\/span><\/sub>\u2019 – 5<\/span><\/span><\/p>\n

2 = v<\/span><\/span>1<\/span><\/sub>\u2019 – 5<\/span><\/span><\/p>\n

2 + 5 = v<\/span><\/span>1<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

v<\/span><\/span>1<\/span><\/sub>\u2019 = 7 m\/s <\/span><\/span><\/p>\n

The speed of object 1 after collision <\/span><\/span>(v<\/span><\/span>1<\/span><\/sub>\u2019) <\/span><\/span>is <\/span><\/span>3 m\/s. <\/span><\/span><\/p>\n

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

<\/p>\n

3. <\/span><\/span>A 1-kg ball 1 and 2-kg ball 2 have the same direction and collide inelastically. Before the collision, ball 1 moves with speed of 10 m\/s and ball 2 moves with speed of 5 m\/s. The speed of ball 2 after the collision is 4 m\/s. Determine the speed of ball 1 after the collision.<\/span><\/span><\/p>\n

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

Mass <\/span><\/span>ball <\/span><\/span>1 (m<\/span><\/span>1<\/span><\/sub>) = 1 kg<\/span><\/span><\/p>\n

Mass <\/span><\/span>ball <\/span><\/span>2 (m<\/span><\/span>2<\/span><\/sub>) = 2 kg<\/span><\/span><\/p>\n

The speed of ball <\/span><\/span>1 (v<\/span><\/span>1<\/span><\/sub>) = 10 m\/s<\/span><\/span><\/p>\n

The speed of ball 2 <\/span><\/span>(v<\/span><\/span>2<\/span><\/sub>) = 5 m\/s<\/span><\/span><\/p>\n

The final speed of ball 2 <\/span><\/span>(v<\/span><\/span>2<\/span><\/sub>\u2019) = 4 m\/s<\/span><\/span><\/p>\n

The plus sign of the velocity indicates that the balls have the same direction.<\/span><\/span><\/i><\/p>\n

Wanted <\/u><\/span><\/span>:<\/u><\/span><\/span> the final velocity of ball 1 <\/span><\/span>(v<\/span><\/span>1<\/span><\/sub>\u2019)<\/span><\/span><\/p>\n

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

m<\/span><\/span>1<\/span><\/sub> v<\/span><\/span>1<\/span><\/sub> + m<\/span><\/span>2<\/span><\/sub> v<\/span><\/span>2<\/span><\/sub> = m<\/span><\/span>1<\/span><\/sub> v<\/span><\/span>1<\/span><\/sub>\u2019 + m<\/span><\/span>2<\/span><\/sub> v<\/span><\/span>2<\/span><\/sub>\u2019<\/span><\/span><\/p>\n

(1)(10) + (2)(5) = (1)(v<\/span><\/span>1<\/span><\/sub>\u2019) + (2)(4)<\/span><\/span><\/p>\n

10 + 10 = v<\/span><\/span>1<\/span><\/sub>\u2019 + 8<\/span><\/span><\/p>\n

20 \u2013 8 = v<\/span><\/span>1<\/span><\/sub>\u2019 <\/span><\/span><\/p>\n

v<\/span><\/span>1<\/span><\/sub>\u2019 = 12 m\/s<\/span><\/span><\/p>\n

The speed of ball 1 after collision is <\/span><\/span>12 m\/s. <\/span><\/span><\/p>\n

[wpdm_package id=’1190′]<\/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 500-gram object, A, moving at 10 m\/s and 200-gram object, B, moving at 12 m\/s. The objects approach each other and collide. If the speed of object A after the collision is 6 m\/s, what is the speed of object B after the collision? Known : Mass of object 1 (m1) = 500 … 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":"Partially inelastic collisions in one dimension - 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-1124","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\/1124","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=1124"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1124\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1124"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1124"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}