{"id":1116,"date":"2018-02-25T10:06:37","date_gmt":"2018-02-25T02:06:37","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1116"},"modified":"2018-02-25T10:06:37","modified_gmt":"2018-02-25T02:06:37","slug":"perfectly-elastic-collisions-in-one-dimension-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/perfectly-elastic-collisions-in-one-dimension-problems-and-solutions.htm","title":{"rendered":"Perfectly elastic collisions in one dimension \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. A 200-gram ball, A, moving at a speed of 10 m\/s strikes a 200-gram ball, B, at rest. What is the speed of ball A and ball B after the collision<\/a>?<\/span><\/span><\/p>\n

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

Mass<\/a> of ball A (m<\/span><\/span>A<\/span><\/sub>) = 200 gram = 0.2 kg<\/span><\/span><\/p>\n

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

Speed of ball A before collision (v<\/span><\/span>A<\/span><\/sub>) = 10 m\/s<\/span><\/span><\/p>\n

Speed of ball B before collision (v<\/span><\/span>B<\/span><\/sub>) = 0<\/span><\/span><\/p>\n

Wanted: speed of ball A (v<\/span><\/span>A<\/span><\/sub>\u2019) and speed of ball B (v<\/span><\/span>B<\/span><\/sub>\u2019) after a collision<\/span><\/span><\/p>\n

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

v<\/span><\/span>A<\/span><\/sub>\u2019 = v<\/span><\/span>B <\/span><\/sub>= 0<\/span><\/span><\/p>\n

v<\/span><\/span>B<\/span><\/sub>\u2019 = v<\/span><\/span>A <\/span><\/sub>= 10 m\/s <\/span><\/span><\/p>\n

<\/p>\n

2. Two equal-mass objects approach each other, collide and then bounce off. The speed of mass A before the collision is 8 m\/s and speed of mass B before the collision is 12 m\/s. What is the magnitude and direction of the velocity<\/a> of mass A and mass B after the collision!<\/span><\/span><\/p>\n

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

Mass A (m<\/span><\/span>A<\/span><\/sub>) = m<\/span><\/span><\/p>\n

Mass B (m<\/span><\/span>B<\/span><\/sub>) = m<\/span><\/span><\/p>\n

Speed of mass A before collision (v<\/span><\/span>A<\/span><\/sub>) = -8 m\/s<\/span><\/span><\/p>\n

Speed of mass B before collision (v<\/span><\/span>B<\/span><\/sub>) = 12 m\/s<\/span><\/span><\/p>\n

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

Wanted: the magnitude and direction of the velocity of mass A (v<\/span><\/span>A<\/span><\/sub>\u2019) and mass B (v<\/span><\/span>B<\/span><\/sub>\u2019) after a collision<\/span><\/span><\/p>\n

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

In a perfectly elastic collision, if the objects of equal mass then the speed of A after the collision (v<\/span><\/span>A<\/span><\/sub>\u2019) = the speed of B before collision (v<\/span><\/span>B<\/span><\/sub>) and the speed of B after the collision (v<\/span><\/span>B<\/span><\/sub>\u2019) = the speed of A before collision (v<\/span><\/span>A<\/span><\/sub>). <\/span><\/span><\/p>\n

If before collision, A moving rightward and B moving leftward, then, after collision, A moving leftward and B moving rightward. <\/span><\/span><\/p>\n

The objects have equal mass and the <\/span><\/span>collision is perfectly elastic so the both objects exchanged speed. <\/span><\/span><\/p>\n

v<\/span><\/span>A<\/span><\/sub>\u2019 = -v<\/span><\/span>B <\/span><\/sub>= -12 m\/s<\/span><\/span><\/p>\n

v<\/span><\/span>B<\/span><\/sub>\u2019 = v<\/span><\/span>A <\/span><\/sub>= 8 m\/s <\/span><\/span><\/p>\n

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

<\/p>\n

3. A 2-kg object, A, moving at a speed of 10 m\/s strikes a 4-kg ball, B, moving at a speed of 20 m\/s. If the collision is perfectly elastic, what is the speed of object A and object B after the collision?<\/span><\/span><\/p>\n

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

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

Mass B (m<\/span><\/span>B<\/span><\/sub>) = 4 kg <\/span><\/span><\/p>\n

Speed of object A before collision (v<\/span><\/span>A<\/span><\/sub>) = 10 m\/s<\/span><\/span><\/p>\n

Speed of object B before collision (v<\/span><\/span>B<\/span><\/sub>) = 20 m\/s<\/span><\/span><\/p>\n

Wanted<\/u><\/span><\/span> : the speed of object A (v<\/span><\/span>A<\/span><\/sub>\u2019) and the speed of object B (v<\/span><\/span>B<\/span><\/sub>\u2019) after collision<\/span><\/span><\/p>\n

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

In perfectly elastic collision<\/a>, if the objects have equal mass and approach each other, the speed of the object after collision calculated using this formula :<\/span><\/span><\/p>\n

\"Perfectly<\/p>\n

Speed of object A after collision :<\/span><\/span><\/p>\n

\"Perfectly<\/p>\n

<\/p>\n

4. A 100-gram moving at 20 m\/s strikes a wall perfectly elastic collision. What is the magnitude and direction of object’s velocity after collision.<\/span><\/span><\/p>\n

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

Mass (m<\/span><\/span>A<\/span><\/sub>) = 100 gram = 0.1 kg<\/span><\/span><\/p>\n

Mass of wall (m<\/span><\/span>B<\/span><\/sub>) = infinity<\/span><\/span><\/p>\n

The speed of mass before collision (v<\/span><\/span>A<\/span><\/sub>) = 20 m\/s <\/span><\/span><\/p>\n

The speed of mass after collision (v<\/span><\/span>B<\/span><\/sub>) = 0 <\/span><\/span><\/p>\n

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

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

If v<\/span><\/span>B<\/span><\/sub> = 0, m<\/span><\/span>A<\/span><\/sub> very small and m<\/span><\/span>2<\/span><\/sub> very big then v<\/span><\/span>A<\/span><\/sub>\u2019 = -v<\/span><\/span>A<\/span><\/sub> and v<\/span><\/span>2<\/span><\/sub>\u2019 = 0.<\/span><\/span><\/p>\n

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

5. <\/span><\/span>Two balls, <\/span><\/span>A <\/span><\/span>with a mass of <\/span><\/span>2-kg <\/span><\/span>and ball B with a mass of <\/span><\/span>5-kg, <\/span><\/span>before and after the collision are shown in the figure below. If the collision is perfectly elastic, what is the speed of ball A before the collision?<\/span><\/span><\/p>\n

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

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

Mass of ball <\/span><\/span>B (m<\/span><\/span>B<\/span><\/sub>) = 5 kg<\/span><\/span><\/p>\n

Speed of ball <\/span><\/span>B <\/span><\/span>before collision <\/span><\/span>(v<\/span><\/span>B<\/span><\/sub>) = 2 m\/s<\/span><\/span><\/p>\n

Speed of ball A after collision <\/span><\/span>(v<\/span><\/span>A<\/span><\/sub>‘) = 5 m\/s<\/span><\/span><\/p>\n

Speed of ball B after collision <\/span><\/span>(v<\/span><\/span>B<\/span><\/sub>‘) = 4 m\/s<\/span><\/span><\/p>\n

Both balls are move to the right so their speed signed positive.<\/i><\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Speed of ball A before collision <\/span><\/span>(v<\/span><\/span>A<\/span><\/sub>)<\/span><\/span><\/p>\n

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

m<\/span><\/span>A<\/span><\/sub> v<\/span><\/span>A<\/span><\/sub> + m<\/span><\/span>B<\/span><\/sub> v<\/span><\/span>B<\/span><\/sub> = m<\/span><\/span>A<\/span><\/sub> v<\/span><\/span>A<\/span><\/sub>‘ + m<\/span><\/span>B<\/span><\/sub> v<\/span><\/span>B<\/span><\/sub>‘<\/span><\/span><\/p>\n

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

2(v<\/span><\/span>A<\/span><\/sub>) + 10 = 10 + 20<\/span><\/span><\/p>\n

2(v<\/span><\/span>A<\/span><\/sub>) + 10 = 30<\/span><\/span><\/p>\n

2(v<\/span><\/span>A<\/span><\/sub>) = 30 \u2013 10<\/span><\/span><\/p>\n

2(v<\/span><\/span>A<\/span><\/sub>) = 20<\/span><\/span><\/p>\n

v<\/span><\/span>A <\/span><\/sub>= 20\/2<\/span><\/span><\/p>\n

v<\/span><\/span>A<\/sub> <\/span><\/span>= 10 m\/s<\/span><\/span><\/p>\n

<\/p>\n

6. <\/span><\/span>Object A and B travel along horizontal plane, as shown in figure below. If the collision is perfectly elastic and the speed of object B after collision is <\/span><\/span>15 m\/s<\/span><\/span>1<\/span><\/span><\/sup>, <\/span><\/span>what is the speed of object A after collision.<\/span><\/span><\/p>\n

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

Mass of object <\/span><\/span>A (m<\/span><\/span>A<\/span><\/sub>) = 5 kg\"Perfectly<\/span><\/span><\/p>\n

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

Speed of object A before collision <\/span><\/span>(v<\/span><\/span>A<\/span><\/sub>) = 12 m\/s<\/span><\/span><\/p>\n

Speed of object B before collision <\/span><\/span>(v<\/span><\/span>B<\/span><\/sub>) = 10 m\/s<\/span><\/span><\/p>\n

Speed of object B after collision <\/span><\/span>(v<\/span><\/span>B<\/span><\/sub>‘) = 15 m\/s<\/span><\/span><\/p>\n

Both objects, before and after collision, move to right so their velocity signed positive.<\/i><\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Speed of object A after collision <\/span><\/span>(v<\/span><\/span>A<\/span><\/sub>‘)<\/span><\/span><\/p>\n

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

m<\/span><\/span>A<\/span><\/sub> v<\/span><\/span>A<\/span><\/sub> + m<\/span><\/span>B<\/span><\/sub> v<\/span><\/span>B<\/span><\/sub> = m<\/span><\/span>A<\/span><\/sub> v<\/span><\/span>A<\/span><\/sub>‘ + m<\/span><\/span>B<\/span><\/sub> v<\/span><\/span>B<\/span><\/sub>‘<\/span><\/span><\/p>\n

(5)(12) + (2)(10) = (5)v<\/span><\/span>A<\/span><\/sub>‘ + (2)(15)<\/span><\/span><\/p>\n

60 + 20 = (5)v<\/span><\/span>A<\/span><\/sub>‘ + 30<\/span><\/span><\/p>\n

80 = (5)v<\/span><\/span>A<\/span><\/sub>‘ + 30<\/span><\/span><\/p>\n

80 \u2013 30 = (5)v<\/span><\/span>A<\/span><\/sub>‘<\/span><\/span><\/p>\n

50 = (5)v<\/span><\/span>A<\/span><\/sub>‘<\/span><\/span><\/p>\n

v<\/span><\/span>A<\/span><\/sub>‘ = 50\/5<\/span><\/span><\/p>\n

v<\/span><\/span>A<\/span><\/sub>‘ = 10 m\/s<\/span><\/span><\/p>\n

[wpdm_package id=’1156′]<\/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 200-gram ball, A, moving at a speed of 10 m\/s strikes a 200-gram ball, B, at rest. What is the speed of ball A and ball B after the collision? Known : Mass of ball A (mA) = 200 gram = 0.2 kg Mass of ball B (mB) = 200 gram = 0.2 … 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":"Perfectly elastic collisions in one dimension \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-1116","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\/1116","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=1116"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1116\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}