{"id":1031,"date":"2018-02-23T07:49:52","date_gmt":"2018-02-22T23:49:52","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=1031"},"modified":"2018-02-23T07:49:52","modified_gmt":"2018-02-22T23:49:52","slug":"gravitational-potential-energy-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/gravitational-potential-energy-problems-and-solutions.htm","title":{"rendered":"Gravitational potential energy \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>A 1-kg body free fall<\/a> from rest, from a height of 10 m. <\/span><\/span><\/p>\n

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

(a) Work done by force<\/a> of gravity <\/a><\/span><\/span><\/p>\n

(b) The change in gravitational potential energy<\/a><\/span><\/span><\/p>\n

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

\"GravitationalKnown :<\/u><\/span><\/span><\/p>\n

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

Height (h) = 10 m<\/span><\/span><\/p>\n

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

Weight<\/a> (w) = m g = (1 kg)(10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>) = 10 N<\/span><\/span><\/p>\n

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

(a)<\/span><\/span> Work done by force of gravity<\/b><\/span><\/span><\/p>\n

W = w h = m g h<\/span><\/span><\/p>\n

W = (1)(10)(10) = 100 Joule<\/span><\/span><\/p>\n

(b) <\/span><\/span>The change in gravitational potential energy<\/b><\/span><\/span><\/p>\n

The change in gravitational potential energy is equal to the work done by gravity. <\/span><\/span><\/p>\n

\u0394<\/span><\/span>EP = 100 Joule<\/span><\/span><\/p>\n

<\/p>\n

2. A 10 N object slides down on the smooth inclined plane along 2 meters. Determine work done by weight force!<\/span><\/span><\/p>\n

\"GravitationalKnown :<\/u><\/span><\/span><\/p>\n

weight (w) = 10 N<\/span><\/span><\/p>\n

w<\/span><\/span>x<\/span><\/sub> = w sin <\/span><\/span>\u03b8<\/span><\/span> = (10)(sin 30<\/span><\/span>o<\/span><\/span><\/sup>) = (10)(0.5) = 5 N<\/span><\/span><\/p>\n

d = 2 m<\/span><\/span><\/p>\n

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

Wanted :<\/u><\/span><\/span> work done by weight force<\/span><\/span><\/p>\n

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

W = F d = w<\/span><\/span>x<\/span><\/span><\/sub> d = (5)(2) = 10 Joule<\/span><\/span><\/p>\n

Alternative solution :<\/b><\/span><\/span><\/p>\n

Sin 30<\/span><\/span>o<\/span><\/span><\/sup> = h \/ d<\/span><\/span><\/p>\n

0.5 = h \/ 2 <\/span><\/span><\/p>\n

h = (0.5)(2) <\/span><\/span><\/p>\n

h = 1 m<\/span><\/span><\/p>\n

Work done by weight force ;<\/span><\/span><\/p>\n

W = F d = w h = (10 N)(1 m) = 10 N m = 10 Joule <\/span><\/span><\/p>\n

<\/p>\n

3. A 1,500 gram object <\/span><\/span>at 20 meters above the ground<\/span><\/span>, free fall to the ground. What is the gravitational potential energy of the object. Acceleration due to gravity is 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>.<\/span><\/span><\/p>\n

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

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

Mass (m) = 1500 gram = 1500\/1000 kilogram = 1.5 kilogram<\/span><\/span><\/p>\n

Height (h) = 20 meters<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The gravitational potential energy<\/span><\/span><\/p>\n

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

PE = m g h = (1.5 kg)(10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>)(20 m) = 300 kg m<\/span><\/span>2<\/span><\/span><\/sup>\/s<\/span><\/span>2<\/span><\/span><\/sup> = 300 Joule <\/span><\/span><\/p>\n

4. Based on figure below, if mass of object 1 is 2 kg and mass of object 2 is 4 kg, comparison of potential energy of object 1 and object 2 is …..<\/span><\/span><\/span><\/p>\n

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

Mass of object 1 (m1<\/sub>) = 2 kilogram\"Gravitational<\/span><\/span><\/p>\n

Mass of object 2 (m2<\/sub>) = 4 kilogram<\/span><\/span><\/p>\n

Height 1 (h1<\/sub>) = 12 meters<\/span><\/span><\/p>\n

Height 2 (h2<\/sub>) = 9 meters<\/span><\/span><\/p>\n

Wanted:<\/u> Comparison of potential energy of object 1 and object 2<\/span><\/span><\/span><\/p>\n

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

PE = m g h<\/span><\/span><\/p>\n

m = mass (its international unit is kilogram, abbreviated kg)<\/span><\/span><\/p>\n

g = acceleration due to gravity (its international unit is meter per second squared, abbreviated m\/s2<\/sup>)<\/span><\/span><\/p>\n

h = height (its international unit is meter, abbreviated m)<\/span><\/span><\/p>\n

PE = gravitational potential energy (its international unit is kg m2<\/sup>\/s2 <\/sup>or Joule)<\/span><\/span><\/p>\n

The gravitational potential energy of object 1 :<\/span><\/span><\/p>\n

EP1 <\/sub>= m1 <\/sub>g h1<\/sub>= (2)(g)(12) = 24 g<\/span><\/span><\/p>\n

The gravitational potential energy of object 2 :<\/span><\/span><\/p>\n

EP2 <\/sub>= m2<\/sub> g h2<\/sub> = (4)(g)(9) = 36 g<\/span><\/span><\/p>\n

Comparison of the potential energy of object 1 and object 2 :<\/span><\/span><\/span><\/p>\n

PE1 <\/sub>: PE2 <\/sub><\/span><\/span><\/p>\n

24 g : 36 g<\/span><\/span><\/p>\n

24 : 36<\/span><\/span><\/p>\n

24\/12 : 36\/12<\/span><\/span><\/p>\n

2 : 3<\/span><\/span><\/p>\n

[wpdm_package id=’1175′]<\/p>\n

    \n
  1. Work done by force problems and solutions<\/a><\/li>\n
  2. Work-kinetic energy problems and solutions<\/a><\/li>\n
  3. Work-mechanical energy principle problems and solutions<\/a><\/li>\n
  4. Gravitational potential energy problems and solutions<\/a><\/li>\n
  5. The potential energy of elastic spring problems and solutions<\/a><\/li>\n
  6. Power problems and solutions<\/a><\/li>\n
  7. Application of conservation of mechanical energy for free fall motion<\/a><\/li>\n
  8. Application of conservation of mechanical energy for up and down motion in free fall motion<\/a><\/li>\n
  9. Application of conservation of mechanical energy for motion on a curved surface<\/a><\/li>\n
  10. Application of conservation of mechanical energy for motion on an inclined plane<\/a><\/li>\n
  11. Application of conservation of mechanical energy for projectile motion<\/a><\/li>\n<\/ol>\n

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

    1. A 1-kg body free fall from rest, from a height of 10 m. Determine : (a) Work done by force of gravity (b) The change in gravitational potential energy Acceleration due to gravity (g) = 10 m\/s2 Known : Mass (m) = 1 kg Height (h) = 10 m Acceleration due to gravity (g) … 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":"Gravitational potential energy \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-1031","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\/1031","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=1031"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/1031\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=1031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=1031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=1031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}