{"id":557,"date":"2018-02-10T07:23:12","date_gmt":"2018-02-09T23:23:12","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=557"},"modified":"2018-02-10T07:23:12","modified_gmt":"2018-02-09T23:23:12","slug":"stress-strain-youngs-modulus-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/stress-strain-youngs-modulus-problems-and-solutions.htm","title":{"rendered":"Stress Strain Young’s modulus – Problems and Solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Stress Strain Young’s modulus – Problems and Solutions<\/strong><\/p>\n

1. A nylon string has a diameter of 2 mm, pulled by a force of 100 N. Determine the stress!<\/span><\/span><\/p>\n

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

Force<\/a> (F) = 100 N<\/span><\/span><\/p>\n

Diameter (d) = 2 mm = 0.002 m<\/span><\/span><\/p>\n

Radius (r) = 1 mm = 0.001 m<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The stress<\/span><\/span><\/p>\n

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

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

A = \u03c0 r<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

A = (3.14)(0.001 m)<\/span><\/span>2<\/span><\/span><\/sup> = 0.00000314 m<\/span><\/span>2 <\/span><\/span><\/sup><\/p>\n

A = 3.14 x 10<\/span><\/span>-6<\/span><\/span><\/sup> m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

The stress :<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

<\/p>\n

2. A cord has original length of 100 cm is pulled by a force. The change in length of the cord is 2 mm. Determine the strain!<\/span><\/span><\/p>\n

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

Original length (l<\/span><\/span>0<\/span><\/sub>) = 100 cm = 1 m<\/span><\/span><\/p>\n

The change in length (\u0394l) = 2 mm = 0.002 m<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> The strain<\/span><\/span><\/p>\n

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

The s<\/span><\/span>train :<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

<\/p>\n

3. A string 4 mm in diameter has original length 2 m. The string is pulled by a force of 200 N. If the final length of the spring is 2.02 m, determine : (a) stress (b) strain (c) Young’s modulus <\/a><\/span><\/span><\/p>\n

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

Diameter (d) = 4 mm = 0.004 m<\/span><\/span><\/p>\n

Radius (r) = 2 mm = 0.002 m <\/span><\/span><\/p>\n

Area (A) = \u03c0 r<\/span><\/span>2<\/span><\/span><\/sup> = (3.14)(0.002 m)<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Area (A) = 0.00001256 m<\/span><\/span>2 <\/span><\/span><\/sup>= 12.56 x 10<\/span><\/span>-6<\/span><\/span><\/sup> m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Force (F) = 200 N<\/span><\/span><\/p>\n

Original length of spring (l<\/span><\/span>0<\/span><\/sub>) = 2 m<\/span><\/span><\/p>\n

The change in length (\u0394l) = 2.02 \u2013 2 = 0.02 m <\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> (a) The stress (b) The strain c) Young’s modulus<\/span><\/span><\/p>\n

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

(a) The s<\/span><\/span>tress<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

(b) The Strain<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

(c) <\/span><\/span>Young’s modulus<\/u><\/span><\/span><\/p>\n

\"Stress,<\/p>\n

<\/p>\n

4. A string has a diameter of 1 cm and the original length of 2 m. The string is pulled by a force of 200 N. Determine the change in length of the string! Young’s modulus of the string = 5 x 10<\/span><\/span>9<\/span><\/span><\/sup> N\/m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

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

Young’s modulus (E) = 5 x 10<\/span><\/span>9<\/span><\/span><\/sup> N\/m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Original length (l<\/span><\/span>0<\/span><\/sub>) = 2 m<\/span><\/span><\/p>\n

Force (F) = 200 N<\/span><\/span><\/p>\n

Diameter (d) = 1 cm = 0.01 m<\/span><\/span><\/p>\n

Radius (r) = 0.5 cm = 0.005 m = 5 x 10<\/span><\/span>-3<\/span><\/span><\/sup> m <\/span><\/span><\/p>\n

Area (A) = \u03c0 r<\/span><\/span>2<\/span><\/span><\/sup> = (3.14)(5 x 10<\/span><\/span>-3<\/span><\/span><\/sup> m)<\/span><\/span>2 <\/span><\/span><\/sup>= (3.14)(25 x 10<\/span><\/span>-6<\/span><\/span><\/sup> m<\/span><\/span>2<\/span><\/span><\/sup>) <\/span><\/span><\/p>\n

Area (A) = 78.5 x 10<\/span><\/span>-6<\/span><\/span><\/sup> m<\/span><\/span>2 <\/span><\/span><\/sup>= 7.85 x 10<\/span><\/span>-5<\/span><\/span><\/sup> m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Wanted <\/u><\/span><\/span>: The change in length (\u0394l)<\/span><\/span><\/p>\n

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

Young’s modulus formula :<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

The change in length <\/u><\/span><\/span>:<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

<\/p>\n

5. A concrete has a height of 5 meters and has unit area of 3 m<\/span><\/span>3<\/span><\/span><\/sup> supports a mass<\/a> of 30,000 kg. Determine (a) The stress (b) The strain (c) The change in height! Acceleration due to gravity<\/a> (g) = 10 m\/s<\/span><\/span>2<\/span><\/span><\/sup>. Young’s modulus of concrete = 20 x 10<\/span><\/span>9<\/span><\/span><\/sup> N\/m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

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

Young’s modulus of concrete = 20 x 10<\/span><\/span>9<\/span><\/span><\/sup> N\/m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Initial height (l<\/span><\/span>0<\/span><\/sub>) = 5 meters<\/span><\/span><\/p>\n

Unit area (A) = 3 m<\/span><\/span>2<\/span><\/span><\/sup><\/p>\n

Weight<\/a> (w) = m g = (30,000)(10) = 300,000 N<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> (a) The stress (b) The strain (c) The change in height!<\/span><\/span><\/p>\n

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

(a) The stress<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

(b) The Strain<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

(c) The change in height<\/span><\/span><\/p>\n

\"Stress,<\/p>\n

<\/p>\n

    \n
  1. Hooke’s law<\/a><\/li>\n
  2. Stress, strain, Young’s modulus <\/a><\/li>\n<\/ol>\n

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

    Stress Strain Young’s modulus – Problems and Solutions 1. A nylon string has a diameter of 2 mm, pulled by a force of 100 N. Determine the stress! Known : Force (F) = 100 N Diameter (d) = 2 mm = 0.002 m Radius (r) = 1 mm = 0.001 m Wanted : The stress … 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":"Stress strain Young's modulus - 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-557","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\/557","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=557"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/557\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=557"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=557"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}