{"id":570,"date":"2018-02-10T07:37:57","date_gmt":"2018-02-09T23:37:57","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=570"},"modified":"2018-02-10T07:37:57","modified_gmt":"2018-02-09T23:37:57","slug":"hookes-law-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/hookes-law-problems-and-solutions.htm","title":{"rendered":"Hooke’s law – problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>A graph of force (F) versus elongation (x<\/span><\/span>) shown in the figure below. Find the spring constant!<\/span><\/span><\/p>\n

\"Hooke'sSolution<\/span><\/span><\/p>\n

Hooke’s law<\/a> formula :<\/span><\/span><\/p>\n

k = F \/ x<\/span><\/span><\/p>\n

F = force<\/a> (Newton)<\/i><\/span><\/span><\/p>\n

k = spring constant (Newton\/meter)<\/i><\/span><\/span><\/p>\n

x = the change in length (meter) <\/i><\/span><\/span><\/p>\n

Spring constant :<\/span><\/span><\/p>\n

k = 10 \/ 0.02 = 20 \/ 0.04 <\/span><\/span><\/p>\n

k = 500 N\/m<\/span><\/span><\/p>\n

<\/p>\n

2. Determine the spring<\/a> constant.<\/span><\/span><\/p>\n

\"Hooke's<\/p>\n

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

Spring constant :<\/span><\/span><\/p>\n

k = F \/ x<\/span><\/span><\/p>\n

k = 5 \/ 0.01 = 10 \/ 0.02 = 15 \/ 0.03 = 20 \/ 0.04<\/span><\/span><\/p>\n

k = 500 N\/m<\/span><\/span><\/p>\n

<\/p>\n

3. Spring A has the original length of 60 cm and spring B has the original length of 90 cm. Spring A has constant 100 N\/m, spring B has constant 200 N\/m. The ratio of the change in length of spring A to the change in length of spring B is…<\/span><\/span><\/p>\n

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

Constant of spring A (k<\/span><\/span>A<\/span><\/sub>) = 100 N\/m<\/span><\/span><\/p>\n

Constant of spring B (k<\/span><\/span>B<\/span><\/sub>) = 200 N\/m<\/span><\/span><\/p>\n

Force on spring A (F<\/span><\/span>A<\/span><\/sub>) = F<\/span><\/span><\/p>\n

Force on spring B (F<\/span><\/span>B<\/span><\/sub>) = F<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> \u0394l<\/span><\/span>A <\/span><\/sub>: <\/span><\/span>\u0394l<\/span><\/span>B<\/span><\/sub><\/p>\n

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

Hooke’s law formula :<\/span><\/span><\/p>\n

\u0394l<\/span><\/span> = F \/ k<\/span><\/span><\/p>\n

\u0394l<\/i><\/span><\/span> = the change in length, F = force, k = constant <\/i><\/span><\/span><\/p>\n

The change in length of spring A :<\/span><\/span><\/p>\n

\u0394l<\/span><\/span>A<\/span><\/sub> = F<\/span><\/span>A<\/span><\/sub> \/ k<\/span><\/span>A<\/span><\/sub> = F \/ 100<\/span><\/span><\/p>\n

The change in length of spring B :<\/span><\/span><\/p>\n

\u0394l<\/span><\/span>B<\/span><\/sub> = F<\/span><\/span>B<\/span><\/sub> \/ k<\/span><\/span>B<\/span><\/sub> = F \/ 200<\/span><\/span><\/p>\n

The ratio of the change in length of spring A to the change in length of spring B :<\/span><\/span><\/p>\n

\u0394l<\/span><\/span>A<\/span><\/sub> : <\/span><\/span> \u0394l<\/span><\/span>B<\/span><\/sub><\/p>\n

F \/ 100 : F \/ 200<\/span><\/span><\/p>\n

1 \/ 100 : 1 \/ 200<\/span><\/span><\/p>\n

1 \/ 1 : 1 \/ 2<\/span><\/span><\/p>\n

2 : 1<\/span><\/span><\/p>\n

<\/p>\n

4. A nylon string with original length 20 cm, is pulled by a force of 10 N. The change in length of the string is 2 cm. Determine the magnitude of force if the change in length is 6 cm.<\/span><\/span><\/p>\n

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

Force (F) = 10 N<\/span><\/span><\/p>\n

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

Wanted :<\/u><\/span><\/span> the magnitude of force (F) if <\/span><\/span>\u0394l = 0.06 m. <\/span><\/span><\/p>\n

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

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

k = F \/ <\/span><\/span>\u0394l<\/span><\/span><\/p>\n

k = 10 \/ 0.02 = 500 N\/m<\/span><\/span><\/p>\n

The magnitude of force (F) if <\/span><\/span>\u0394l = 0.06 m :<\/span><\/span><\/p>\n

F = k x <\/span><\/span><\/p>\n

F = (500)(0.06) <\/span><\/span><\/p>\n

F = 30 N<\/span><\/span><\/p>\n

<\/p>\n

[wpdm_package id=’689′]<\/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":"

    1. A graph of force (F) versus elongation (x) shown in the figure below. Find the spring constant! Solution Hooke’s law formula : k = F \/ x F = force (Newton) k = spring constant (Newton\/meter) x = the change in length (meter) Spring constant : k = 10 \/ 0.02 = 20 \/ … 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":"Hooke's law - 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-570","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\/570","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=570"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/570\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}