{"id":2368,"date":"2018-05-01T13:44:19","date_gmt":"2018-05-01T05:44:19","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=2368"},"modified":"2023-08-06T15:43:31","modified_gmt":"2023-08-06T15:43:31","slug":"work-mechanical-energy-principle","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/work-mechanical-energy-principle.htm","title":{"rendered":"Work-mechanical energy principle","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Work-mechanical energy principle<\/span><\/p>\n

The work-kinetic energy theorem states that the net work or the work done by the net force is equal to the change in kinetic energy.<\/span><\/p>\n

Wnet <\/sub>= KEt<\/sub> – KEo <\/sub>= 1\u20442 m(vt<\/sub>2<\/sup> \u2013 vo<\/sub>2<\/sup>)<\/span><\/p>\n

Wnet<\/sub> = There are two types of forces, namely conservative force, and non-conservative force. Thus, net work can be considered to be comprised of the work done by a conservative force and the work done by a non-conservative force.<\/span><\/p>\n

Wc<\/sub> + Wnc<\/sub> = \u0394KE<\/span><\/p>\n

The work done by a conservative force is equal to the negative change in potential energy:<\/span><\/p>\n

Wc<\/sub>= -\u0394PE <\/span><\/p>\n

– \u0394PE + Wnc<\/sub> = \u0394KE<\/span><\/p>\n

Wnc<\/sub> = \u0394PE + \u0394KE<\/span><\/p>\n

Wnc = \u0394ME<\/span><\/p>\n

The equation above states that the work done by a non-conservative force on an object is equal to the change in the mechanical energy of the object. Mechanical energy = potential energy + kinetic energy. Potential energy can take the form of gravitational potential energy or elastic potential energy.<\/span><\/p>\n

Example question: The work-mechanical energy theorem<\/span><\/p>\n

A 2 kg box initially moves at a speed of 10 m\/s. Shortly after, the box stops. The coefficient of kinetic friction between the box and the floor is 0.2. The gravitational acceleration is 10 m\/s2<\/sup>. How much is the box\u2019s displacement?<\/span><\/p>\n

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

Identified: m = 2 kg, vo<\/sub> = 10 m\/s, vt = 0, k = 0.2, w = m g = (1 kg)(10 m\/s2<\/sup>) = 10 kg m\/s2<\/sup> = 10 Newton,<\/span><\/p>\n

Asked: the amount of the box\u2019s displacement (s)\"Work-mechanical<\/span><\/p>\n

The work-mechanical energy theorem:<\/span><\/p>\n

Wnc<\/sub> = \u0394ME<\/span><\/p>\n

Wnc<\/sub> = \u0394PE + \u0394KE<\/span><\/p>\n

The height (h) remains constant or there is no change in the height, so there is no change in the gravitational potential energy.<\/span><\/p>\n

Wnc = \u0394KE<\/span><\/p>\n

The work done by the kinetic frictional force is:<\/span><\/p>\n

Wnc <\/sub>= – fk<\/sub> s = \u03bck<\/sub> N -s = \u03bck<\/sub> w -s = \u03bck m g -s<\/span><\/p>\n

Wnc<\/sub> = – (0.2)(2)(10)(s) = – (4)(s)<\/span><\/p>\n

The kinetic frictional force does negative work (the kinetic frictional force is in opposite direction from the object\u2019s displacement)<\/span><\/p>\n

Change in the kinetic energy:<\/span><\/p>\n

\u0394KE = 1\u20442 m (vt<\/sub>2<\/sup> \u2013 vo<\/sub>2<\/sup>) = 1\u20442 (2)(02 <\/sup>– 102<\/sup>) = (0 – 100) = – 100<\/span><\/p>\n

Object\u2019s displacement:<\/span><\/p>\n

Wnc<\/sub> = \u0394KE<\/span><\/p>\n

– (4)(s) = – 100<\/span><\/p>\n

s = – 100 \/ – 4 = 25 meters<\/span><\/p>\n

20 conceptual questions and answers about the work-mechanical energy principle:<\/span><\/p>\n

1. Question:<\/strong> What is the work-mechanical energy principle? Answer:<\/strong> The work-mechanical energy principle states that the work done on an object is equal to the change in its mechanical energy.<\/span><\/p>\n

2. Question:<\/strong> How is work defined in physics? Answer:<\/strong> Work is defined as the product of the force applied to an object and the distance it moves in the direction of the force<\/span><\/p>\n

3. Question:<\/strong> What constitutes mechanical energy? Answer:<\/strong> Mechanical energy consists of an object’s kinetic energy and potential energy.<\/span><\/p>\n

4. Question:<\/strong> In the absence of non-conservative forces, what can be said about the total mechanical energy of a closed system? Answer:<\/strong> The total mechanical energy remains constant.<\/span><\/p>\n

5. Question:<\/strong> Give an example of a conservative force. Answer:<\/strong> Gravitational force is an example of a conservative force.<\/span><\/p>\n

6. Question:<\/strong> How is potential energy different from kinetic energy? Answer:<\/strong> Potential energy is the energy due to position, like height above the ground, while kinetic energy is due to motion.<\/span><\/p>\n

7. Question:<\/strong> How does the work done by a conservative force relate to potential energy? Answer:<\/strong> The work done by a conservative force is equal to the negative change in potential energy.<\/span><\/p>\n

9. Question:<\/strong> How does the work-mechanical energy principle explain the conversion of potential energy to kinetic energy in a free-falling object? Answer:<\/strong> As an object falls, its potential energy decreases and its kinetic energy increases by an equivalent amount, keeping the total mechanical energy constant.<\/span><\/p>\n

10. Question:<\/strong> What happens to the mechanical energy of a system when non-conservative forces, like friction, act on it? Answer:<\/strong> The mechanical energy decreases because non-conservative forces dissipate energy, often as heat.<\/span><\/p>\n

11. Question:<\/strong> Can the mechanical energy of a system increase? Answer:<\/strong> Yes, when external work is done on the system.<\/span><\/p>\n

12. Question:<\/strong> How is the concept of work related to energy? Answer:<\/strong> Work is the means by which energy is transferred or transformed in a system.<\/span><\/p>\n

13. Question:<\/strong> If an object is moving at a constant velocity, what can be said about the net work done on it? Answer:<\/strong> The net work done on it is zero because no acceleration is happening.<\/span><\/p>\n

15. Question:<\/strong> Why does a compressed spring have potential energy? Answer:<\/strong> When a spring is compressed, work is done on it, which is stored as potential energy. This energy can be released when the spring is let go.<\/span><\/p>\n

16. Question:<\/strong> What is the work-energy theorem? Answer:<\/strong> The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.<\/span><\/p>\n

17. Question:<\/strong> How is power related to work? Answer:<\/strong> Power is the rate at which work is done or energy is transferred. It’s calculated as P<\/span>=<\/span><\/span>W<\/span>\/<\/span>t<\/span><\/span><\/span><\/span><\/span>, where W<\/span><\/span><\/span><\/span><\/span> is work and t<\/span><\/span><\/span><\/span><\/span> is time.<\/span><\/p>\n

18. Question:<\/strong> Can work have a negative value? Answer:<\/strong> Yes, work is negative when the force and the direction of motion are opposite.<\/span><\/p>\n

19. Question:<\/strong> If the angle between the force and the direction of motion is 90 degrees, what is the work done? Answer:<\/strong> The work done is zero because the force has no component in the direction of motion.<\/span><\/p>\n

20. Question:<\/strong> How does a simple machine, like a lever, make work easier? Answer:<\/strong> A lever doesn’t change the total work done but changes the way the force is applied, making the task more manageable or efficient.<\/span><\/p>\n

The concept of work and the mechanical energy principle are fundamental in physics and provide a foundational understanding of how energy is transferred and transformed in various systems.<\/span><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

Work-mechanical energy principle The work-kinetic energy theorem states that the net work or the work done by the net force is equal to the change in kinetic energy. Wnet = KEt – KEo = 1\u20442 m(vt2 \u2013 vo2) Wnet = There are two types of forces, namely conservative force, and non-conservative force. Thus, net work … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"closed","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":"Work-mechanical energy principle","_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":[2],"tags":[],"class_list":["post-2368","post","type-post","status-publish","format-standard","hentry","category-basic-physics-tutorials"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/2368","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=2368"}],"version-history":[{"count":2,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/2368\/revisions"}],"predecessor-version":[{"id":8581,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/2368\/revisions\/8581"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=2368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=2368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=2368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}