{"id":576,"date":"2020-04-08T04:03:55","date_gmt":"2020-04-08T04:03:55","guid":{"rendered":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/?p=576"},"modified":"2020-06-01T05:06:04","modified_gmt":"2020-06-01T05:06:04","slug":"section-9-2","status":"publish","type":"post","link":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/2020\/04\/08\/section-9-2\/","title":{"rendered":"Chapter 9: Force"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">9.2 Newton&#8217;s laws<\/h2>\n\n\n\n<p>In the late 1600&#8217;s and early 1700&#8217;s, Isaac Newton published the&nbsp;<em>Principia Mathematica<\/em>&nbsp;in which he built upon discoveries of scientists (at the time called \u201cnatural philosophers\u201d) before him, laying the foundation of classical mechanics. In the&nbsp;<em>Principia<\/em>, he described three laws of motion:<\/p>\n\n\n<ol>\n<li>An object&#8217;s momentum will only change if the object is acted on by some force. This is known as the principle of inertia.<\/li>\n<li>The total force acting on an object is equal to the rate of change of the object\u2019s momentum:\n<p align=\"center\"><em><strong>F<\/strong><sub>net<\/sub> = <sup>\u0394<strong>p<\/strong><\/sup>\u2044<sub>\u0394t<\/sub><\/em><\/p>\n<\/li>\n<li>For every force acting on an object, there is a reaction force equal in magnitude and opposite in direction acting on another object.<\/li>\n<\/ol>\n\n\n<p>We have already discussed the first law in the context of energy; if you can understand inertia, you can explain many phenomena you observe. The second law is a mathematical statement which we can use to quantitatively solve problems. The third law, as we\u2019ll see in the following example, is a result of conservation of momentum.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example<\/h4>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_book_ch9_2_EXMPL\" width=\"100%\" height=\"1000\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<p>Note: in the previous example, in the last line of math before the final answer, each velocity should be multiplied by its respective mass. The calculated result is correct, however.<\/p>\n\n\n\n<p>Remember: all forces describe&nbsp;<em>interactions<\/em>&nbsp;between two objects; all forces come in pairs.<\/p>\n\n\n\n<p>Finally, let&#8217;s take another look at the second law. Consider a situation where an object&#8217;s mass remains constant (which is often the case). The change in momentum would be:<\/p>\n<p align=\"center\"> <em>\u0394<b>p<\/b> = <b>p<\/b><sub>f<\/sub> &#8211; <b>p<\/b><sub>i<\/sub> = m<b>v<\/b><sub>f<\/sub> &#8211; m<b>v<\/b><sub>i<\/sub><\/em><\/p>\n<p>Since the mass is not changing, we can factor it out:<\/p>\n<p align=\"center\"> <em>\u0394<b>p<\/b> = m(<b>v<\/b><sub>f<\/sub> &#8211; m<b>v<\/b><sub>i<\/sub>) = m&nbsp;\u0394<b>v<\/b><\/em><\/p>\n<p>And substituting this into Newton&#8217;s second law gives us<\/p>\n<p align=\"center\"> <em><b>F<\/b><sub>net<\/sub> = <sup>\u0394<b>p<\/b><\/sup>\u2044<sub>\u0394t<\/sub> = m&nbsp;<sup>\u0394<b>v<\/b><\/sup>\u2044<sub>\u0394t<\/sub><\/em><\/p>\n<p>but <em><sup>\u0394<b>v<\/b><\/sup>\u2044<sub>\u0394t<\/sub><\/em> is the object&#8217;s acceleration! So, when mass is constant, Newton&#8217;s second law can be written as<\/p>\n<p align=\"center\"><em><b>F<\/b><sub>net<\/sub> = m<b>a<\/b><\/em><\/p>\n\n\n\n<p>Remember that force, momentum, and acceleration are all <em>vector<\/em> quantities. To work with them, we must separate into <em>x<\/em> and <em>y<\/em> components:<\/p>\n\n\n\n<p align=\"center\"><em> F<sub>net, x<\/sub> = <sup>\u0394p<sub>x<\/sub><\/sup>\u2044<sub>\u0394t<\/sub> = m&nbsp;a<sub>x<\/sub><\/em><\/p>\n<p>and<\/p>\n<p align=\"center\"><em> F<sub>net, y<\/sub> = <sup>\u0394p<sub>y<\/sub><\/sup>\u2044<sub>\u0394t<\/sub> = m&nbsp;a<sub>y<\/sub><\/em><\/p>\n\n\n\n<p>The SI unit of force is named the <em>newton <\/em>(N) in honor of Isaac Newton. Using Newton&#8217;s second law, we can break the newton down into base SI units:<\/p>\n\n\n\n<p class=\"has-text-align-center\">N = kg \u00b7 m\/s<sup>2<\/sup><\/p>\n\n\n\n<p>For comparison, one newton is approximately the force required to push down one key on a computer keyboard.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Example<\/h4>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_book_ch9_1_EXMPL\" width=\"100%\" height=\"600\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<h4 class=\"wp-block-heading\">Practice<\/h4>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_HW3A_q1\" width=\"100%\" height=\"600\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<h4 class=\"wp-block-heading\">Practice<\/h4>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_HW3A_q2\" width=\"100%\" height=\"600\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<h4 class=\"wp-block-heading\">Practice<\/h4>\n\n\n\n<!-- iframe plugin v.6.0 wordpress.org\/plugins\/iframe\/ -->\n<iframe loading=\"lazy\" src=\"https:\/\/my.compclassnotes.com\/canonical\/PHYS110\/PHYS110_HW3A_q5\" width=\"100%\" height=\"600\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n","protected":false},"excerpt":{"rendered":"<p>9.2 Newton&#8217;s laws In the late 1600&#8217;s and early 1700&#8217;s, Isaac Newton published the&nbsp;Principia Mathematica&nbsp;in which he built upon discoveries of scientists (at the time called \u201cnatural philosophers\u201d) before him, laying the foundation of classical mechanics. In the&nbsp;Principia, he described <span class=\"readmore\"><a href=\"https:\/\/books.compclassnotes.com\/rothphys110-2e\/2020\/04\/08\/section-9-2\/\">Continue Reading<\/a><\/span><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-576","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/576","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/comments?post=576"}],"version-history":[{"count":12,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/576\/revisions"}],"predecessor-version":[{"id":694,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/576\/revisions\/694"}],"wp:attachment":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/media?parent=576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/categories?post=576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/tags?post=576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}