{"id":669,"date":"2020-05-21T19:50:12","date_gmt":"2020-05-21T19:50:12","guid":{"rendered":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/?p=669"},"modified":"2021-06-29T18:54:49","modified_gmt":"2021-06-29T18:54:49","slug":"section-9-3","status":"publish","type":"post","link":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/2020\/05\/21\/section-9-3\/","title":{"rendered":"Chapter 9: Force"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">9.3 Types of forces<\/h2>\n\n\n\n<p>In the classical model of physics, we describe many different forces depending on what things are interacting. A few of these forces have a distinct mathematical expression.<\/p>\n\n\n\n<p><strong><em>Weight<\/em><\/strong> is the force of gravity of the Earth pulling on an object. See <a href=\"https:\/\/books.compclassnotes.com\/rothphys110-2e\/2020\/04\/08\/sections-9-7-9-8#gravitation\" target=\"_blank\" rel=\"noreferrer noopener\">section 9.8<\/a> for the full story. An object\u2019s weight is given by the expression:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"math display\"><em>F<\/em><sup><em> G<\/em><\/sup>\u2004=\u2004<em>mg<\/em><\/span><\/p>\n\n\n\n<p>The <strong><em>spring force<\/em><\/strong> is the force exerted by a spring that is stretched or compressed a distance <span class=\"math inline\"><em>x<\/em><\/span>  from its equilibrium position:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"math display\"><em>F<\/em><sup><em> sp<\/em><\/sup>\u2004=\u2004<em>kx<\/em><\/span><\/p>\n\n\n\n<p>This equation is known as <em>Hooke\u2019s Law<\/em> after Robert Hooke. The <em>k<\/em> is the same spring constant that we use to determine spring potential energy. We now see that the spring constant has units of N\/m; the spring exerts some force for any given distance it is stretched or compressed from equilibrium. The spring force is always directed towards the equilibrium position of the spring. Hooke\u2019s Law is a very powerful tool that is used to model many situations involving things which have a tendency to return to some equilibrium position.<\/p>\n\n\n\n<p>Some of the forces we\u2019ll use do not have a set equation to determine their strength. These forces will depend on everything else acting on a given object:<\/p>\n\n\n\n<p><strong><em>Normal force<\/em><\/strong> (<span class=\"math inline\"><em>F<\/em><sup><em> N<\/em><\/sup><\/span> ) is the \u201cforce of contact\u201d between two surfaces. It is always perpendicular to the interface of the two surfaces.<\/p>\n\n\n\n<p>We can actually use Hooke\u2019s law to better understand the normal force. A reliable way to model solids is to image the atoms as very small, hard spheres that are connected by springs. When something pushes down on this object, you can imagine those springs compressing. The animation below shows a simplified example:<\/p>\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_force_ANIME\" width=\"100%\" height=\"500\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<p>Following Hooke\u2019s law, the molecules then exert a force back up, towards their equilibrium position; this force is perpendicular to the surface itself. When taken over the many many <em>many<\/em> atoms that make up a solid, we have the effect which we call the normal force.<\/p>\n\n\n\n<p><strong><em>Friction<\/em><\/strong> (<span class=\"math inline\"><em>F<\/em><sup><em> f<\/em> <\/sup><\/span>) is the force between two surfaces that resists motion. It is always parallel to the interface of the two surfaces, and points in a direction to oppose motion. Ask yourself, \u201cif there were no friction, which way would the object move?\u201d The frictional force points in the opposite direction.<\/p>\n\n\n\n<p>On a microscopic level, \u201csmooth\u201d surfaces are not smooth. When two surfaces rub against each other, the jagged \u201cpeaks and valleys\u201d snag on each other; this resists the motion of the objects.<\/p>\n\n\n\n<p><strong><em>Tension<\/em><\/strong> (<span class=\"math inline\"><em>F<\/em><sup><em> T <\/em><\/sup><\/span>) is the force that a rope\/wire\/string\/etc.&nbsp;exerts. It acts in the direction that the rope (or string, or wire&#8230;) is pulling.<\/p>\n\n\n\n<p>Sometimes we will refer to a force being &#8220;<strong><em>applied<\/em><\/strong>.&#8221; We use this somewhat generically, though it often is used to describe the force exerted by a push. We use the symbol <em>F<sup> app<\/sup><\/em>.  In the case of a push, this is technically a normal force! But it sometimes conceptually useful to just think of it on its own terms, as the force that you yourself are intentionally applying to an object.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Practice: friction<\/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_q4\" width=\"100%\" height=\"600\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"yes\" class=\"iframe-class\" frameborder=\"0\"><\/iframe>\n\n\n\n\n<p>Hint: you don&#8217;t need to do any math for this problem.<\/p>\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>9.3 Types of forces In the classical model of physics, we describe many different forces depending on what things are interacting. A few of these forces have a distinct mathematical expression. Weight is the force of gravity of the Earth <span class=\"readmore\"><a href=\"https:\/\/books.compclassnotes.com\/rothphys110-2e\/2020\/05\/21\/section-9-3\/\">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-669","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/669","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=669"}],"version-history":[{"count":11,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/669\/revisions"}],"predecessor-version":[{"id":1239,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/posts\/669\/revisions\/1239"}],"wp:attachment":[{"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/media?parent=669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/categories?post=669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/books.compclassnotes.com\/rothphys110-2e\/wp-json\/wp\/v2\/tags?post=669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}