{"id":1262,"date":"2019-01-14T02:59:48","date_gmt":"2019-01-14T02:59:48","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ivytech-sci111\/chapter\/free-falling-objects\/"},"modified":"2019-01-14T03:54:37","modified_gmt":"2019-01-14T03:54:37","slug":"free-falling-objects","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-sci111\/chapter\/free-falling-objects\/","title":{"raw":"Module 2 Free-Falling Objects","rendered":"Module 2 Free-Falling Objects"},"content":{"raw":"<div class=\"boundless-concept\">\r\n<h2>Free-Falling Objects<\/h2>\r\nFree fall is the motion of a body where its weight is the only force acting on an object.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nSolve basic problems concerning free fall and distinguish it from other kinds of motion\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Takeaways<\/h3>\r\n<h4>Key Points<\/h4>\r\n<ul>\r\n \t<li>The acceleration of free-falling objects is called the acceleration due to gravity, since objects are pulled towards the center of the earth.<\/li>\r\n \t<li>The acceleration due to gravity is constant on the surface of the Earth and has the value of 9.80 [latex]\\displaystyle \\frac{\\text{m}}{\\text{s}^2}[\/latex].<\/li>\r\n<\/ul>\r\n<h4>Key Terms<\/h4>\r\n<ul>\r\n \t<li><strong>acceleration<\/strong>: The amount by which a speed or velocity changes within a certain period of time (and so a scalar quantity or a vector quantity).<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Free Fall<\/h3>\r\nThe motion of falling objects is the simplest and most common example of motion with changing velocity. If a coin and a piece of paper are simultaneously dropped side by side, the paper takes much longer to hit the ground. However, if you crumple the paper into a compact ball and drop the items again, it will look like both the coin and the paper hit the floor simultaneously. This is because the amount of force acting on an object is a function of not only its mass, but also area. Free fall is the motion of a body where its weight is the only force acting on an object.\r\n<div class=\"wp-caption alignright\" style=\"width: 158px;\" data-global-id=\"gid:\/\/boundless\/Image\/17491\">\r\n<div class=\"figure-cont\">\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2548\/2019\/01\/14025947\/free-fall.gif\" alt=\"image\" width=\"148\" height=\"330\" \/>\r\n<p class=\"wp-caption-text\"><strong>Free Fall<\/strong>: This clip shows an object in free fall.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nGalileo also observed this phenomena and realized that it disagreed with the Aristotle principle that heavier items fall more quickly. Galileo then hypothesized that there is an upward force exerted by air in addition to the downward force of gravity. If air resistance and friction are negligible, then in a given location (because gravity changes with location), all objects fall toward the center of Earth with the <em>same constant acceleration<\/em>, <em>independent of their mass<\/em>, that constant acceleration is gravity. Air resistance opposes the motion of an object through the air, while friction opposes motion between objects and the medium through which they are traveling. The acceleration of free-falling objects is referred to as the acceleration due to gravity [latex]\\text{g}[\/latex]. As we said earlier, gravity varies depending on location and altitude on Earth (or any other planet), but the average acceleration due to gravity on Earth is 9.8 [latex]\\displaystyle \\frac{\\text{m}}{\\text{s}^2}[\/latex]<sup>. <\/sup>This value is also often expressed as a negative acceleration in mathematical calculations due to the downward direction of gravity.\r\n<h3>Equations<\/h3>\r\nThe best way to see the basic features of motion involving gravity is to start by considering straight up and down motion with no air resistance or friction. This means that if the object is dropped, we know the initial velocity is zero. Once the object is in motion, the object is in free-fall. Under these circumstances, the motion is one-dimensional and has constant acceleration, [latex]\\text{g}[\/latex]. The kinematic equations for objects experiencing free fall are:\r\n\r\n[latex]\\text{v}=\\text{v}_0-\\text{gt}\\\\\\text{y}=\\text{y}_0+\\text{v}_0\\text{t}-\\frac12\\text{gt}^2\\\\\\text{v}^2=\\text{v}_0^2-2\\text{g}(\\text{y}-\\text{y}_0),[\/latex]\r\n\r\nwhere [latex]\\text{v} = \\text{velocity}[\/latex], [latex]\\text{g}=\\text{gravity}[\/latex], [latex]\\text{t}=\\text{time}[\/latex], and [latex]\\text{y}=\\text{vertical displacement}[\/latex].\r\n<div class=\"embed-wrap\" data-global-id=\"gid:\/\/boundless\/Embed\/21499\">\r\n<div class=\"figure-cont\">\r\n<div>http:\/\/www.youtube.com\/watch?v=C6-AxMc9mig&amp;stop=513<\/div>\r\n<strong>Free Fall Motion - YouTube<\/strong>: Describes how to calculate the time for an object to fall if given the height and the height that an object fell if given the time to fall.\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Examples<\/h3>\r\nSome examples of objects that are in free fall include:\r\n<ul>\r\n \t<li>A spacecraft in continuous orbit. The free fall would end once the propulsion devices turned on.<\/li>\r\n \t<li>An stone dropped down an empty well.<\/li>\r\n \t<li>An object, in projectile motion, on its descent.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"boundless-concept\">\n<h2>Free-Falling Objects<\/h2>\n<p>Free fall is the motion of a body where its weight is the only force acting on an object.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Solve basic problems concerning free fall and distinguish it from other kinds of motion<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Takeaways<\/h3>\n<h4>Key Points<\/h4>\n<ul>\n<li>The acceleration of free-falling objects is called the acceleration due to gravity, since objects are pulled towards the center of the earth.<\/li>\n<li>The acceleration due to gravity is constant on the surface of the Earth and has the value of 9.80 [latex]\\displaystyle \\frac{\\text{m}}{\\text{s}^2}[\/latex].<\/li>\n<\/ul>\n<h4>Key Terms<\/h4>\n<ul>\n<li><strong>acceleration<\/strong>: The amount by which a speed or velocity changes within a certain period of time (and so a scalar quantity or a vector quantity).<\/li>\n<\/ul>\n<\/div>\n<h3>Free Fall<\/h3>\n<p>The motion of falling objects is the simplest and most common example of motion with changing velocity. If a coin and a piece of paper are simultaneously dropped side by side, the paper takes much longer to hit the ground. However, if you crumple the paper into a compact ball and drop the items again, it will look like both the coin and the paper hit the floor simultaneously. This is because the amount of force acting on an object is a function of not only its mass, but also area. Free fall is the motion of a body where its weight is the only force acting on an object.<\/p>\n<div class=\"wp-caption alignright\" style=\"width: 158px;\" data-global-id=\"gid:\/\/boundless\/Image\/17491\">\n<div class=\"figure-cont\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2548\/2019\/01\/14025947\/free-fall.gif\" alt=\"image\" width=\"148\" height=\"330\" \/><\/p>\n<p class=\"wp-caption-text\"><strong>Free Fall<\/strong>: This clip shows an object in free fall.<\/p>\n<\/div>\n<\/div>\n<p>Galileo also observed this phenomena and realized that it disagreed with the Aristotle principle that heavier items fall more quickly. Galileo then hypothesized that there is an upward force exerted by air in addition to the downward force of gravity. If air resistance and friction are negligible, then in a given location (because gravity changes with location), all objects fall toward the center of Earth with the <em>same constant acceleration<\/em>, <em>independent of their mass<\/em>, that constant acceleration is gravity. Air resistance opposes the motion of an object through the air, while friction opposes motion between objects and the medium through which they are traveling. The acceleration of free-falling objects is referred to as the acceleration due to gravity [latex]\\text{g}[\/latex]. As we said earlier, gravity varies depending on location and altitude on Earth (or any other planet), but the average acceleration due to gravity on Earth is 9.8 [latex]\\displaystyle \\frac{\\text{m}}{\\text{s}^2}[\/latex]<sup>. <\/sup>This value is also often expressed as a negative acceleration in mathematical calculations due to the downward direction of gravity.<\/p>\n<h3>Equations<\/h3>\n<p>The best way to see the basic features of motion involving gravity is to start by considering straight up and down motion with no air resistance or friction. This means that if the object is dropped, we know the initial velocity is zero. Once the object is in motion, the object is in free-fall. Under these circumstances, the motion is one-dimensional and has constant acceleration, [latex]\\text{g}[\/latex]. The kinematic equations for objects experiencing free fall are:<\/p>\n<p>[latex]\\text{v}=\\text{v}_0-\\text{gt}\\\\\\text{y}=\\text{y}_0+\\text{v}_0\\text{t}-\\frac12\\text{gt}^2\\\\\\text{v}^2=\\text{v}_0^2-2\\text{g}(\\text{y}-\\text{y}_0),[\/latex]<\/p>\n<p>where [latex]\\text{v} = \\text{velocity}[\/latex], [latex]\\text{g}=\\text{gravity}[\/latex], [latex]\\text{t}=\\text{time}[\/latex], and [latex]\\text{y}=\\text{vertical displacement}[\/latex].<\/p>\n<div class=\"embed-wrap\" data-global-id=\"gid:\/\/boundless\/Embed\/21499\">\n<div class=\"figure-cont\">\n<div>http:\/\/www.youtube.com\/watch?v=C6-AxMc9mig&amp;stop=513<\/div>\n<p><strong>Free Fall Motion &#8211; YouTube<\/strong>: Describes how to calculate the time for an object to fall if given the height and the height that an object fell if given the time to fall.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Examples<\/h3>\n<p>Some examples of objects that are in free fall include:<\/p>\n<ul>\n<li>A spacecraft in continuous orbit. The free fall would end once the propulsion devices turned on.<\/li>\n<li>An stone dropped down an empty well.<\/li>\n<li>An object, in projectile motion, on its descent.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1262\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Curation and Revision. <strong>Provided by<\/strong>: Boundless.com. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Light and Matter. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/lightandmatter.com\/lmb.pdf\">http:\/\/lightandmatter.com\/lmb.pdf<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Free fall. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Free_fall\">http:\/\/en.wikipedia.org\/wiki\/Free_fall<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>acceleration. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/acceleration\">http:\/\/en.wiktionary.org\/wiki\/acceleration<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Free-fall. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/File:Free-fall.gif\">http:\/\/en.wikipedia.org\/wiki\/File:Free-fall.gif<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Free Fall Motion - YouTube. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.youtube.com\/watch?v=C6-AxMc9mig\">http:\/\/www.youtube.com\/watch?v=C6-AxMc9mig<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em>. <strong>License Terms<\/strong>: Standard YouTube license<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":18,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"\",\"author\":\"\",\"organization\":\"Light and Matter\",\"url\":\"http:\/\/lightandmatter.com\/lmb.pdf\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Free fall\",\"author\":\"\",\"organization\":\"Wikipedia\",\"url\":\"http:\/\/en.wikipedia.org\/wiki\/Free_fall\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"acceleration\",\"author\":\"\",\"organization\":\"Wiktionary\",\"url\":\"http:\/\/en.wiktionary.org\/wiki\/acceleration\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Free-fall\",\"author\":\"\",\"organization\":\"Wikipedia\",\"url\":\"http:\/\/en.wikipedia.org\/wiki\/File:Free-fall.gif\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Free Fall Motion - 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