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App\Entity\MediaTranslation {#1381 -id: 1405 -title: "Inclined plane theory" -description: """ <p>A simple machine functions without a motor and offers a mechanical advantage. An inclined plane is a flat surface that forms an angle with the horizontal plane. This is a simple machine since it modifies the intensity and the direction of the force needed to move an object.</p>\r\n \r\n <p>As the slope of the inclined plane decreases, so does the force needed to move the object. However, the distance to travel with the objet increases.</p> """ -legends: """ 1 m\n 2 m\n 3 m\n 4 m\n 5 m\n Work =\n Distance\n .\n Force\n Theory\n Mechanical\nAdvantage\n MA\n Effort\nForce\n Fe\n Resistance\nForce\n Fr\n Fw\n N\n 50 kg\n 100 kg """ -goals: """ <ul>\r\n \t<li>Understand the concepts of the inclined plane theory.</li>\r\n \t<li>Introduce the notion of mechanical energy (work)</li>\r\n \t<li>Know how to use the formula of energy W = F × D</li>\r\n </ul> """ -more: """ <p>To lift a load, one must apply a force upwards with the same intensity as the weight of the object.</p>\r\n \r\n <p>The weight of the object acts as the <strong>resistance force</strong>. The <strong>effort force</strong> here is the muscular force.</p>\r\n \r\n <p>Remember: The intensity of a force is expressed in <strong>Newton</strong> (N). A force of 9.81 N is needed to lift an object of 1 kg on Earth. This force is rounded to 10 N in this animation. Friction is negligible.</p>\r\n \r\n <p>How to move a heavy object 1 m vertically?</p>\r\n \r\n <p>When human strength isn't enough to lift an object, an apparatus must be introduced to minimize the resistance of that object.</p>\r\n \r\n <p>An inclined plane acts as such since it allows you to pull or push with a lower intensity force than that of the object's weight. Less force is needed with a smaller <strong>slope</strong>.</p>\r\n \r\n <p>When the ratio between the weight of the objet and the intensity of the effort force allowing the displacement is greater than 1, the inclined plane presents a <strong>mechanical advantage</strong> (or a <strong>gain</strong>).</p>\r\n \r\n <p>Theory:</p>\r\n \r\n <p>Consider the case of a 50 kg box being pushed on an inclined plane, 5 m long and 1 m high. F<sub>W</sub> = 500 N</p>\r\n \r\n <p>Due to the inclined plane, the effort force (<strong>F<sub>E</sub></strong> vector) is no longer vertical but parallel to the inclined plane.</p>\r\n \r\n <p>In this case, the weight (<strong>F</strong><sub><strong>W</strong></sub> vector) is divided into two components, one parallel and the other perpendicular to the inclined plane.</p>\r\n \r\n <p>The resistance force (<strong>F<sub>R</sub></strong> vector) is a component of the weight parallel to the plane in a downwards direction. Its intensity depends on the angle α<em> </em>of the slope:</p>\r\n \r\n <p>F<sub>R</sub> = F<sub>W</sub> × sin(α) = 500 × 1/5 = 100 N</p>\r\n \r\n <p>Hence, the intensity of the resistance force F<sub>R</sub> is 5 times smaller than that of the weight. In order to move the box, the effort force (<strong>F</strong><sub><strong>E</strong></sub> vector) must equally compensate the resistance force (<strong>F</strong><sub><strong>R</strong></sub> vector).</p>\r\n \r\n <p><strong>F</strong><sub><strong>E </strong></sub>= <strong>- F</strong><sub><strong>R</strong></sub></p>\r\n \r\n <p>The mechanical advantage of the inclined plane is expressed as follows:</p>\r\n \r\n <p>G = F<sub>E</sub>/F<sub>M</sub> = 1/sin(α) = 5</p>\r\n \r\n <p><strong>Work</strong> is the <strong>mechanical energy</strong> dispensed for a displacement. It's expressed in <strong>Joule</strong> (J). By definition, the work of a force intensity F<sub>E</sub> applied over a distance D in the direction of the displacement is given by the formula:</p>\r\n \r\n <p>Work = F<sub>E</sub> × D</p>\r\n \r\n <p>The work needed to push a 50 kg box along the 5 m of the inclined plane to a height of 1 m is:</p>\r\n \r\n <p>Work = 100 × 5 = 500 J</p>\r\n \r\n <p>The work needed to lift a 50 kg box vertically to a height of 1 m is:</p>\r\n \r\n <p>Work = 500 × 1 = 500 J</p>\r\n \r\n <p>These results correspond with the <strong>energy conservation principle</strong>. An inclined plane doesn't change the amount of energy required, but simply lowers the intensity of the force required. However, this lower intensity force is applied over a longer distance. </p>\r\n \r\n <p>Simple machines derived from inclined planes:</p>\r\n \r\n <ul>\r\n \t<li>A <strong>wedge</strong> is made of two inclined planes, one on either side, and is used to separate objects in half (an axe, a blade of a knife, the bow of a boat).</li>\r\n \t<li>A <strong>screw</strong> is an inclined plane wrapped around a cylinder; it exerts a pressure on an object to stabilize them (a screw, container lid). The closer the threads (a long inclined plane) of the screw are, the easier it is to drive the screw.</li>\r\n </ul> """ -scenario: null -features: "<p><strong>Select</strong> the variables of the experiment (force, load, plane inclination) using the buttons.</p>" -publishedAt: DateTimeImmutable @1431388800 {#1377 : 2015-05-12 00:00:00.0 UTC (+00:00) } -preventIndexForSearch: false #locale: "en" #translatable: App\Entity\Media {#1308 …} #status: "published" #createdAt: DateTime @1421622000 {#1379 : 2015-01-18 23:00:00.0 UTC (+00:00) } #updatedAt: DateTime @1699086598 {#1380 : 2023-11-04 08:29:58.0 UTC (+00:00) } } |
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