{"id":107,"date":"2017-09-04T04:30:04","date_gmt":"2017-09-04T04:30:04","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/general-science\/?page_id=107"},"modified":"2017-09-19T16:28:55","modified_gmt":"2017-09-19T16:28:55","slug":"work-energy-power-and-momentum","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/general-science\/work-energy-power-and-momentum\/","title":{"rendered":"Work, Energy, Power, and Momentum"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\"><a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/general-science\/physics\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/general-science\/mechanics-of-fluids\">Next Lesson \u27a1<\/a><\/div>\n<p><!-- CONTENT BEGINS HERE --><\/p>\n<h1 id=\"title\">Work, Energy, Power, and Momentum<\/h1>\n<h4>Objective<\/h4>\n<p>The lesson will cover the basics of energy, work, power, and momentum.<\/p>\n<section>\n<h3>Energy<\/h3>\n<p>Energy is everywhere around us. It is a fundamental quantity that all physical systems contain in one form or another. The concept of energy is not difficult to understand. Energy is a quantity that can be moved or transferred from one place or from one form to another, and like mass, it cannot be created or destroyed. The simplest way to define energy is that energy is the ability to do work. All energy and work can be interconverted between actual work done, potential energy, and kinetic energy. Energy is also defined as the amount of work required to change the state of a physical system (e.g., from liquid to gas) Potential energy is sometimes called &#8220;stored energy.&#8221;<\/p>\n<p>Here are some of the ways that energy is stored:<\/p>\n<ul>\n<li>Chemical energy &#8211; Energy that is stored in chemical bonds. For example, remember the breakfast that you ate this morning? The calories contained in the chemical bonds are now available to your muscles as chemical potential energy.<\/li>\n<li>Gravitational energy &#8211; Energy that is stored in the gravitational field between two masses. This is sometimes also called potential energy.<\/li>\n<li>Elastic energy &#8211; Energy that is stored in objects that stretch or bend, like your skin, trees, rubber bands, strings, and diving boards.<\/li>\n<li>Kinetic energy is sometimes viewed as energy of motion, or expressed energy.<\/li>\n<li>A moving object has kinetic energy due to its motion.<\/li>\n<li>A falling object possesses both potential and kinetic energy.<\/li>\n<li>A hot stove possesses both potential and kinetic energy.<\/li>\n<\/ul>\n<p>How do we change energy between its various forms? Sometime this occurs naturally, as when an object falls toward the earth. \u201cworking.\u201d <abbr title=\"The product of the force applied to an object multiplied by the distance the object moved under the influence of the force. Also known as the amount energy that is transferred from one storage mode into another.\">Work<\/abbr> is done when energy is transferred from one place to another. More specifically, the amount of work done equals the amount of transferred energy. Here are a few examples of when work is done:<\/p>\n<ul>\n<li>Chemical energy stored in a battery transfers to radiant energy from a light bulb.<\/li>\n<li>Gravitational potential energy of elevated water transfers into kinetic energy as the water cascades over a water wheel.<\/li>\n<li>Chemical energy stored in the muscles of a mountain climber transfers into lifting energy as she climbs up a mountain.<\/li>\n<li>Random kinetic energy of individual water molecules in steam transfers into kinetic energy in a turbine.<\/li>\n<\/ul>\n<p>In a parallel fashion, energy can be transferred from one form of storage into another. Using the examples from above, the electromotive force in a battery enables the energy to transfer from chemical energy to radiant and heat energies in the circuit. Similarly, the gravitational force enables energy to transfer from potential energy into kinetic and heat energies through the turning of a water wheel.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>How would you explain the operation of a car in terms of energy and work? Think about all the ways that energy is converted, used, and stored during the car\u2019s operation. Also consider how forces enable the energy to transfer from one mode into another. Click on the following link to check your explanation:<\/p>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">Chemical energy is stored as chemical bonds in the gasoline. When gasoline combusts, the liquid is changed to a gas through combustion, and the gas expands to do work on the pistons. The pistons transfer the energy into kinetic energy that turns the drive shaft and the tires. The frictional force between the tires and the road transfers that kinetic energy to the kinetic energy of the car. Hence, the car moves.<\/p>\n<\/section>\n<p>How do we calculate work? When objects are moved, work is done when the applied force is in the same direction that the object will be moved. Motion in any other direction than the proposed direction of motion does not count toward the work being done. For example, when an object is lifted vertically, work (W) is calculated by taking the product of the force applied (F) and height that it is lifted (h). In this case the height the object is lifted against gravity becomes the distance, and the work is called &#8220;gravitational work.&#8221; Thus the normal work equation Work = force(f) x distance(d) becomes:<\/p>\n<p class=\"center formula\">W = F h<\/p>\n<p>The force that we\u2019re lifting against is, of course, the gravitational force. This force is calculated by taking the product of an object\u2019s mass (m) times the strength of the gravitational field (g = 9.8 N\/kg on the surface of the earth). So, our equation becomes:<\/p>\n<p class=\"center formula\">Work = m g h<\/p>\n<p>For example, how much work would it take to lift a 40 kg barbell to a height of 2 meters from the ground?<\/p>\n<p class=\"center formula\">W = m g h = 40 kg \u00b7 (9.8 N\/kg) \u00b7 2 m = 784 J<\/p>\n<p class=\"center\">Note: m x g is the weight of an object<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Practice Question: How much work would it take to carry the same barbell 5 meters across the room?<\/p>\n<ol>\n<li>784 J<\/li>\n<li>3784 J<\/li>\n<li>0 J<\/li>\n<li>5 J<\/li>\n<\/ol>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">The correct answer is C. No work is done because the applied force (gravity in this case) is not in the direction of the motion. The calculation looks like this: W = mgh = 40 kg \u00b7 (9.8 N\/kg) \u00b7 0 m = 0 J<\/p>\n<\/section>\n<h3>Working Simply<\/h3>\n<p>Sometimes we don\u2019t have the physical strength or mechanical power to apply enough force to get a job done. <abbr title=\"any device that requires the single application of a force to work. Archimedes' screw, an inclined plane, a lever, a pulley, and a wedge are all simple machines used everyday and can convert a small force to a greater force (or vice versa) by changing the distance the force is exerted. The ratio of output force to the input force is the mechanical advantage.\">Simple machines<\/abbr> are devices that make work easy. They can help us by changing the direction of the applied force, reducing the magnitude of the input force, or helping to add speed to the rate at which work is done. This sounds almost magical, like we\u2019re getting something from nothing. But, alas, the law of energy conservation still governs the universe. Reduced forces applied through simple machines are a consequence of increasing distances. For example, the equation<\/p>\n<p class=\"center\">Work in = Work out<\/p>\n<p class=\"formula\">(F d) in = (F d ) out<\/p>\n<p>Where F = force, and d = distance, the formula shows how an ideal machine transfers no energy to heat by frictional forces, since \u201cwork in\u201d equals \u201cwork out.\u201d<\/p>\n<p>A classic example, the lever, can significantly reduce the input forces and yield large output forces. The handle is easily moved over a large distance and an object is pried through a small distance as shown in the following figure:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/Mod5Fig01s.jpg\" alt=\"A simple fulcrum\" \/><\/center>The work equation can be written as follows in this case:<\/p>\n<p class=\"formula\">(F d) in = (F d ) out<\/p>\n<p>The mechanical advantage (MA) of a simple machine is the ratio between the output force (F out) to the input force (F in):<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0001M.gif\" alt=\"Mechanical Advantage formula\" \/><\/center>For example, we can calculate the mechanical advantage for a worker using a hammer to pry out a nail. A 20 N force is applied to the handle that results in an 80 N force that pulls up on the nail. The mechanical advantage (MA) is calculated as follows:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/image06.gif\" alt=\"MA\" \/><\/center>The inclined plane is another example of a simple machine. Instead of lifting directly up against the gravitational force, the inclined plane enables the user to push with a smaller force a greater distance diagonally up the ramp. For example, a 130N box is pushed up the incline shown in the picture below.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/Mod5Fig02s.jpg\" alt=\"Incline\" \/><\/center>We can calculate the force needed to push it up the ramp as follows:<\/p>\n<p class=\"formula\">(F d) in = (F d ) out<\/p>\n<p class=\"formula\">F \u00b713m = 130N \u00b7 5m<\/p>\n<p class=\"formula\">F = 50 N<\/p>\n<section class=\"question\">Calculate the mechanical advantage for this inclined plane.<a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\"><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0003MP.gif\" alt=\"\" \/><\/p>\n<\/section>\n<p>Pulleys, wedges, ramps, and screws are some other examples of simple machines that offer a mechanical advantage. It is a good exercise to think about how these simple machines save us work in our everyday lives.<\/p>\n<h3>Working Powerfully<\/h3>\n<p>What is the relationship between energy, work, and power? <abbr title=\"the rate at which energy is transferred.\">Power (P)<\/abbr> is the rate at which work is done. For example, 100-Watt light bulb uses twice as much energy in a second as a 50-Watt light bulb. The following equation can be used to calculate power:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0004M.gif\" alt=\"Power formula\" \/><\/center>Where <em>E transferred<\/em> is the energy that is transferred in the process of doing work and <strong>P<\/strong> is the total power of the system.<\/p>\n<p>To calculate the power output of a 150N child that climbs 5 meters up a rope in 10 seconds, the following calculation is made:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0005M.gif\" alt=\"Example power\" \/><\/center><\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>Who is more powerful: a man who lifts a 200-N barbell 2 meters vertically in 2 seconds, or a boy who lifts a 100-N barbell 1 meter in 0.5 seconds?<\/p>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\">They both have the SAME power:<br \/>\n<img decoding=\"async\" class=\"center\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0006M.gif\" alt=\"Question power\" \/><br \/>\n<img decoding=\"async\" class=\"center\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0007M.gif\" alt=\"Question power 2\" \/><\/p>\n<\/section>\n<h3>Conserving Momentum<\/h3>\n<p>Like energy and mass, the momentum of a system is also conserved. <abbr title=\"the product of an object's mass and velocity.\">Momentum (p)<\/abbr> is a product of an object\u2019s mass (m) and its velocity (v):<\/p>\n<p class=\"formula\">p = m v<\/p>\n<p>In other words, momentum is a product of a mass in motion. Momentum also has direction associated with it and is considered a vector. For example, we can calculate the momentum of a 2000 kg car heading north at a speed of 20 m\/s.<\/p>\n<p class=\"formula\">p = m v = 2000kg \u00b7 20 m\/s = 40,000 kg m\/s north<\/p>\n<p>But what about momentum being conserved? This concept is a consequence of Newton\u2019s second law and can be written as:<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0008M.gif\" alt=\"Net force\" \/><\/center>The equation now becomes:<\/p>\n<p class=\"formula\">F<sub>net<\/sub> = m\u0394v \/ \u0394t = \u0394p<\/p>\n<p class=\"formula\">or F<sub>net<\/sub>(\u0394t)= m(\u0394v) = \u0394p<\/p>\n<p>F<sub>net<\/sub> is the net force of the system, \u0394v is the change in velocity, \u0394t is the change in time, and \u0394p is the change in momentum. The term F<sub>net<\/sub> (\u0394t) is called impulse, and is exactly the same quantity as m(\u0394v) . It gives us another way to view momentum.<\/p>\n<p>If there is no net force applied to a system, then this implies that \u0394p is zero. In other words, with no unbalanced force on a system there is no momentum change.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0009M.gif\" alt=\"\" \/><\/center>where p<sub>i<\/sub> is the initial momentum of the system and p<span style=\"font-size: 13.3333px;\">f<\/span>\u00a0is the final momentum of the system.<\/p>\n<p>For example, consider a billiard ball moving at 2 m\/s that squarely strikes an identical billiard ball that\u2019s at rest. The moving ball stops and the momentum is completely transferred to the other ball, which picks up a speed of 2 m\/s. Momentum is NOT conserved for the first billiard ball alone because it experiences a net force. Momentum IS conserved for the SYSTEM of both balls because the collision forces are internal to the system.<\/p>\n<p>What if two objects of different masses collide? For example, what if a 2000-kg boxcar moving at 30 m\/s hits and links with a 1000-kg boxcar that\u2019s initially at rest? How fast does the combination move after the collision? To answer this, we must note that the amount of moving mass increases after the collision. This means that the speed of the system must decrease so that the momentum is conserved.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0010M.gif\" alt=\"\" \/><\/center>Another example of momentum conservation is in the operation of rockets. As a rocket ejects combusted gases rearward at high velocities, the more massive rocket is propelled forwards at a lesser velocity. In other words, the backward momentum of the exhaust gases equals the forward momentum of the rocket.<\/p>\n<section class=\"question\">Try this one on your own. A 20-kg child holding a 2-kg brick is standing still on the slick surface of an ice skating rink. She throws the brick forward at a speed of 5 m\/s. Completely describe her resulting motion and calculate her speed.<a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\"><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/Images\/gensci\/img\/eq0011MP.gif\" alt=\"answer\" \/><\/p>\n<\/section>\n<\/section>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<div class=\"advance\"><a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/general-science\/physics\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/general-science\/mechanics-of-fluids\">Next Lesson \u27a1<\/a><\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Workshop Index\u00a0Next Lesson \u27a1 Work, Energy, Power, and Momentum Objective The lesson will cover the basics of energy, work, power, and momentum. Energy Energy is everywhere around us. It is a fundamental quantity that all physical systems contain in one form or another. The concept of energy is not difficult to understand. Energy is a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-107","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/general-science\/wp-json\/wp\/v2\/pages\/107","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/general-science\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/general-science\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/general-science\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/general-science\/wp-json\/wp\/v2\/comments?post=107"}],"version-history":[{"count":12,"href":"https:\/\/americanboard.org\/Subjects\/general-science\/wp-json\/wp\/v2\/pages\/107\/revisions"}],"predecessor-version":[{"id":625,"href":"https:\/\/americanboard.org\/Subjects\/general-science\/wp-json\/wp\/v2\/pages\/107\/revisions\/625"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/general-science\/wp-json\/wp\/v2\/media?parent=107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}