{"id":418,"date":"2020-04-19T15:59:21","date_gmt":"2020-04-19T19:59:21","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/chapter\/7-6-conservation-of-energy-2\/"},"modified":"2020-09-03T14:18:36","modified_gmt":"2020-09-03T18:18:36","slug":"7-6-conservation-of-energy-2","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/chapter\/7-6-conservation-of-energy-2\/","title":{"raw":"7.6 Conservation of Energy","rendered":"7.6 Conservation of Energy"},"content":{"raw":"\n<div>\n<div class=\"bcc-box bcc-highlight\">\n<h3>Summary<\/h3>\n<div>\n<ul>\n \t<li>Explain the law of the conservation of energy.<\/li>\n \t<li>Describe some of the many forms of energy.<\/li>\n \t<li>Define efficiency of an energy conversion process as the fraction left as useful energy or work, rather than being transformed, for example, into thermal energy.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<section id=\"fs-id2568702\">\n<h1>Law of Conservation of Energy<\/h1>\n<p id=\"import-auto-id2610565\">Energy, as we have noted, is conserved, making it one of the most important physical quantities in nature. The <strong><span id=\"import-auto-id2096012\">law of conservation of energy<\/span><\/strong> can be stated as follows:<\/p>\n<p id=\"import-auto-id2689220\"><em>Total energy is constant in any process. It may change in form or be transferred from one system to another, but the total remains the same.<\/em><\/p>\n<p id=\"import-auto-id1957364\">We have explored some forms of energy and some ways it can be transferred from one system to another. This exploration led to the definition of two major types of energy\u2014mechanical energy <strong>(KE + PE)<\/strong> and energy transferred via work done by nonconservative forces <strong>(<em>W<\/em><sub>nc<\/sub>)<\/strong>. But energy takes <em>many<\/em> other forms, manifesting itself in <em>many<\/em> different ways, and we need to be able to deal with all of these before we can write an equation for the above general statement of the conservation of energy.<\/p>\n\n<\/section><section id=\"fs-id2206024\">\n<h1>Other Forms of Energy than Mechanical Energy<\/h1>\n<p id=\"import-auto-id1698850\">At this point, we deal with all other forms of energy by lumping them into a single group called <strong>other energy (OE)<\/strong>. Then we can state the conservation of energy in equation form as<\/p>\n\n<div style=\"text-align: center\" class=\"equation\" id=\"fs-id2198866\">[latex]\\boldsymbol{\\textbf{KE}_{\\textbf{i}}+\\textbf{PE}_{\\textbf{i}}+W_{\\textbf{nc}}+\\textbf{OE}_{\\textbf{i}}=\\textbf{KE}_{\\textbf{f}}+\\textbf{PE}_{\\textbf{f}}+\\textbf{OE}_{\\textbf{f}}}.[\/latex]<\/div>\n<p id=\"import-auto-id1466947\">All types of energy and work can be included in this very general statement of conservation of energy. Kinetic energy is <strong>KE<\/strong>, work done by a conservative force is represented by <strong>PE<\/strong>, work done by nonconservative forces is <strong><em>W<\/em><sub>nc<\/sub><\/strong>, and all other energies are included as <strong>OE<\/strong>. This equation applies to all previous examples; in those situations <strong>OE<\/strong> was constant, and so it subtracted out and was not directly considered.<\/p>\n\n<div class=\"note\" id=\"fs-id2580294\">\n<div class=\"textbox shaded\">\n<div class=\"note\">\n<h3 class=\"title\">MAKING CONNECTIONS: USEFULNESS OF THE ENERGY CONSERVATION PRINCIPLE<span style=\"text-decoration: underline\">\n<\/span><\/h3>\n<div class=\"title\"><\/div>\n<p id=\"import-auto-id1158363\">The fact that energy is conserved and has many forms makes it very important. You will find that energy is discussed in many contexts, because it is involved in all processes. It will also become apparent that many situations are best understood in terms of energy and that problems are often most easily conceptualized and solved by considering energy.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<p id=\"import-auto-id2198022\">When does <strong>OE<\/strong> play a role? One example occurs when a person eats. Food is oxidized with the release of carbon dioxide, water, and energy. Some of this chemical energy is converted to kinetic energy when the person moves, to potential energy when the person changes altitude, and to thermal energy (another form of <strong>OE<\/strong>).<\/p>\n\n<\/section><section id=\"fs-id2166527\">\n<h1>Some of the Many Forms of Energy<\/h1>\n<p id=\"import-auto-id1895848\">What are some other forms of energy? You can probably name a number of forms of energy not yet discussed. Many of these will be covered in later chapters, but let us detail a few here. <strong><span id=\"import-auto-id2771762\">Electrical energy<\/span><\/strong> is a common form that is converted to many other forms and does work in a wide range of practical situations. Fuels, such as gasoline and food, carry <strong><span id=\"import-auto-id2094176\">chemical energy<\/span><\/strong> that can be transferred to a system through oxidation. Chemical fuel can also produce electrical energy, such as in batteries. Batteries can in turn produce light, which is a very pure form of energy. Most energy sources on Earth are in fact stored energy from the energy we receive from the Sun. We sometimes refer to this as <strong><span id=\"import-auto-id2739439\">radiant energy<\/span><\/strong>, or electromagnetic radiation, which includes visible light, infrared, and ultraviolet radiation. <strong><span id=\"import-auto-id2580734\">Nuclear energy<\/span><\/strong> comes from processes that convert measurable amounts of mass into energy. Nuclear energy is transformed into the energy of sunlight, into electrical energy in power plants, and into the energy of the heat transfer and blast in weapons. Atoms and molecules inside all objects are in random motion. This internal mechanical energy from the random motions is called <strong><span id=\"import-auto-id2393416\">thermal energy<\/span><\/strong>, because it is related to the temperature of the object. These and all other forms of energy can be converted into one another and can do work.<\/p>\n<p id=\"import-auto-id2568214\"><a href=\"#import-auto-id2866785\" class=\"autogenerated-content\">Table 1<\/a> gives the amount of energy stored, used, or released from various objects and in various phenomena. The range of energies and the variety of types and situations is impressive.<\/p>\n\n<\/section><section id=\"fs-id1309904\">\n<h1>Efficiency<\/h1>\n<p id=\"import-auto-id2061613\">Even though energy is conserved in an energy conversion process, the output of <em>useful energy<\/em> or work will be less than the energy input. The <strong><span id=\"import-auto-id2408157\">efficiency <\/span><em>Eff <\/em><\/strong>of an energy conversion process is defined as<\/p>\n\n<div style=\"text-align: center\" class=\"equation\" id=\"fs-id2849499\">[latex]\\boldsymbol{\\textbf{Efficiency}(Eff)\\:=}\\boldsymbol{\\frac{\\textbf{useful energy or work output}}{\\textbf{total energy input}}}\\boldsymbol{=}\\boldsymbol{\\frac{W_{\\textbf{out}}}{E_{\\textbf{in}}}}.[\/latex]<\/div>\n<p id=\"import-auto-id1615246\"><a href=\"#import-auto-id1330125\" class=\"autogenerated-content\">Table 2<\/a> lists some efficiencies of mechanical devices and human activities.<\/p>\n\n<table id=\"import-auto-id1330125\" summary=\"A table titled efficiency of the human body and mechanical devices, containing two columns. One column lists a human activity or a mechanical device and the corresponding cell in the next column lists the efficiency in percentage associated with the respective human activity or mechanical device.\">\n<thead>\n<tr>\n<th>Activity\/device<\/th>\n<th>Efficiency (%)<a name=\"footnote-ref1\" href=\"#footnote1\"><sup>1<\/sup><\/a><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Cycling and climbing<\/td>\n<td>20<\/td>\n<\/tr>\n<tr>\n<td>Swimming, surface<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>Swimming, submerged<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>Shoveling<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>Weightlifting<\/td>\n<td>9<\/td>\n<\/tr>\n<tr>\n<td>Steam engine<\/td>\n<td>17<\/td>\n<\/tr>\n<tr>\n<td>Gasoline engine<\/td>\n<td>30<\/td>\n<\/tr>\n<tr>\n<td>Diesel engine<\/td>\n<td>35<\/td>\n<\/tr>\n<tr>\n<td>Nuclear power plant<\/td>\n<td>35<\/td>\n<\/tr>\n<tr>\n<td>Coal power plant<\/td>\n<td>42<\/td>\n<\/tr>\n<tr>\n<td>Electric motor<\/td>\n<td>98<\/td>\n<\/tr>\n<tr>\n<td>Compact fluorescent light<\/td>\n<td>20<\/td>\n<\/tr>\n<tr>\n<td>Gas heater (residential)<\/td>\n<td>90<\/td>\n<\/tr>\n<tr>\n<td>Solar cell<\/td>\n<td>10<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td colspan=\"2\"><strong>Table 2.<\/strong> Efficiency of the Human Body and Mechanical Devices.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"note\" id=\"fs-id1398490\">\n<figure>\n<p style=\"text-align: left\"><\/p>\n<\/figure>\n<\/div>\n<\/section><section id=\"fs-id1911538\" class=\"section-summary\">\n<h1>Section Summary<\/h1>\n<ul id=\"fs-id1897388\">\n \t<li id=\"import-auto-id1537867\">The law of conservation of energy states that the total energy is constant in any process. Energy may change in form or be transferred from one system to another, but the total remains the same.<\/li>\n \t<li id=\"import-auto-id1839690\">When all forms of energy are considered, conservation of energy is written in equation form as <strong>KE<sub>i<\/sub> + PE<sub>i<\/sub> + <em>W<\/em>nc + OE<sub>i<\/sub> = KE<sub>f<\/sub> + PE<sub>f<\/sub> + OE<sub>f<\/sub><\/strong>, where <strong>OE<\/strong> is all <strong>other forms of energy<\/strong> besides mechanical energy.<\/li>\n \t<li id=\"import-auto-id1317294\">Commonly encountered forms of energy include electric energy, chemical energy, radiant energy, nuclear energy, and thermal energy.<\/li>\n \t<li id=\"import-auto-id1787512\">Energy is often utilized to do work, but it is not possible to convert all the energy of a system to work.<\/li>\n \t<li id=\"import-auto-id1628394\">The efficiency <em><strong>Eff<\/strong><\/em> of a machine or human is defined to be [latex]\\boldsymbol{Eff=\\frac{W_{\\textbf{out}}}{E_{\\textbf{in}}}},[\/latex] where <strong><em>W<\/em><sub>out<\/sub><\/strong> is useful work output and <strong><em>E<\/em><sub>in<\/sub><\/strong> is the energy consumed.<\/li>\n<\/ul>\n<\/section><section id=\"fs-id1758921\" class=\"conceptual-questions\">\n<h1><\/h1>\n<div class=\"bcc-box bcc-info\">\n<h3>Conceptual Questions<\/h3>\n<div class=\"exercise\" id=\"fs-id1471362\">\n<div class=\"problem\" id=\"fs-id1698457\">\n<p id=\"import-auto-id1848389\"><strong>1: <\/strong>Describe the energy transfers and transformations for a javelin, starting from the point at which an athlete picks up the javelin and ending when the javelin is stuck into the ground after being thrown.<\/p>\n\n<\/div>\n<\/div>\n<div class=\"exercise\" id=\"fs-id1528780\">\n<div class=\"problem\" id=\"fs-id2045976\">\n<p id=\"import-auto-id1502617\"><strong>2: <\/strong>List the energy conversions that occur when riding a bicycle.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/section><section id=\"fs-id1703148\" class=\"problems-exercises\">\n<div class=\"bcc-box bcc-info\">\n<h3>Problems &amp; Exercises<\/h3>\n<div class=\"exercise\" id=\"eip-309\">\n<div class=\"problem\">\n\n<strong>1: <\/strong>Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m\/s strikes the water with a speed of 24.8 m\/s independent of the direction thrown.\n\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<div>\n<h2>Footnotes<\/h2>\n<ol>\n \t<li><a name=\"footnote1\" href=\"#footnote-ref1\">1<\/a> Representative values<\/li>\n<\/ol>\n<\/div>\n<div>\n<h2>Glossary<\/h2>\n<dl id=\"import-auto-id2748477\" class=\"definition\">\n \t<dt id=\"import-auto-id2866094\">law of conservation of energy<\/dt>\n \t<dd id=\"fs-id1455501\">the general law that total energy is constant in any process; energy may change in form or be transferred from one system to another, but the total remains the same<\/dd>\n<\/dl>\n<dl id=\"import-auto-id2101389\" class=\"definition\">\n \t<dt id=\"import-auto-id2187394\">electrical energy<\/dt>\n \t<dd id=\"fs-id1593493\">the energy carried by a flow of charge<\/dd>\n<\/dl>\n<dl id=\"import-auto-id2688755\" class=\"definition\">\n \t<dt id=\"import-auto-id684982\">chemical energy<\/dt>\n \t<dd id=\"fs-id2012484\">the energy in a substance stored in the bonds between atoms and molecules that can be released in a chemical reaction<\/dd>\n<\/dl>\n<dl id=\"import-auto-id2584269\" class=\"definition\">\n \t<dt id=\"import-auto-id1856658\">radiant energy<\/dt>\n \t<dd id=\"fs-id1964070\">the energy carried by electromagnetic waves<\/dd>\n<\/dl>\n<dl id=\"import-auto-id1582487\" class=\"definition\">\n \t<dt id=\"import-auto-id1389125\">nuclear energy<\/dt>\n \t<dd id=\"fs-id1745402\">energy released by changes within atomic nuclei, such as the fusion of two light nuclei or the fission of a heavy nucleus<\/dd>\n<\/dl>\n<dl id=\"import-auto-id2009020\" class=\"definition\">\n \t<dt id=\"import-auto-id2582378\">thermal energy<\/dt>\n \t<dd id=\"fs-id2187325\">the energy within an object due to the random motion of its atoms and molecules that accounts for the object's temperature<\/dd>\n<\/dl>\n<dl id=\"fs-id1636613\" class=\"definition\">\n \t<dt id=\"import-auto-id1290297\">efficiency<\/dt>\n \t<dd id=\"fs-id1116189\">a measure of the effectiveness of the input of energy to do work; useful energy or work divided by the total input of energy<\/dd>\n<\/dl>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Solutions<\/h3>\n<strong>Problems &amp; Exercises<\/strong>\n\n<strong>2: <\/strong>Equating[latex]\\boldsymbol{\\Delta\\textbf{PE}_{\\textbf{g}}}[\/latex]and[latex]\\boldsymbol{\\Delta\\textbf{KE}},[\/latex]we obtain[latex]\\boldsymbol{v=\\sqrt{2gh+v_0^2}=\\sqrt{2(9.80\\textbf{ m\/s}^2)(20.0\\textbf{ m})+(15.0\\textbf{ m\/s})^2}=24.8\\textbf{ m\/s}}[\/latex]\n\n<\/div>\n","rendered":"<div>\n<div class=\"bcc-box bcc-highlight\">\n<h3>Summary<\/h3>\n<div>\n<ul>\n<li>Explain the law of the conservation of energy.<\/li>\n<li>Describe some of the many forms of energy.<\/li>\n<li>Define efficiency of an energy conversion process as the fraction left as useful energy or work, rather than being transformed, for example, into thermal energy.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<section id=\"fs-id2568702\">\n<h1>Law of Conservation of Energy<\/h1>\n<p id=\"import-auto-id2610565\">Energy, as we have noted, is conserved, making it one of the most important physical quantities in nature. The <strong><span id=\"import-auto-id2096012\">law of conservation of energy<\/span><\/strong> can be stated as follows:<\/p>\n<p id=\"import-auto-id2689220\"><em>Total energy is constant in any process. It may change in form or be transferred from one system to another, but the total remains the same.<\/em><\/p>\n<p id=\"import-auto-id1957364\">We have explored some forms of energy and some ways it can be transferred from one system to another. This exploration led to the definition of two major types of energy\u2014mechanical energy <strong>(KE + PE)<\/strong> and energy transferred via work done by nonconservative forces <strong>(<em>W<\/em><sub>nc<\/sub>)<\/strong>. But energy takes <em>many<\/em> other forms, manifesting itself in <em>many<\/em> different ways, and we need to be able to deal with all of these before we can write an equation for the above general statement of the conservation of energy.<\/p>\n<\/section>\n<section id=\"fs-id2206024\">\n<h1>Other Forms of Energy than Mechanical Energy<\/h1>\n<p id=\"import-auto-id1698850\">At this point, we deal with all other forms of energy by lumping them into a single group called <strong>other energy (OE)<\/strong>. Then we can state the conservation of energy in equation form as<\/p>\n<div style=\"text-align: center\" class=\"equation\" id=\"fs-id2198866\">[latex]\\boldsymbol{\\textbf{KE}_{\\textbf{i}}+\\textbf{PE}_{\\textbf{i}}+W_{\\textbf{nc}}+\\textbf{OE}_{\\textbf{i}}=\\textbf{KE}_{\\textbf{f}}+\\textbf{PE}_{\\textbf{f}}+\\textbf{OE}_{\\textbf{f}}}.[\/latex]<\/div>\n<p id=\"import-auto-id1466947\">All types of energy and work can be included in this very general statement of conservation of energy. Kinetic energy is <strong>KE<\/strong>, work done by a conservative force is represented by <strong>PE<\/strong>, work done by nonconservative forces is <strong><em>W<\/em><sub>nc<\/sub><\/strong>, and all other energies are included as <strong>OE<\/strong>. This equation applies to all previous examples; in those situations <strong>OE<\/strong> was constant, and so it subtracted out and was not directly considered.<\/p>\n<div class=\"note\" id=\"fs-id2580294\">\n<div class=\"textbox shaded\">\n<div class=\"note\">\n<h3 class=\"title\">MAKING CONNECTIONS: USEFULNESS OF THE ENERGY CONSERVATION PRINCIPLE<span style=\"text-decoration: underline\"><br \/>\n<\/span><\/h3>\n<div class=\"title\"><\/div>\n<p id=\"import-auto-id1158363\">The fact that energy is conserved and has many forms makes it very important. You will find that energy is discussed in many contexts, because it is involved in all processes. It will also become apparent that many situations are best understood in terms of energy and that problems are often most easily conceptualized and solved by considering energy.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"import-auto-id2198022\">When does <strong>OE<\/strong> play a role? One example occurs when a person eats. Food is oxidized with the release of carbon dioxide, water, and energy. Some of this chemical energy is converted to kinetic energy when the person moves, to potential energy when the person changes altitude, and to thermal energy (another form of <strong>OE<\/strong>).<\/p>\n<\/section>\n<section id=\"fs-id2166527\">\n<h1>Some of the Many Forms of Energy<\/h1>\n<p id=\"import-auto-id1895848\">What are some other forms of energy? You can probably name a number of forms of energy not yet discussed. Many of these will be covered in later chapters, but let us detail a few here. <strong><span id=\"import-auto-id2771762\">Electrical energy<\/span><\/strong> is a common form that is converted to many other forms and does work in a wide range of practical situations. Fuels, such as gasoline and food, carry <strong><span id=\"import-auto-id2094176\">chemical energy<\/span><\/strong> that can be transferred to a system through oxidation. Chemical fuel can also produce electrical energy, such as in batteries. Batteries can in turn produce light, which is a very pure form of energy. Most energy sources on Earth are in fact stored energy from the energy we receive from the Sun. We sometimes refer to this as <strong><span id=\"import-auto-id2739439\">radiant energy<\/span><\/strong>, or electromagnetic radiation, which includes visible light, infrared, and ultraviolet radiation. <strong><span id=\"import-auto-id2580734\">Nuclear energy<\/span><\/strong> comes from processes that convert measurable amounts of mass into energy. Nuclear energy is transformed into the energy of sunlight, into electrical energy in power plants, and into the energy of the heat transfer and blast in weapons. Atoms and molecules inside all objects are in random motion. This internal mechanical energy from the random motions is called <strong><span id=\"import-auto-id2393416\">thermal energy<\/span><\/strong>, because it is related to the temperature of the object. These and all other forms of energy can be converted into one another and can do work.<\/p>\n<p id=\"import-auto-id2568214\"><a href=\"#import-auto-id2866785\" class=\"autogenerated-content\">Table 1<\/a> gives the amount of energy stored, used, or released from various objects and in various phenomena. The range of energies and the variety of types and situations is impressive.<\/p>\n<\/section>\n<section id=\"fs-id1309904\">\n<h1>Efficiency<\/h1>\n<p id=\"import-auto-id2061613\">Even though energy is conserved in an energy conversion process, the output of <em>useful energy<\/em> or work will be less than the energy input. The <strong><span id=\"import-auto-id2408157\">efficiency <\/span><em>Eff <\/em><\/strong>of an energy conversion process is defined as<\/p>\n<div style=\"text-align: center\" class=\"equation\" id=\"fs-id2849499\">[latex]\\boldsymbol{\\textbf{Efficiency}(Eff)\\:=}\\boldsymbol{\\frac{\\textbf{useful energy or work output}}{\\textbf{total energy input}}}\\boldsymbol{=}\\boldsymbol{\\frac{W_{\\textbf{out}}}{E_{\\textbf{in}}}}.[\/latex]<\/div>\n<p id=\"import-auto-id1615246\"><a href=\"#import-auto-id1330125\" class=\"autogenerated-content\">Table 2<\/a> lists some efficiencies of mechanical devices and human activities.<\/p>\n<table id=\"import-auto-id1330125\" summary=\"A table titled efficiency of the human body and mechanical devices, containing two columns. One column lists a human activity or a mechanical device and the corresponding cell in the next column lists the efficiency in percentage associated with the respective human activity or mechanical device.\">\n<thead>\n<tr>\n<th>Activity\/device<\/th>\n<th>Efficiency (%)<a name=\"footnote-ref1\" href=\"#footnote1\"><sup>1<\/sup><\/a><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Cycling and climbing<\/td>\n<td>20<\/td>\n<\/tr>\n<tr>\n<td>Swimming, surface<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>Swimming, submerged<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>Shoveling<\/td>\n<td>3<\/td>\n<\/tr>\n<tr>\n<td>Weightlifting<\/td>\n<td>9<\/td>\n<\/tr>\n<tr>\n<td>Steam engine<\/td>\n<td>17<\/td>\n<\/tr>\n<tr>\n<td>Gasoline engine<\/td>\n<td>30<\/td>\n<\/tr>\n<tr>\n<td>Diesel engine<\/td>\n<td>35<\/td>\n<\/tr>\n<tr>\n<td>Nuclear power plant<\/td>\n<td>35<\/td>\n<\/tr>\n<tr>\n<td>Coal power plant<\/td>\n<td>42<\/td>\n<\/tr>\n<tr>\n<td>Electric motor<\/td>\n<td>98<\/td>\n<\/tr>\n<tr>\n<td>Compact fluorescent light<\/td>\n<td>20<\/td>\n<\/tr>\n<tr>\n<td>Gas heater (residential)<\/td>\n<td>90<\/td>\n<\/tr>\n<tr>\n<td>Solar cell<\/td>\n<td>10<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td colspan=\"2\"><strong>Table 2.<\/strong> Efficiency of the Human Body and Mechanical Devices.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"note\" id=\"fs-id1398490\">\n<figure>\n<p style=\"text-align: left\">\n<\/figure>\n<\/div>\n<\/section>\n<section id=\"fs-id1911538\" class=\"section-summary\">\n<h1>Section Summary<\/h1>\n<ul id=\"fs-id1897388\">\n<li id=\"import-auto-id1537867\">The law of conservation of energy states that the total energy is constant in any process. Energy may change in form or be transferred from one system to another, but the total remains the same.<\/li>\n<li id=\"import-auto-id1839690\">When all forms of energy are considered, conservation of energy is written in equation form as <strong>KE<sub>i<\/sub> + PE<sub>i<\/sub> + <em>W<\/em>nc + OE<sub>i<\/sub> = KE<sub>f<\/sub> + PE<sub>f<\/sub> + OE<sub>f<\/sub><\/strong>, where <strong>OE<\/strong> is all <strong>other forms of energy<\/strong> besides mechanical energy.<\/li>\n<li id=\"import-auto-id1317294\">Commonly encountered forms of energy include electric energy, chemical energy, radiant energy, nuclear energy, and thermal energy.<\/li>\n<li id=\"import-auto-id1787512\">Energy is often utilized to do work, but it is not possible to convert all the energy of a system to work.<\/li>\n<li id=\"import-auto-id1628394\">The efficiency <em><strong>Eff<\/strong><\/em> of a machine or human is defined to be [latex]\\boldsymbol{Eff=\\frac{W_{\\textbf{out}}}{E_{\\textbf{in}}}},[\/latex] where <strong><em>W<\/em><sub>out<\/sub><\/strong> is useful work output and <strong><em>E<\/em><sub>in<\/sub><\/strong> is the energy consumed.<\/li>\n<\/ul>\n<\/section>\n<section id=\"fs-id1758921\" class=\"conceptual-questions\">\n<h1><\/h1>\n<div class=\"bcc-box bcc-info\">\n<h3>Conceptual Questions<\/h3>\n<div class=\"exercise\" id=\"fs-id1471362\">\n<div class=\"problem\" id=\"fs-id1698457\">\n<p id=\"import-auto-id1848389\"><strong>1: <\/strong>Describe the energy transfers and transformations for a javelin, starting from the point at which an athlete picks up the javelin and ending when the javelin is stuck into the ground after being thrown.<\/p>\n<\/div>\n<\/div>\n<div class=\"exercise\" id=\"fs-id1528780\">\n<div class=\"problem\" id=\"fs-id2045976\">\n<p id=\"import-auto-id1502617\"><strong>2: <\/strong>List the energy conversions that occur when riding a bicycle.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"fs-id1703148\" class=\"problems-exercises\">\n<div class=\"bcc-box bcc-info\">\n<h3>Problems &amp; Exercises<\/h3>\n<div class=\"exercise\" id=\"eip-309\">\n<div class=\"problem\">\n<p><strong>1: <\/strong>Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m\/s strikes the water with a speed of 24.8 m\/s independent of the direction thrown.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<div>\n<h2>Footnotes<\/h2>\n<ol>\n<li><a name=\"footnote1\" href=\"#footnote-ref1\" id=\"footnote1\">1<\/a> Representative values<\/li>\n<\/ol>\n<\/div>\n<div>\n<h2>Glossary<\/h2>\n<dl id=\"import-auto-id2748477\" class=\"definition\">\n<dt id=\"import-auto-id2866094\">law of conservation of energy<\/dt>\n<dd id=\"fs-id1455501\">the general law that total energy is constant in any process; energy may change in form or be transferred from one system to another, but the total remains the same<\/dd>\n<\/dl>\n<dl id=\"import-auto-id2101389\" class=\"definition\">\n<dt id=\"import-auto-id2187394\">electrical energy<\/dt>\n<dd id=\"fs-id1593493\">the energy carried by a flow of charge<\/dd>\n<\/dl>\n<dl id=\"import-auto-id2688755\" class=\"definition\">\n<dt id=\"import-auto-id684982\">chemical energy<\/dt>\n<dd id=\"fs-id2012484\">the energy in a substance stored in the bonds between atoms and molecules that can be released in a chemical reaction<\/dd>\n<\/dl>\n<dl id=\"import-auto-id2584269\" class=\"definition\">\n<dt id=\"import-auto-id1856658\">radiant energy<\/dt>\n<dd id=\"fs-id1964070\">the energy carried by electromagnetic waves<\/dd>\n<\/dl>\n<dl id=\"import-auto-id1582487\" class=\"definition\">\n<dt id=\"import-auto-id1389125\">nuclear energy<\/dt>\n<dd id=\"fs-id1745402\">energy released by changes within atomic nuclei, such as the fusion of two light nuclei or the fission of a heavy nucleus<\/dd>\n<\/dl>\n<dl id=\"import-auto-id2009020\" class=\"definition\">\n<dt id=\"import-auto-id2582378\">thermal energy<\/dt>\n<dd id=\"fs-id2187325\">the energy within an object due to the random motion of its atoms and molecules that accounts for the object&#8217;s temperature<\/dd>\n<\/dl>\n<dl id=\"fs-id1636613\" class=\"definition\">\n<dt id=\"import-auto-id1290297\">efficiency<\/dt>\n<dd id=\"fs-id1116189\">a measure of the effectiveness of the input of energy to do work; useful energy or work divided by the total input of energy<\/dd>\n<\/dl>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Solutions<\/h3>\n<p><strong>Problems &amp; Exercises<\/strong><\/p>\n<p><strong>2: <\/strong>Equating[latex]\\boldsymbol{\\Delta\\textbf{PE}_{\\textbf{g}}}[\/latex]and[latex]\\boldsymbol{\\Delta\\textbf{KE}},[\/latex]we obtain[latex]\\boldsymbol{v=\\sqrt{2gh+v_0^2}=\\sqrt{2(9.80\\textbf{ m\/s}^2)(20.0\\textbf{ m})+(15.0\\textbf{ m\/s})^2}=24.8\\textbf{ m\/s}}[\/latex]<\/p>\n<\/div>\n","protected":false},"author":71,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-418","chapter","type-chapter","status-publish","hentry"],"part":388,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/pressbooks\/v2\/chapters\/418","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/wp\/v2\/users\/71"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/pressbooks\/v2\/chapters\/418\/revisions"}],"predecessor-version":[{"id":1041,"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/pressbooks\/v2\/chapters\/418\/revisions\/1041"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/pressbooks\/v2\/parts\/388"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/pressbooks\/v2\/chapters\/418\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/wp\/v2\/media?parent=418"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/pressbooks\/v2\/chapter-type?post=418"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/wp\/v2\/contributor?post=418"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/humanbiomechanics\/wp-json\/wp\/v2\/license?post=418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}