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#555" title="Suggested study time: 20 minutes"><i class="fa fa-clock-o"></i> 20'</span> </ol> <article id="main-article"> <p><img alt="" src="../../mechanics/bulb-sma-1.jpg" style="width: 250px; height: 165px; float: left;">In the previous topics of <a href="../219/forces.html" title="Forces">Forces</a> and <a href="../240/conservation-of-momentum.html" title="Conservation of momentum">Conservation of momentum</a> we learned that an understanding of <em>kinetic energy</em> was required to fully predict the outcome of a collision.</p> <p>In this section, we'll attempt to define energy (easier said than done - as it's a relative concept) and the types that can be calculated and converted.</p> <p>Work done and energy changed are equivalent.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div class="panel panel-has-border panel-turquoise panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Energy</p> </div> </div> <div class="panel-body"> <div> <p><em>Energy</em> is a scalar quantity that is conserved; the total energy contained in a system is constant. However, the energy possessed by an object can increase (e.g. if a force is exerted on it) or decrease (e.g. if heat dissipates into the surroundings).</p> <p style="text-align: center;">Energy gained = work done</p> <p style="text-align: center;">The unit of energy is Joules (J)</p> <p style="text-align: center;"><img class="sibico" src="../../../img/sibico/exam-style.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Exam-style question"> Can you work out what this is in SI base units?</p> <p>Energy is not an absolute measure. Nothing has zero energy. On these pages you will learn how to calculate quantities of energy, but it is more helpful to think of these as the amount by which energy has changed:</p> <ul> <li>A book resting on a table has kinetic energy, even if it is "at rest", as the Earth is moving in orbit around the Sun</li> <li>A nebula far out in space still has mass, and therefore gravitational potential energy, and the small amount of heat caused by vibrations of the particles requires kinetic energy.</li> </ul> <div class="magenta"> <h4>Conservation of energy</h4> <p>The law of <em>conservation of energy </em>states that energy can neither be created nor destroyed - it can only be changed from one form to another. This is also known as the first law of thermodynamics.</p> <p>This means that if body A does work on body B the energy lost by A equals the energy gained by B.</p> </div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Work</p> </div> </div> <div class="panel-body"> <div> <p>Work is done when a force moves its point of application in the direction of the force</p> <p style="text-align: center;"><span class="math-tex">\(\text{work} = \text{force} \times \text{ distance moved in direction of force}\)</span></p> <p style="text-align: center;">OR: <span class="math-tex">\(\text {work} = \text{displacement} \times \text{ component of force in the direction of displacement}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(W=Fs\cos\theta\)</span></p> <p style="text-align: center;">The unit of energy or work is N m or J.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-expandable panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Power</p> </div> </div> <div class="panel-body"> <div> <p>Power is defined as the rate at which work is done. It is a scalar quantity.</p> <p style="text-align: center;"><span class="math-tex">\(P={W\over t}\)</span></p> <p style="text-align: center;">The unit of power is J s<sup>-1</sup> or Watt (W)</p> <p>Note that the symbol for the quantity 'work' is the same as the unit of power 'Watt'.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-expandable panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Efficiency</p> </div> </div> <div class="panel-body"> <div> <p>Efficiency is defined as the ratio of useful energy output to the total energy input:</p> <p style="text-align: center;"><span class="math-tex">\(\text {efficiency} = {\text {useful energy output}\over \text{ total energy input}}\)</span></p> <p>Efficiency is a <em>dimensionless</em> quantity (no units).</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Using graphs</p> </div> </div> <div class="panel-body"> <div> <h4> </h4> <p>Since work done is the product of force and displacement, the area under a force-displacement graph is equal to work done.</p> <p>Hooke's law states that force is proportional to extension. For a spring that obeys Hooke's law the graph will be linear as shown.</p> <p><img alt="" src="../../../ib/physics/activities/workande3.jpg" style="width: 244px; height: 215px; float: left;">The equation of the line is <span class="math-tex">\(F=kx\)</span> where <span class="math-tex">\(k\)</span> is the <em>spring constant</em>. Using the area under the graph:</p> <p style="text-align: center;"><span class="math-tex">\(W={1\over 2} k{\Delta x}^2\)</span></p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Energy types</p> </div> </div> <div class="panel-body"> <div> <p><em>Kinetic</em> energy (E<sub>k</sub>) is due to movement, equal to the amount of work required to make a body move.</p> <p style="text-align: center;"><span class="math-tex">\(E_k={1\over 2} mv^2\)</span></p> <p><em>Potential</em> energy (E<sub>p</sub>) is positional, equal to the amount of work done in taking a body from a place of zero potential energy to the place in question.</p> <p style="text-align: center;"><span class="math-tex">\(E_p=mgh\)</span></p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Elastic collisions</p> </div> </div> <div class="panel-body"> <div> <p>During an <i>elastic</i> collision, both momentum and kinetic energy are conserved.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/208777850"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><i>Use flashcards to practise your recall.</i></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="1" data-mode="Normal" data-topics="492" data-subject-id="6" data-n-flashcards="13" style="text-align:center">Show flashcards</a></div><hr> </div> </div> </div> <div class="panel panel-has-colored-body panel-red"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Just for Fun</p> </div> </div> <div class="panel-body"> <div> <p><em>Check out this πg physics summary.</em></p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/208777850"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="220"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>Work and energy</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/physics/page/220/work-and-energy"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> <div id="fc-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"><div class="modal-dialog" role="document"><div class="modal-content"><div class="modal-header" style="background-color: #fafafa;"><div class="row" style="width: 100%;"><div class="col-md-12 tags-heading"><div style="display: flex; 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