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class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../217/mechanics.html">Mechanics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../220/work-and-energy.html">Work and energy</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Conservation of energy</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 10 minutes"><i class="fa fa-clock-o"></i> 10'</span> </ol> <article id="main-article"> <p><img alt="" src="../../mechanics/jump-small-1.jpg" style="float: left; width: 250px; height: 191px;">Energy is always conserved, but to find out where it has gone we sometimes need to look inside matter. Macroscopic processes can lead to microscopic changes.</p> <hr class="hidden-separator"> <div class="panel panel-has-colored-body panel-purple"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-purple panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Mass pushed up a frictionless slope</p> </div> </div> <div class="panel-body"> <div> <p>When work is done on a block on a slope it gains both kinetic and potential energy but when the force is removed the kinetic energy is converted to potential energy. At the top, the potential energy gained is equal to the total work that was done:</p> <p style="text-align: center;"><span class="math-tex">\(Fd = mgh + {1\over2}mv^2\)</span></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/162164714"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-purple 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>Ball thrown vertically</p> </div> </div> <div class="panel-body"> <div> <p>When a ball leaves your hand it has kinetic energy. As it rises <span class="math-tex">\(E_k\rightarrow E_p\)</span>.</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/162165044"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-purple 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>Energy lost when bouncing</p> </div> </div> <div class="panel-body"> <div> <p>When a ball bounces some energy is lost. The energy goes to the kinetic and potential energy of the atoms.</p> <p><img class="sibico" src="../../../img/sibico/video.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Video"> If the ball itself could squash, the energy could be considered to have transferred to elastic potential energy.</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/162165619"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-purple 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>Mass on a spring</p> </div> </div> <div class="panel-body"> <div> <p>When a spring is stretched, work is done, so energy is transferred. This energy is stored in the spring as elastic potential energy.</p> <p style="text-align: center;"><span class="math-tex">\(E_p = {1\over2}kx^2\)</span></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/162181474"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <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><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#b9c1d7d6"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="b9c1d7d6"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Conservation of energy <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-56-251" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>A constant force of 100 N is applied to a block as shown.</p><p style="text-align: center;"><img alt="" src="../../images/conq1.png" style="width: 350px; height: 153px;"></p><p>If the frictional force is 10 N calculate</p></div><div class="q-answer"><p>The work done on the block by the person pulling it = <input type="text" style="height: auto;" data-c="500"> <span class="review"></span> J</p><p>The work done against friction = <input type="text" style="height: auto;" data-c="50"> <span class="review"></span> J</p><p>The increase in PE when the block is at the top of the slope = <input type="text" style="height: auto;" data-c="200"> <span class="review"></span> J</p><p>The gain in KE when the block is at the top = <input type="text" style="height: auto;" data-c="250"> <span class="review"></span> J</p></div><div class="q-explanation"><p>Work = 5 x 100 = 500 J<br>Work against friction = 5 x 10 = 50 J<br>gain in PE = 10 x 10 x 2 = 200 J<br>Work done = gain in PE + KE + work against friction, KE = 500 - 200 - 50 = 250 J</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A constant force of 100 N is applied to a block as shown.</p><p style="text-align: center;"><img alt="" src="../../images/conq1.png" style="width: 350px; height: 153px;"></p><p>If there is no friction calculate</p></div><div class="q-answer"><p>The work done on the block by the person pulling it = <input type="text" style="height: auto;" data-c="500"> <span class="review"></span> J</p><p>The increase in PE when the block is at the top of the slope = <input type="text" style="height: auto;" data-c="200"> <span class="review"></span> J</p><p>The gain in KE when the block is at the top = <input type="text" style="height: auto;" data-c="300"> <span class="review"></span> J</p></div><div class="q-explanation"><p>Work = 5 x 100 = 500 J<br>gain in PE = 10 x 10 x 2 = 200 J<br>Work done = gain in PE + KE KE = 500 - 200 = 300 J</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A block is sent up the hill shown with a velocity v.</p><p style="text-align: center;"><img alt="" src="../../images/conq2.png" style="width: 350px; height: 123px;"></p><p>The block just reaches the top of the hill and falls off the other side</p><p>The frictional force is 60 N.</p></div><div class="q-answer"><p>The statement that the block "just reaches the top" implies that the velocity at the top = <input type="text" style="height: auto;" data-c="0"> <span class="review"></span> ms<sup>-1</sup></p><p>The work done against friction = <input type="text" style="height: auto;" data-c="300"> <span class="review"></span> J</p><p>The gain in PE = <input type="text" style="height: auto;" data-c="200"> <span class="review"></span> J</p><p>The loss in KE = <input type="text" style="height: auto;" data-c="500"> <span class="review"></span> J</p><p>The original KE = <input type="text" style="height: auto;" data-c="500"> <span class="review"></span> J</p><p>The original velocity = <input type="text" style="height: auto;" data-c="10"> <span class="review"></span> ms<sup>-1</sup></p></div><div class="q-explanation"><p>Work done against friction = 60 x 5 = 300 J</p><p>Gain in PE = 10 x 10 x 2 = 200 J</p><p>Loss in KE = 500 J</p><p>1/2mv<sup>2</sup><sup> </sup>= 500 = 5 v<sup>2</sup></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A block travelling at 10 ms<sup>-1</sup> travels up the hill shown arriving at the top with a velocity of 4 ms<sup>-1</sup></p><p style="text-align: center;"><img alt="" src="../../images/conq2.png" style="width: 350px; height: 123px;"></p><p>Calculate</p></div><div class="q-answer"><p>The KE of the block at the bottom = <input type="text" style="height: auto;" data-c="500"> <span class="review"></span> J</p><p>The KE at the top = <input type="text" style="height: auto;" data-c="80"> <span class="review"></span> J</p><p>The PE at the top = <input type="text" style="height: auto;" data-c="200"> <span class="review"></span> J</p><p>The work done against friction = <input type="text" style="height: auto;" data-c="220"> <span class="review"></span> J</p><p>The frictional force = <input type="text" style="height: auto;" data-c="44"> <span class="review"></span> N</p></div><div class="q-explanation"><p>1/2 x 10 x 10<sup>2</sup><sup> </sup>= 500 J</p><p>1/2 x 10 x 4<sup>2</sup><sup> </sup>= 80 J</p><p>10 x 10 x 2 = 200 J</p><p>Loss of KE = gain in PE + work against friction</p><p>Work against friction = 500 -80 -200 = 220 J</p><p>Force = work / dist = 220 / 5 = 44 N</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A ball drops from a height of 10 m as shown</p><p style="text-align: center;"><img alt="" src="../../images/conq3.png" style="width: 150px; height: 248px;"></p><p>When the ball bounces its velocity is reduced to half what it was.</p><p>Calculate</p></div><div class="q-answer"><p>The KE just before hitting the ground = <input type="text" style="height: auto;" data-c="500"> <span class="review"></span> J</p><p>The KE just after the bounce = <input type="text" style="height: auto;" data-c="125"> <span class="review"></span> J</p><p>The energy lost in the form of thermal energy = <input type="text" style="height: auto;" data-c="375"> <span class="review"></span> J</p><p>The height reached after the bounce = <input type="text" style="height: auto;" data-c="2.5"> <span class="review"></span> m</p></div><div class="q-explanation"><p>gain in KE = loss of PE = mgh = 5 x 10 x 10 = 500 J</p><p>If velocity is 1/2 the KE is 1/4 = 125 J</p><p>mgh = 125 = 2.5 m</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> 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