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title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol 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="../219/forces.html">Forces</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Conservation of momentum</span></li> <span class="pull-right" style="color: #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="../../cradle-small.jpg" style="width: 250px; height: 175px; float: left;">Momentum is a quantity that is <em>conserved</em>. This means that the total amount is constant throughout an interaction, such as a collision, provided that there are no external forces acting.</p> <p>Since velocity is a vector quantity, so too is momentum, and so momenum in the reverse direction will be negative.</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"> <p>By applying Newton's three laws to a collision between two balls, we can show that the total momentum for isolated bodies is constant. Momentum is 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/161468804"></iframe></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-yellow panel-has-colored-body panel-has-border"> <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> <h4>Identical bodies</h4> <p>An elastic collision means that total kinetic energy is constant. Recall that kinetic energy is a scalar (since the velocity term is squared) and so energies are added together no matter what the direction.</p> <p>When two identical balls collide elastically they swap velocity, so if one was stationary before the other will be stationary after.</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/161477946"></iframe></div> <h4>Non-identical bodies</h4> <p>The momentum before a collision always equals the momentum after, provided the bodies are isolated.</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/161486580"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-yellow 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>Explosions</p> </div> </div> <div class="panel-body"> <div> <p>There is no momentum before an explosion. After the explosion, the bodies have velocities in different directions.</p> <p>If the system is isolated, the momentum is conserved. Therefore, the bits going left are balanced by the bits going right (and the same could be said up and down).</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/161755217"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-yellow 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>2-dimensional collisions</p> </div> </div> <div class="panel-body"> <div> <p>Momentum is conserved in 2-dimensions. To show this we can either make a triangle of the vectors or take components.</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/161632734"></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><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#bf2f6cc7"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="bf2f6cc7"> <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 momentum <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="6-50-240" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>Two balls collide as shown</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="http://www.thinkib.net/files/physics/capture-256.gif" style="width: 388px; height: 132px;"></p><p>Which of the following statements is true</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> The total momentum of the two balls is conserved.</label></p><p><label class="radio"><input type="radio"> Momentum isn't conserved</label></p><p><label class="radio"><input type="radio"> The momentum of the red ball is conserved.</label></p><p><label class="radio"><input type="radio"> The momentum of the grey ball is conserved.</label></p></div><div class="q-explanation"><p>The momentum of each ball is not conserved as they are not isolated</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>Consider the following collision.</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="http://www.thinkib.net/files/physics/capture-256.gif" style="width: 388px; height: 132px;"></p><p>If the mass of the red ball is 1 kg and the grey is 4 kg calculate the following values</p></div><div class="q-answer"><p>Change of momentum of the red ball <input type="text" style="height: auto;" data-c="-3.6"> <span class="review"></span> Ns</p><p>Change of momentum of the grey ball <input type="text" style="height: auto;" data-c="3.6"> <span class="review"></span>Ns</p><p>Change in momentum of the two balls <input type="text" style="height: auto;" data-c="0"> <span class="review"></span>Ns </p></div><div class="q-explanation"><p>Change in momentum = mass x change in velocity</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 footballer kicks a ball. Which of the following statements is true.</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> The momentum of the ball is conserved but not the footballer</label></p><p><label class="radio"><input type="radio"> Momentum of the footballer and ball is conserved</label></p><p><label class="radio"><input class="c" type="radio"> Momentum of the footballer and ball are not conserved because they are not isolated.</label></p><p><label class="radio"><input type="radio"> Momentum of the footballer and ball are not conserved because they are not elastic.</label></p></div><div class="q-explanation"><p>The footballer and ball interact with the ground.</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>There following diagram represents the before position and 4 possible after positions for a collision</p><p style="text-align: center;"><img alt="" src="../../images/collsq1.png" style="width: 363px; height: 301px;"></p><p>Which are possible</p></div><div class="q-answer"><p><label class="checkbox" style=" float: left; margin-right: 40px; "><input class="c" type="checkbox"> A</label></p><p><label class="checkbox" style=" float: left; margin-right: 40px; "><input class="c" type="checkbox"> B</label></p><p><label class="checkbox" style=" float: left; margin-right: 40px; "><input type="checkbox"> C</label></p><p><label class="checkbox" style=" float: left; margin-right: 40px; "><input type="checkbox"> D</label></p></div><div class="q-explanation"><p>C implies zero momentum</p><p>D implies negative momentum</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>The diagram shows two possible outcomes for a collision between 2 balls of equal mass</p><p style="text-align: center;"><img alt="" src="../../images/collsq2.png" style="width: 362px; height: 185px;"></p><p>The velocity of the balls in each case is:</p></div><div class="q-answer"><p>A: Red ball <input type="text" style="height: auto;" data-c="v/2"> <span class="review"></span> Blue ball <input type="text" style="height: auto;" data-c="v/2"> <span class="review"></span></p><p>B: Red ball<input type="text" style="height: auto;" data-c="0"> <span class="review"></span> Blue ball <input type="text" style="height: auto;" data-c="v"> <span class="review"></span></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>1 ball hits 4 identical balls as shown</p><p><img alt="" class="gifffer" data-gifffer="/media/physics/images/momq1.gif" style="width: 800px; height: 200px;"></p></div><div class="q-answer"><p>The velocity of the 4 balls after the collision = <input type="text" style="height: auto;" data-c="1.5"> <span class="review"></span> ms<sup>-1</sup></p></div><div class="q-explanation"><p>momentum before = 5m</p><p>momentum after = 4mv -m = 5m</p><p>4v = 6</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>2 boxes hit 4 identical boxes as shown</p><p><img alt="" class="gifffer" data-gifffer="/media/physics/images/6-boxes.gif" style="width: 700px; height: 116px;"></p></div><div class="q-answer"><p>The velocity after the collision is <input type="text" style="height: auto;" data-c="1"> <span class="review"></span> ms<sup>-1</sup></p></div><div class="q-explanation"><p>2mx3 =6mv</p><p>v=6/6</p></div><div 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