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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">Inertia, momentum and impulse</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 15 minutes"><i class="fa fa-clock-o"></i> 15'</span> </ol> <article id="main-article"> <p><img alt="" src="../../mechanics/equipment-gym-hard-669577-small.jpg" style="float: left; width: 190px; height: 126px;">While Physics problems usually explore the interactions between force and motion with a focus on velocity and acceleration, we mustn't forget that <em>mass</em> has an equally significant part to play. </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> <div class="panel panel-turquoise panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Inertia</p> </div> </div> <div class="panel-body"> <div> <p>Heavy bodies require a larger force to get them moving than smaller bodies. They also require more force to make them stop. We say the body has a large <em>inertia </em>(mass), a measure of its reluctance to change velocity.</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/161272574"></iframe></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>Momentum</p> </div> </div> <div class="panel-body"> <div> <p>Momentum is defined as the product of a body's mass and velocity.</p> <p style="text-align: center;">momentum (<em>p</em>) = mass (<em>m</em>) x velocity (<em>v</em>)</p> <p>The unit of momentum is a combination of what it is calculated from, usually kg m s<sup>-1</sup></p> <p>The effect that a ball has when it hits a wall depends on its momentum.</p> <div class="smart-object center" data-id="63"> <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/161195963"></iframe></div> </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>Impulse</p> </div> </div> <div class="panel-body"> <div> <p>Impulse is the change of momentum (and, consequently, is the product of force and time) during a collision. This is greater when a ball bounces on a hard floor than when it lands in soft sand.</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/161272881"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> </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="#4aa5513d"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="4aa5513d"> <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%;"> 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="6-47-237" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>A ball with mass m has velocity v just before hitting the ground. Just after hitting the ground it has velocity 1/2v.</p><p>The initial momentum is:</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> -mv</label></p><p><label class="radio"><input type="radio"> +1/2 mv</label></p><p><label class="radio"><input type="radio"> +mv</label></p><p><label class="radio"><input type="radio"> -3/2 mv</label></p></div><div class="q-explanation"><p>Down is normally negative</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 with mass m has velocity v just before hitting the ground. Just after hitting the ground it has velocity 1/2v.</p><p>The impulse is:</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> +3/2mv</label></p><p><label class="radio"><input type="radio"> -1/2 mv</label></p><p><label class="radio"><input type="radio"> -3/2mv</label></p><p><label class="radio"><input type="radio"> +1/2 mv</label></p></div><div class="q-explanation"><p>final - initial = 1/2mv - -mv</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 with mass m has velocity v just before hitting the ground. Just after hitting the ground it has velocity 1/2v.</p><p>The direction of the impulse is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> doesn't have direction</label></p><p><label class="radio"><input class="c" type="radio"> up</label></p><p><label class="radio"><input type="radio"> down</label></p><p><label class="radio"><input type="radio"> parallel to the ground</label></p></div><div class="q-explanation"><p>positive is up</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 density of the red balls is twice that of the blue balls</p><p style="text-align: center;"><img alt="" src="../../images/momq1.png" style="width: 269px; height: 279px;"></p><p>Which ball has the biggest momentum?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> D</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p></div><div class="q-explanation"><p>the red balls have bigger mass</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 density of the red balls is twice that of the blue balls</p><p style="text-align: center;"><img alt="" src="../../images/momq1.png" style="width: 269px; height: 279px;"></p>What is the ratio momentum of D/momentum of A</div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 4</label></p><p><label class="radio"><input type="radio"> 2</label></p><p><label class="radio"><input type="radio"> 1/4</label></p><p><label class="radio"><input type="radio"> 1</label></p></div><div class="q-explanation"><p>The velocity vector is twice as long so velocity of D is twice as big.<br>radius of all balls is equal so volume the same. if density 2x the mass 2x</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>Which of the following (more than one) are possible units for impulse?</p></div><div class="q-answer"><p><label class="checkbox"><input type="checkbox"> N s<sup>-1</sup></label></p><p><label class="checkbox"><input type="checkbox"> Pa s<sup>-1</sup></label></p><p><label class="checkbox"><input class="c" type="checkbox"> kg ms<sup>-1</sup> </label></p><p><label class="checkbox"><input class="c" type="checkbox"> N s</label></p></div><div class="q-explanation"><p>mv - kg ms<sup>-1 </sup></p><p>Ns - kg ms<sup>-2</sup> s = kg ms<sup>-1 </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>The motion of a 3 kg ball is represented by the following graph.</p><p style="text-align: center;"><img alt="" src="../../images/momq2.png" style="width: 273px; height: 277px;"></p><p>The momentum after 4s wil be</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 36 Ns</label></p><p><label class="radio"><input type="radio"> 12 Ns</label></p><p><label class="radio"><input type="radio"> 4 Ns</label></p><p><label class="radio"><input type="radio"> 9 Ns</label></p></div><div class="q-explanation"><p>acceleration is 3 ms<sup>-2</sup> so in 4s velocity will be 12 ms<sup>-1</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>The motion of a 2 kg ball is represented by the following graph</p><p style="text-align: center;"><img alt="" src="../../images/momq3.png" style="width: 275px; height: 279px;"></p><p>The momentum of the ball is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> +6 Ns</label></p><p><label class="radio"><input type="radio"> -3 Ns</label></p><p><label class="radio"><input type="radio"> 3 Ns</label></p><p><label class="radio"><input class="c" type="radio"> -4 Ns</label></p></div><div class="q-explanation"><p>velocity = gradient = -2 ms<sup>-1</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> 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