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href="../244/collisions.html">Collisions</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../245/power.html">Power</a></label></li></ul></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Forces <a href="#" class="mark-page-favorite pull-right" data-pid="219" 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><span class="gray">Forces</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="../../mechanics/jump-small-1.jpg" style="float: left; width: 250px; height: 191px;">Take a moment to consider your body right now - the movement of your eyes across the screen, your lungs as they expand and contract, the muscles keeping you upright... and that's before you consider playing sport, or an instrument, or the workings of the brain. Every new movement, direction, squash or stretch requires a force.</p> <p>Real-world objects are complex, with moving parts, lumps, axles and volume. To simplify things, in Physics most things can be considered as a small ball with forces acting at the centre or contact surfaces.</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-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Definitions</p> </div> </div> <div class="panel-body"> <div> <p>A <em>force</em> is a push or a pull.</p> <p>The unit of force is the newton, 1 N, is approximately the force required to hold a mass of 100 g still.</p> <p>A force is an example of a vector quantity, and so is represented with an arrow. Some forces act when two bodies come into contact; some act at a distance.</p> <p>Forces are said to be <em>balanced</em> if the resultant force is zero. The body is then in <em>equilibrium</em>.</p> <p><em>Equal</em> forces are balanced only if they act in opposite directions.</p> <p>The resultant can be found of two or more forces in 2-dimensions by vector addition. NB: See <a href="../188/pythagoras-and-trigonometry.html" title="Pythagoras and trigonometry">Pythagoras and trigonometry</a> for help.</p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Examples</p> </div> </div> <div class="panel-body"> <div> <p>When a string is attached to body and pulled the force is called <em>tension</em> (<em>T</em>).</p> <p>Gravitational force (or weight, <em>W</em>) is the force that attracts bodies with mass to the Earth. The force is proportional to the mass.</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(W=mg\)</span></p> <p>In this equation, we can consider <em>g</em> to have two possible names:</p> <ul> <li>Gravitational field strength = 9.81 N kg<sup>-1</sup></li> <li>Acceleration due to gravity = 9.81 m s<sup>-2</sup></li> </ul> <p>Weight acts on the centre of mass of a body.</p> </div> <p>The <em>normal </em>force (<em>N</em> or <em>R</em>) acts perpendicular to two surfaces that are in contact.</p> <p><em>Friction</em> is a force that opposes the motion of a body in contact with a surface.</p> <div class="box"> <p>Friction acts parallel to and along the contact surface. However, it is proportional to the normal force between the surfaces:</p> <p style="text-align: center;"><span class="math-tex">\(F=\mu N\)</span></p> <p>The constant of proportionality, <span class="math-tex">\(\mu\)</span> = the coefficient of friction, and varies depending on whether the body is stationary (static friction, <span class="math-tex">\(\mu_s\)</span>) or moving (dynamic friction, <span class="math-tex">\(\mu_d\)</span>).</p> </div> <p><em>Buoyancy</em> or <em>upthrust</em> (<em>F<sub>B</sub></em>) is the force experienced when a body is totally or partially immersed in a fluid.</p> <div class="box"> <p><img class="sibico" src="../../../img/sibico/hl-red.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="HL difficult"> This is caused by the displacement of fluid particles and is equal to the weight of fluid that would fill the same volume.</p> <p>F<sub>B</sub> = weight of fluid displaced</p> </div> <p><em>Air resistance</em> is the force that opposes the motion of bodies through the air. This force can be referred to as 'drag' for a body moving through an unspecified fluid.</p> <div class="box"> <p><img class="sibico" src="../../../img/sibico/hl-red.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="HL difficult"> There are different models of air resistance:</p> <ul> <li>for slow-moving spheres, the force is proportional to velocity, where <em>η</em> is a constant called viscosity and r is the radius</li> </ul> <p style="text-align: center;"><span class="math-tex">\(F=6\pi \eta vr\)</span></p> <ul> <li>for faster-moving objects, the force is proportional to <em>v</em><sup>2</sup><sup> </sup></li> </ul> <p style="text-align: center;"><span class="math-tex">\(F={1\over 2}A\rho C v^2\)</span></p> </div> </div> </div> <div class="panel-footer"> <div> <p><a class="expander" href="#"><span class="fa fa-plus"></span></a></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> <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>Newton's laws of motion</p> </div> </div> <div class="panel-body"> <div> <p>Newton's laws explain the effects of forces on the motion of bodies.</p> <ol> <li> <p>The first law states that a body will remain at rest or moving with constant velocity unless acted upon by an unbalanced force.</p> </li> </ol> <div class="box"> <p>In simple terms, things don't move or stop moving unless pushed.</p> <p><img alt="" src="../../mechanics/newt11.png" style="width: 721px; height: 139px;"></p> </div> <ol start="2"> <li>Let's start with a simple statement that applies to bodies with constant mass: The acceleration of a body is proportional to the unbalanced force applied and inversely proportional to its mass.</li> </ol> <div class="box"> <p>Considering Newton's first and second laws together, we gather that a body won't move unless pushed, and that for a moving body, the harder you push the faster it will go. This tells us that force and acceleration are related:</p> <p style="text-align: center;"><span class="math-tex">\(a\propto{F\over M}\)</span></p> <p><img class="sibico" src="../../../img/sibico/notes.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Notes (summary/recap)"> 1 newton is defined as the force required to accelerate a 1 kg mass at a rate of 1 ms<sup>-2</sup> and so the constant of proportionality = 1 (<img class="sibico" src="../../../img/sibico/tok.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Theory if Knowledge"> unusual in physics!). We can therefore write:</p> <p style="text-align: center;"><span class="math-tex">\(F=ma\)</span></p> </div> <ol start="3"> <li> <p>If body A exerts a force on body B, then body B will exert an equal and opposite force on body A.</p> </li> </ol> <div class="box"> <p>It is important to note that Newton's third law only applies in the following circumstances:</p> <ul> <li>The forces act on different bodies.</li> <li>The forces are the same type.</li> <li>The forces are the same size.</li> <li>The forces act in opposite directions.</li> </ul> </div> </div> </div> <div class="panel-footer"> <div> </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>Momentum</p> </div> </div> <div class="panel-body"> <div> <p><em>Momentum</em> is defined as the product of mass and velocity, and (since <em>m</em> was already taken) is given the symbol <em>p</em>:</p> <p style="text-align: center;"><span class="math-tex">\(p=mv\)</span></p> <p style="text-align: center;">The derived SI unit of momentum is kg m s<sup>-1</sup> or N s.</p> <p><img class="sibico" src="../../../img/sibico/quiz.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Quiz"> Can you confirm that kg ms<sup>-1</sup> and Ns are dimensionally equivalent?</p> <p><img class="sibico" src="../../../img/sibico/notes.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Notes (summary/recap)"> Momentum is a vector quantity, as it is proportional to one other vector quantity.</p> <p><em>Impulse</em> is defined as the change of momentum, <span class="math-tex">\(\Delta p =\Delta mv\)</span></p> <div class="box"> <p>Since forces cause objects to accelerate, and therefore to gain momentum, we can relate force to change in momentum:</p> <p style="text-align: center;"><span class="math-tex">\(F = ma = m{(v-u) \over t}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow F={mv-mu\over t}={\Delta p\over t}\)</span></p> </div> <p>The rate of change of momentum of a body is directly proportional to the unbalanced force acting on that body and takes place in the same direction.</p> <p><img alt="" src="../../mechanics/newt28.png" style="width: 234px; height: 236px; float: left;">If we plot a simple force-time graph, we can see that the area under the graph = FΔt. Therefore, the area under a force-time graph is equal to the change in momentum or impulse.</p> <hr class="hidden-separator"> <div class="magenta"> <h4>Conservation of momentum</h4> <p>For an <em>isolated system </em>of bodies (no external forces) the total momentum is always the same.</p> <p style="text-align: center;"><span class="math-tex">\(m_1u_1+m_2u_2=m_1v_1+m_2u_2\)</span></p> <p>This applies in each of the following situations:</p> <ul> <li>Explosion (no initial momentum)</li> <li>Elastic collision (no change in total kinetic energy)</li> <li>Coalescing collision (reduction in kinetic energy as one object sticks to the other)</li> </ul> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <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> <p><em>Check out this recap of the concepts so far.</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/208693481"></iframe></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"> <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="485" data-subject-id="6" data-n-flashcards="18" style="text-align:center">Show flashcards</a></div><hr> </div> <div class="panel-footer"> <div> </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/208693481"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="219"> <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>Forces</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/219/forces"> <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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