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233 lines
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<title>Force</title>
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 class="center">Force</h1>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/jet.jpg" width="360" height="168" alt="jet" /></p>
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<p> </p>
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<p>Force is push or pull.</p>
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<p> </p>
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<p>Unbalanced forces make an object <a href="../measure/metric-acceleration.html">accelerate</a></p>
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<div style="clear:both"></div>
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<h2>Balanced</h2>
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<p>Forces on an object are usually <b>balanced</b>: forces in one direction are equal to forces in the opposite direction:</p>
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<p class="center"><img src="images/forces-balanced.gif" width="135" height="206" alt="forces balanced" /><br>
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Examples of
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<b>Balanced</b> Forces<br>
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<i>No acceleration. </i></p>
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<div style="clear:both"></div>
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<div class="example">
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<h3> Example: The forces are in balance at the top of this bridge tower. </h3>
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<p class="center"><img src="images/suspension-bridge.jpg" width="240" height="142" alt="suspension bridge" /></p>
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<p>The cables pull <b>downwards</b> equally to the left and right, and that is balanced by the tower's <b>upwards</b> push. (Does the tower push? Yes! Imagine you stand there instead of the tower.) </p>
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<p>We can <a href="../algebra/mathematical-models.html">model</a> the forces like this:</p>
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<p class="center"><img src="images/suspension-bridge-forces1.svg" alt="suspension bridge forces" /></p>
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<p>By putting them <b>head-to-tail </b>we see they <b>close back on themselves</b>, meaning the net effect is zero:</p>
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<p class="center">
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<img src="images/suspension-bridge-forces2.svg" alt="suspension bridge forces" /><br>
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The forces are in balance.</p>
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</div>
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<h2>Unbalanced</h2>
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<p> But when forces are <b>unbalanced</b> the object <a href="../measure/metric-acceleration.html">accelerates</a>. </p>
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<p class="center"><img src="images/forces-unbalanced.gif" width="132" height="187" alt="forces unbalanced" /> <br>
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Examples of <b>Unbalanced</b> Forces.<i><br>
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There is acceleration. </i></p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/ball-kick.jpg" width="360" height="201" alt="ball kick" /></p>
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<p> </p>
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<p>Kicking a ball is an unbalanced force that makes it accelerate very quickly.</p>
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<p>Once it loses contact with your foot that force (and its acceleration) stops. </p>
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<p> </p>
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<div style="clear:both"></div>
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<p>The ball would continue to travel in a straight line at a fixed velocity, except that <b>other forces</b> act on the ball:</p>
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<ul>
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<li>Gravity is now an unbalanced force that makes the ball accelerate downwards.</li>
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<li>Air resistance is also an unbalanced force which gradually reduces the velocity of the ball.</li>
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</ul>
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<p class="center"><img src="images/ball-forces.svg" alt="ball forces: kick, gravity, air" /></p>
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<div style="clear:both"></div>
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<div class="words">
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<p><b>Acceleration</b>: an increase <i>or decrease</i> in velocity</p>
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<p>A decrease in velocity can also be called <i>deceleration</i>. </p>
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</div>
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<p>Force and Acceleration are linked.</p>
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<p class="so">The more force, the more acceleration.</p>
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<p>But objects with more mass are harder to accelerate</p>
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<p class="so">The more mass, the less acceleration.</p>
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<p>Imagine trying to kick a stone ball:</p>
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<p class="center"><img src="images/ball-kick-mass.jpg" width="320" height="186" alt="ball kick massive stone" /></p>
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<p>The famous formula is:</p>
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<div class="def">
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<p class="center large"><b>F</b> = m<b>a</b></p>
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<p class="center"><i>"Newton's Second Law of Motion"</i><br>
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(<b>F</b> is force, m is mass and <b>a</b> is acceleration) </p>
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</div>
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<p>Dividing both sides by m makes it clearer:</p>
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<p class="center"><img src="images/fm-a.svg" alt="f/m = a" /></p>
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<div class="words">
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<p style="float:right; margin: 0 0 5px 10px;"> </p>
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<p>The idea that mass resists acceleration is called <b class="larger">inertia</b>. </p>
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</div>
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<p>Inertia means the object wants to <b>continue</b> to do what it does. </p>
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<p>If it is at rest (in relation to us), it continues to be at rest. If it is moving East at 20 m/s, it continues moving East at 20 m/s. etc.</p>
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<p class="center"><img src="images/hdr-container-ship.jpg" width="723" height="100" alt="container ship" /> </p>
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<p> This oil tanker has a <b> large inertia</b>. It is:</p>
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<ul>
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<li>hard to speed up</li>
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<li>hard to slow down when it is moving (can take many kilometers to stop)</li>
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<li>hard to change direction </li>
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</ul>
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<p class="center"><span style="float:right; margin: 0 0 5px 10px;"><img src="images/walrus.jpg" width="250" height="123" alt="walrus" /></span></p>
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<p class="center">It seems that mass doesn't like being pushed around!</p>
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<div style="clear:both"></div> <h2>Newtons</h2>
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<p>In honor of Sir Isaac Newton the unit of force is the <b>Newton</b> (abbreviation is N).</p>
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<p>A Newton is the force it takes to make <b>1 kg</b> change its velocity by <b>1 m/s every second</b>.</p>
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<div class="tbl">
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<div class="row"><span class="left">In other words:</span><span class="right"><i>1 kg changes its velocity by 1 m/s every second</i></span></div>
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<div class="row"><span class="left">Or:</span><span class="right"><i>1 kg changes 1 m/s per second</i></span></div>
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<div class="row"><span class="left">Or:</span><span class="right"><i>1 kg m/s /s </i></span></div>
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</div>
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<p>The two lots of "/s" (per second) become "/s<sup>2</sup>" (per second squared), so:</p>
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<p class="so">1 <b>Newton</b> is 1 <b>kg m/s<sup>2</sup></b> (kilogram meter per second squared)</p>
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<div class="example">
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<h3>Example: A 2000kg car goes from 0 to 15 m/s in 5 seconds. What is the force?</h3>
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<p>The acceleration is 15 m/s over 5 seconds, or <span class="intbl">
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<em>15 m/s</em>
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<strong>5 s
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</strong>
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</span> = <span class="intbl">
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<em>3 m/s</em>
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<strong>s
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</strong>
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</span> = 3 m/s<sup>2</sup></p>
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<p>Now let's calculate the force:</p><div class="tbl">
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<div class="row"><span class="left"><b>F</b> =</span><span class="right"> m<b>a</b></span></div>
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<div class="row"><span class="left">=</span><span class="right"> 2000 kg × <b>3 m/s<sup>2</sup></b></span></div>
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<div class="row"><span class="left"> =</span><span class="right"> <b>6000 kg m/s<sup>2</sup></b></span></div>
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<div class="row"><span class="left">=</span><span class="right"> <b>6000 N</b></span></div>
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<div class="row"><span class="left"> =</span><span class="right"> <b>6 kN</b></span></div>
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</div>
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<p>The force is <b>6 kN</b> (6 kiloNewtons).</p>
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</div>
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<h2>Forces are Interactions</h2>
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<p style="float:left; margin: 0 10px 5px 0;"> <img src="images/stone-force.jpg" width="150" height="255" alt="stone finger force" /></p>
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<p> </p>
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<p>In the words of Sir Isaac Newton (his Third Law of Motion):</p>
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<p class="center larger">"To every action there is always opposed an equal reaction"</p>
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<p>Today we say "Every action has an equal and opposite reaction"</p>
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<p>He also gave this example:</p>
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<p class="center">"If you press a stone with your finger, the finger is also pressed by the stone."</p>
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<div style="clear:both"></div>
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<h2>Vector</h2>
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<p>Force has magnitude <b>and</b> direction.
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So it is a <a href="../algebra/vectors.html">vector</a>:</p>
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<p class="center">
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<img src="../algebra/images/vector-mag-dir.svg" alt="vector magnitude and direction" /></p>
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<p>Acceleration also has magnitude and direction.
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So it too is a vector.</p>
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<p> </p>
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<p style="float:left; margin: 0 10px 5px 0;"><a href="force-calculations.html"><img src="images/force-ex2c.svg" alt="force beam strut" /></a></p>
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<h3>Calculations</h3>
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<p>Read the page devoted to <a href="force-calculations.html">Force Calculations</a></p><div style="clear:both"></div>
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<h2>Relative</h2>
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<p>Note: when we say something is "at rest" or "moving at 4 m/s" we forget to say "in relation to me" or "in relation to the ground", etc.</p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="../measure/images/earth-rotate.gif" width="128" height="128" alt="earth rotate" /></p>
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<p>Think about this: are you really standing still? You are on planet Earth which is spinning at 40,075 km per day (about 1675 km/h or 465 m/s), and moving around the Sun at about 100,000 km/h, which is itself moving through the Galaxy.</p>
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<p><b>It is all relative!</b></p>
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<div style="clear:both"></div>
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<h2>Summary</h2>
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<ul class="larger">
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<li>Force is a push or pull</li>
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<li>Forces on an object can be balanced or unbalanced</li>
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<li>Unbalanced forces make an object accelerate
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<ul>
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<li>More force, more acceleration</li>
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<li>More mass, less acceleration (inertia)</li>
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</ul>
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</li>
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<li>"To every action there is always opposed an equal reaction" </li>
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</ul>
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<p> </p>
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<div class="def">
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<h3>Newton's Three Laws</h3>
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<p>Back in 1687 Newton wrote three laws about motion, which basically are:</p>
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<ul>
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<li>First Law: Inertia (force is needed to change an object's velocity)</li>
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<li>Second Law: <b>F</b> = m<b>a</b></li>
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<li>Third Law: Every action has an equal and opposite reaction</li>
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</ul>
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</div>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(11923, 11924, 11925, 11926, 11927, 11928, 11929, 11930, 11931, 11932);</script>
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</div>
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<div class="related"> <a href="../measure/metric-acceleration.html">Acceleration</a> <a href="force-calculations.html">Force Calculations</a> <a href="index.html">Physics Index</a></div>
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Copyright © 2018 MathsIsFun.com
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