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<title>Potential and Kinetic Energy</title>
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<h1 class="center">Potential and Kinetic Energy</h1>
<h2>Energy</h2>
<p><a href="energy-work.html">Energy</a> is the capacity to do <b>work</b>.</p>
<p>The unit of energy is <b>J</b> (Joule) which is also <b>kg m<sup>2</sup>/s<sup>2</sup></b> (kilogram meter squared per second squared)</p>
<p>Energy can be in many forms! Here we look at Potential Energy (PE) and Kinetic Energy (KE).</p>
<h2>Potential Energy and Kinetic Energy</h2>
<p style="float:left; margin: 0 20px 5px 0;"><img src="images/hammer.jpg" alt="hammer" height="163" width="150"></p>
<p>&nbsp;</p>
<p>A hammer:</p>
<ul>
<li>when raised up has <b>potential</b> energy (the energy of position or state)</li>
<li>when falling down has <b>kinetic</b> energy (the energy of motion)</li>
</ul>
<div style="clear:both"></div>
<h3>Potential energy (PE) is <b>stored energy</b> due to position&nbsp;or state</h3>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/bow-arrow.jpg" alt="bow and arrow" height="121" width="250"><br>
</p><ul>
<li>a raised hammer has PE due to gravity.</li>
<li>fuel and explosives have Chemical PE</li>
<li>a coiled spring or a drawn bow also have PE due to their state</li>
</ul><p></p>
<div style="clear:both"></div>
<h3>Kinetic energy (KE) is energy of <b>motion</b></h3>
<p class="center"><img src="images/car-moving.jpg" alt="car moving" height="89" width="250"><br>
A moving car has a lot of <b>kinetic energy</b></p>
<h3>From PE to KE</h3>
<p class="center"><img src="images/skydivers.jpg" alt="skydivers" height="156" width="360"><br>
These skydivers have <b>potential energy</b> due to being high up.<br>
After they jump this potential energy gets<br>
converted into <b>kinetic energy</b> (and heat) as they speed up.</p>
<h2>Pendulum</h2>
<p>For a good example of PE and KE have a play with a <a href="pendulum.html">pendulum</a>.</p>
<h2>Gravitational Potential Energy</h2>
<p>When the PE is due to an objects height then:</p>
<p class="center large">PE due to gravity = m g h</p>
<p>Where:</p>
<ul>
<li>m is the objects mass (kg)</li>
<li>g is the "gravitational field strength" of <b>9.8 m/s<sup>2</sup></b> near the Earth's surface</li>
<li>h is height (m)</li>
</ul>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/hammer.jpg" alt="hammer" height="163" width="150"></p>
<h3>Example: This 2 kg hammer is 0.4 m up. What is it's PE?</h3>
<div class="tbl">
<div class="row"><span class="left">PE =</span><span class="right"> m g h</span></div>
<div class="row"><span class="left"> =</span><span class="right"> 2 kg × 9.8 m/s<sup>2</sup> × 0.4 m</span></div>
<div class="row"><span class="left"> =</span><span class="right"> 7.84 kg m<sup>2</sup>/s<sup>2</sup></span></div>
<div class="row"><span class="left"> =</span><span class="right"> <b>7.84 J</b></span></div>
</div>
</div>
<h2>Kinetic Energy</h2>
<p>The formula is:</p>
<p class="center large">KE = ½ m v<sup>2</sup></p>
<p>Where</p>
<ul>
<li>m is the object's mass (kg)</li>
<li>v is the object's speed (m/s)</li>
</ul>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/car-moving.jpg" alt="car moving" height="89" width="250"></p>
<h3>Example: What is the KE of a 1500 kg car going at suburban speed of <b>14 m/s</b> (about 50 km/h or 30 mph)?</h3>
<p class="so">KE = ½ m v<sup>2</sup></p>
<p class="so">KE = ½ × 1500 kg × (14 m/s)<sup>2</sup></p>
<p class="so">KE = 147,000 kg m<sup>2</sup>/s<sup>2</sup></p>
<p class="so">KE = <b>147 kJ</b></p>
</div>
<p>Let's double the speed!</p>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/car-moving.jpg" alt="car moving" height="89" width="250"></p>
<h3>Example: The same car is now going at highway speed of <b>28 m/s</b> (about 100 km/h or 60 mph)?</h3>
<p class="so">KE = ½ m v<sup>2</sup></p>
<p class="so">KE = ½ × 1500 kg × (28 m/s)<sup>2</sup></p>
<p class="so">KE = 588,000 kg m<sup>2</sup>/s<sup>2</sup></p>
<p class="so">KE = <b>588 kJ</b></p>
<p>Wow! that is a big increase in energy! Highway speed is way more dangerous.</p>
</div>
<p><b>Double</b> the speed and the KE increases by <b>four</b> times. Very important to know</p>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/moon.jpg" alt="moon" height="191" width="200"></p>
<h3>A 1 kg meteorite strikes the Moon at 11 km/s. How much KE is that?</h3>
<p class="so">KE = ½ m v<sup>2</sup></p>
<p class="so">KE = ½ × 1 kg × (11,000 m/s)<sup>2</sup></p>
<p class="so">KE = 60,500,000 J</p>
<p class="so">KE = 60.5 MJ</p>
<p>That is 100 times the energy of a car going at highway speed.</p>
</div>
<h2>From PE to KE</h2>
<p>When falling, an object's <b>PE due to gravity</b> converts into <b>KE</b> and also <b>heat</b> due to air resistance.</p>
<p>Let's drop something!</p>
<div class="example">
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/apple-1m.svg" alt="apple 1m"></p>
<h3>Example: We drop this 0.1 kg apple 1 m. What speed does it hit the ground with?</h3>
<p>At 1 m above the ground it's Potential Energy is</p>
<p class="so">PE = m g h</p>
<p class="so">PE = 0.1 kg × 9.8 m/s<sup>2</sup> × 1 m</p>
<p class="so">PE = 0.98 kg m<sup>2</sup>/s<sup>2</sup></p>
<p>Ignoring air resistance (which is small for this little drop anyway) that PE gets converted into KE:</p>
<p class="so">KE = ½ m v<sup>2</sup></p>
<p>Swap sides and rearrange:</p>
<p class="so">½ m v<sup>2</sup> = KE</p>
<p class="so">v<sup>2</sup> = 2 × KE / m</p>
<p class="so">v = √( 2 × KE / m )</p>
<p>Now put PE into KE and&nbsp;we get:</p>
<p class="so">v = √( 2 × 0.98 kg m<sup>2</sup>/s<sup>2</sup> / 0.1 kg )</p>
<p class="so">v = √( 19.6 m<sup>2</sup>/s<sup>2</sup> )</p>
<p class="so">v = 4.427... m/s</p>
</div>
<div class="fun">
<p>Note: for velocity we can combine the formulas like this:</p>
<table style="border: 0; margin:auto;">
<tbody>
<tr>
<td align="right">Velocity from KE:</td>
<td width="20">&nbsp;</td>
<td>v = √( 2 × KE / m )</td>
</tr>
<tr>
<td align="right">Put in formula for PE:</td>
<td>&nbsp;</td>
<td>v = √( 2 × mgh / m )</td>
</tr>
<tr>
<td align="right">Cancel m/m:</td>
<td>&nbsp;</td>
<td>v = √( 2gh )</td>
</tr>
</tbody></table>
<p><b>The mass does not matter!</b> It is all about height and gravity. For&nbsp;our earlier example:</p>
<p class="so">v = √( 2gh )</p>
<p class="so">v = √( 2 × 9.8 m/s<sup>2</sup> × 1 m )</p>
<p class="so">v = 4.427... m/s</p>
</div>
<h2>Summary</h2>
<ul class="larger">
<li>Energy is the ability to do work</li>
<li>Potential Energy (PE) is <b>stored energy</b> due to position&nbsp;or state</li>
<p class="center large">PE due to gravity = m g h</p>
<li>Kinetic Energy (KE) is energy of <b>motion</b></li>
<p class="center large">KE = ½ m v<sup>2</sup></p>
<p>&nbsp;</p>
</ul>
<p>&nbsp;</p>
<div class="questions">
<script>getQ(11975, 17599, 11977, 11983, 17606, 11979, 11982, 17601, 17605, 17608);</script>&nbsp; </div>
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<a href="energy-work.html">Energy</a>
<a href="index.html">Physics Index</a>
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