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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Energy and Work</h1>
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<p class="center larger"><b>Work</b> is done when force moves through a distance.</p>
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<p class="center"><img src="images/push-box.jpg" alt="push box" height="112" width="383"><br></p>
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<p>If no movement, then no work!</p>
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<p class="center large"><img src="images/lifting-weights.jpg" alt="lifting weights" height="250" width="250"><br>
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These people are doing work, because they are lifting weights</p>
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<p class="center large"><img src="images/weight-hold.jpg" alt="weight hold" height="267" width="250"><br>
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This guy did work to get the weights up,<br>
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but right now he is <b>not doing any work</b> as the weights aren't moving</p>
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<p class="center large"><img src="images/weight-lift-statue.jpg" alt="weight lift statue" height="242" width="200"><br>
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This guy is also <b>not doing any work</b></p>
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<p class="center large"><img src="images/tractor-pull.jpg" alt="tractor pull" height="93" width="360"><br>
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This tractor <b>is doing work</b> as it pulls the hay bales along.</p>
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<h2>Same Direction!</h2>
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<p>The force and movement are measured <b>in the same direction</b>.</p>
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<div class="def">
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<p class="center larger">Work = <b>Force</b> × <b>Distance</b> × cos θ</p>
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<p class="center large">Where <b>θ is the angle between</b> the force and the direction of motion.</p>
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</div>
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So any force that is sideways to the movement is not included.
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<div class="example">
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<h3>Example: John pushes a box 3 m straight forward using 200 N of force. But his push is a little upwards by 20°.</h3>
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<p class="center"><img src="images/push-box-20.jpg" alt="push box 20 degrees" height="123" width="385"></p>
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<p>Start with:</p>
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<p class="center larger">Work = <b>Force</b> × <b>Distance</b> × cos θ</p>
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<p>Put in the values we know:</p>
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<p class="center larger">Work = <b>200 N</b> × <b>3 m</b> × cos 20°</p>
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<p class="center larger">Work = <b>200 N</b> × <b>3 m</b> × 0.9397...</p>
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<p class="center larger">Work = 564 N m (to nearest N m)</p>
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<p>1 N m is <b>1 Joule</b> (J) the preferred unit for work and energy (more on this later):</p>
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<p class="center larger"><b>Work = 564 J</b></p>
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<p>(Without cos θ, the <i><b>wrong</b></i> value would be 600 J)</p>
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</div>
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<p>Here are some other angles:</p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr valign="bottom">
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<td style="text-align:center;">cos(0°)=1</td>
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<td style="text-align:center; width:20px;"> </td>
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<td style="text-align:center;">cos(60°)=0.5</td>
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<td style="text-align:center; width:20px;"> </td>
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<td style="text-align:center;">cos(90°)=0</td>
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</tr>
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<tr valign="bottom">
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<td style="text-align:center;"><img src="images/work-fd-0.svg" alt="force along distance" height="48" width="130"><br>
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</td>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;"><img src="images/work-fd-60.svg" alt="force at 60 degrees to distance" height="86" width="130"><br>
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</td>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;"><img src="images/work-fd-90.svg" alt="force at 90 degrees to distance" height="100" width="140"><br>
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</td>
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</tr>
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<tr>
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<td style="text-align:center;"><span class="large">W = Fd</span></td>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;"><span class="large">W = Fd × 0.5</span></td>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;"><span class="large">W = 0</span></td>
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</tr>
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</tbody></table>
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</div>
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<p>So remember:</p>
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<ul>
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<li>Without movement there is no work</li>
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<li>Force and movement in the same direction</li>
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<li>Work = <b>Force</b> × <b>Distance</b> × cos θ</li>
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</ul>
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<h2>Energy</h2>
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<p><b>Energy</b> is the capacity to <b>do work</b>.</p>
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<p>It is like energy is <b>stored up work</b>.</p>
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<ul>
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<li>When work is done <b>by</b> something it <b>loses</b> energy</li>
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<li>When work is done <b>on</b> something it <b>gains</b> energy</li>
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</ul>
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<p>Energy can be in many forms:</p>
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<p class="center"><img src="images/spring4.jpg" alt="spring" height="359" width="195"><br>
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A coiled spring has elastic energy.</p>
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<p class="center"><img src="images/batteries2.jpg" alt="batteries" height="199" width="360"><br>
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Batteries store chemical energy.<br>
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They convert that to electrical energy,<br>
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which we can use to do work.</p>
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<p>Fuel also contains chemical energy. An engine can turn that fuel (with oxygen) into work, making your car go!</p>
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<p style="float:left; margin: 0 20px 5px 0;"><img src="images/hammer.jpg" alt="hammer" height="163" width="150"></p>
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<p>A hammer has mechanical energy:</p>
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<ul>
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<li>when raised up it has <b>potential</b> energy (the energy of position)</li>
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<li>when falling down it has <b>kinetic</b> energy (the energy of motion)</li>
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</ul>
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<div style="clear:both"></div>
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<p class="center large">Energy goes from one storage to another, or goes to heat:</p>
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<p class="center"><img src="images/energy-work-heat.svg" alt="energy work heat" height="91" width="338"></p>
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<p>Heat is a type of energy, too. In fact the total amount of energy stays the same:</p>
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<p class="center large">Energy can't be created or destroyed.</p>
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<p>This is called <a href="conservation.html">Conservation of Energy</a>: energy just gets transformed and the total stays constant.</p>
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<p>Energy is <b>lost to a system</b> when it leaves it. A battery loses energy when it powers a light. Our bodies lose heat all the time.</p>
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<p>And when we say "energy is lost as heat" we really mean the energy is <b>dissipated</b> (spread out) into the environment, it is <b>not gone from the Universe</b>.</p>
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<h2>Sankey Diagrams</h2>
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<p>A "Sankey Diagram" shows where the energy goes. The width of the arrow shows how much goes where.</p>
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<p class="center"><img src="images/car-moving.jpg" alt="car moving" height="89" width="250"><br>
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<br>
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Here is a Sankey Diagram for a car's gasoline engine:</p>
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<p class="center"><img src="images/sankey-car-engine.svg" alt="sankey diagram for car engine" height="145" width="335"><br></p>
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<p>Note: "MJ" is Megajoule (Million Joules). Add them up to make sure the totals match!</p>
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<h2>The Joule</h2>
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<p>The basic unit of energy and work is the <b>Joule</b> (J):</p>
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<div class="def">
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<p class="center larger">1 Joule is the work done by 1 Newton moving 1 meter</p>
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<p class="center larger">1 J = 1 N × 1 m</p>
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<p>The Joule has the units <b>N m</b>, or <b>kg m<sup>2</sup>/s<sup>2</sup></b> (because a Newton is kg m/s<sup>2</sup>)</p>
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</div>
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<p>Only force and movement in <b>the same direction</b> count, so a more accurate description is:</p>
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<div class="def">
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<p class="center large">1 J is the work done to an object when a force of 1 N acts on that object in the direction of its motion through a distance of 1 meter.</p>
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</div>
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<div class="example">
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/apple-1m.svg" alt="apple 1m" height="441" width="107"></p>
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<h3>Example: How much energy is needed to lift an 0.1 kg apple up 1 meter?</h3>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/gravity-apple2.svg" alt="gravity apple force" height="197" width="128"></p>
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<p>To <b>hold</b> a 0.1 kg apple against <a href="gravity.html">gravity</a> needs 1 Newton of <a href="force.html">force</a>:</p>
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<p class="center"><b>F</b> = m<b><i>g</i></b></p>
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<p class="center"><b>F</b> = 0.1 kg × <b>9.8 m/s<sup>2</sup></b></p>
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<p class="center"><b>F</b> ≈ <b>1 N</b></p>
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<p>But holding an apple is not work, the apple needs to <b>move</b>!</p>
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<p>So, raising it using <b>1 N</b> for <b>1 m</b> (both in same direction!) gives:</p>
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<p class="center larger">Work = <b>1 N</b> × <b>1 m</b> × cos 0°<br>
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<br>
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= 1 J</p>
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</div>
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<h2>How Much?</h2>
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<h3>One joule is about:</h3>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="../measure/images/droplet.jpg" alt="droplets" height="112" width="100"></p>
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<ul>
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<li>the energy needed to lift an 0.1 kg apple up 1 meter</li>
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<li>The energy released when the apple falls back down again</li>
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<li>The heat needed to raise a single <b>drop</b> of water by 5° C</li>
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<li>1 watt of electricity for 1 second</li>
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</ul>
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<p>And:</p>
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<ul>
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<li>An LED light uses about <b>3 J</b> every second</li>
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<li>A human at rest releases about <b>60 J</b> of heat every second</li>
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</ul>
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<h3>A kilojoule (kJ) is 1000 J:</h3>
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<ul>
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<li>A fan heater releases about <b>2 kJ</b> of heat every second</li>
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<li>to heat the water for a cup of coffee needs <b>80 kJ</b></li>
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</ul>
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<h3>A Megajoule (MJ) is 1 million J:</h3>
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<ul>
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<li>A 2500 kg car going at highway speed has <b>1 MJ</b> of energy</li>
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<li>A big TV uses about <b>1 MJ</b> of electricity every hour</li>
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<li>One kW h (kilowatt hour) of electricity is <b>3.6 MJ</b></li>
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<li>A fan heater releases about <b>8 MJ</b> of heat every hour</li>
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</ul>
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<h3>A Gigajoule (GJ) is 1 billion J:</h3>
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<ul>
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<li>The solar energy falling on a roof is about <b>1 GJ</b> to <b>5 GJ</b> every day</li>
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<li>A person uses about <b>20 GJ</b> in their home every year</li>
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</ul>
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<h2>Efficiency</h2>
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<p>Efficiency is how much of the energy is <b>useful</b> as a <b>percent of the total energy</b>.</p>
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<p class="center"><span class="large">Efficiency = <span class="intbl">
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<em>Useful Energy</em>
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<strong>Total Energy</strong>
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</span></span> as a percentage</p>
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<div class="example">
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<h3>Example: For every 100 MJ (Megajoule) of energy a gasoline engine uses, only 25 MJ goes to driving it forward.</h3>
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<p class="center larger">Efficiency = <span class="intbl">
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<em>25 MJ</em>
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<strong>100 MJ</strong>
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</span>= 25%</p>
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</div>
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<h2>Summary</h2>
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<ul class="larger">
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<li>Work is force times distance (in the same direction!)</li>
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<li>W = <b>F</b> <b>d</b> cos θ</li>
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<li>Energy is the ability to do work</li>
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<li>Energy goes from one storage to another, or goes to heat</li>
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<li>Energy can't be created or destroyed (Conservation of Energy)</li>
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<li>The basic unit of energy is 1 Joule (J)</li>
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<li>1 J = 1 N m</li>
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</ul>
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<p> </p>
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<div class="questions">11965, 11974, 17589, 17590, 11966, 11967, 11970, 11972, 17591, 17598</div>
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<div class="related">
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<a href="index.html">Physics Index</a>
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</div>
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