e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
321 lines
14 KiB
HTML
321 lines
14 KiB
HTML
<!DOCTYPE html>
|
||
<html lang="en"><!-- #BeginTemplate "/Templates/Advanced.dwt" --><!-- DW6 -->
|
||
|
||
<!-- Mirrored from www.mathsisfun.com/physics/gravity.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:39:31 GMT -->
|
||
<head>
|
||
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
|
||
|
||
|
||
<!-- #BeginEditable "doctitle" -->
|
||
<title>Gravity</title>
|
||
|
||
<script>reSpell=[["meters","metres"],["center","centre"],["centers","centres"]];</script>
|
||
|
||
<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents.">
|
||
<!-- #EndEditable -->
|
||
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
||
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
||
<meta name="HandheldFriendly" content="true">
|
||
<meta name="referrer" content="always">
|
||
<link rel="preload" href="../images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin="">
|
||
<link rel="preload" href="../style4.css" as="style">
|
||
<link rel="preload" href="../main4.js" as="script">
|
||
<link rel="stylesheet" href="../style4.css">
|
||
<script src="../main4.js" defer="defer"></script>
|
||
<!-- Global site tag (gtag.js) - Google Analytics -->
|
||
<script async="" src="https://www.googletagmanager.com/gtag/js?id=UA-29771508-1"></script>
|
||
<script>
|
||
window.dataLayer = window.dataLayer || [];
|
||
function gtag(){dataLayer.push(arguments);}
|
||
gtag('js', new Date());
|
||
gtag('config', 'UA-29771508-1');
|
||
</script>
|
||
</head>
|
||
|
||
<body id="bodybg" class="adv">
|
||
|
||
<div id="stt"></div>
|
||
<div id="adTop"></div>
|
||
<header>
|
||
<div id="hdr"></div>
|
||
<div id="tran"></div>
|
||
<div id="adHide"></div>
|
||
<div id="cookOK"></div>
|
||
</header>
|
||
|
||
<div class="mid">
|
||
|
||
<nav>
|
||
<div id="menuWide" class="menu"></div>
|
||
<div id="logo"><a href="../index.html"><img src="../images/style/logo-adv.svg" alt="Math is Fun Advanced"></a></div>
|
||
|
||
<div id="search" role="search"></div>
|
||
<div id="linkto"></div>
|
||
|
||
<div id="menuSlim" class="menu"></div>
|
||
<div id="menuTiny" class="menu"></div>
|
||
</nav>
|
||
|
||
<div id="extra"></div>
|
||
|
||
<article id="content" role="main">
|
||
|
||
<!-- #BeginEditable "Body" -->
|
||
|
||
|
||
<h1 class="center">Gravity</h1>
|
||
|
||
|
||
<h2>Falling Apple</h2>
|
||
|
||
<p>Gravity is all around us. It can, for example, make an apple fall to the ground:</p>
|
||
<p class="center"><img src="images/gravity-apple1.svg" alt="gravity apple" height="197" width="128"></p>
|
||
<p>Gravity constantly acts on the apple so it goes faster and faster ... in other words it <a href="../measure/metric-acceleration.html">accelerates</a>.</p>
|
||
<p>Ignoring air resistance, its <a href="../measure/metric-speed.html">velocity</a> increases by <b>9.8 meters per second</b> every second. So we get this:</p>
|
||
<table style="text-align:right; margin:auto;" border="0">
|
||
<tbody>
|
||
<tr>
|
||
<td style="width:150px;">After 1 second:</td>
|
||
<td style="width:90px;">9.8 m/s</td></tr>
|
||
<tr>
|
||
<td>After 2 seconds:</td>
|
||
<td>19.6 m/s</td></tr>
|
||
<tr>
|
||
<td>After 3 seconds:</td>
|
||
<td>29.4 m/s</td></tr>
|
||
<tr>
|
||
<td>etc...</td>
|
||
<td><br></td></tr></tbody></table>
|
||
<p></p>
|
||
<p><b>9.8 meters per second</b> per second (yes, that is two lots of "per second") can be written
|
||
9.8 m/s/s, but is usually written:</p>
|
||
<p class="center larger"> <b>9.8 m/s<sup>2</sup></b></p>
|
||
<p><b>9.8 m/s<sup>2</sup></b> is the <b>acceleration due to gravity</b> near the Earth's surface. Nearly everything in our lives happens near the Earth's surface, so that value gets used a lot, and is written as a <b>little</b> <b><i>g</i></b>:</p>
|
||
<p class="center large"><b><i>g</i></b> = 9.8 m/s<sup>2</sup></p>
|
||
<div class="fun">
|
||
<p>The average value is <b>9.80665 m/s<sup>2</sup></b>, but values are different around the world, such as Calcutta at 9.78548, London at 9.81599 and Tokyo at 9.79805.</p>
|
||
<p>So most people just use <b>9.8 m/s<sup>2</sup></b></p>
|
||
</div>
|
||
<p> </p>
|
||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/gravity-apple2.svg" alt="gravity apple" height="197" width="128"></p>
|
||
<p> </p>
|
||
<p>To hold an apple against gravity needs <a href="force.html">force</a>.</p>
|
||
<p>Force is mass times acceleration (<b>F</b> = m<b>a</b>), and in this case the acceleration is <b><i>g</i></b>:</p>
|
||
<p class="center larger"><b>F</b> = m<b><i>g</i></b></p>
|
||
<div style="clear:both"></div>
|
||
|
||
<div class="example">
|
||
|
||
<h3>Example: how much force to hold an apple with a mass of 0.1 kg?</h3>
|
||
<p class="center"><b>F</b> = m<b><i>g</i></b></p>
|
||
<p class="center"><b>F</b> = 0.1 kg × <b>9.8 m/s<sup>2</sup></b></p>
|
||
<p class="center"><b>F</b> = <b>0.98 kg m/s<sup>2</sup></b></p>
|
||
<p>Force is measured in Newtons (<b>N</b>) which are the same as <b> kg m/s<sup>2</sup></b></p>
|
||
<p class="center"><b>F</b> = <b>0.98 N</b></p>
|
||
<p>So it needs a force of <b>about 1 Newton</b> to hold up an apple.</p>
|
||
<p>We also say the apple has a <a href="../measure/weight-mass.html">weight</a> of 0.98 N.</p>
|
||
</div>
|
||
<div class="def">
|
||
<p class="center larger">To convert a mass in kg to a force in Newtons multiply by<b> 9.8 m/s<sup>2</sup></b></p>
|
||
</div><p>Another example:</p>
|
||
|
||
<div class="example">
|
||
|
||
<h3>Example: a 100kg steel beam sits evenly on two supports. How much force is on each support?</h3>
|
||
<p class="center"><img src="images/beam-100kg.gif" alt="beam 100kg" height="58" width="200"></p>
|
||
<p>The beam exerts a downwards force due to gravity:</p>
|
||
<p class="center"><b>F</b> = m<b><i>g</i></b></p>
|
||
<p class="center"><b>F</b> = 100 kg × <b>9.8 m/s<sup>2</sup></b> = <b>980 N</b></p>
|
||
<p>As it sits evenly on the support, each support bears half the weight (980/2=490):</p>
|
||
<p class="center"><img src="images/beam-100kg-forces.gif" alt="beam 100kg forces: 980N balances 2 of 490 N" height="154" width="200"></p>
|
||
</div>
|
||
|
||
|
||
<h2>But What Is Gravity?</h2>
|
||
|
||
<p>Now you know how to deal with gravity here on Earth (just multiply mass by <span class="center"><b>9.8 m/s<sup>2</sup></b></span> to get force), but what is gravity really?</p>
|
||
<p>Well, mass and energy make space curved (or distorted), so it is natural for objects to follow a path towards each other.</p>
|
||
<p class="center"><img src="images/space-time-curve2.jpg" alt="space time curve" height="187" width="360"><br>
|
||
<i>Here an object naturally follows space-time towards
|
||
Earth</i></p>
|
||
<p>This results in objects being <b>attracted to each other</b>, which we call <b>Gravity</b>.</p>
|
||
<div class="words">
|
||
<p><b>Gravity</b>: the attraction of objects with mass or energy towards each other.</p>
|
||
</div>
|
||
<p>This attraction shows as a <a href="force.html">force</a> that is:</p>
|
||
<ul>
|
||
<li>less for objects that are further away</li>
|
||
<li>more for objects of greater mass (like the Sun)</li>
|
||
</ul>
|
||
<p>Imagine just two balls:</p>
|
||
<p class="center"><img src="images/gravity-m1-m2-only.svg" alt="gravity mass 1 and 2" height="" width=""></p>
|
||
<p>Each ball is made of lots of bits of mass and energy that are all attracted to each other:</p>
|
||
<p class="center"><img src="images/gravity-parts.svg" alt="gravity all bits" height="" width=""><br>
|
||
<i>(Actually needs <b>lots</b> more particles!)</i></p>
|
||
<p>But we normally simplify it by imagining each ball's mass and energy is at its center, called the <a href="../geometry/centroid.html">Center of Gravity</a>.</p>
|
||
<p class="center"><img src="images/gravity-m1-m2.svg" alt="gravity mass 1 force = mass 2 force" height="" width=""></p>
|
||
<p>(But remember we just imagine all the mass is at the center, to make calculations easier.)</p>
|
||
<p>Newton worked out a formula for the force of attraction:</p>
|
||
<div class="def">
|
||
<p class="center large"><b>F</b> = G <span class="intbl"><em>m<sub>1</sub> m<sub>2</sub></em>
|
||
<strong>d<sup>2</sup>
|
||
</strong></span></p>
|
||
</div>
|
||
<ul>
|
||
<li><b>F</b> is the force (in Newtons), <b>which is equal but opposite in direction</b> for both objects</li>
|
||
<li>G is the gravitational constant, approximately 6.674×10<sup>-11</sup> N m<sup>2</sup>/kg<sup>2</sup></li>
|
||
<li>m<sub>1</sub> and m<sub>2</sub> are the two masses (in kg)</li>
|
||
<li>d is the distance <b>between the centers</b> of each mass (in meters)</li>
|
||
</ul>
|
||
<p> </p>
|
||
|
||
<div class="example">
|
||
|
||
<h3>Example: Two cars with masses of 800 kg and 1500 kg are 3 m apart</h3>
|
||
<p class="center"><img src="images/gravity-cars.jpg" alt="gravity between cars of 800 and 1500 mass" height="207" width="300"></p>
|
||
<p>The gravitational attraction <b>between the two cars</b> is:</p>
|
||
<p class="center large"><b>F</b> = G <span class="intbl">
|
||
<em>m<sub>1</sub> m<sub>2</sub></em>
|
||
<strong>d<sup>2</sup></strong>
|
||
</span></p>
|
||
<p class="center large"><b>F</b> = 6.674×10<sup>-11</sup> N m<sup>2</sup>/kg<sup>2</sup> × <span class="intbl">
|
||
<em>800 kg × 1500 kg</em>
|
||
<strong>(3 m)<sup>2</sup></strong>
|
||
</span></p>
|
||
<p class="center large"><b>F</b> ≈ 0.000009 N</p>
|
||
<p>They are <b>very slightly</b> (only 9 millionths of a Newton) attracted towards each other! </p>
|
||
</div>
|
||
|
||
<div class="example">
|
||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/gravity-earth-apple.svg" alt="gravity betwen earth and apple" height="151" width="261"></p>
|
||
|
||
<h3>Example: An Apple and the Earth</h3>
|
||
<p>The apple has a mass of 0.1 kg</p>
|
||
<p>The Earth has a mass of 5.972×10<sup>24</sup> kg</p>
|
||
<p>From the <b>center of the apple</b> to the <b>center of the Earth</b> is 6371 km (6.371×10<sup>6</sup> m)</p>
|
||
<p class="center large"><b>F</b> = G <span class="intbl">
|
||
<em>m<sub>1</sub> m<sub>2</sub></em>
|
||
<strong>d<sup>2</sup> </strong>
|
||
</span></p>
|
||
<p class="center large"><b>F</b> = 6.674×10<sup>-11</sup> N m<sup>2</sup>/kg<sup>2</sup> × <span class="intbl">
|
||
<em>0.1 kg × 5.972×10<sup>24</sup> kg</em>
|
||
<strong>(6.371×10<sup>6</sup> m)<sup>2</sup> </strong>
|
||
</span></p>
|
||
<p class="center large"><b>F</b> = 0.98 N</p>
|
||
<p><i>(This is the same value as the earlier apple calculation, so that's good!)</i></p>
|
||
</div>
|
||
|
||
<h3>Goes Both Ways</h3>
|
||
<p>The Earth is also attracted to the apple!</p>
|
||
<p>But the Earth is so ridiculously more massive that it hardly affects it.</p>
|
||
<p>Let's calculate the acceleration for the apple <b>and</b> for the Earth:</p>
|
||
|
||
<div class="example">
|
||
|
||
<h3>Example (continued): Knowing the force is 0.98 N what is the acceleration for the apple <b>and</b> the Earth?</h3>
|
||
<p>For the <b>apple</b>:</p>
|
||
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr>
|
||
<td style="text-align:right;"> </td>
|
||
<td> </td>
|
||
<td><b>F</b> = m<b>a</b></td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">We know F is 0.98 N, and m is 0.1 kg</td>
|
||
<td> </td>
|
||
<td><b>0.98 N</b> = 0.1 kg <b>a</b></td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">Divide both sides by 0.1 kg </td>
|
||
<td> </td>
|
||
<td><b>0.98 N</b> / 0.1 kg = <b>a</b></td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">Swap sides</td>
|
||
<td> </td>
|
||
<td><b>a</b> = <b>0.98 N</b> / 0.1 kg</td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">Answer: </td>
|
||
<td> </td>
|
||
<td><b>a</b> = <b>9.8 m/s<sup>2</sup></b></td>
|
||
</tr>
|
||
</tbody></table>
|
||
<p>That is the acceleration due to gravity "g" that we all experience every day.</p>
|
||
<p>And for the <b>Earth</b>:</p>
|
||
|
||
<table style="border: 0; margin:auto;">
|
||
<tbody>
|
||
<tr>
|
||
<td style="text-align:right;"> </td>
|
||
<td> </td>
|
||
<td><b>F</b> = m<b>a</b></td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">F is 0.98 N, and m is 5.972×10<sup>24</sup> kg</td>
|
||
<td> </td>
|
||
<td><b>0.98 N</b> = 5.972×10<sup>24</sup> kg <b>a</b></td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">Divide both sides by 5.972×10<sup>24</sup> kg</td>
|
||
<td> </td>
|
||
<td><b>0.98 N</b> / 5.972×10<sup>24</sup> kg = <b>a</b></td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">Swap sides</td>
|
||
<td> </td>
|
||
<td><b>a</b> = <b>0.98 N</b> / 5.972×10<sup>24</sup> kg</td>
|
||
</tr>
|
||
<tr>
|
||
<td style="text-align:right;">Answer: </td>
|
||
<td> </td>
|
||
<td><b>a</b> = <b>1.64×10<sup>-25 </sup>m/s<sup>2</sup></b></td>
|
||
</tr>
|
||
</tbody></table>
|
||
<p>That is an <i>extremely small acceleration</i>, no wonder we don't notice the Earth moving due to the apple.</p>
|
||
</div>
|
||
<div class="fun">
|
||
<p>But a much larger object such as the Moon (with a mass of <b>7.342×10<sup>22</sup> kg</b>) does have a noticeable effect on the Earth.</p>
|
||
<p>The Moon orbits the Earth at about <b>384,000 km</b> every 27.3 days</p>
|
||
<p>And the Earth also has an "orbit" (more like a wobble) with the Moon of about 5000 km (which is actually less than the Earth's radius), also every 27.3 days.</p>
|
||
</div>
|
||
<p>Your turn: try to work out the force of attraction between the Earth and the Moon.</p>
|
||
|
||
|
||
<h2>Have a Play</h2>
|
||
|
||
<p>Have a play with gravity at <a href="../numbers/gravity-freeplay.html">Gravity Freeplay</a>.</p>
|
||
|
||
|
||
<h2>Summary</h2>
|
||
|
||
<ul class="larger">
|
||
<li>mass and energy curve space, which naturally makes objects move towards each other</li>
|
||
<li>this attraction we call <b>gravity</b></li>
|
||
<li>this constant attraction makes objects accelerate towards each other</li>
|
||
<li>the acceleration has a matching force (<b>F</b>=m<b>a</b>)</li>
|
||
<li>near the surface of the Earth the acceleration due to gravity is <b>9.8 m/s<sup>2</sup></b></li>
|
||
<li>so a <b>1 kg mass</b> experiences a gravitational pull of <b>9.8 Newtons</b> of force</li>
|
||
</ul>
|
||
<p> </p>
|
||
<div class="questions">11939, 11941, 17544, 11942, 11947, 17546, 17550, 11945, 17548, 17551, 17552</div>
|
||
|
||
<div class="related">
|
||
<a href="gravity-ball.html">Ball Physics Animation</a>
|
||
<a href="../measure/metric-acceleration.html">Acceleration</a>
|
||
<a href="index.html">Physics Index</a>
|
||
</div>
|
||
<!-- #EndEditable -->
|
||
|
||
</article>
|
||
|
||
<div id="adend" class="centerfull noprint"></div>
|
||
<footer id="footer" class="centerfull noprint"></footer>
|
||
<div id="copyrt">Copyright © 2022 Rod Pierce</div>
|
||
|
||
</div>
|
||
</body><!-- #EndTemplate -->
|
||
<!-- Mirrored from www.mathsisfun.com/physics/gravity.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:39:34 GMT -->
|
||
</html> |