File "ahl-gravitational-fields.html"
Path: /StudyIB/physics/page/1148/ahl-gravitational-fieldshtml
File size: 72.16 KB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html><html lang="EN"><head> <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-PZBWZ8J');</script> <title>AHL Gravitational fields</title><!-- Removed by WebCopy --><!--<base href="/">--><!-- Removed by WebCopy --><meta http-equiv="x-ua-compatible" content="IE=Edge"><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1"><link href="../../../css/bootstrap.flatly.min.css" rel="stylesheet" media="screen"><link rel="stylesheet" href="../../../fonts/awesome/css/font-awesome.min.css"><link href="../../../js/jquery-fancybox/jquery.fancybox.min.css" type="text/css" rel="stylesheet"><link rel="stylesheet" href="../../../css/style.min.css?v=202301301645"><meta name="robots" content="index, follow"><meta name="googlebot" content="noarchive"><meta prefix="og: http://ogp.me/ns#" property="og:title" name="og:title" content="StudyIB Physics: AHL Gravitational fields"> <meta prefix="og: http://ogp.me/ns#" property="og:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta prefix="og: http://ogp.me/ns#" property="og:description" name="og:description" content="Close to the surface of a large mass (like Earth), the effects of gravitation are uniform. Further out, we realise the the gravitational field of a spherical mass is in fact radial. This has implications for how we calculate forces, field strength, potenti"> <meta prefix="og: http://ogp.me/ns#" property="og:url" name="og:url" content="https://studyib.net/physics/page/1148/ahl-gravitational-fields"> <meta prefix="og: http://ogp.me/ns#" property="og:site_name" name="og:site_name" content="StudyIB - Your IB learning companion"> <meta prefix="og: http://ogp.me/ns#" property="og:locale" name="og:locale" content="en"> <meta prefix="og: http://ogp.me/ns#" property="og:type" name="og:type" content="website"> <meta name="description" content="Close to the surface of a large mass (like Earth), the effects of gravitation are uniform. Further out, we realise the the gravitational field of a spherical mass is in fact radial. This has implications for how we calculate forces, field strength, potenti"> <meta name="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="keywords" content="StudyIB, Physics, Site overview, Self-study, Videos, Virtual tutor, Practices, Multiple Choice, IB, IBDP, InThinking, International Baccalaureate, Revision, Revision websites, Student Sites, Students, Learning, Guidance, Exam, Questions"> <meta itemprop="name" content="StudyIB Physics: AHL Gravitational fields"> <meta itemprop="description" content="Close to the surface of a large mass (like Earth), the effects of gravitation are uniform. Further out, we realise the the gravitational field of a spherical mass is in fact radial. This has implications for how we calculate forces, field strength, potenti"> <meta itemprop="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:title" content="StudyIB Physics: AHL Gravitational fields"> <meta name="twitter:description" content="Close to the surface of a large mass (like Earth), the effects of gravitation are uniform. Further out, we realise the the gravitational field of a spherical mass is in fact radial. This has implications for how we calculate forces, field strength, potenti"> <meta name="twitter:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:creator" content="@inthinker"><link rel="stylesheet" href="../../../css/snippets.min.css?v=202209111300"><link rel="stylesheet" href="../../../css/article.min.css?v=202211221000"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick.min.css"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick-theme.min.css"><link rel="stylesheet" type="text/css" href="../../../css/flashcards/flashcards.min.css?v=202211221000"><link rel="stylesheet" href="../../../css/flashcards/magic.min.css"><style type="text/css">.filter-sl-only { display: none; }</style><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script src="../../../js/ifvisible.min.js"></script><script>ifvisible.setIdleDuration(300);</script><link rel="apple-touch-icon-precomposed" sizes="57x57" href="../../../img/favicon/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon-precomposed" sizes="114x114" href="../../../img/favicon/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon-precomposed" sizes="72x72" href="../../../img/favicon/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon-precomposed" sizes="144x144" href="../../../img/favicon/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon-precomposed" sizes="60x60" href="../../../img/favicon/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon-precomposed" sizes="120x120" href="../../../img/favicon/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon-precomposed" sizes="76x76" href="../../../img/favicon/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon-precomposed" sizes="152x152" href="../../../img/favicon/apple-touch-icon-152x152.png"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-196x196.png" sizes="196x196"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-16x16.png" sizes="16x16"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-128.png" sizes="128x128"> <meta name="application-name" content="StudyIB: Your IB Learning Companion"> <meta name="msapplication-TileColor" content="#A5BED5"> <meta name="msapplication-TileImage" content="/img/favicon/mstile-144x144.png"> <meta name="msapplication-square70x70logo" content="/img/favicon/mstile-70x70.png"> <meta name="msapplication-square150x150logo" content="/img/favicon/mstile-150x150.png"> <meta name="msapplication-wide310x150logo" content="/img/favicon/mstile-310x150.png"> <meta name="msapplication-square310x310logo" content="/img/favicon/mstile-310x310.png"><script>var stdHash = "6da675cbcb3d25f050b05557349abc79", stdTicket = "082b9c9c4ae3624d";</script><script src="../../../js/user/local-stats.min.js?v=202205311700"></script><link href="../../../css/subjects-frontpage.min.css?v=202302031000" rel="stylesheet"></head><body class="public physics"> <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PZBWZ8J" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <div id="top-header"> <div class="wmap general hidden-sm hidden-xs subjects"> <div class="layout-wrapper"> <div class="container-fluid"> <a href=""> <img class="header-thinker" src="../../../img/header-thinker.svg"> </a> <h1> <a href="../../../physics.html"> IBDP Physics </a> <a href="https://inthinking.net" title="inthinking.net" class="inthinking-logo pull-right"> <img src="../../../img/header-logo.svg" style="height: 80px; width: auto;"> </a> </h1> <p class="slogan">InThinking Revision Sites for students</p> <p class="author">Website by <strong>Chris Hamper & Emma Mitchell</strong></p> <p class="updated">Updated 3 February 2023</p> </div> </div> </div> <nav id="public-topnav" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <a class="navbar-brand hidden-md hidden-lg" href="../../../index.htm"> <img class="header-xs-thinker" src="../../../img/header-thinker.svg"> </a> <button type="button" class="collapsed navbar-toggle" data-toggle="collapse" data-target="#subject-navbar-collapse" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <i class="fa fa-fw fa-2x fa-user"></i> </button> <div class="brand hidden-lg hidden-md hidden-sm"> <a class="brand-xs" href="../../../physics.html"> <strong class="title" style="white-space: nowrap;font-size: 18px;">Physics</strong> </a> </div> </div> <div class="collapse navbar-collapse" id="subject-navbar-collapse"> <ul class="nav navbar-bar navbar-userbox hidden-md hidden-lg"><li class="dropdown"><a href="#" class="dropdown-toggle" data-toggle="dropdown"><i class="fa fa-fw fa-lg fa-user-circle" style="margin-right: 5px;"></i><span style="font-size: 16px;"></span></a><ul class="dropdown-menu"><li class="dropdown-submenu"><a class="dropdown-toggle" href="#" data-toggle="dropdown"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class=""><a href="../../../mathsanalysis.html">DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class="active"><a href="../../../physics.html"><i class="fa fa-caret-right"></i> DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="menu-item"><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li class="menu-item"><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li class="menu-item"><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li><li class="menu-item hidden-md hidden-lg mt-xs-3"><a href="../../../index.htm?logout=1" class="btn btn-primary btn-xs-block"><i class="fa fa-fw fa-lg fa-power-off text-danger"></i>Log out</a></li></ul></li></ul> <ul class="nav navbar-bar"><li class=""><a class="home" href="../../../physics.html"><i class="fa fa-fw fa-home"></i> Home</a></li><li class=""><a class="topics" href="#"><i class="fa fa-fw fa-th-large"></i> Topics</a></li><li class=""><a class="favorites" href="../../../physics.html"><i class="fa fa-fw fa-star"></i> My favorites</a></li><li class=""><a class="" href="../../flashcards.html"><i class="fa fa-fw fa-bolt"></i> Flashcards</a></li><li class=""><a class="qbank" href="../../test-your-knowledge.html"><i class="fa fa-fw fa-question"></i> Question bank</a></li><li class=""><a class="networks" href="../../networks.html"><i class="fa fa-fw fa-graduation-cap"></i> Virtual tutor</a></li><li class=""><a class="" href="../../blogs.html"><i class="fa fa-fw fa-paperclip"></i> Blog</a></li><li class=""><a class="sitemap" href="../../sitemap.html"><i class="fa fa-fw fa-sitemap"></i> Sitemap</a></li><li class=""><a class="activity" href="../../../physics.html"><i class="fa fa-fw fa-calendar-check-o"></i> My activity</a></li></ul> <ul class="nav navbar-bar navbar-right"> <li> <form class="navbar-form hidden-md hidden-lg" role="search" method="get" action="physics/search"> <div class="input-group"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search..."> <span class="input-group-btn"> <button type="submit" class="btn bg-blue"> <i class="fa fa-search"> </i> </button> </span> </div> </form> <a href="#" class="toggle-menu-search hidden-sm hidden-xs" data-toggle="dropdown"> <i class="fa fa-lg fa-search"></i> </a> </li></ul> </div> </div></nav><nav id="nav-menu-search" class="shadow-bottom hidden-sm hidden-xs" style="display: none;"> <div class="container-fluid"> <form class="" role="search" method="get" action="physics/search"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search Physics..."> <button class="btn btn-sm btn-primary" type="submit"> Search </button> </form> </div></nav><div class="modal fade" tabindex="-1" role="dialog" id="modal-mini-login"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-body"> <button aria-hidden="true" data-dismiss="modal" class="close hidden-xs login-button-close" type="button">×</button> <form method="post"> <div class="form-group"> <input name="user-email" class="form-control" type="text" placeholder="Email"> </div> <div class="form-group"> <input name="user-password" class="form-control" type="password" placeholder="Password"> <input name="user-fp" class="fp" value="d8c893da5db7501669ffeeac46273ba6" type="hidden"> </div> <div class="form-group"> <a href="../../../reset-password.html" class="reset-password" style="font-weight: normal;"> Forgot your password? </a> </div> <div class="form-group"> <button type="submit" name="submit-login" value="1" class="btn btn-primary btn-block text-center"> <i class="fa fa-user fa-fw"></i> Log in </button> </div> </form> </div> </div> </div></div></div><div class="modal fade" id="show-topics" tabindex="-1" role="dialog"><div id="dialog-topics" class="modal-dialog modal-dialog-topics"><div class="modal-content"><div class="modal-body modal-body-topics"><div id="new-frontpage-toplevels-topics" class="frontpage-box"><div class="row"><div class="col-md-4 col-sm-4"><div class="item"><a href="../3015/free-access-weekend.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Free Access Weekend!</h3></div><div class="body"><div class="cropper" style="background-image: url('../../free.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../814/start-here.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Start here</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/getting-started/getting-started.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../819/revision-tips.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Revision tips</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/getting-started/exam-tips.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../2885/exam-questions.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Exam questions</h3></div><div class="body"><div class="cropper" style="background-image: url('../../practice-papers/flash-front.png'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../204/basics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Basics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/basics/basics.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../217/mechanics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Mechanics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/mechanics/mechanics.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../252/thermal.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Thermal</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/thermal/thermal.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../444/oscillations-and-waves.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Oscillations & waves</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/waves/waves.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../445/electricity-and-magnetism.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Electricity & magnetism</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/electricity/electricity.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../443/circular-motion-and-gravity.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Circular motion & gravity</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/circular-motion/circular.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../354/atomic-nuclear-and-particles.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Atomic, nuclear & particles</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/atomic/atomic.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../446/energy-production.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Energy production</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/energy-production/energy.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../848/options.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Options</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/astro/options.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../823/astrophysics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Astrophysics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/astro/black-hole.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../849/engineering.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Engineering</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/engineering/lift-off.jpg'); height: 10vw;"></div></div></a></div></div></div></div></div></div></div></div><div class="container-fluid shadow-ith"><div class="row frontpage"> <div class="col-md-3" id="left-column"> <p class="visible-xs-block"></p><div class="dropdown user-menu hidden-xs" style="margin-bottom: 20px;"> <button type="button" class="btn btn-default dropdown-toggle" data-toggle="dropdown" style="border-radius: 0; padding: 6px 18px;"> <i class="fa fa-fw fa-user-circle"></i> <small><i class="fa fa-caret-down"></i></small> </button> <ul class="dropdown-menu"> <li class="dropdown-submenu"><a href="#"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul id="user-subjects-menu" class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class=""><a href="../../../mathsanalysis.html">DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class="active"><a href="../../../physics.html"><i class="fa fa-caret-right"></i> DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="divider"></li><li><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li> <li class="divider"></li> <li> <a href="../../../index.htm?logout=1"> <i class="fa fa-fw fa-power-off"></i> Log out </a> </li> </ul></div> <div id="side-nav"><h4 class="side-nav-title dropdown"><a href="../443/circular-motion-and-gravity.html" class="dropdown-toggle toplevel-dropdown" data-toggle="dropdown"><i class="fa fa-ellipsis-v"></i></a> <a href="../443/circular-motion-and-gravity.html">Circular motion and gravity</a><ul class="dropdown-menu"><li><a href="../../../physics.html" style="padding-left: 5px; border-bottom: solid 1px #ddd"><i class="fa fa-fw fa-home"></i> Home</a></li><li><a href="../3015/free-access-weekend.html"><i class="fa fa-fw fa-caret-right"></i> Free Access Weekend!</a></li><li><a href="../814/start-here.html"><i class="fa fa-fw fa-caret-right"></i> Start here</a></li><li><a href="../819/revision-tips.html"><i class="fa fa-fw fa-caret-right"></i> Revision tips</a></li><li><a href="../2885/exam-questions.html"><i class="fa fa-fw fa-caret-right"></i> Exam questions</a></li><li><a href="../204/basics.html"><i class="fa fa-fw fa-caret-right"></i> Basics</a></li><li><a href="../217/mechanics.html"><i class="fa fa-fw fa-caret-right"></i> Mechanics</a></li><li><a href="../252/thermal.html"><i class="fa fa-fw fa-caret-right"></i> Thermal</a></li><li><a href="../444/oscillations-and-waves.html"><i class="fa fa-fw fa-caret-right"></i> Oscillations and waves</a></li><li><a href="../445/electricity-and-magnetism.html"><i class="fa fa-fw fa-caret-right"></i> Electricity and magnetism</a></li><li><a href="../354/atomic-nuclear-and-particles.html"><i class="fa fa-fw fa-caret-right"></i> Atomic, nuclear and particles</a></li><li><a href="../446/energy-production.html"><i class="fa fa-fw fa-caret-right"></i> Energy production</a></li><li><a href="../848/options.html"><i class="fa fa-fw fa-caret-right"></i> Options</a></li><li><a href="../823/astrophysics.html"><i class="fa fa-fw fa-caret-right"></i> Astrophysics</a></li><li><a href="../849/engineering.html"><i class="fa fa-fw fa-caret-right"></i> Engineering</a></li></ul><div class="pull-right"><a class="sidenav-expand" title="Expand all" href="#"><i class="fa fa-plus-circle"></i></a> <a class="sidenav-compress" title="Compress all" href="#"><i class="fa fa-minus-circle"></i></a></div></h4><ul class="side-nav level-0"><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../264/circular-motion.html">Circular motion</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../265/centripetal-force.html">Centripetal force</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../266/examples-of-circular-motion.html">Examples of circular motion</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../268/gravitation.html">Gravitation</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../269/newtons-law-of-gravitation.html">Newton's law of gravitation</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../270/uniform-fields.html">Uniform fields</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../271/orbits.html">Orbits</a></label></li></ul></li><li class="expanded parent selected"><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="ahl-gravitational-fields.html">AHL Gravitational fields</a></label></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"> AHL Gravitational fields <a href="#" class="mark-page-favorite pull-right" data-pid="1148" 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="../443/circular-motion-and-gravity.html">Circular motion and gravity</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">AHL Gravitational fields</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <p><img alt="" src="../../fields/earth-field.jpg" style="float: left; width: 250px; height: 250px;">Close to the surface of a large mass (like Earth), the effects of gravitation are uniform. Further out, we realise the the gravitational field of a spherical mass is in fact radial. This has implications for how we calculate forces, field strength, potential and energies. </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>Uniform fields</div> <div> <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>Field strength</p> </div> </div> <div class="panel-body"> <div> <p>Close to the surface of a large spherical mass, the surface appears horizontal and the gravitational field is uniform. Gravitational field strength is constant (9.81 Nkg<sup>-1</sup> on Earth) and field lines are equidistant and parallel.</p> <p style="text-align: center;"><img alt="" src="../../small-images/screen-shot-2016-11-03-at-05.42.27.png" style="width: 200px; height: 172px;"></p> <p>The direction of field lines is towards the mass producing the field (gravitational forces are always attractive). Because field strength is constant, the force acting on a given mass is constant. We call this <em>weight</em>:</p> <p style="text-align: center;"><span class="math-tex">\(F_g=W=mg\)</span></p> <ul> <li><span class="math-tex">\(F_g\)</span> is gravitational force (N)</li> <li><span class="math-tex">\(W\)</span> is weight (N)</li> <li><span class="math-tex">\(m\)</span> is mass (kg)</li> <li><span class="math-tex">\(g\)</span> is gravitational field strength (9.81 Nkg<sup>-1</sup> on Earth)</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-expandable panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Calculating energy changes</p> </div> </div> <div class="panel-body"> <div> <p>The work done by a mass against a gravitational field can be calculated by multiplying the gravitational force by the displacement. This work done becomes gravitational potential energy in the mass placed in the field.</p> <p style="text-align: center;"><span class="math-tex">\(\Delta E_p=mg\Delta h\)</span></p> <ul> <li><span class="math-tex">\(\Delta E_p\)</span> is the change in potential energy (J)</li> <li><span class="math-tex">\(m\)</span> is the mass in the field (kg)</li> <li><span class="math-tex">\(g\)</span> is gravitational field strength (Nkg<sup>-1</sup>)</li> <li><span class="math-tex">\(\Delta h\)</span> is the change in height (m)</li> </ul> <p>If a mass is released in a gravitational field, it loses potential energy equal to the kinetic energy gained.</p> <p>Gravitational potential at a position in the field is the potential energy per unit mass:</p> <p style="text-align: center;"><span class="math-tex">\(V_g=gh\)</span></p> <ul> <li><span class="math-tex">\(V_g\)</span> is gravitational potential (Jkg<sup>-1</sup>)</li> <li><span class="math-tex">\(g\)</span> is gravitational field strength (Nkg<sup>-1</sup>)</li> <li><span class="math-tex">\(h\)</span> is the height above zero potential (m)</li> </ul> <p>We can define zero potential arbitrarily but in such a way as to simplify the calculation, such as at the surface of the mass producing the field.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-expandable panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Equipotential surfaces</p> </div> </div> <div class="panel-body"> <div> <p>Equipotential surfaces are perpendicular to the gravitational field lines. For a uniform gravitational field, the equipotentials are horizontal, parallel and equidistant (shown in pale gray):</p> <p style="text-align: center;"><img alt="" src="../../images/flashcard-images/uniform.png" style="width: 200px; height: 142px;"></p> <p>Potential gradient is the ratio of the potential difference to the height and is a constant equal to the magnitude of the field strength.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </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>Radial fields</div> <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>Field strength</p> </div> </div> <div class="panel-body"> <div> <p>Beyond the distance from a mass at which fields can be assumed to be uniform, gravitational fields from point or spherical masses are radial.</p> <p style="text-align: center;"><img alt="" src="../../fields/radial-grav.png" style="width: 200px; height: 200px;"></p> <p>Gravitational force can be calculated from Newton's law:</p> <p style="text-align: center;"><span class="math-tex">\(F_g=G{Mm\over r^2}\)</span></p> <p>Gravitational field strength is the force per unit mass for a test mass placed in the field:</p> <p style="text-align: center;"><span class="math-tex">\(g={F_g\over m}=G{M\over r^2}\)</span></p> <ul> <li><span class="math-tex">\(g\)</span> is gravitational field strength (Nkg<sup>-1</sup>)</li> <li><span class="math-tex">\(F_g\)</span> is gravitational force (N)</li> <li><span class="math-tex">\(m\)</span> is the mass placed in the field (kg)</li> <li><span class="math-tex">\(G\)</span> is the universal gravitational constant (6.67 × 10<sup>-11</sup> m<sup>3</sup>kg<sup>-1</sup>s<sup>-2</sup>)</li> <li><span class="math-tex">\(M\)</span> is the mass producing the field (kg)</li> <li><span class="math-tex">\(r\)</span> is the distance between the centers of masses (m)</li> </ul> <p>Both force and field strength are vector quantities that obey inverse-square law behaviour.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </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>Potential</p> </div> </div> <div class="panel-body"> <div> <p>Gravitational potential is the work done per unit mass when a mass is brought from infinity to a point in space at a small constant speed.</p> <p>As force is not constant, the work done is found by integrating the force with respect to the distance from infinity.</p> <p style="text-align: center;"><span class="math-tex">\(V_g= {\int_\infty^r F_g\,\mathrm{d}r\over m}={\int_\infty^r {GMm\over r^2}\,\mathrm{d}r\over m}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow V_g=-G{M\over r}\)</span></p> <ul> <li><span class="math-tex">\(V_g\)</span> is gravitational potential (Nkg<sup>-1</sup>)</li> <li><span class="math-tex">\(G\)</span> is the universal gravitational constant (6.67 × 10<sup>-11</sup> m<sup>3</sup>kg<sup>-1</sup>s<sup>-2</sup>)</li> <li><span class="math-tex">\(M\)</span> is the mass producing the field (kg)</li> <li><span class="math-tex">\(r\)</span> is the distance between the centers of the masses (m)</li> </ul> <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/380476367"></iframe></div> <p>NB: Gravitational potential is negative as energy is released as the mass is brought from infinity to within the field. This is because gravitational forces are attractive.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </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>Equipotential surfaces</p> </div> </div> <div class="panel-body"> <div> <p>Since gravitational potential varies with <span class="math-tex">\(1\over r\)</span> from the center of the mass, the equipotential surfaces for a radial field increase in spacing outward from the mass producing the field. They are always at right angles to the field lines (shown in red):</p> <p style="text-align: center;"><img alt="" src="../../fields/equi-grav.png" style="height: 200px; width: 200px;"></p> <p>No energy is changed when the mass moves along an equipotential surface.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </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>Potential energy</p> </div> </div> <div class="panel-body"> <div> <p>When a mass moves parallel to a field line, its potential energy changes. Potential energy is the product of potential and the mass placed in the field:</p> <p style="text-align: center;"><span class="math-tex">\(E_p=mV_g=-G{Mm\over r}\)</span></p> <p>Change in potential energy can be calculated as follows:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta E_p=m\Delta V_g=m\times GM({1\over r_f}-{1\over r_i})\)</span></p> <ul> <li><span class="math-tex">\(\Delta E_p\)</span> is change in potential energy (J)</li> <li><span class="math-tex">\(m\)</span> is the mass moving in the field (kg)</li> <li><span class="math-tex">\(\Delta V_g\)</span> is the change in potential (Jkg<sup>-1</sup>)</li> <li><span class="math-tex">\(G\)</span> is the universal gravitational constant (6.67 × 10<sup>-11</sup> m<sup>3</sup>kg<sup>-1</sup>s<sup>-2</sup>)</li> <li><span class="math-tex">\(M\)</span> is the mass producing the field (kg)</li> <li><span class="math-tex">\(r\)</span> is the initial or final distance between the centers of the masses (m)</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </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>Potential gradient</p> </div> </div> <div class="panel-body"> <div> <p>Potential gradient between two equipotential surfaces is the ratio of the potential difference to the distance between the equipotentials:</p> <p style="text-align: center;"><span class="math-tex">\({\Delta V_g\over \Delta r}=-G{M\over r^2}\)</span></p> <p>Notice that potential gradient is equal to negative gravitational field strength:</p> <p style="text-align: center;"><span class="math-tex">\(g=-{\Delta V_g\over \Delta r} =G{M\over r^2}\)</span></p> <ul> <li><span class="math-tex">\(g\)</span> is gravitational field strength (Nkg<sup>-1</sup>)</li> <li><span class="math-tex">\(\Delta V_g\)</span> is the change in potential (Jkg<sup>-1</sup>)</li> <li><span class="math-tex">\(\Delta r\)</span> is the distance between the equipotentials (m)</li> <li><span class="math-tex">\(G\)</span> is the universal gravitational constant (6.67 × 10<sup>-11</sup> m<sup>3</sup>kg<sup>-1</sup>s<sup>-2</sup>)</li> <li><span class="math-tex">\(M\)</span> is the mass producing the field (kg)</li> <li><span class="math-tex">\(r\)</span> is the distance between the centers of masses (m)</li> </ul> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p>Gravity in space </p> <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>Orbits</p> </div> </div> <div class="panel-body"> <div> <p>A mass in orbit in a gravitational field possesses two types of energy:</p> <ul> <li>Kinetic energy due to its motion, <span class="math-tex">\(E_k={1\over 2}mv^2\)</span></li> <li>Gravitational potential energy due to its position in the field, <span class="math-tex">\(E_p=-G{Mm\over r}\)</span></li> </ul> <p>Total energy, <span class="math-tex">\(E_T=E_k+E_p\)</span>:</p> <p style="text-align: center;"><span class="math-tex">\(E_T={1\over 2}mv^2-G{Mm\over r}\)</span></p> <p>We can reduce the number of variables by considering the implication of circular orbital motion, that the resultant centripetal force is equal to the gravitational force:</p> <p style="text-align: center;"><span class="math-tex">\(F_g=G{Mm\over r^2}=m{v^2\over r}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(v^2=G{M\over r}\)</span></p> <p>Substituting into the total energy:</p> <p style="text-align: center;"><span class="math-tex">\(E_T={1\over 2}G{Mm\over r}-G{Mm\over r}=-{1\over 2}G{Mm\over r}\)</span></p> <p>NB: We bypassed a Data Booklet equation en route, which gives the size of the velocity for an orbtting body:</p> <p style="text-align: center;"><span class="math-tex">\(v_\text{orbit}=\sqrt{G{M\over r}}\)</span></p> </div> </div> <div class="panel-footer"> <div> <p> </p> </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>Escape speed</p> </div> </div> <div class="panel-body"> <div> <p>A ballistic object (i.e. a particle without its own engine) can theoretically be given sufficient kinetic energy to fully escape the gravitational field of the mass on which it is situated. The escape speed is the speed that would just be enough to escape the field.</p> <p>To derive an expression for this escape velocity, we use conservation of energy. The kinetic energy at the surface added to the gravitational potential energy at the surface is equal to the energy at infinity. The energy at infinity is zero because the object will <em>just</em> have lost its kinetic energy and because of how gravitational potential is defined when the field is escaped.</p> <p style="text-align: center;"><span class="math-tex">\(E_k+E_p=0\)</span></p> <p style="text-align: center;"><span class="math-tex">\({1\over 2}mv^2-G{Mm\over r}=0\)</span></p> <p style="text-align: center;"><span class="math-tex">\({1\over 2}mv^2=G{Mm\over r}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow v_\text{esc}=\sqrt{2G{M\over r}}\)</span></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/380475730"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </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><em>Use flashcards to practise your recall.</em></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="3" data-mode="Normal" data-topics="1030" data-subject-id="6" data-n-flashcards="11" style="text-align:center">Show flashcards</a></div><hr> <p><em>Use quizzes to practise application of theory.</em></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#328a35e7"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="328a35e7"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> AHL Gravitational potential and escape velocity <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-375-1148" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>Two balls are placed in a uniform gravitational field.</p><p style="text-align: center;"><img alt="" height="210" src="../../screenshot-2019-11-27-at-06.19.23.png" width="268"></p><p>The green ball has one quarter the mass of the blue ball but the same potential energy.</p><p>The ratio <span class="math-tex">\(\text{acceleration of green ball}\over \text{acceleration of blue ball}\)</span> and the direction of acceleration is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>1 - down</span></label> </p><p><label class="radio"> <input type="radio"> <span>4 - down</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1 - up</span></label> </p><p><label class="radio"> <input type="radio"> <span>1/4 - up</span></label> </p></div><div class="q-explanation"><p>The field is uniform so the gravitational field strength and, hence, acceleration of each is the same.</p><p>The potential at the green ball's position is higher than that of the blue (since the potential energy is greater for a smaller mass) so the potential is increasing downwards. The field is therefore directed up.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Two balls of equal mass are arranged in a uniform gravitational field as shown.</p><p style="text-align: center;"><img alt="" height="165" src="../../screenshot-2019-11-27-at-07.00.26.png" width="330"></p><p>They have the same acceleration but the red one has higher potential energy.</p><p>The direction of the field is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>towards the right</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>towards the left</span></label> </p><p><label class="radio"> <input type="radio"> <span>down</span></label> </p><p><label class="radio"> <input type="radio"> <span>up</span></label> </p></div><div class="q-explanation"><p>Potential increases from left to right so work has been done to move the red further than the green. Gravitational force is to the left.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The red mass is in the gravitational field of the blue mass.</p><p style="text-align: center;"><img alt="" height="135" src="../../screenshot-2019-11-27-at-15.41.29.png" width="167"></p><p>If the potential energy of the red mass is <span class="math-tex">\(E\)</span>, the potential of the field at that position is:</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(E\over m\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(E\over r\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(Em\over r\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(E\over M\)</span></span></label></p></div><div class="q-explanation"><p>Potential is defined as the work done per unit mass. The work done is equal to the potential energy.</p><p><span class="math-tex">\(E=G{Mm\over r}\)</span></p><p><span class="math-tex">\(V = G{M\over r}={E\over m}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The red mass is in the gravitational field of the blue mass.</p><p style="text-align: center;"><img alt="" height="135" src="../../screenshot-2019-11-27-at-15.41.29.png" width="167"></p><p>If the force experienced by the red mass is <span class="math-tex">\(F\)</span>, the magnitude of the potential of the field at that position is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(Fr\over M\)</span></span></label></p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(Fr\over m\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(F\over mr\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(F\over m\)</span></span></label></p></div><div class="q-explanation"><p><span class="math-tex">\(F = G{Mm\over r^2}\)</span></p><p><span class="math-tex">\(V = G{M\over r}={Fr\over m}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A small mass is moved in a straight line from point A to point B.</p><p style="text-align: center;"><img alt="" height="139" src="../../screenshot-2019-11-27-at-16.00.42.png" width="363"></p><p>At point X:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Potential energy is zero; force is maximum</span></label> </p><p><label class="radio"> <input type="radio"> <span>Potential energy is minimum; force is zero</span></label> </p><p><label class="radio"> <input type="radio"> <span>Potential energy is maximum; force is maximum</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Potential energy is maximum; force is zero</span></label> </p></div><div class="q-explanation"><p>Force is a vector quantity and is balanced due to the opposite and equal forces.</p><p>The magnitude of potential energy is maximised at X as the mass would have to be pushed to X then it would be attracted by the right hand mass to B. NB: potential energy is a scalar quantity that would be reduced if closer to the center of either mass.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A small mass travels from A to B through a tunnel passing through the <span class="scayt-misspell-word" data-scayt-word="centre" data-wsc-id="k3hfmoar5ks92ctqj" data-wsc-lang="en_US">centre</span> of a large mass.</p><p style="text-align: center;"><img alt="" height="175" src="../../screenshot-2019-11-27-at-16.15.35.png" width="204"></p><p>At point X:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Potential energy is maximum; force is zero</span></label> </p><p><label class="radio"> <input type="radio"> <span>Potential energy is minimum; force is maximum</span></label> </p><p><label class="radio"> <input type="radio"> <span>Potential energy is maximum; force is maximum</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Potential energy is minimum; force is zero</span></label> </p></div><div class="q-explanation"><p>Forces are balanced so resultant force is zero.</p><p>The mass would fall down the hole, then once past the <span class="scayt-misspell-word" data-scayt-word="centre" data-wsc-id="k3hfunkeg3bwx2slh" data-wsc-lang="en_US">centre</span> be attracted back down the hole.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>In an <span class="scayt-misspell-word" data-scayt-word="Algodoo" data-wsc-id="k3i9xt0jh1563eoca" data-wsc-lang="en_US">Algodoo</span> simulation where <span class="math-tex">\(G\)</span> = 1 Nm<sup>2</sup>kg<sup>-2 </sup>, what would the potential be on the surface of a 100 kg sphere of radius 2 m?</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>-50 Jkg<sup>-1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>-200 Jkg<sup>-1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>-100 Jkg<sup>-1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>-25 Jkg<sup>-1</sup></span></label> </p></div><div class="q-explanation"><p>We can calculate potential using the equation direct from the Data Booklet: <span class="math-tex">\(V_g = -G{M\over r}\)</span></p><p>It is not necessary to recall the derivation using the integration of force from infinity!</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>In an <span class="scayt-misspell-word" data-scayt-word="Algodoo" data-wsc-id="k3i9xt0isjr29fq5c" data-wsc-lang="en_US">Algodoo</span> simulation where G = 1 Nm<sup>2</sup>kg<sup>-2 </sup>, what would the escape velocity be from the surface of a 100 kg sphere of radius 2 m?</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>10 ms<sup>-1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>50 ms<sup>-1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>100 ms<sup>-1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>it depends on the mass of the escaping body</span></label> </p></div><div class="q-explanation"><p><span class="scayt-misspell-word" data-scayt-word="ΔPE" data-wsc-id="k3i9xt7glq7gv4rgo" data-wsc-lang="en_US">Since the kinetic energy provided must be sufficient just to escape the gravitational field, <span class="math-tex">\(E_k=E_p\)</span></span></p><p><span class="math-tex">\({1\over 2}mv^2=G{Mm\over r}\)</span></p><p><span class="math-tex">\(v_\text{esc} = \sqrt{2G{M\over r}} = \sqrt{100}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Stars A and B have the same radius but the density of star A is four times that of B.</p><p>What is the ratio <span class="math-tex">\(v_\text{esc, A}\over v_\text{esc, B}\)</span>?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(\sqrt2\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over 2\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(4\)</span></span></label></p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(2\)</span></span></label></p></div><div class="q-explanation"><p><span class="math-tex">\(v_\text{esc} = \sqrt{2G{M\over r}}\)</span></p><p>The radius is the same so <span class="math-tex">\(v_\text{esc}\propto\sqrt M\)</span></p><p><span class="math-tex">\(M_A = 4M_B\)</span></p><p><span class="math-tex">\({v_A\over v_B} = \sqrt{4M_B\over M_B} =2\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A satellite of mass, <span class="math-tex">\(m\)</span> has an orbit of radius <span class="math-tex">\(r\)</span> around the Earth. If the mass of the Earth is <span class="math-tex">\(M\)</span>, the kinetic energy of the satellite is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(GMm\over r\)</span></span></label></p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(GMm\over 2r\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(GMm\over r^2\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(-GMm\over r\)</span></span></label></p></div><div class="q-explanation"><p><span class="math-tex">\({mv^2\over r} = {GMm\over r^2}\)</span></p><p><span class="math-tex">\({1\over 2}mv^2 = {GMm\over 2r}\)</span></p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>A satellite of mass, <span class="math-tex">\(m\)</span> has an orbit of radius <span class="math-tex">\(r\)</span> round the Earth. If the mass of the Earth is <span class="math-tex">\(M\)</span>, the potential energy of the satellite is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(GMm\over r\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(-GMm\over r^2\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(GMm\over 2r\)</span></span></label></p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(-GMm\over r\)</span></span></label></p></div><div class="q-explanation"><p>Don't be put off by the long description of the problem. No matter what type of orbit the body was in, it would have this potential energy as a result of its position.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="1148"> <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>AHL Gravitational fields</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/1148/ahl-gravitational-fields"> <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; justify-content: space-between; align-items: center;"><p id="fc-viewer-info" style="width: 80%;"></p><button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button></div></div></div></div><div id="flashcard-body" class="modal-body"><div class="row" style="margin: 0;"><div class="col-md-8 fc-viewer-main"><div class="fc-viewer-inner"><div id="fc-viewer-main-front"><div class="fc-viewer-content"></div><span class="mark-favorite" style="position: absolute; top: 10px; right: 10px; font-size: 22px;"><i class="fa fa-lg fa-star-o"></i></span><span id="issue-report" class="issue-report hidden-xs hidden-sm" title="Report a problem"><i class="fa fa-fw fa-lg fa-exclamation-circle" style="font-size: 1.5em;"></i> </span> </div><div id="fc-viewer-main-back" class="reverse-flashcard green-bg"><div class="fc-viewer-content"></div><span class="mark-favorite" style="position: absolute; top: 10px; right: 10px; font-size: 22px;"><i class="fa fa-lg fa-star-o"></i></span></div></div></div><div class="col-md-4 fc-viewer-controls"><div class="fc-viewer-controls-middle"> <div class="fc-viewer-controls-middle-inner fc-back"><div class="fc-viewer-controls-answers mt-xs-0 mx-xs-0"><button id="right-answer" class="btn btn-success text-center btn-block" title="Mark this flashcard as CORRECT"><i class="fa fa-check"></i> Correct</button><button id="wrong-answer" class="btn text-center bg-red btn-block" title="Mark this flashcard as INCORRECT"><i class="fa fa-remove"></i> Incorrect</button></div><table class="table stats"><tr><td>Times flipped</td><td id="fc-viewer-tflipped" class="text-right">0</td></tr><tr><td>Marked as <em>correct</em></td><td id="fc-viewer-right" class="text-right">0</td></tr><tr><td>Marked as <em>incorrect</em></td><td id="fc-viewer-wrong" class="text-right">0</td></tr></table><a href="#" class="btn btn-default btn-sm btn-block text-center reset-stats hidden-xs hidden-sm" title="Reset stats for this flashcard" style="margin: 10px 0;"><i class="fa fa-undo"></i> Reset</a> <div class="fc-notes-container hidden-xs hidden-sm"><textarea class="form-control notes fc-back card-notes" rows="4" placeholder="Write your own notes here..." style="resize: none;">
</textarea><a href="#" class="btn btn-default btn-sm btn-block text-center save-notes" title="Save personal notes for this flashcard" style="margin-bottom: 10px;"><i class="fa fa-pencil"></i> Save notes</a> </div><div class="fc-viewer-actions-sm hidden-md hidden-lg"><button type="button" class="btn btn-sm btn-xs-block reset-stats"><i class="fa fa-fw fa-undo"></i>Reset</button> <button type="button" class="btn btn-sm btn-xs-block" data-toggle="modal" data-target="#card-notes-sm-modal"><i class="fa fa-fw fa-pencil"></i>Notes</button><button type="button" class="btn btn-sm btn-xs-block" data-toggle="modal" data-target="#report-problem-sm-modal"><i class="fa fa-fw fa-exclamation-circle"></i>Report error</button></div> </div></div><div class="fc-viewer-controls-bottom hidden-xs hidden-sm"><div class="fc-move"> <button class="btn bg-turquoise text-center disabled" rel="prev" title="Previous flashcard"><i class="fa fa-fw fa-chevron-left"></i>Prev</button><button class="btn bg-turquoise text-center disabled" rel="next" title="Next flashcard">Next<i class="fa fa-fw fa-chevron-right"></i></button></div><div class="fc-actions"><button class="btn btn-default btn-block text-center shuffle"><i class="fa fa-random"></i> Shuffle</button><div class="fc-progress"><div class="progress"><div class="progress-bar"></div></div><div class="text-right"><span class="fc-viewer-results-counter"></span></div></div></div></div><div class="fc-close-sm hidden-md hidden-lg"><button id="fc-xs-close" type="button" class="btn btn-default btn-block text-center" data-dismiss="modal" aria-label="Close">Close</button> <hr class="thin"> <div class="fc-actions" style="width: 100%;"> <button class="btn btn-default btn-block text-center shuffle"> <i class="fa fa-random"></i> Shuffle </button><div class="fc-progress"><div class="progress"><div class="progress-bar"></div></div><div class="text-right"><span class="fc-viewer-results-counter hidden-md hidden-lg"></span></div></div> </div></div></div></div></div><div class="modal-footer"><div id="report-error-container" class="report-problem"><div class="row"><div class="col-md-8"><div class="msg"></div><div class="form-group"><label>Report a problem for flashcard <span class="fc-viewer-id"></span></label><textarea class="form-control issue-description" cols="4"></textarea></div><button type="button" class="btn btn-primary pull-right send-report disabled"><i class="fa fa-paper-plane"></i>Send</button><button id="close-send-report" type="button" class="btn btn-default" style="margin-left: 0;">Close</button></div></div></div></div></div></div></div><div id="card-notes-sm-modal" class="modal fade overlay-modal" tabindex="-1" role="dialog"><div class="modal-dialog modal-sm" role="document"><div class="modal-content"><div class="modal-header p-xs-3"><h4 class="modal-title text-center my-xs-2">Notes</h4></div><div class="modal-body p-xs-3"><textarea class="form-control notes fc-back card-notes p-xs-3" rows="8" style="resize: none;">
</textarea></div><div class="modal-footer p-xs-3"><button type="button" class="btn btn-sm btn-primary btn-xs-block save-notes"><i class="fa fa-fw fa-pencil"></i>Save</button><button type="button" class="btn btn-sm btn-default btn-xs-block mx-xs-0" data-dismiss="modal" aria-label="Close">Close</button></div></div></div></div><div id="report-problem-sm-modal" class="modal fade overlay-modal report-problem" tabindex="-1" role="dialog"><div class="modal-dialog modal-sm" role="document"><div class="modal-content"><div class="modal-header p-xs-3"><h4 class="modal-title text-center my-xs-2">Report a problem for flashcard <span class="fc-viewer-id"></span></h4></div><div class="modal-body p-xs-3"><div class="msg"></div><div class="form-group mb-xs-0"><textarea class="form-control issue-description p-xs-3" rows="8"></textarea></div></div><div class="modal-footer p-xs-3"><button type="button" class="btn btn-sm btn-primary text-center btn-xs-block mb-xs-3 disabled send-report"><i class="fa fa-fw fa-paper-plane"></i>Send</button><button type="button" class="btn btn-sm btn-default text-center btn-xs-block mx-xs-0" data-dismiss="modal" aria-label="Close">Close</button></div></div></div></div> <div id="fcgame-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"> <div class="modal-dialog modal-lg modal-dialog-fcgame" role="document"> <div class="modal-content mc-flashcard modal-content-fcgame"> <div class="modal-header" style="background-color: #fafafa;"> <div class="row text-center" style="width: 100%;"> <div class="col-md-12"> <div style="display: flex; justify-content: space-between; align-items: center;"> <div class="text-left"> Your time: <span class="chronometer c-mobile" id="chronometer">00:00:</span> <span class="chronometer msec c-mobile" id="chronometer-msec">000</span> <br> Your best time: <span class="chronometer c-mobile" id="best-record"></span> </div> <button type="button" class="close" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> </div> </div> </div> <div id="fcgame-body" class=" modal-body modal-body-fcgame"> <div class="row-fluid"> <div class="col-lg-12 col-md-12 col-sm-12 fc-content" id="fc-content" style="padding: 15px;"></div> </div> </div> <div id="end-game" style="display: none;"> <div class="col-lg-10 col-lg-offset-1 col-md-10 col-md-offset-1 col-sm-10 col-sm-offset-1 result shadow-bottom"> <div id="end-game-dismiss"></div> <div id="end-game-results"></div> <div id="show-percent" style="margin-bottom: 30px;font-size: 16px;"></div> </div> <div id="end-game-fc" class="col-lg-12"></div> </div> <div id="start-game" class="col-lg-12 col-md-12 col-sm-12 centered"> <div style="width: 200px;"> <button class="btn btn-success btn-xs-block" id="play-game" style="display: block; width: 100%; margin: 10px 0;">Start</button> <button class="btn btn-default btn-xs-block" id="cancel-game" style="display: block; width: 100%; margin: 10px 0;">Cancel</button> </div> </div> <div class="modal-footer"></div> </div> </div></div><div id="fcgame-modal-issue-report" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title">Report error</h4> </div> <div class="modal-body"> <textarea id="issue-description-fcgame" class="form-control"></textarea> </div> <div class="modal-footer"> <button id="send-report-fcgame" type="button" class="btn btn-primary">Send Report</button> </div> </div> </div></div> </article> <hr class="hidden-md hidden-lg"> <div class="hidden-md hidden-lg mt-xs-3"> <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> <input type="hidden" id="user-id" value="38342"></div><input id="ticket" type="hidden" value="082b9c9c4ae3624d"><input id="tzoffset" type="hidden" value="new"><input id="fp" class="fp" type="hidden" value=""></div><div id="std-footer"> <div class="wmap"> <div class="layout-wrapper"> <p> <a href="https://www.inthinking.net"> © <span id="footer-year"></span> <em>InThinking</em> <script>document.getElementById("footer-year").innerHTML = new Date().getFullYear();</script> </a> | <a target="_self" href="../../../about.html"> About us </a> | <a target="_self" href="../../../terms-and-conditions.html"> Legal </a> | <a target="_self" href="../../../contact.html"> Contact </a> </p> <p> <a class="social" target="_blank" href="https://twitter.com/#!/inthinker"> <img src="../../../img/social/twitter-square.svg"> Twitter </a> <a class="social" target="_blank" href="https://www.facebook.com/inthinking.net"> <img src="../../../img/social/facebook-square.svg"> Facebook </a> <a class="social" target="_blank" href="https://www.linkedin.com/profile/view?id=139741989"> <img src="../../../img/social/linkedin-square.svg"> LinkedIn </a> </p> </div> </div></div><script src="../../../js/jquery-1.11.3.min.js"></script><script src="../../../js/bootstrap.min.js"></script><script src="../../../js/jquery-fancybox/jquery.fancybox.min.js"></script><script>var pageId = 1148;</script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui-custom.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.js"></script><script type="text/javascript" src="../../../js/std-quizzes-helpers.min.js?v=20220406"></script><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script type="text/javascript" src="../../../js/slick-carousel/slick.min.js"></script><script type="text/javascript" src="../../../js/std-slide-quizzes.min.js?v=20220406"></script><script type="text/javascript" src="../../../js/jq-boxfit/jquery.boxfit.min.js"></script><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script type="text/javascript" src="../../../js/flashcards/flashcards-utils.min.js?v=202211221200"></script><script type="text/javascript" src="../../../js/flashcards/std-flashcards.min.js?v=202211221000"></script><script type="text/javascript" src="../../../js/hammerjs/hammerjs.min-1.js?v=20220414"></script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.min.js"></script><script src="../../../js/user/page-my-progress.min.js?v=202211221000"></script><script>var sAJAX='/pages/subjects/activity/user-stats-page.php?t=082b9c9c4ae3624d&p=1148&s=6&x=29490';var sData='k4iA6GSB03BgPm1yOUCNIxiA6GSB0bfq7Y9FwFiA6GSBPFAF7YcHEKvrZ0fREzP5PgcPUxpV7nc3Z0fsSYBhWncRPYEjEGyg74PRPHpsE3KeSYcH74P5k4iRE0EBWVOFwBRD00rRPnLsSYK4ZGcR74P5EncR739RPHaL6nfhWGcjWFP5PFPRPHpsSYlFwFi7Ibp1k0aj6ba7IbpsE3K7IDuyads7I3c1WxLH7nc3Z0fsSYBhWncRIGEjEGyg74iv';var loopSecs = 30;var minSecsLog = 60;var lsKey = '6-83610-1148';</script><script src="../../../js/subjects/activity/user-stats-page.min.js?v=202205311700"></script><script src="../../../js/subjects/activity/my-favorites.min.js?v=20220610"></script><script src="../../../js/subjects/feedback.min.js?v=202211221000"></script><script>var sessionUpdateSecs = 300;</script><script type="text/javascript" src="../../../js/session-updater.js"></script><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');ga('create', 'UA-98480796-3', 'auto');ga('send', 'pageview');</script><script src="../../../js/devicefp/devicefp.min.js"></script><script src="../../../js/jq-quickfit/jq-quickfit.min.js?v=20220201"></script><script src="../../../js/frontpage-subjects.min.js?v=202211161300"></script><script type="text/javascript" src="../../../js/studyib-jq.min.js?v=202211241300"></script><script type="text/javascript">$(document).ready(function(){ $('#trigger-modal-video-overview').click(function() { if( $('#modal-video-overview .modal-body iframe').attr('src').length == 0 ) { $('#modal-video-overview .modal-body iframe').attr('src', 'https://www.youtube.com/embed/hxxtdiLdTFk?rel=0'); } }); $('#modal-video-overview').on('hidden.bs.modal', function() { $('#modal-video-overview .modal-body iframe').attr('src', ''); }); });</script></body></html>