{"id":287,"date":"2026-06-21T02:02:36","date_gmt":"2026-06-21T02:02:36","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=287"},"modified":"2026-06-21T02:02:37","modified_gmt":"2026-06-21T02:02:37","slug":"potential-energy","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/potential-energy\/","title":{"rendered":"Potential Energy: Definition, Types &amp; Formula"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\nPotential energy is the energy stored in an object because of its position, shape, or configuration, ready to be released as motion or another form of energy. For an object of mass m at height h, gravitational potential energy equals mgh, where g is the gravitational field strength. Its SI unit is the joule (J).\n<\/p><\/div>\n\n<p>Lift a book over your head and hold it perfectly still. Nothing is moving, no engine is running \u2014 yet something has changed. You have loaded that book with energy, and the floor will find out the instant you let go.<\/p>\n\n<p>That waiting, stored energy is potential energy. It hides in a drawn bow, in water trapped behind a dam, in the food on your plate, even in the charge sitting on your phone battery. None of it does anything visible \u2014 until it is released.<\/p>\n\n<h2>What Is Potential Energy?<\/h2>\n\n<p>Potential energy is the energy an object stores because of <em>where<\/em> it is or <em>how<\/em> it is arranged, rather than because it is moving. Stretch a spring, raise a mass, push two magnets together: each time you do work, and that work is banked as energy the system can pay back later.<\/p>\n\n<p>It is one of the two great families of mechanical energy \u2014 the other being <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/kinetic-energy-formula\/\">kinetic energy<\/a>, the energy of motion. For the wider map of how all the forms fit together, see our guide to <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/what-is-energy-in-physics\/\">energy in physics<\/a>.<\/p>\n\n<p>The word <em>potential<\/em> is the clue. The energy is latent, not active. A boulder resting on a clifftop isn&#8217;t doing a thing \u2014 but it holds the <em>potential<\/em> to do a great deal the moment it tips over the edge.<\/p>\n\n<svg role=\"img\" aria-label=\"Diagram showing a ball of mass m held at height h above a reference level, illustrating that gravitational potential energy equals m times g times h\" viewBox=\"0 0 640 380\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;max-width:640px;display:block;margin:0 auto;background:#0A1628;border-radius:6px;\">\n  <defs>\n    <marker id=\"pe-gold\" markerWidth=\"9\" markerHeight=\"9\" refX=\"5.5\" refY=\"3\" orient=\"auto\" markerUnits=\"strokeWidth\"><path d=\"M0,0 L6,3 L0,6 Z\" fill=\"#C8932A\"><\/path><\/marker>\n    <marker id=\"pe-mist\" markerWidth=\"9\" markerHeight=\"9\" refX=\"5.5\" refY=\"3\" orient=\"auto\" markerUnits=\"strokeWidth\"><path d=\"M0,0 L6,3 L0,6 Z\" fill=\"#C5D0DC\"><\/path><\/marker>\n  <\/defs>\n  <rect x=\"0\" y=\"0\" width=\"640\" height=\"380\" fill=\"#0A1628\"><\/rect>\n  <rect x=\"0\" y=\"305\" width=\"640\" height=\"75\" fill=\"#142139\"><\/rect>\n  <line x1=\"0\" y1=\"305\" x2=\"640\" y2=\"305\" stroke=\"#D9CFB8\" stroke-width=\"2\"><\/line>\n  <text x=\"22\" y=\"332\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" fill=\"#C5D0DC\">Reference level (h = 0)<\/text>\n  <text x=\"28\" y=\"74\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"34\" font-weight=\"800\" fill=\"#FAF6EE\">PE = <tspan fill=\"#C8932A\">mgh<\/tspan><\/text>\n  <text x=\"30\" y=\"104\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"15\" fill=\"#C5D0DC\">energy stored by position<\/text>\n  <line x1=\"500\" y1=\"305\" x2=\"500\" y2=\"95\" stroke=\"#C8932A\" stroke-width=\"2\" stroke-dasharray=\"6 5\" marker-start=\"url(#pe-gold)\" marker-end=\"url(#pe-gold)\"><\/line>\n  <text x=\"514\" y=\"206\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"22\" font-weight=\"700\" fill=\"#FAF6EE\">h<\/text>\n  <text x=\"514\" y=\"227\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#C5D0DC\">height<\/text>\n  <circle cx=\"440\" cy=\"95\" r=\"26\" fill=\"#C8932A\" stroke=\"#FAF6EE\" stroke-width=\"2\"><\/circle>\n  <text x=\"440\" y=\"50\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"16\" fill=\"#FAF6EE\" text-anchor=\"middle\">mass m<\/text>\n  <line x1=\"392\" y1=\"78\" x2=\"392\" y2=\"162\" stroke=\"#C5D0DC\" stroke-width=\"2.5\" marker-end=\"url(#pe-mist)\"><\/line>\n  <text x=\"372\" y=\"120\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"18\" fill=\"#C5D0DC\" text-anchor=\"end\">g<\/text>\n  <text x=\"372\" y=\"138\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#C5D0DC\" text-anchor=\"end\">9.81 m\/s\u00b2<\/text>\n  <circle cx=\"440\" cy=\"298\" r=\"14\" fill=\"none\" stroke=\"#7A1F2B\" stroke-width=\"2\" stroke-dasharray=\"4 4\"><\/circle>\n<\/svg>\n<p style=\"text-align:center;font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Gravitational potential energy depends on mass, gravity, and height above a chosen reference level.<\/p>\n\n<h2>The Potential Energy Formula<\/h2>\n\n<p>There isn&#8217;t one single formula for potential energy, because energy can be stored in different ways. But three formulas cover almost everything you will meet, and the first is the one most people mean by &#8220;the PE formula&#8221;.<\/p>\n\n<h3>Gravitational potential energy: PE = mgh<\/h3>\n\n<p>Near the Earth&#8217;s surface, the gravitational potential energy of a raised object is the product of just three quantities:<\/p>\n\n<div class=\"pf-formula\">PE = m \u00d7 g \u00d7 h<\/div>\n\n<p>Each symbol, with its SI unit:<\/p>\n\n<ul>\n  <li><strong>PE<\/strong> \u2014 gravitational potential energy, measured in <strong>joules (J)<\/strong>.<\/li>\n  <li><strong>m<\/strong> \u2014 the object&#8217;s mass, in <strong>kilograms (kg)<\/strong>.<\/li>\n  <li><strong>g<\/strong> \u2014 the gravitational field strength, about <strong>9.81 m\/s\u00b2<\/strong> near Earth&#8217;s surface (equivalently 9.81 N\/kg).<\/li>\n  <li><strong>h<\/strong> \u2014 the height above your chosen reference level, in <strong>metres (m)<\/strong>.<\/li>\n<\/ul>\n\n<h3>Elastic potential energy: E\u209a = \u00bdkx\u00b2<\/h3>\n\n<p>Squash or stretch a spring and you store energy in it. The further you push, the more you store \u2014 and because the resisting force grows as you go, the energy rises with the <em>square<\/em> of the displacement.<\/p>\n\n<div class=\"pf-formula\">E\u209a = \u00bd \u00d7 k \u00d7 x\u00b2<\/div>\n\n<ul>\n  <li><strong>E\u209a<\/strong> \u2014 elastic potential energy, in <strong>joules (J)<\/strong>.<\/li>\n  <li><strong>k<\/strong> \u2014 the spring constant, or stiffness, in <strong>newtons per metre (N\/m)<\/strong>.<\/li>\n  <li><strong>x<\/strong> \u2014 the extension or compression from the natural length, in <strong>metres (m)<\/strong>.<\/li>\n<\/ul>\n\n<p>This formula comes straight from <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/hookes-law\/\">Hooke&#8217;s law<\/a>, which tells us the restoring force of a spring is proportional to how far it is stretched.<\/p>\n\n<h3>Far from Earth: U = \u2212GMm\/r<\/h3>\n\n<p>The tidy PE = mgh only works while gravity is roughly constant \u2014 that is, near the surface. Travel out towards orbit and beyond, and you need the full expression:<\/p>\n\n<div class=\"pf-formula\">U = \u2212 G \u00d7 M \u00d7 m \/ r<\/div>\n\n<ul>\n  <li><strong>U<\/strong> \u2014 the gravitational potential energy of the two-mass system, in <strong>joules (J)<\/strong>.<\/li>\n  <li><strong>G<\/strong> \u2014 the gravitational constant, <strong>6.674 \u00d7 10\u207b\u00b9\u00b9 N\u00b7m\u00b2\/kg\u00b2<\/strong> (<a href=\"https:\/\/physics.nist.gov\/cuu\/pdf\/wallet_2022.pdf\" target=\"_blank\" rel=\"noopener\">NIST CODATA value<\/a>).<\/li>\n  <li><strong>M, m<\/strong> \u2014 the two masses, in <strong>kilograms (kg)<\/strong>.<\/li>\n  <li><strong>r<\/strong> \u2014 the distance between their centres, in <strong>metres (m)<\/strong>.<\/li>\n<\/ul>\n\n<p>The minus sign looks strange, but it simply sets the zero of energy at infinite separation. We will unpack that in the misconceptions below.<\/p>\n\n<h2>Types of Potential Energy<\/h2>\n\n<p>Because energy can be banked in several ways, &#8220;potential energy&#8221; is really an umbrella term. Here are the five forms you are most likely to meet.<\/p>\n\n<h3>Gravitational<\/h3>\n<p>Energy stored by lifting a mass against gravity \u2014 the dam, the diver on the high board, the apple before it falls. This is the PE = mgh form near the ground.<\/p>\n\n<h3>Elastic (strain)<\/h3>\n<p>Energy stored when a material is stretched, compressed, or bent: a drawn bow, a wound clock spring, a trampoline mat at full sag.<\/p>\n\n<h3>Electric (electrostatic)<\/h3>\n<p>Energy stored in the arrangement of charged particles. Pull unlike charges apart or push like charges together and you store electric potential energy \u2014 the principle behind a charged capacitor, and a direct cousin of <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/coulombs-law\/\">Coulomb&#8217;s law<\/a>.<\/p>\n\n<h3>Chemical<\/h3>\n<p>Energy locked in the bonds between atoms. Petrol, food, and a battery all hold chemical potential energy, released as heat, motion, or electricity during a reaction.<\/p>\n\n<h3>Nuclear<\/h3>\n<p>Energy stored in the nucleus of an atom, released in fission or fusion. It is what powers nuclear reactors \u2014 and the Sun.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n  <thead>\n    <tr style=\"background:#142139;color:#FAF6EE;\">\n      <th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Type<\/th>\n      <th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Typical formula<\/th>\n      <th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Energy is stored in\u2026<\/th>\n      <th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Everyday example<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Gravitational<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">PE = mgh (or U = \u2212GMm\/r)<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">an object&#8217;s height in a gravitational field<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">water held behind a dam<\/td>\n    <\/tr>\n    <tr style=\"background:#F5F2EA;\">\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Elastic<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">E\u209a = \u00bdkx\u00b2<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">a stretched or compressed material<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">a drawn bow or trampoline<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Electric<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">U = kq\u2081q\u2082 \/ r<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">the arrangement of charges<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">a charged capacitor<\/td>\n    <\/tr>\n    <tr style=\"background:#F5F2EA;\">\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Chemical<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">no single formula<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">bonds between atoms<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">food, petrol, a battery<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Nuclear<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">E = \u0394mc\u00b2 (binding energy)<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">the nucleus of an atom<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">uranium fuel, the Sun<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>\n\n<h2>How Potential Energy Works<\/h2>\n\n<p>Where does the stored energy actually come from? From work. Whenever you push against a force that wants to pull something back \u2014 gravity pulling a mass down, a spring trying to snap shut \u2014 the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/work-done-in-physics\/\">work you do<\/a> is converted into potential energy.<\/p>\n\n<p>Lift a mass <em>m<\/em> straight up at steady speed and the force you apply equals its weight, <em>mg<\/em>. Work is force times distance, so raising it through a height <em>h<\/em> takes work mg \u00d7 h = mgh. That is exactly the energy now stored \u2014 which is <a href=\"https:\/\/courses.lumenlearning.com\/suny-physics\/chapter\/7-3-gravitational-potential-energy\/\" target=\"_blank\" rel=\"noopener\">why PE = mgh<\/a>.<\/p>\n\n<h3>It always needs a reference level<\/h3>\n\n<p>Here is a subtlety worth pinning down early. Potential energy is never an absolute number \u2014 it is always measured <em>from somewhere<\/em>. The book is 1.5 m above the desk, but 4 m above the floor, and 30 m above the street.<\/p>\n\n<p>So you choose a reference level (often the ground) and call its energy zero. Only the <strong>change<\/strong> in potential energy between two points has physical meaning, and that change is the same whichever zero you pick.<\/p>\n\n<h3>Energy that converts and conserves<\/h3>\n\n<p>Release the stored energy and it has to go somewhere. As the book falls, its potential energy turns into kinetic energy: the lower it gets, the faster it moves. Add the two together and \u2014 if we ignore air resistance \u2014 the total never changes.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Energy Conservation Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:560px}@media(max-width:760px){.pf-sim-frame{height:840px}}<\/style><iframe src=\"\/labs\/energy.html\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<svg role=\"img\" aria-label=\"Bar chart showing potential energy converting to kinetic energy as an object falls, with total energy staying constant\" viewBox=\"0 0 640 360\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:100%;height:auto;max-width:640px;display:block;margin:0 auto;background:#0A1628;border-radius:6px;\">\n  <rect x=\"0\" y=\"0\" width=\"640\" height=\"360\" fill=\"#0A1628\"><\/rect>\n  <text x=\"320\" y=\"38\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"20\" font-weight=\"800\" fill=\"#FAF6EE\">Total energy stays constant as it falls<\/text>\n  <line x1=\"80\" y1=\"120\" x2=\"600\" y2=\"120\" stroke=\"#D9CFB8\" stroke-width=\"1.5\" stroke-dasharray=\"5 5\"><\/line>\n  <text x=\"600\" y=\"113\" text-anchor=\"end\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"12\" fill=\"#D9CFB8\">total energy (constant)<\/text>\n  <rect x=\"120\" y=\"120\" width=\"64\" height=\"180\" fill=\"#C8932A\"><\/rect>\n  <text x=\"152\" y=\"216\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#0A1628\">PE<\/text>\n  <text x=\"152\" y=\"325\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" fill=\"#FAF6EE\">At the top<\/text>\n  <rect x=\"300\" y=\"210\" width=\"64\" height=\"90\" fill=\"#C5D0DC\"><\/rect>\n  <rect x=\"300\" y=\"120\" width=\"64\" height=\"90\" fill=\"#C8932A\"><\/rect>\n  <text x=\"332\" y=\"172\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#0A1628\">PE<\/text>\n  <text x=\"332\" y=\"262\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#0A1628\">KE<\/text>\n  <text x=\"332\" y=\"325\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" fill=\"#FAF6EE\">Halfway down<\/text>\n  <rect x=\"480\" y=\"120\" width=\"64\" height=\"180\" fill=\"#C5D0DC\"><\/rect>\n  <text x=\"512\" y=\"216\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" font-weight=\"700\" fill=\"#0A1628\">KE<\/text>\n  <text x=\"512\" y=\"325\" text-anchor=\"middle\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"14\" fill=\"#FAF6EE\">At the bottom<\/text>\n  <line x1=\"90\" y1=\"300\" x2=\"590\" y2=\"300\" stroke=\"#D9CFB8\" stroke-width=\"2\"><\/line>\n  <rect x=\"150\" y=\"336\" width=\"14\" height=\"14\" fill=\"#C8932A\"><\/rect>\n  <text x=\"170\" y=\"348\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#C5D0DC\">Potential energy<\/text>\n  <rect x=\"340\" y=\"336\" width=\"14\" height=\"14\" fill=\"#C5D0DC\"><\/rect>\n  <text x=\"360\" y=\"348\" font-family=\"Manrope, Arial, sans-serif\" font-size=\"13\" fill=\"#C5D0DC\">Kinetic energy<\/text>\n<\/svg>\n<p style=\"text-align:center;font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">As an object falls, potential energy converts into kinetic energy while the total mechanical energy stays the same (ignoring air resistance).<\/p>\n\n<p>One more idea ties this together neatly: a force always points &#8220;downhill&#8221; in energy. Mathematically, force is the negative slope of potential energy (F = \u2212dU\/dx) \u2014 which is just a precise way of saying things naturally move towards lower potential energy, like that boulder rolling off the cliff.<\/p>\n\n<h2>Real-World Examples of Potential Energy<\/h2>\n\n<p><strong>1. Water behind a dam.<\/strong> A reservoir holds enormous gravitational potential energy simply by sitting high up. Let it fall through turbines and that energy becomes electricity \u2014 the basis of every hydroelectric plant.<\/p>\n\n<p><strong>2. A drawn bow.<\/strong> Pull the string back and the limbs store elastic potential energy. Release, and it flings into the arrow&#8217;s kinetic energy in a fraction of a second.<\/p>\n\n<p><strong>3. A roller coaster at the crest.<\/strong> The first big climb does nothing but load the car with gravitational potential energy. Every thrilling drop afterwards is that energy being spent as speed.<\/p>\n\n<p><strong>4. A pendulum clock.<\/strong> At the top of each swing the bob is momentarily still \u2014 all potential energy. At the bottom it is fastest \u2014 all kinetic. The endless trade keeps the clock ticking.<\/p>\n\n<p><strong>5. A charged phone battery.<\/strong> Charging stores chemical potential energy; using the phone releases it as electrical energy. Same idea, different storehouse.<\/p>\n\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/06\/energies-18-01812-g002.png\"\n       alt=\"Hydroelectric dam storing gravitational potential energy in water held at height\"\n       loading=\"lazy\"\n       style=\"width:100%;height:auto;border-radius:4px;\" \/>\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Water held high behind a dam is a vast store of gravitational potential energy.<\/figcaption>\n<\/figure>\n\n\n<h2>Common Misconceptions About Potential Energy<\/h2>\n\n<p><strong>Myth: potential energy belongs to a single object.<\/strong> It is really a property of a <em>system<\/em>. Gravitational potential energy belongs to the object\u2013Earth pair, and electric potential energy to a set of charges. We say &#8220;the book&#8217;s PE&#8221; only as a convenient shorthand.<\/p>\n\n<p><strong>Myth: there is an absolute zero of potential energy.<\/strong> The zero is a choice, not a fact of nature. Put it at the floor, the desk, or sea level \u2014 your numbers shift, but every <em>change<\/em> in PE stays identical, and only changes affect the physics.<\/p>\n\n<p><strong>Myth: PE = mgh works everywhere, even in deep space.<\/strong> It holds only where g is roughly constant \u2014 close to the surface. Far out, gravity weakens with distance and you must switch to U = \u2212GMm\/r, which is why that formula carries its negative sign.<\/p>\n\n<p><strong>Myth: heavier objects fall faster because they store more energy.<\/strong> A heavier object does store more PE and arrives with more kinetic energy \u2014 but not more <em>speed<\/em>. Mass cancels in mgh = \u00bdmv\u00b2, leaving v = \u221a(2gh). On the airless Moon, a hammer and a feather hit the ground together.<\/p>\n\n<h2>How Potential Energy Relates to Kinetic Energy, Work, and Conservation of Energy<\/h2>\n\n<p>Potential energy never lives alone. Add it to kinetic energy and you get an object&#8217;s <strong>mechanical energy<\/strong>. When only conservative forces (like gravity) act, that total is conserved:<\/p>\n\n<div class=\"pf-formula\">KE + PE = constant<\/div>\n\n<p>This is what makes energy methods so powerful. Instead of tracking forces moment by moment, you compare energy at the start and the end. A pendulum and a mass on a spring show it beautifully \u2014 both forever swap PE and KE, as we explore in <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/simple-harmonic-motion\/\">simple harmonic motion<\/a>.<\/p>\n\n<p>Work is the bridge between them. The <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/work-done-in-physics\/\">work done<\/a> against gravity becomes stored PE; releasing it does work that becomes <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/kinetic-energy-formula\/\">kinetic energy<\/a>. Energy is simply passed along the chain, never created or destroyed.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n  <thead>\n    <tr style=\"background:#142139;color:#FAF6EE;\">\n      <th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Feature<\/th>\n      <th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Kinetic energy<\/th>\n      <th style=\"padding:10px;border:1px solid #D9CFB8;text-align:left;\">Potential energy<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Depends on<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">motion (speed)<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">position or configuration<\/td>\n    <\/tr>\n    <tr style=\"background:#F5F2EA;\">\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Typical formula<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">KE = \u00bdmv\u00b2<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">PE = mgh<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Is zero when<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">the object is at rest<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">it sits at the chosen reference level<\/td>\n    <\/tr>\n    <tr style=\"background:#F5F2EA;\">\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Quantity type<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">scalar, in joules (J)<\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\">scalar, in joules (J)<\/td>\n    <\/tr>\n    <tr>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>Together they form<\/strong><\/td>\n      <td style=\"padding:10px;border:1px solid #D9CFB8;\" colspan=\"2\">mechanical energy (KE + PE)<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<\/div>\n\n<h2>Worked Problems<\/h2>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">A 2.0 kg textbook is placed on a shelf 1.8 m above the floor. Taking g = 9.81 m\/s\u00b2, how much gravitational potential energy does it gain relative to the floor?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\n<strong>Step 1:<\/strong> Use the gravitational PE formula, PE = mgh.<br>\n<strong>Step 2:<\/strong> Substitute with units: PE = (2.0 kg)(9.81 m\/s\u00b2)(1.8 m).<br>\n<strong>Step 3:<\/strong> Multiply: PE = 35.3 J.<br>\n<strong>Answer: PE \u2248 35 J (2 significant figures).<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">A 0.50 kg ball has 24.5 J of gravitational potential energy relative to the ground. Using g = 9.8 m\/s\u00b2, how high is it?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\n<strong>Step 1:<\/strong> Rearrange PE = mgh to make h the subject: h = PE \/ (mg).<br>\n<strong>Step 2:<\/strong> Substitute: h = 24.5 J \/ [(0.50 kg)(9.8 m\/s\u00b2)] = 24.5 \/ 4.9.<br>\n<strong>Step 3:<\/strong> Divide: h = 5.0 m.<br>\n<strong>Answer: h = 5.0 m.<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">A spring with a spring constant of 200 N\/m is compressed by 0.15 m. How much elastic potential energy is stored in it?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\n<strong>Step 1:<\/strong> Use the elastic PE formula, E\u209a = \u00bdkx\u00b2.<br>\n<strong>Step 2:<\/strong> Substitute: E\u209a = \u00bd \u00d7 (200 N\/m) \u00d7 (0.15 m)\u00b2.<br>\n<strong>Step 3:<\/strong> Evaluate: \u00bd \u00d7 200 \u00d7 0.0225 = 2.25 J.<br>\n<strong>Answer: E\u209a = 2.25 J.<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">A 0.20 kg ball is dropped from a height of 5.0 m. Ignoring air resistance and using g = 9.81 m\/s\u00b2, how fast is it moving just before it hits the ground?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\n<strong>Step 1:<\/strong> All the potential energy becomes kinetic energy: mgh = \u00bdmv\u00b2.<br>\n<strong>Step 2:<\/strong> Mass cancels, giving v = \u221a(2gh) = \u221a(2 \u00d7 9.81 \u00d7 5.0).<br>\n<strong>Step 3:<\/strong> Evaluate: v = \u221a98.1 = 9.9 m\/s.<br>\n<strong>Answer: v \u2248 9.9 m\/s (and KE at the ground \u2248 9.8 J).<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">A 1500 kg roller-coaster car starts from rest at the top of a 45 m hill. Assuming friction is negligible and g = 9.81 m\/s\u00b2, find its kinetic energy and its speed at the bottom.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\n<strong>Step 1:<\/strong> The PE at the top all converts to KE at the bottom: KE = mgh.<br>\n<strong>Step 2:<\/strong> Substitute: KE = (1500 kg)(9.81 m\/s\u00b2)(45 m) = 662 175 J.<br>\n<strong>Step 3:<\/strong> For speed, use \u00bdmv\u00b2 = mgh, so v = \u221a(2gh) = \u221a(2 \u00d7 9.81 \u00d7 45) = \u221a882.9.<br>\n<strong>Answer: KE \u2248 6.6 \u00d7 10\u2075 J and v \u2248 29.7 m\/s.<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">A 60 kg hiker climbs from an elevation of 200 m to a summit at 1500 m. Using g = 9.81 m\/s\u00b2, what is her change in gravitational potential energy?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\n<strong>Step 1:<\/strong> Use \u0394PE = mg\u0394h, where \u0394h is the change in height.<br>\n<strong>Step 2:<\/strong> Find \u0394h = 1500 \u2212 200 = 1300 m, then substitute: \u0394PE = (60 kg)(9.81 m\/s\u00b2)(1300 m).<br>\n<strong>Step 3:<\/strong> Multiply: \u0394PE = 765 180 J.<br>\n<strong>Answer: \u0394PE \u2248 7.7 \u00d7 10\u2075 J (about 765 kJ).<\/strong>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">A 1000 kg satellite orbits 400 km above Earth&#039;s surface. Using G = 6.674 \u00d7 10\u207b\u00b9\u00b9 N\u00b7m\u00b2\/kg\u00b2, Earth&#039;s mass M = 5.972 \u00d7 10\u00b2\u2074 kg and Earth&#039;s radius R = 6.371 \u00d7 10\u2076 m, find its gravitational potential energy relative to infinity.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<strong>Solution:<\/strong><br>\n<strong>Step 1:<\/strong> Far from the surface use U = \u2212GMm\/r, with r = R + altitude.<br>\n<strong>Step 2:<\/strong> Find r = 6.371 \u00d7 10\u2076 + 0.400 \u00d7 10\u2076 = 6.771 \u00d7 10\u2076 m, then substitute: U = \u2212(6.674 \u00d7 10\u207b\u00b9\u00b9 \u00d7 5.972 \u00d7 10\u00b2\u2074 \u00d7 1000) \/ (6.771 \u00d7 10\u2076).<br>\n<strong>Step 3:<\/strong> Evaluate the top (3.986 \u00d7 10\u00b9\u2077) and divide: U = \u22125.89 \u00d7 10\u00b9\u2070 J.<br>\n<strong>Answer: U \u2248 \u22125.9 \u00d7 10\u00b9\u2070 J \u2014 the negative sign means energy must be supplied to move the satellite infinitely far away.<\/strong>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is potential energy in simple terms?<\/summary><div class=\"pf-faq-item-answer\">\nPotential energy is stored energy an object has because of where it is or how it is arranged. A ball held above the ground, a stretched spring, and the chemicals in a battery all hold potential energy that can be released later \u2014 usually as movement, heat, light, or electricity. Its SI unit is the joule (J).\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the SI unit of potential energy?<\/summary><div class=\"pf-faq-item-answer\">\nThe SI unit of potential energy is the joule (J), the same unit used for every form of energy and for work. One joule equals one newton-metre (1 J = 1 N\u00b7m = 1 kg\u00b7m\u00b2\/s\u00b2). As a feel for the size, lifting a 1 kg object about 10 cm against gravity stores roughly one joule.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Can potential energy be negative?<\/summary><div class=\"pf-faq-item-answer\">\nYes. Because potential energy is always measured from a chosen reference level, it can be positive, zero, or negative depending on where that zero sits. In the formula U = \u2212GMm\/r, gravitational potential energy is negative by convention, reaching zero only at infinite separation. Only differences in potential energy carry physical meaning.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the difference between kinetic and potential energy?<\/summary><div class=\"pf-faq-item-answer\">\nKinetic energy is the energy of motion (KE = \u00bdmv\u00b2), while potential energy is stored energy due to position or configuration (for example PE = mgh). A moving car has kinetic energy; a car parked at the top of a hill has potential energy. Added together, they make up an object&#8217;s mechanical energy.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Is potential energy a vector or a scalar?<\/summary><div class=\"pf-faq-item-answer\">\nPotential energy is a scalar: it has a size, measured in joules, but no direction. You combine potential energies as ordinary numbers, not as arrows. This is one reason energy methods are often simpler than force methods \u2014 you avoid resolving directions into components.\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why is gravitational potential energy equal to mgh?<\/summary><div class=\"pf-faq-item-answer\">\nLifting an object of mass m straight up at steady speed needs a force equal to its weight, mg. Work equals force times distance, so the work done over a height h is W = mg \u00d7 h = mgh. That work is stored as gravitational potential energy, which is exactly why PE = mgh.\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>Potential energy is stored energy an object has due to its position or configuration. Learn the PE = mgh formula, the main types, real-world examples and step-by-step worked problems.<\/p>\n","protected":false},"author":1,"featured_media":288,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[15,138,143,45,144,16],"class_list":["post-287","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanics","tag-conservation-of-energy","tag-elastic-potential-energy","tag-gravitational-potential-energy","tag-mechanics","tag-pe-formula","tag-potential-energy"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/287","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/comments?post=287"}],"version-history":[{"count":1,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/287\/revisions"}],"predecessor-version":[{"id":290,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/287\/revisions\/290"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/288"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}