6.3: Potential Energy
- Page ID
- 122907
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Potential energy is the energy an object has stored up due to its position or state. Think of it as "potential" to do work. An object with potential energy isn't moving right now, but it has the ability to move and do something later.
There are a few different types of potential energy, but the two main ones you'll encounter are:
Gravitational Potential Energy
This is the most common type. It's the energy an object stores because of its height above some reference location such as the ground.
Think of it this way:
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A bowling ball on the top shelf of a closet: It has a lot of gravitational potential energy because if it falls, it can do some serious damage (like breaking a tile on the floor). If you lift the ball higher, you're increasing its potential energy. All of this potential energy becomes kinetic energy when the ball falls. The further the ball falls, the more kinetic energy gained from the larger initial potential energy. We say that gravity does work on the ball to convert potential energy into kinetic energy.
Figure \(\PageIndex{1}\): A bowling ball falling from a shelf and converting gravitational potential energy to kinetic energy. Image created by Gemini AI.
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A roller coaster at the top of the first hill: It's not moving very fast horizontally, but it has a massive amount of potential energy. As it goes down the hill, this potential energy is converted into kinetic energy (energy of motion), which is what makes it go so fast.
Figure \(\PageIndex{2}\): A roller coaster with large potential energy. Image created by Gemini AI.
The formula for gravitational potential energy is \(PE=mgh\), where:
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\(m\) is the mass of the object (how much "stuff" it's made of)
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\(g\) is the acceleration due to gravity (a constant number, usually about 9.8m/s2 on Earth)
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\(h\) is the height of the object
Elastic Potential Energy
This is the energy stored in something that is stretched, compressed, or twisted.
Think of it this way:
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A stretched rubber band: It has elastic potential energy. When you let it go, that stored energy is released, and it snaps back to its original shape. You've converted the potential energy into kinetic energy.
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A compressed spring: When you press down on a spring, you are storing energy in it. If you let it go, the spring will "spring" back, releasing that stored potential energy. This is how things like trampolines and pogo sticks work.
The formula for elastic potential energy in a spring is \(PE=\frac{1}{2}kx^2\), where:
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\(k\) is the spring constant (a number that tells you how stiff the spring is)
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\(x\) is the distance the spring is stretched or compressed from its resting position.
Chemical potential energy is somewhat connected to elastic potential energy. When chemical bonds are very strong, it is as if they have a large spring constant. Stiff chemical bonds have a lot of chemical potential energy.
The Big Picture
The key takeaway is that potential energy is all about stored energy. It's the energy an object has waiting to be used. When that energy is released, it is usually converted into another form of energy, most often kinetic energy (the energy of motion). This constant conversion between potential and kinetic energy is fundamental to understanding how things move and interact in the physical world.
In the PhET simulation below,
- click the "Measure" tab.
- Place the skateboarder at one of the red dots at the top of the ramp and release them.
- Move the energy sensor to one of the red dots at the top of the ramp.
- What are the energies (kinetic, potential, thermal, total)?
- Move the sensor to the red dot at the bottom of the ramp.
- What are the energies (kinetic, potential, thermal, total)?
- Explain what has happened to the energy of the skateboarder between the top and the bottom of the ramp.
- Does it appear that \(mgh\) and \(1/2 mv^2\) are constant values, i.e., each are always the same value?
- Does it appear that total energy is a constant value?
- Does the gravitational force appear to uphold the work-energy theorem? Explain.
- Adjust the friction slider so there is some friction.
- Does it appear that \(mgh\) and \(1/2 mv^2\) are constant values?
- Does it appear that total energy is a constant value?
- Friction is a force. How is it different from gravitational force in terms of its effect on energy?
- Does the frictional force appear to uphold the work-energy theorem? Explain.