Potential Energy - Revision history

Jogola3: /* References */

2025-12-03T04:09:48Z

References

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	==References==		==References==

			“3.5: Conservative Forces, Potential Energy, and Conservation of Energy.” Physics LibreTexts, Libretexts, 12 Mar. 2024, phys.libretexts.org/Bookshelves/Conceptual_Physics/Introduction_to_Physics_(Park)/03%3A_Unit_2-_Mechanics_II_-_Energy_and_Momentum_Oscillations_and_Waves_Rotation_and_Fluids/03%3A_Work_and_Energy/3.05%3A_Conservative_Forces_Potential_Energy_and_Conservation_of_Energy.

	“Potential Energy.” The Physics Classroom, https://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy.<be>		“Potential Energy.” The Physics Classroom, https://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy.<be>
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	“What Is Gravitational Potential Energy? (Article).” Khan Academy, Khan Academy, https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-gravitational-potential-energy.<be>		“What Is Gravitational Potential Energy? (Article).” Khan Academy, Khan Academy, https://www.khanacademy.org/science/physics/work-and-energy/work-and-energy-tutorial/a/what-is-gravitational-potential-energy.<be>


	https://www.khanacademy.org/test-prep/mcat/physical-processes/electrostatics-1/a/electric-potential#:~:text=Electric%20potential%20energy%20is%20the,through%20a%20stronger%20electric%20field.		https://www.khanacademy.org/test-prep/mcat/physical-processes/electrostatics-1/a/electric-potential#:~:text=Electric%20potential%20energy%20is%20the,through%20a%20stronger%20electric%20field.

Jogola3: /* Gravitational Potential Energy */

2025-12-03T04:05:11Z

Gravitational Potential Energy

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	where <math>m</math> is the object's mass, <math>g = GM_{\oplus}/R_{\oplus}^2</math> is the [[gravity of Earth]], and <math>h</math> is the height of the object's [[center of mass]] above a chosen reference level.<ref name=gpe/>		where <math>m</math> is the object's mass, <math>g = GM_{\oplus}/R_{\oplus}^2</math> is the [[gravity of Earth]], and <math>h</math> is the height of the object's [[center of mass]] above a chosen reference level.<ref name=gpe/>

	~~''Examples of Gravitational Energy''~~		When using the near-Earth approximation, <math>U = mgh</math>, the location where the potential energy is zero <math>U = 0</math> is arbitrary. Since gravity is a conservative force, what matters is the change in potential energy, not the value of U itself. For any given system, the difference in potential energy between two points remains the same regardless of where you set <math>U = 0</math>.The only physically meaningful quantity is the change in potential energy, and therefore the work done by the gravitational force.

	*A raised weight
	*Water that is ~~behind~~ a ~~dam~~
	*A car that is ~~parked at~~ the ~~top of a hill~~
	*A yoyo before it is released
	*River water at the ~~top~~ of ~~a waterfall~~
	*A book on a table before it falls
	*A child at the ~~top of a slide~~
	*Ripe fruit before it falls

	~~''m represents~~ the ~~mass~~ of the ~~object~~, ~~h represents the height of the object~~ and ~~g represents~~ the ~~gravity of~~ the ~~earth surface which is (9.8 N/kg on Earth)~~.''

	== Elastic Potential Energy ==		== Elastic Potential Energy ==

Jogola3 at 03:24, 3 December 2025

2025-12-03T03:24:04Z

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	Nuclear potential energy also exists, and is the potential energy of the particles inside an atomic nucleus. Most nuclear elements like Pd and Ur have unstable nucleus due to a disproportion of nuclear particles like protons and neutrons. Unstable nucleus means a nucleus which is susceptible to change to another configuration: they have a potential. Elements used in nuclear reactions thus have kernels with a high potential energy. As we previously discussed, nature always try to go to the most stable state of energy, the state where it has the least potential energy. That's why most radioactive elements naturally decay and change composition to be in a more stable stage. The difference of energy between previous and next stage is the energy liberated in nuclear reactions as rays.		Nuclear potential energy also exists, and is the potential energy of the particles inside an atomic nucleus. Most nuclear elements like Pd and Ur have unstable nucleus due to a disproportion of nuclear particles like protons and neutrons. Unstable nucleus means a nucleus which is susceptible to change to another configuration: they have a potential. Elements used in nuclear reactions thus have kernels with a high potential energy. As we previously discussed, nature always try to go to the most stable state of energy, the state where it has the least potential energy. That's why most radioactive elements naturally decay and change composition to be in a more stable stage. The difference of energy between previous and next stage is the energy liberated in nuclear reactions as rays.



	==History==		==History==
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	== See also ==		== See also ==

	Electric Potential Energy		==Electric Potential Energy==

			Electric potential energy is the energy stored in a system of charges due to their relative positions in space. The potential energy U between two point charges, Q and q, that are separated by a distance d, is given by <math>U= k\frac{Qq}{d}</math> where k is Coulomb's constant. If Q and q have the same sign, U is positive, and the charges repel. Conversely, if Q and q have opposing signs, U is negative, and the charges attract.

	When an electric field accelerates a free positive charge Q, kinetic energy is associated. According to LibreTexts physics, "the electrostatic or Coulomb force is conservative, which means that the work done on q is independent of the path taken, as we will demonstrate later. This is exactly analogous to the gravitational force." (LibreTexts).		When an electric field accelerates a free positive charge Q, kinetic energy is associated. According to LibreTexts physics, "the electrostatic or Coulomb force is conservative, which means that the work done on q is independent of the path taken, as we will demonstrate later. This is exactly analogous to the gravitational force." (LibreTexts).

Jogola3: /* The Main Idea */

2025-12-03T02:46:48Z

The Main Idea

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	<math> \vartriangle \!\, Kball + \vartriangle \!\, Kearth + \vartriangle \!\, Uball/earth = 0 </math>		<math> \vartriangle \!\, Kball + \vartriangle \!\, Kearth + \vartriangle \!\, Uball/earth = 0 </math>


			===Conservative Forces===
			Potential energy can only be used for '''conservative forces'''. A force can be defined as conservative if the work done on an object by a force depends on just the final and initial position, rather than the entire path in between.
			As an example, lifting a chair upwards a distance d, vs sliding it across
			If a force is conservative, the negative work the force does on an object is the potential energy of that system <math>U = -W</math>

			'''Non-Conservative forces'''
			Forces like friction and air resistance are non-conservative.
			For these forces, the work done depends directly on the path length
			When a non-conservative force does work, the energy is converted into thermal energy and therefore, no potential energy can be said for these forces

Jogola3: /* A Mathematical Model */

2025-12-03T02:22:46Z

A Mathematical Model

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	<math>\frac{-dU}{dx} = F(x)</math>		<math>\frac{-dU}{dx} = F(x)</math>

	~~Which means~~ that the force on an object is the negative of the ~~derivative of the~~ potential energy ~~function~~ U. ~~Therefore~~, the force ~~on an object~~ is ~~the~~ negative of the ~~slope~~ of ~~the~~ potential energy ~~curve~~. ~~Plots of potential functions are valuable aids to visualizing~~ the ~~change of~~ the force ~~in a given region of space~~.		From this fundamental relationship <math>\frac{-dU}{dx} = F(x)</math>, it can be concluded that the force exerted on an object is equal to the negative slope of the potential energy curve at a given point.

			'''Gravitational Potential Energy'''
			The near-Earth gravitational potential energy, <math>U(y) = mgy</math>, is a straight line graph when plotted against height (y). The given line has a constant positive slope <math>\frac{-dU}{dy} = mg</math>. Meaning, the force is negative and constant: <math>F_y = \frac{-mgy}{dy} = -mg</math>, which corresponds to the force of gravity pointing downward.

			'''Elastic Potential Energy'''
			The elastic potential energy, <math>U(x)= \frac{1}{2}kx^2</math>, when plotted against displacement (x), forms a parabola centred at the equilibrium position (x=0).
			At this equilibrium position (x=0), the slope is zero, and therefore the force is zero.
			When the spring is stretched (x>0), the slope is positive, so the force <math>F_x = \frac{-dU}{dx}</math> is negative
			When the spring is compressed (x<0), the slope is negative, so the force <math>F_x = \frac{-dU}{dx}</math> is positive


	Let's apply this relationship. If the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential. Let's consider gravitational potential and elastic potential.		Let's apply this relationship. If the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential. Let's consider gravitational potential and elastic potential.

Jogola3: /* A Computational Model */

2025-12-03T01:24:26Z

A Computational Model

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	===A Computational Model===		===A Computational Model===

	A spring is like a rubber band, as you stretch it, it stores potential energy.~~{{#widget:Iframe\|url=https://trinket.io/embed/glowscript/fa7fbeaf3b\|width=100%\|height=450}}~~ Once released, this stored energy is converted to kinetic energy. The simulation at this link shows it https://trinket.io/embed/glowscript/fa7fbeaf3b[https://trinket.io/embed/glowscript/fa7fbeaf3b]		A spring is like a rubber band, as you stretch it, it stores potential energy. Once released, this stored energy is converted to kinetic energy. The simulation at this link shows it https://trinket.io/embed/glowscript/fa7fbeaf3b[https://trinket.io/embed/glowscript/fa7fbeaf3b]

Jogola3: /* A Computational Model */

2025-12-03T00:39:47Z

A Computational Model

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	===A Computational Model===		===A Computational Model===

	A spring is like a rubber band, as you stretch it, it stores potential energy. Once released, this stored energy is converted to kinetic energy. The simulation at this link shows it https://trinket.io/embed/glowscript/fa7fbeaf3b[https://trinket.io/embed/glowscript/fa7fbeaf3b]		A spring is like a rubber band, as you stretch it, it stores potential energy.{{#widget:Iframe\|url=https://trinket.io/embed/glowscript/fa7fbeaf3b\|width=100%\|height=450}} Once released, this stored energy is converted to kinetic energy. The simulation at this link shows it https://trinket.io/embed/glowscript/fa7fbeaf3b[https://trinket.io/embed/glowscript/fa7fbeaf3b]


	~~<iframe src="https://trinket.io/embed/glowscript/fa7fbeaf3b" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>~~

	''It is interesting to see how potential(yellow) and kinetic(cyan) energy alter. When U is at a maximum, K is at a minimum. When K is at a maximum, U is at a minimum. This suggests an energy transfer: U is transformed into kinetic energy which causes the ball to move. Also total Energy is constant because there are no surroundings.''		''It is interesting to see how potential(yellow) and kinetic(cyan) energy alter. When U is at a maximum, K is at a minimum. When K is at a maximum, U is at a minimum. This suggests an energy transfer: U is transformed into kinetic energy which causes the ball to move. Also total Energy is constant because there are no surroundings.''

Jogola3: /* A Computational Model */

2025-12-03T00:31:47Z

A Computational Model

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	'''~~Ismail Elsissi~~ (~~ielsissi3~~) ~~Spring~~ 2025'''		'''Joyce Ogola (jogola3) Fall 2025'''

	Potential energy (referred as <math>U</math>) is the stored energy of position possessed by an object and is that some body possesses due to their position relative to other bodies, configuration or stresses within itself, electric charges, and other factors. These factors can include a variety of many things, the main one being the pull of the earth. However, other common sources of potential energy include springs and other planets.		Potential energy (referred as <math>U</math>) is the stored energy of position possessed by an object and is that some body possesses due to their position relative to other bodies, configuration or stresses within itself, electric charges, and other factors. These factors can include a variety of many things, the main one being the pull of the earth. However, other common sources of potential energy include springs and other planets.

Jogola3: /* A Computational Model */

2025-12-03T00:31:20Z

A Computational Model

← Older revision		Revision as of 20:31, 2 December 2025
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	A spring is like a rubber band, as you stretch it, it stores potential energy. Once released, this stored energy is converted to kinetic energy. The simulation at this link shows it https://trinket.io/embed/glowscript/fa7fbeaf3b[https://trinket.io/embed/glowscript/fa7fbeaf3b]		A spring is like a rubber band, as you stretch it, it stores potential energy. Once released, this stored energy is converted to kinetic energy. The simulation at this link shows it https://trinket.io/embed/glowscript/fa7fbeaf3b[https://trinket.io/embed/glowscript/fa7fbeaf3b]

			<iframe src="https://trinket.io/embed/glowscript/fa7fbeaf3b" width="100%" height="356" frameborder="0" marginwidth="0" marginheight="0" allowfullscreen></iframe>

	''It is interesting to see how potential(yellow) and kinetic(cyan) energy alter. When U is at a maximum, K is at a minimum. When K is at a maximum, U is at a minimum. This suggests an energy transfer: U is transformed into kinetic energy which causes the ball to move. Also total Energy is constant because there are no surroundings.''		''It is interesting to see how potential(yellow) and kinetic(cyan) energy alter. When U is at a maximum, K is at a minimum. When K is at a maximum, U is at a minimum. This suggests an energy transfer: U is transformed into kinetic energy which causes the ball to move. Also total Energy is constant because there are no surroundings.''

Ielsissi3: I added a summary table. I think this section can be of great help to a student, especially before a test, when they need a quick recap/reminder.

2025-04-13T16:49:19Z

I added a summary table. I think this section can be of great help to a student, especially before a test, when they need a quick recap/reminder.

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-'''Author: Matthew Lewine (mlewine3)'''
+'''Ismail Elsissi (ielsissi3) Spring 2025'''
 Potential energy (referred as <math>U</math>) is the stored energy of position possessed by an object and is that some body possesses due to their position relative to other bodies, configuration or stresses within itself, electric charges, and other factors. These factors can include a variety of many things, the main one being the pull of the earth. However, other common sources of potential energy include springs and other planets.
@@ Line 27: / Line 22: @@
 It is interesting to note, that the universe naturally prefers lower potential configuration of systems.  This peculiarity is partly why balancing a pencil on one finger is so hard; the pencil contains potential energy that can be released easily. As taught in many engineering classes, this can be explained by one of the thermodynamic laws, where the universe always increase randomness, or entropy.
 ==The Main Idea==