Potential energy Definition and 1000 Threads

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.Common types of potential energy include the gravitational potential energy of an object that depends on its mass and its distance from the center of mass of another object, the elastic potential energy of an extended spring, and the electric potential energy of an electric charge in an electric field. The unit for energy in the International System of Units (SI) is the joule, which has the symbol J.
The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called conservative forces, can be represented at every point in space by vectors expressed as gradients of a certain scalar function called potential.
Since the work of potential forces acting on a body that moves from a start to an end position is determined only by these two positions, and does not depend on the trajectory of the body, there is a function known as potential that can be evaluated at the two positions to determine this work.

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  1. P

    QHO: Time dependant expectation value of the potential energy

    Summary:: Linear Quantum harmonic oscillator and expectation value of the potential energy (time dependent) Hello, I have attached a picture of the full question, but I am stuck on part b). I have found the expectation value of the <momentum> and the <total energy> However I am struggling with...
  2. cahill

    I Change in chemical potential energy from nuclear decay

    I have been amateur reading about beta decay. The example given for electron capture was krypton-81 into bromine-81. Going from a noble gas to a halogen gives rise to a big change in chemical potential energy. How is this energy accounted for in the equations of the reactant particles and...
  3. A

    Energy conservation for objects hanging from a pulley

    I have some conceptual questions about this task. In order to get the correct result (I checked the textbook answer) in part (a) I had to assume that the speed for each block is the same at all instants. And that if one block moves down x meters, the other one will move up that same amount of...
  4. M

    Potential Energy: Rigorous Understanding & E=mc²

    I used to believe that potential energy of a particular particle is of no meaning. It is always linked with a system, and Potential Energy of a system means negative of work done by INTERNAL conservative forces from an initial stage of assumed zero potential energy. And energy cannot be said to...
  5. Saptarshi Sarkar

    I Why does Special Theory of Relativity leave out Potential Energy?

    While studying Special Theory of Relativity I came across the formula for the energy of a particle. The total energy of a relativistic particle in STR contains the Rest Mass energy and the Kinetic energy. But, in Classical and Quantum Mechanics, we consider the total energy of the particle to be...
  6. L

    Why Do Physical Systems Seek Minimum Potential Energy?

    Many, many years ago while in engineering graduate school I was studying calculus of variations. One classic problem was to determine the shape of a hanging cable supported at its two ends. After minimizing the integral, the catenary curve was the solution. The basic assumption in setting up...
  7. N

    Exploring the Role of Gravity in Spring Potential Energy: A Scientific Analysis

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  8. E

    Not sure why my method doesn't work: Springs, Potential Energy and Work

    I know that you can get the answer through using Fs as 18 and solving for K, then subbing it into the equation for elastic energy. I was just wondering why another method wouldn't work. I tried doing it using the concept that Work is an equal to the Change in Elastic Energy, therefore Ee=xF...
  9. S

    Finding the potential energy if force depends on both position and time

    How to find potential energy if force depends on both position of particle and time ? Suppose force is : f(r,t) = (k/r^2) * exp(-alpha*t), k, alpha = positive constants, r = position of the particle from force-centre t = time Is this force a conservative or non-conservative ?
  10. C

    Why Potential Energy cannot be included twice?

    If for example I have two charged particles q_1 , q_2 with distance 'r' between them, then: The potential energy that results from particle q_1 exerting force on particle q_2 is $$ k\frac{q_1 q_2}{r} $$ If I do the same process for particle q_2: The potential energy that results...
  11. n3pix

    What does this mean ##U=\int F\times d\vec{r}## in the Work-Energy Theorem?

    Hello, I'm newly discovering the world of the Energy. My question is about the equation ##U=\int \vec{F}\times d\vec{r}=-\int \vec{F}_{s}\times d\vec{r}##. Can you tell me what does this equation means? Thanks!
  12. n3pix

    A question about potential energy and work

    Hello, I'm confusing about the basic terms about Conservation of Energy, Potential Energy and Work. Consider that we have a mass ##M## above the ground (zero point) distance of ##y_{0}=h##. When we release the mass it will accelerate through it's way to ground. So the work is made by a field...
  13. Sofa

    Issues Determining Change in Elastic Potential Energy

    I've attached a screengrab of the problem (Specifically, Part B, as indicated in the image) and my attempt at a solution. Summarized, my thinking was based on using ##-\Delta U=\frac{Kx_i^2-Kx_f^2}{2}##. After using up all my attempts, the solution, as it turns out, was U2=4.91J. No variation...
  14. maistral

    Ergun equation for beds + rising fluid + potential energy

    I am quite familiar with the Ergun equation's formulation. My question is, do I need to subtract the potential term ΔP/Δz = -ρg/gc after the Ergun equation's own ΔP/Δz , assuming that the fluid is to be pumped upward, from the bottom of the bed to the top of the bed? I was thinking it should be...
  15. U

    Catapult spring, Kinetic and Potential energy

    My solutions: When ball is launched horizontally, assuming its velocity is entirely in the horizontal dimension, there is no interaction of the ball with the gravitational field, thus no change in GPE, so all of the EPE (elastic potential energy ) of the spring is transferred to KE of the ball...
  16. Samanko

    Potential energy of an electric dipole

    This is a problem from a textbook, and I can't solve it. I know that the equation of Potential energy of electric dipole. Since the configuration is a little bit complicated. I'm confused applying which electric fields.
  17. H

    What Determines Gravitational Potential Energy?

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  18. C

    Interactions and Potential Energy

    Usps=1/2(1.8x10^6)(0.03)^2=810J Ke=1/2mv^2=1/2(0.05)(300)^2=2250J I don't know how to take it farther than this, or if this is the correct way to start the problem. If this is correct, would it be correct to assume that the bullet does penetrate the creature because Ke overcomes Usps?
  19. EEristavi

    Calculate this Spring's Potential Energy

    I know that gravitational potential energy is decreased by E = -m g h = -1 10 0.02 = -0.2. So, the spring potential energy must be E=0.2 (Joule). However, in the answer's sheet I have E=0.1 What mistake do I make?
  20. SLTH02

    Determine the potential energy function of the charged particle

    I understand that you need to integrate f(x), and the negative of that is U(x). But the last part of the problem says "Clearly state any assumptions you make." And the answer is just the antiderivative of that f(x) without any constant from integrationHow does that make sense
  21. J

    B Exploring Force & Potential Energy of a Donut-Shaped Planet

    So, let's say you have a donut - shaped planet, so a second object can move right on top of the center of mass of the first object. Does force go to infinity? How about potential energy? Or, just take one object, divide it into elements, what happens to the central element of mass within the...
  22. SpaceThoughts

    What Does Negative Potential Energy Indicate in Colliding Iron Balls in Space?

    Hi Everyone. I am hoping to get a little help with this: Two equal balls of iron each with a mass of 1000 kg are placed in rest in space 10 meters from each other. Because of gravity they start to accelerate towards each other, and collide in the end. I would like to know how to calculate the...
  23. Kaushik

    Negative potential energy vs Positive potential energy

    What is the physical difference between negative potential energy and positive potential energy? PS- When I was reading about surface tension I came through the following line - ' The molecules at bulk inside the fluid has lesser negative potential energy than those on the surface.' In this...
  24. peguerosdc

    How to relate the gravitational potential energy zero to the axes?

    (Throughout all my post, I will refer to “gravitational potential energy” just as “potential energy”) Hi! I have this confusion about when is potential energy positive/negative and how it is related to how we define our axes. I think it is easier to understand my confusion with the following...
  25. Kaushik

    A few questions about Potential Energy

    Is it possible to briefly explain the potential energy concept? Why is potential energy only associated with conservative forces? Does potential energy really exist? Or Is it just kinetic energy from different reference frame?
  26. Stormzy67

    Elastic potential energy and natural length of a spring- relation?

    I figured out that the spring constant is inversely proportional to the natural length, but there’s still an unknown change in a quantity( most likely extension).
  27. TheQuestionGuy14

    How does gravitational potential energy work?

    Gravitational energy is the potential energy a physical object with mass has in relation to another massive object due to gravity, so, does an object outside a gravitational field have no gravitational potential energy? For example, the Earth is 4.5 billion years old, so it's gravity stretches...
  28. L

    Man jumping onto a see-saw to launch bricks vertically

    I drew a diagram for the a) part The person is h meters high So GPE= 100 x 9.8x h GPE= 980h j KE = 980h when the person hits the see saw KE=1/2mv² 980h=0.5 x 5 x v² Now it v²=u²+2as For the brick going up to 10m v = 0 u=? a=-9.8ms-² s=10m u²=2 x 9.8 x 10 u=14m/s We can assume that u=14m/s is...
  29. W

    Regarding the idea of potential energy

    I am studying basic mechanics and have reached the chapter on potential energy. However I am a bit confused about the difference between potential energy and the formula for the potential energy due to work done by a conservative force. I am not sure which of the following interpretations is...
  30. A

    An electron is placed at Point P, Calculate the Potential Energy

    Not quite sure how to approach this question - do I need to calculate -qEd for all three charges and then the electron and add them together? Thanks
  31. K

    I Gravitational Potential Energy in GR

    Hi, folks. Several years ago I made a YouTube video with a new demonstration of GR for a general audience ("How Gravity Makes Things Fall"). It won a pretty prestigious physics award. I still get comments and questions on it. One today stumped me: "How do we account for potential energy if...
  32. J

    Understanding the derivation for Elastic Potential Energy.

    Elastic Potential Energy of a Strained Body (A) Using ## Y = \frac {stress}{strain}## we get ##F = \frac {AY}{L} * x## where ##F## is the restoring force, ##x## is the distance the body is stretched by. Since Work = PE (spring force/ stress is conservative?) Thus ##W = \int_{0}^{x} \frac...
  33. Terrycho

    The Potential Energy Function in Three-Dimensional Motion

    I set the location of the particle (x,y,z); therefore, → the force F_1 is (z^2/root(x^2+y^2) * x/root(x^2+y^2) , z^2/root(x^2+y^2) * y/root(x^2+y^2), 0), since cosΘ is x/root(x^2+y^2). →...
  34. alicia12131415

    How do I calculate elastic potential energy?

    Is this the correct formula to use, if not what is. I really just don't know where to start. I really just need to know where and how to start.
  35. Harperchisari

    The energy conservation issue with parallel charged plates with a hole.

    A while back I thought of an issue with parallel charged plates. Imagine this: a set of opposite charged resistive plates with holes in the center. In theory, there is a finite amount of energy required to push a positive charged particle through the hole in the positive plate (in theory it...
  36. L

    I Definition of the potential energy operator

    In quantum mechanics, I can write the hamiltonian as ##\hat{H} = \hat{p}^{2}/2m + \hat{V}##. I am confusing with the definition of the operator ##\hat{V}##, who represents the potential energy. If the potential energy depend only on the position, is it correct write ##\hat{V} = V(\hat{x})##...
  37. B

    AQA physics paper On potential energy in mass spring system

    The spring constant of a helical spring is 28 N mñ1. A 0.40 kg mass is suspended from the spring and set into simple harmonic motion of amplitude 60 mm. i use the equation 1/2 change in extension times by force where the force i assume is mass times by 9.8 but the mark scheme uses 1/2 kx ^2 and...
  38. archaic

    Is the 'test charge' in electric potential energy defined as immobile?

    Hello, quick question, when EPE was defined, did we decide that the "test charge" is immobile in the field? Otherwise a force equal and opposite to that of the electric field would just stop the charge from accelerating.
  39. Gursimran Singh

    Potential energy of a shell and a disc, both covered uniformly with charge

    Double integration maybe?? I calculated potential due to shell on plate's center but not on other points on it's surface.
  40. Lone Wolf

    Potential Energy and Equilibrium Position for a Circular Trajectory

    a) Solution given: F = - x î - y j b) The equilibrium position happens when F = 0. x = 0 and y = 0 is the point of equilibrium. Solution given: (0, 0) c) Since the particle has a circular trajectory the trajectory equation becomes x^2 + y^2 = R^2. The maximum potential energy the...
  41. M

    Force on a pin from a pendulum and a string

    1. Determine the velocity of the ball when it is 30degrees from the horizontal: U1 = mgh = mg(0.8m) U2 = mgh = mg(0.4+0.4cos(30)) = mg(.74641) ΔU = U2 - U1 = mg(.74641 - .8) = mg(-0.051433) T1 =0 T2 = 0.5mv^2 ΔT = T2 - T1 = 0.5mv^2 ΔU = ΔT mg(-0.051433) = 0.5mv^2 ====> v = 1.025394 2. Use...
  42. M

    How far does the block slide? (work, spring, incline)

    Homework Statement The system is released from rest with no slack in the cable and with the spring stretched 225 mm. Determine the distance s traveled by the 3.2-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 2.5 kg. Assume no mechanical interference and no friction...
  43. Thorscira

    Expression for effective potential energy

    << Mentor Note -- Poster has been reminded to use the Template when starting new schoolwork threads >> Two particles of identical mass m interact with each other via central potential energy Vcentral(r) = -V0(1-|r|/a), if 0 <= |r| <= a 0, if a < |r| Constants are V0 > 0...
  44. tinesi

    Voltage, electric field and potential energy for concentric shells

    1. Homework Statement the a shell is charged Va=120v shell b is grounded, Vb=0V What is the voltage in the center of shells (vo)? The electric field in the center of shells? The potential energy in the center of shells? Homework Equations Vr=Va+(1/r-1/a)/(1/a-1/b)Vab (from integrals) though I...
  45. L

    Potential Energy and Potential -- Systems versus Particles

    When I first learned about these subjects, I did what was intuitive to me and treated particles as if they carried potential energy. I would do this similarly for rigid bodies where I would also treat them as a particles with their body's mass at the center of mass. This wasn't helped by...
  46. Interdimensional

    Potential Energy of a Finite Proton

    Homework Statement This was in a problem set I found. Suppose that the proton in a hydrogen atom is not a pointlike object, but instead described by a uniform spherical charge distribution with charge e and radius R = 8.7 x 10^-16 m. Using Gauss's law and the definition for the electric...
  47. S

    I Relativistic mass and gravitational potential

    Hello everyone, Any object has a gravitational potential energy as a function of the distance from the Earth (R). Does this energy depend only on the rest mass of the object; or one must take into account it's relativistic mass? In other words, if we imagine two identical bullets on the top...
  48. Bheshaj

    Potential Energy Explained: In-Depth Guide

    Can someone please explain me the concept of potential energy correctly and in detail.
  49. stockzahn

    Apparent vanishing of (magnetic) potential energy

    Dear all, I cannot figure out my mistake with this thought experiment: Consider a ferromagnetic material (e.g.iron) in a magnetic field - or just any iron anywhere, since the range of magnetic fields is infinite. Between the ferromagnetic material and (permanent) magnets potential energy is...
  50. hilbert2

    Delta potential in classical mechanics

    In quantum mechanics, there exist some systems where the potential energy of some particle is a Dirac delta function of position: ##V(x) = A\delta (x-x_0 )##, where ##A## is a constant with proper dimensions. Is there any classical mechanics application of this? It would seem that if I...
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