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. J

    Velocity of two masses due to electric potential energy

    We can find the potential energy by finding the potential difference between the two masses. the minimum distance between the two masses is 10 cm. The maximum is 30 cm because they can be 3 string lengths apart as they repulse each other once the string is cut. So, to get potential difference...
  2. A

    I How to interpret this definition of potential energy?

    Hello everyone, I'd like to share a doubt I am currently struggling with. So we know that ΔU=−W, where ΔU is the difference of potential energy and Wthe work done by the force to move the body from point A to point B. When analyzing this for the gravitational force, since we have U=−GmM/R, with...
  3. rudransh verma

    Potential energy in case of Atwood machine

    ##T-2mg=2ma_1## (acceleration of heavier mass) ##T-mg=ma_2## (##-a_1=a_2##) On solving the eqns, ##a_1=-g/3=-a_2## ##s=1/2at^2## ##s=-g/6## , distance covered by heavier mass. ##s=g/6## , covered by lighter mass. Edit: ##\Delta U_1=mgh=-2mg^2/6## (decrease in U of heavier mass) ##\Delta...
  4. B

    Potential Energy of the Atmosphere

    Summary:: I have been trying to do this question for a while using the hydrostatic relationship to put rho and z in terms of p, however, I can not seem to end up with an answer. Can anyone suggest where to start. The question is as follows:
  5. Danny_aero

    Change in potential energy of expanded air in piston-cylinder

    Air is heated in a vertical piston–cylinder assembly fitted with an electrical resistor. The volume of the air slowly increases by 1.6 ft^3 while its pressure remains constant. The area of the piston is 1 ft^2. The mass of the air is 0.6 lb. The local acceleration of gravity is g = 32.0 ft/s^2...
  6. Dario56

    I Potential Energy of an Electron-Nuclei Interaction in DFT

    In density functional theory (DFT), electron density is a central quantity. Because of this, we want to calculate electron - nuclei potential energy as functional on electron density. If we know how potential energy varies across space, we can calculate this functional with plugging particular...
  7. Dario56

    I Kinetic Energy and Potential Energy of Electrons

    Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ [(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)] \Psi = E \Psi $$ Terms in...
  8. Anmoldeep

    Time dependant Potential Energy in ion trap

    Ion traps are very complex, but one of my Physics Olympiad textbooks presents a simplified model of a resonating charged particle in an ion trap A tuned circuit consists of an inductor and a parallel plate capacitor (capacitance C and plate separation d). It has a resonating frequency ##\nu...
  9. S

    Work done on dipole and potential energy in uniform electric field

    I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help. The torque on a dipole can be defined as τ=PEsinθ The work done on a dipole to move it from an angle ##\theta_0##...
  10. V

    Kinetic & Potential Energy of a Pendulum

    When the pendulum is released, the Kinetic Energy should be 0. When the pendulum is at the bottom/hits the rod, it should have 0 potential energy. However, I don't quite understand what happens after it hits the rod.
  11. M

    Engineering Spring Deformation: Potential Energy Balance Incorrect?

    In the initial position the spring is previously compressed, then the block adds a force, and the spring is again deformed. I think the energy balance is incorrect; the potential energy of the spring is repeated.
  12. A

    Gravitational potential energy traveling from earth to mars

    My attempt: Let ##M_e## be the mass of the Earth and ##M_m## be the mass of the person. Let ##D_{EM}## be the distance from Earth to Mars and let ##R_e## be the radius of the earth. Defining these constants (leaving off units for brevity): Masses in Kilograms (G is not a mass but I'll leave...
  13. bluesteels

    Does work = neg or pos change in potential energy?

    u = (9*10^9)(1.61*10^-19)^2 * (1/[3*10^-15 ]- 1/[2*10^-10]) u = 7.68*10^-14 J but here the question. I have been taught that W= -U so shouldn't the answer be negative?? When i look up at the solution all other sources say that the W = U and therefore the answer is in postive.
  14. H

    Potential energy, Wave function, Quantum physics

    I am totally confused about the task. Any help will be nice. Thank you so much
  15. Iwanttolearnphysics

    About KE and PE of a stone falling down a tube filled with oil

    This question does not have numbers, so I'm stumped. Here's my thinking. (I), the gain in KE is less than the loss in GPE is correct according to the key, but I think I don't understand this conceptually. Can you ask me questions to make me think about this a bit more? I can't even form...
  16. ergospherical

    I System, potential energy, and nonconservative forces: The whole story

    [Mentors' note: This thread was split off from https://www.physicsforums.com/threads/system-potential-energy-and-nonconservative-forces.1009237/] This is not a particularly helpful way to think about things; For a general mechanical system, you usually split the specified forces into external...
  17. F

    I System, potential energy, and nonconservative forces

    Hello, I am trying to get my head around the idea of nonconservative forces doing work and changing the potential energy of a system. First of all, forces acting on a system can be: a) internal and conservative b) internal and nonconservative (friction, pushes, pulls, thrust, etc.) c) external...
  18. san12345

    Spring potential and kinetic energy

    please help me
  19. H

    I Image for increase in gravitational potential energy in radial field

    A question to physicists: What sort of real world scenario / image would *best* depict the increase in gravitational potential energy in a radial field? Would a rocket traveling through the Earth's atmosphere suffice or are there better alternatives? This image would have to be relevant to the...
  20. E

    What is the definition of potential energy of a system?

    hi guys i am encountered with a question that is : two protons in a helium atom stand close together,approximately at a distance of 2 fm. what is the potential energy of this system ? i can understand the concepts that are potential of a particle or potentail of a object etc but can't...
  21. Anonymous243

    Electrostatic potential energy of a non-uniformly charged sphere

    Hi, I'm new here, so I don't know how to write mathematical equations, and I may not be fully aware of the rules here, so I'm sorry if I made a mistake. I know how to calculate the electrostatic potential energy of a countable number of charged particles, but I don't know how to calculate the...
  22. Danimal

    Potential Energy Storage: Investigating the Mechanics of a Heavy Weight Drop

    I read about a proposal for storing potential energy by hoisting heavy weights that can be dropped when needed to generate electric power. So using the numbers from a hydraulic turbine from Hoover dam, how heavy would a hanging weight have to be to generate 178,000 horsepower as it descended...
  23. F

    Potential Energy of three charged particles

    I set up an equation for the sum of all the potential energies and when cancelling out ##k## and ##q^2##, I got ##\frac{1}{0.05}-\frac{1}{x}-\frac{1}{0.05-x}=0##. However, this has no solutions, so I must've gone wrong somewhere. Could someone just give me a hint, not a solution, that would put...
  24. V

    Confusing definition of electrical potential energy

    If the book had said that electrical potential energy is the negative of work done by electrical force on a charge, then the definition would be very clear and easy to understand. So, why should the book give this confusing definition instead.
  25. S

    B L = 0 in the equation for effective potential energy?

    Hi, What would happen if I set L in this equation to zero? I can have an L that is zero right?
  26. R

    Misunderstanding of Gravitational Potential Energy

    Here is my solution, which is correct. The tilt of the water at the top can be described in terms of ##x## and ##y## as ##y = \frac{2y_0}{L}x##. The height of the water at any given x is then equal to ##h + \frac{2y_0}{L}x## where ##x \in [-\frac{L}{2}, \frac{L}{2}]##. So the potential...
  27. T

    Exponential potential energy state diagram

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  28. P

    I Is there a negative sign in front of the centrifugal potential energy?

    In orbital mechanics, the effective potential is given by ##\frac {1} {2} m r^2 w^2##, which can be expressed in terms of angular momentum ##L## which is conserved. Yet, https://web.njit.edu/~gary/321/Lecture17.html apparently shows the centrifugal potential as the negative of the above...
  29. Anmoldeep

    I Work Done in Changing Shape of Current Carrying Loop

    How would you go about calculating the work done in morphing a square current-carrying loop into a circular current-carrying loop, without change in length while maintaining the same angular orientation with an external magnetic field. My book suggests defining P(potential energy) = M.B (dot...
  30. P

    I Confusion over the "centrifugal potential energy"

    I understand that potential energies are energies relative to reference points. For example, gravitational/electrical potential energy is relative to a point at infinity. What is the reference point for centrifugal potential energies? In the case of planetary orbits, must the reference point...
  31. Leo Liu

    Equation connecting potential and potential energy of a distribution

    The equation below allows us to calculate the potential energy of a continuous distribution of electric charge. $$U=\frac {\epsilon_0} 2 \iiint\limits_\text{Entire electric field}\vec E^2\,dV$$ In my textbook, the author states $$U=\frac 1 {8\pi\epsilon_0}\iiint\limits_\text{Entire electric...
  32. Dario56

    I Why Does Molecular Potential Energy Curve Have That Specific Shape?

    Molecular potential energy of hydrogen in dependence with atomic distance for bonding orbital is given by picture below. We can see that at large distances force between atoms is attractive and potential energy drops to minimum which corresponds to bond energy and length. This part of the...
  33. V

    B Potential energy in standing wave compared to traveling wave

    From hyperphysics, "The unique point in the case of the traveling wave in the string is the element of the string that is at the maximum displacement as the wave passes. That element has a zero instantaneous velocity perpendicular to the straight string configuration, and as the wave goes "over...
  34. F

    Kinetic and potential energy of a particle attracted by charged sphere

    Hello, I have a particle at point A with charge ##q_A##, and an unmovable sphere of radius ##R_B## at point B with a volumic charge density ##\rho##. The distance from particle A to the centre of the sphere in B is ##r##. Both objects have opposed charges, so, the particle in A, initially at...
  35. S

    MHB Calculate the Length & Potential Energy of a Sliding Box on a Ramp

    A ramp rises 10cm for every 80cm along the sloping surface. A box of mass 50 kg slides down the ramp starting from rest at the top of the ramp. The coefficient of friction between the ramp and the box is 0.03 and no other resistance acts. The box is traveling at 2 m/s when it reaches the bottom...
  36. S

    MHB Decrease in Potential Energy of a Sliding Tile

    A tile of mass 1.2 kg slides 3m down a roof that makes an angle of 35 degree to the horizontal. Find the decrease in potential energy. Iam getting the ans 24.8J PE = mgh= 1.2× 12 sin 35 ×3 The ans in the textbook is 20.6J
  37. itchybrain

    Question about potential energy: gravity and a vertical spring

    Let's say a mass is gently laid on top of a massless spring. The spring compresses. There is a change in the height of the mass. Therefore, there is a change in the gravitational potential energy: a decrease. The compressed spring now has potential energy (it has gained energy). The change...
  38. S

    How does gravity convert potential energy to kinetic?

    If I hold a ball above the ground, it has potential energy. Once gravity pulls on it, it becomes kinetic. What is gravity and how does it convert one kind of energy to another?
  39. yucheng

    Is the potential energy of an ion in a lattice ##U_0## or ##U_0/2##?

    Potential energy in a two-dimensional crystal Consider the potential energy of a given ion due to the full infinite plane. Call it##U_{0}##. If we sum over all ions (or a very large number##N##) to find the total##U##of these ions, we obtain##N U_{0}##. However, we have counted each pair twice...
  40. R

    How Can I Analyze Particle Movement Given Potential Energy and Force Function?

    Knowing that ##F(x)=-\mathrm{d}V(x)/\mathrm{d}x##, I found that ##F(x)=-2.4x^3+1.35x^2+8x-3##. But it was the only thing I could find. How can I analyze what will be the type of movement with the information presented by the question statement?
  41. R

    Calculating Potential Energy from Force for Non-Linear Systems

    If I have a force that behaves according to the formula ##F(x)=\alpha x-\beta x^3##, how can I get the potential energy from it? I know that: $$-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x),$$ but what about the limits of the integration?
  42. Ebi Rogha

    B Exploring Energy-Mass Equivalence: Converting Energy to Matter in Everyday Life?

    a) Can we convert energy to mass (matter) in every day life? b) When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?
  43. Vash25

    Gravitational potential energy question - normal force on us

    Hi, If we are standing on the ground, the Earth applies a force equal to our weight to us, but why do we feel a greater force when we fall to the ground from a certain height? Our weight is the same along this small height because our mass and acceleration are the same and, even so, the normal...
  44. Vash25

    Gravitational potential energy question -- Ojbect sitting on the Earth

    Good day, If I consider my system to be an object and the earth, and the object is on the surface of the earth, then the system will have gravitational potential energy. Why couldn't I say that only the object (considering it as my system) has gravitational potential energy? Thanks
  45. akashpandey

    Why do we add Kinetic and Potential energy?

    As we know Energy is a scalar quantity. So when we add kinetic and potential energy to get Total energy. So addicting these two energy (kinetic and potential) comes under Scalar addition ? I just wanted to confirm it.
  46. sophiatev

    Electrostatic Potential Energy of a Sphere/Shell of Charge

    So it seems the typical way to approach this problem is to consider the sphere when it has charge q and radius r. With uniform charge density ##\rho##, this becomes ##q = 4/3 \pi r^3 \rho## and so ##dq = 4 \pi r^2 dr \rho##. Using our expression for the potential outside of the sphere, we find...
  47. eloiseh

    Find potential energy using time-independent Schrodinger's equation

    I had found what U(x) was equal to already by plugging in the wave function and simplifying, which is (2h^2/mL^4)(x^2 - 3L^2/2) by the way. But the solution key that I have goes an extra step. After stating the equation of U(x) that I got, it says that: "U(x) is a parabola centred at x = 0 with...
  48. Bob Enyart

    Is there any motion hidden within potential energy?

    Of potential and kinetic energy in their various forms, in their own reference frames, which involve motion? Heat, light, nuclear, kinetic, etc., seem to involve motion. Does potential energy, in any way whatsoever, involve motion? Thermal does. Does nuclear energy involve motion? Seems to...
  49. E

    A Gravitational Potential Energy & the Equivalence Principle

    First, in section 20.4, after listing all the things gravitational potential energy does not do, they say the equivalence principle forbids it being localized. I thought I understood the equivalence principle, but maybe I don’t. Any comments explaining that would be appreciated. Second, they...
  50. Clint0

    Potential energy increase of an expanding stellar object

    How much energy is required to double the radius of a uniformly dense stellar object? Express the answer in terms of mass and the radius of the object.
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