What is Potential energy: Definition and 1000 Discussions

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.

View More On Wikipedia.org
Recent contents Top users
  1. R

    What does negative potential energy mean?

    In the case of lifting a box, I know potential energy is negative because negative work is done by gravity. What does the negative part of -PE denote? Does it denote the direction of the energy or does it mean that energy is being lost? But how is energy being lost if the box gains more...
  2. NoahCygnus

    Net work done on Earth-object system and potential energy

    My book says: "Let us derive an expression for the potential energy associated with an object at a given location above the surface of earth. Consider an external agent lifting an object of mass ##m## from an initial height ##y_{i}##above the ground to a final height ##y_{f}##. We assume the...
  3. Irfan Nafi

    Which ball has more energy halfway through the track?

    2 frictionless tracks have equal length bumps with one going up and the other down. Halfway through the track which one has more energy? Assuming that they started at the same height, I thought that they had the same amount of energy, but since Ball B ends up having a greater velocity at the...
  4. S

    Work done between two points

    work done in taking positive charge from A to B in electric field E= potential energy at B - potential energy at A OR potential at A-potential at B Am i correct in both formula?
  5. J

    Potential energy of a massive string

    How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it? The string is uniform, so I know its center of mass is at L/2.
  6. Irfan Nafi

    General Definition of Potential Energy - Conceptual Help

    My textbook states that an alternative definition of the change in potential energy is the work required of an external force to move an object without acceleration between two points. I am confused on why it says acceleration. Wouldn't that mean that the acceleration is 0 and therefore the...
  7. B

    Formula of potential energy of a nucleus

    Why there is the term ##\frac{3}{5}## in the formula of the electrostatic potential of a nucleus $$U_e = \frac{3}{5} \cdot \frac{(Ze)^2}{4 \pi \epsilon_0 R}$$
  8. A

    Electrical Potential Energy and Potential

    Homework Statement An electron that accelerates from a point near a collection of negative source charges toward a point near a collection of positive source charges experiences A) a decrease in electric potential energy as it moves toward a region at a lower electric potential B) a decrease...
  9. Pushoam

    Deriving the potential energy of a dipole

    Homework Statement Homework EquationsThe Attempt at a Solution In case of uniform E, torque ##\vec N = \vec p \times \vec E \\ U = \int_0 ^ \theta N d \theta = pE \int_0 ^ \theta \sin \theta d \theta = - pE \cos \theta \text { Here, I assumed that the direction of } \vec N ~ and ~ \vec d...
  10. E

    Change in Potential energy equals change in Kinetic energy?

    Homework Statement I'm trying to digest the concept of change in potential energy being set equal to a change in kinetic energy. Does this relationship always hold? Please see below for more details. Homework Equations PE = mgh KE = .5mv^2 W = ΔKE = -ΔPE W = f*d The Attempt at a Solution...
  11. G

    Potential Energy in 3D: Partial Derivatives

    To find potential energy in 3 dimensions why do we take partial derivative and not total derivative?
  12. esha

    Potential energy and equilibrium

    It is said that a negative potential energy gives stable equilibrium but a positive potential energy gives an unstable equilibrium. why is it so?
  13. jlmccart03

    Velocity of a particle kicked into four point charge square

    Homework Statement Consider the arrangment of charges (fixed in place) shown in the figure. The square has side length d. (Figure 1) Now suppose the particle with charge q is released. It is "kicked" so that it's initial speed is v. After an unspecified trajectory, it is observed that the...
  14. P

    Change in potential energy of air in a piston-cylinder system

    1. Homework Statement This is my first question and I'll try to stick to the forum rules as much as possible. imgur.com/a/2JyZC Imagine a cylinder filled with air which is uniformly distributed and a piston above it, so the air can expand vertically. Let the system be the air itself, so the...
  15. R

    Potential energy vs position curve

    Can a potential energy curve be vertical ?
  16. R

    Does Increasing Potential Energy Affect the Gravitational Pull on an Object?

    hey guys! i am very confused about the concept of potential energy and gravity. we know that as an object is continuously lifted above ground, its potential energy increases. but i was wondering if that potential energy is physically affecting the body, like if the potential energy increases...
  17. e2m2a

    Invariance of elastic potential energy

    At non-relativistic speeds is the elastic potential energy of a compressed spring frame-invariant? That is, would all reference frames agree on how much elastic potential energy is stored in the spring?
  18. B

    Kinetic energy and potential energy look very dissimilar

    The more I think about it the less clear the respective natures of kinetic energy and potential energy (and of their sum, the so-called total energy) become. The thing is I have the impression that once you try to go a bit further than the usual description of "scalar values assigned to systems...
  19. J

    Can Elastic Potential Energy Ever Be Negative?

    Homework Statement Which of the following Graphs BEST illustrates the potential energy vs. time for the system in Figure 1, where t=0 is defined as the time at which the incident box 1st contacts the box on the spring? My question is why can't the Elastic PE be negative? The answer is A...
  20. D

    I Kinetic and Potential energy operators commutation

    Hi All, Perhaps I am missing something. Schrodinger equation is HPsi=EPsi, where H is hamiltonian = sum of kinetic energy operator and potential energy operator. Kinetic energy operator does not commute with potential energy operator, then how come they share the same wave function Psi? The...
  21. V

    B Negative potential energy and negative mass

    My question is: If gravitational potential energy is normally negative, and E=m•c^2, doesen't that means that negative mass could exist? (I don't know much about general relativity so please explain as simple as posible)
  22. BTEC Michio Kaku

    GCSE Physics : Temperature & Gravitational potential energy

    Homework Statement Q7. Some lead shot with a mass of 50 grams is placed into a card board box the distance from one end to the other being 1m. The ends are sealed with rubber bungs in order to prevent the lead shots from falling out, the tube is rotated so the lead shots fall down from one end...
  23. esha

    Why is electric potential present inside a conductor?

    potential energy is the work done by an external force in taking a body from a point to another against a force. on the surface of a conductor the electrostatic charges arrange themselves in such a way that the net electric field is always zero. so if there isn't any force to act against why...
  24. G

    The total potential energy of two charges Wikipedia mistake?

    Say, we have two particles of equal and opposite charge in an isolated system in which we neglect gravity. The energy of particle 1 is: E1 = U1 + T1 Where U1 is electrostatic potential energy and T1 is the kinetic energy of particle 1. The energy of particle 2 is: E2 = U2 + T2 Where U2 is...
  25. Pushoam

    Change in electrostatic potential energy of two spheres

    We have two conducting spheres of radius r1 and r2 far away from each other. The first sphere has a charge Q. What is the change in electrostatic potential energy when they are connected together? Before the connection , Ube = ## \frac{Q^2}{8\pi\epsilon_0 r_1} ## After the connection , Uaf = ##...
  26. N

    Clarification between electric field and potential energy

    From my understand, electric field is the force emitting from a charge. This means that if a charge was placed in the vicinity of the charge that was emitting the field of force, that charge placed would experience a force from it. How does potential energy differ from this? I understand that...
  27. phasacs

    Why isn't Kinetic Energy always equal to Potential Energy?

    K= ∫mvdv = ∫m dx/dt dv = ∫m dx/dv dv/dt dv = ∫m dv/dt dx = ∫Fdx = U => K=U, why isn't this true? If it is, wouldn't that mean that Kinetic Energy is always equal to Potential Energy?
  28. E

    Potential energy in a mouse trap

    Homework Statement So I have been building a mouse trap car at my school, and I need to hand in a report on it tomorrow. :biggrin: I don't have all of the measurments at the moment, but the only thing I want to know is how to calculate this. I want to see how much energy is lost to...
  29. B

    Proving that two integrals of potential energy are equal

    I want to prove ##\displaystyle U = {1\over 8\pi}\int \vec E \cdot \vec E dV## and ##\displaystyle U = \frac12 \int \phi \rho dV## are equal. I started with ##\nabla \cdot (\phi \nabla\phi) =(\nabla \phi)^2 + \phi \nabla^2 \phi##' Then ##\displaystyle {1\over 8\pi}\int \vec E \cdot \vec E dV...
  30. B

    Potential energy by concentric shells

    Homework Statement Concentric spherical shell of radius ##a## and ##b##, with ##b > a## carry charge ##Q## and ##-Q## respectively, each charge uniformly distributed. Find the energy stored in the E field of this system. Homework EquationsThe Attempt at a Solution Field between ##a## and...
  31. Nathan phisi

    Stuck on an Electrical Potential Energy Question

    Homework Statement A charge of Q = −1 µC is moved from point A to point B. Which of the following situations will result in an increase in electrical potential energy? I've now uploaded the files below Homework Equations F = qE U = qV a b c d e f g h The Attempt at a Solution I think...
  32. EastWindBreaks

    A car traveling upward on inclined plane

    Homework Statement consider a 3300 lb car whose speed is increased by 35 mph over a distance of 200 ft while traveling up a rectilinear incline with a 15% grade. model the car as a particle, assume the tires do not slip, neglect all sources of frictional losses and drag. find the work done by...
  33. Haynes Kwon

    Electrical Potential Energy and Electric Potential

    Hi. Getting straight to the point, what is the difference between electrical potential energy and electric potential? Please be as specific as you can. Thank you.
  34. gelfand

    Show that potential energy is conserved

    Homework Statement potential energy function of : $$ U(x) = 4x^2 + 3 $$ And have to i) Work out the equation of motion ii) Prove explicitly that the total energy is conservedHomework Equations$$ F = \frac{dU}{dt} $$ The Attempt at a Solution I'm not too sure how to go about this...
  35. L

    Relate rotational kinetic energy to potential energy

    Homework Statement This problem is from the 2015 AP Physics C Mechanics free response, question 3 part b. https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_frq_physics_c-m.pdf Homework Equations K = 1/2Iω2 U = mgh The Attempt at a Solution The potential energy of the bar when...
  36. J

    Electric Field and Potential Scenario

    Homework Statement I was wondering in what situation would the potential and the electric field of the system both be equal to zero at the same time? Homework Equations W=-ΔU=-ΔVq ΔV=-∫Edr V=kQ/r (with reference r->∞) The Attempt at a Solution I know for the middle of a dipole the potential...
  37. R

    Potential energy of rubber bands

    <Mentor's note: moved from a general forum and therefore no template> This is the equation of potential energy in rubber bands, however, I don't know how to calculate the inertia of the arm of catapults or get the k constant. And what does n mean? Basically, i don't understand the whole...
  38. C

    Finding Potential Energy of Oscillation

    How do I find the total potential energy at the highest and lowest points of oscillation without velocity or time?? I do not believe there is any air resistance, only gravity. I also already have the elastic potential energy and the gravitational potential energy.
  39. Metovich

    Question About Potential Energy

    I have two simple examples of potential energy and kinetic energy. First example: Imagine a book on the ground and I want to lift it.At first I apply a force just a little more than the gravitational force of the Earth so that it has some velocity. After the book gets that velocity, I keep my...
  40. C

    Relationship between work and potential energy?

    Homework Statement Imagine a thin tower 4000 miles tall; ı.e. as tall as the earth’s own radius Re, placed at the north pole of the earth. Suppose you start at rest at the base of the tower and climb to the top (wearing a spacesuit and carrying supplies you need, so that your total mass is M)...
  41. Leechie

    Calculating potential energy of hydrogen atom

    Homework Statement Calculate ##\left< \frac 1 r \right>## and ##\left< \frac 1 {r^2} \right>## and the expectation value and uncertainty of the potential energy of the electron and proton for a hydrogen atom in the given state. The given state is: $$ \psi_{2,1,-1} \left( r,\theta,\phi \right)...
  42. J

    How can I show that the bulk modulus is about r^-4?

    Homework Statement Using the equations, show the bulk modulus is about r^-4. Homework Equations The Attempt at a Solution Tried to plug Uij but it is not same as U. To be honest, I don't know where to start.
  43. cheapstrike

    Electrostatic Potential Energy stored outside a shell.

    Homework Statement A point charge +Q is placed at the centre of an isolated conducting shell of radius R. Find the electrostatic potential energy stored outside the spherical shell if the shell also contains a charge +Q distributed uniformly over it. Homework Equations [/B] E=kQ/r2...
  44. E

    Does Compressing a Spring Decrease Its Potential Energy?

    I have just read chapter 7.4 FORCE AND POTENTIAL ENERGY in Sears and Zemansky's university physics 14th edition. There they show that a conservative force always acts to push the system toward lower potential energy in a one-dimensional motion with the equation Fx(x) = - dU(x)/dx. As I...
  45. RavenBlackwolf

    Conservation of Energy, Down an Incline with a Spring

    Homework Statement A 4.0 kg block starts at rest and slides a distance d down a frictionless 35.0 incline, where it runs into a spring. The block slides an additional 16.0 cm before it is brought to rest momentarily by compressing the spring, whose spring constant is 429...
  46. Thinkor

    A Where is Potential Curvature Stored in GR?

    It is commonly said that if you lift an object above the Earth it gains potential energy equal to mgh (m=mass, g=gravitational acceleration, h=height), suggesting that the potential energy is in the lifted mass. This cannot be. Consider the case of two perfectly rigid spheres, isolated in...
  47. D

    Calculating the Potential Energy of a 3-point charge config.

    Homework Statement Charge q1= 8.5 nC is located at the coordinate system origin (0,0), while charge q2= -4.46 nC is located at (a,0), where a= 1.5 m. The point P has coordinates (a,b), where b=0.95 m. A third charge q3= 16.5 nC will b added later. It is a 3 part question, first asking for the...
  48. S

    Potential Energy vs. Position Graphs

    Homework Statement A particle has the potential energy shown in the figure. (Figure 1) What is the x-component of the force on the particle at x =5, 15, 25, and 35 cm? I'm stuck on finding the Fx at 25 & 35 cm.Homework Equations F = -du/dx 100 N = 1J/cm The Attempt at a Solution Slope...
  49. theideasmith

    Difference in potential energy of two charge configurations

    Chapter 24, Question 61 Given two configurations, ##C_1##, ##C_2## of ##N## point charges each, determine the smallest value of ##N## s.t. ##V_1>V_2##. ##C_1##: ##N## point charges are uniformly distributed on a ring s.t. the distance between adjacent electrons is constant ##C_2##: ##N-1##...
  50. S

    Find change in electric potential energy

    Homework Statement A uniform electric field of magnitude 4.1 ✕ 10^5 N/C points in the positive x-direction. Find the change in electric potential energy of a +5.3 µC charge as it moves from the origin to each of the points given below. (a) (0, 6.9 m) __ J (b) (6.9 m, 0) __J (c) (6.9 m...
Back
Top