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.

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  1. 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##...
  2. 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...
  3. D

    Potential energy in Gauss' gun

    Homework Statement For my extended essay as part of the IB, I am investigating the effect of changing the distance and the number of stationary ball bearings in a Gaussian gun. I was hoping to look at the energy transfer during each stage of magnets and therefore calculate the efficiency...
  4. AsadaShino92

    Understanding Potential Energy Graphs for Two-Particle Systems

    Homework Statement The potential energy V(R) of a two particle system exhibiting oscillatory behavior near a local minimum at the equilibrium separation Ro. V(R)= -(A/R)+(B/R^2) , where R is the interparticle separation. A) Sketch V(R), what happens to V(R) as R→0 B) At what value of R is...
  5. fuvest

    Mechanical Energy Problem/non-conservative forces

    Homework Statement A body of mass "m" is let go from on top of a surface A, where it slides down to B(without friction). From that point on, it displaces itself on an horizontal surface 5 meters away from B, where it stops at C. Being "m" a mass in kg "h" in meters and g = 10 m/s^2 The value...
  6. C

    Ball Doing a Loop Min Kin Energy: Find Angle θ

    Homework Statement A ball with radius ##r## is inside a hollow cylinder with radius ##r+R##. In the first part of the assignment, one has to calculate the minimum kinetic energy the ball has to have at the bottom in order to complete a full loop in the cylinder. It turns out to be...
  7. AsadaShino92

    Potential energy of a displaced mass on a spring

    Homework Statement A spring of negligible mass exerts a restoring force on a point mass M given by F(x)= (-k1x)+(k2x^2) where k1 and k2 >0. Calculate the potential energy U(x) stored in the spring for a displacement x. Take U=0 at x=0. Homework Equations ΔU=∫F(x)dx U=½kx^2 The Attempt at a...
  8. J

    Exploring Electrical Potential Energy Across Series Circuits

    Assuming the resistance of a wire in a series circuit, consisting only of 1 component (e.g. filament lamp) and a battery, is negligible; does each Coulomb of charge commit all of its electrical potential energy, supplied by the battery's potential difference, as work done across the component...
  9. D

    How to find the average potential energy given V(x,y) and E?

    Homework Statement A classical particle with total energy E moves under the influence of a potential V(x,y) = 3x3+2x2y+2xy2+y3. What is the average potential energy, calculated over a long time? Homework EquationsThe Attempt at a Solution I think that this can be solved using Virial Theorem...
  10. J

    I Energy transfer during uphill vs downhill running

    Hello Physics Gurus, Please critique the following logic... When a runner hikes/runs to the top of a mountain, the chemical potential energy inside the muscles transferred into the potential energy of the runner's body mass at the higher elevation (Pe = mass*gravity*height = mgh). Energy is...
  11. R

    Maximum potential energy after collision

    Homework Statement : A ball a, moving with kinetic energy E, makes a head on elastic collision with a stationary ball with mass n times that of A. The maximum potential energy stored in the system during the collision is a)nE/(n+1) b)(n+1)E/n c)(n-1)E/n d)E/n[/B]Homework Equations :Principle of...
  12. bdolle

    Confusion with Potential Energy and Work

    In my physics textbook chapter of work 3 statements are made which I am having trouble sorting through. 1. When W>0 the system's energy increases, when W<0 the system's energy decreases. 2. ΔE = ΔK+ΔU+ΔTherm = W 3. ΔU = -W Here is where my confusion begins. If I move a 1kg brick from 0m to 1m...
  13. V

    Physical interpretation of the "total potential energy"

    The principle of minimum total potential energy is frequently used in solid mechanics as an elegant way of deriving the equilibrium equations for an elastic body under conservative forces. This method states that out of all the possible displacement fields that fulfill the boundary conditions...
  14. D

    Why does the potential energy get lower as atoms get closer?

    Hello. I'm new to this forum and to Physics and Chemistry in general and I have a question that's making me go crazy: why does the potential energy decrease as two atoms (say, hydrogen atoms) get closer to form a molecule? I'm talking about this graphic: I've read that it's related to the...
  15. R

    Potential energy of the spring

    A planar object comprises of two masses joined by a linear spring with relaxed length p. The horizontal and the vertical displacements of the two masses are measured relative to a fixed point of reference as shown in the figure. What would be the potential energy of the spring? My initial guess...
  16. Vitani11

    Potential energy as a form of mass?

    Homework Statement Let's say we have a mass of 5kg at a height of 3 m so it's potential energy is mgh = 147J/1.6e-19 = 9.19 e20 eV. Now we know that E = mc^2... so when finding the mass of this potential energy we get 10.2e3 kg. What the hell is that supposed to mean? Homework Equations None...
  17. ikihi

    Building a Clock from a Spring: Exploring Potential Energy

    Homework Statement You are in a spaceship far from any other objects, and you want to build a clock. You decide to build your clock out of a spring with a mass attached to it. You use a spring with spring constant k = 138 N/m, and you initially displace the mass a distance x=25.0 cm from...
  18. P

    Spring's Potential Energy expression

    Homework Statement In an experiment, a student wishes to use a spring to accelerate a cart along a horizontal level track. The spring is attached to the left end of the track and produces a non-linear force of magnitude Fs = Ass + Bs, where s is the distance the spring is compressed in meters...
  19. 1

    Lagrangian of 2 rotating masses on a spring, sliding down plane

    Homework Statement 2 masses are connected by a spring. They are on a frictionless plane inclined relative to the horizontal by ##\alpha##. The masses are free to slide, rotate about their center of mass, and oscillate. 1. Find the Lagrangian as a sum of the Lagrangian for the COM motion and a...
  20. betty0202

    Potential Energy: Find Force, Equilibrium & Conditions

    Homework Statement The potential energy of a system of two particles separated by a distance X is given by the equation below, where A,B,U0 are constant. U(X)=U0exp{[-(x/A)-1)((x/B)-]} (a). Find the force F(x) that each particle exerts on the other. (b). show that the is a X where the system...
  21. A

    Potential energy in a Mass spring system

    Why is the rate of change of potential energy always same the rate of change of kinetic energy in a mass spring system? Additiinally, How do we determine the rate of change of potential energy in such case?
  22. Jules Winnfield

    How come escape velocity isn't imaginary?

    Going through several definitions, it appears that escape velocity is equal to the potential energy. That is:$$\frac{1}{2}m v^2=-\frac{G M m}{r}$$but if I solve for velocity, $v$, I get:$$v=\sqrt{-2\frac{G M}{r}}$$So how do I get an escape velocity that isn't imaginary?
  23. Jules Winnfield

    Potential energy in the presence of two fields

    I'm trying to understand potential energy, especially with regard to gravity. There's a double negative that's difficult to grasp: The direction of the force is negative because the vector points radially outward and the force of gravity is directed inward, and the work done to bring an object...
  24. L

    [Gravitational Potential Energy] In a movie stunt, a 65 kg skier...

    Homework Statement [/B] In a movie stunt, a 65 kg skier starts from a rest position at the top of a hill 30 m high. She slides down the hill to the bottom, where she collides with a 45 kg stationary skier. The collision is completely inelastic. Find the final velocity of the skiers. Homework...
  25. N

    B If an object runs an infinite distance in universe....?

    ...(after infinite distance) falls into earth, would exist infinite potential energy if E=mgh and h is infinite?
  26. LoganNagol

    How can potential energy be negative?

    In my physics class I was told that potential energy can be negative because it relative, but i thought as long as something has room to fall it has a positive amount of potential energy. So how can potential energy be negative?
  27. Pratik89

    Elastic and gravitational potential energy

    X has a mass of 55 kg and hangs from a rope. As a result of this the rope stretches by 0.6 m. Calculate the energy stored in the rope as a result of stretching. Solution: F = kx and E = 0.5x^2. Using this fetches the answer as 161.5 However, the change in potential energy (calculated using mgh )...
  28. EternusVia

    Binding energy / mass deficit of Earth-moon system?

    Homework Statement Consider the earth-moon system (whose constituent pats we take to be the Earth and the moon separately). a) Compute this system's gravitational potential energy (in joules) and the mass deficit (in kilograms). The radius of the moon's orbit is 384,000 km, and its period is...
  29. A

    When does potential energy change?

    Why doesn't the potential energy of a substance change when the pressure changes? Or in what case will the potential energy of a substance change?
  30. S

    Why does this system have zero potential energy and only one degree of freedom?

    the question is : particles m1 and m2 each of mass m are connected by a massless rod with length l , these particles move on a frictionless horizontal plane as shown in the screen shot , the movement of m1 is fixed on a frictionless circular track of radius R , find the E.O.M ! Homework...
  31. 10Exahertz

    Orbital Potential Energy to find r and phi in terms of t.

    Homework Statement A particle in central force field has the orbit r=cφ^2, c is a constant. Find the potential energy, Find r and phi in terms of t. I get how to find the potential energy and found it to be U=-l^2/mu (2c/r^3+l/2r^2) l is angular momentum and mu is the reduced mass But how do I...
  32. B

    Gravitational potential energy problem

    Homework Statement Question :- Two stars, each of a solar mass and radius ##10^7 m## are at a distance of ##10^{12} m## from each other. Find the speed of each star before collision if initial speed is negligible. Homework Equations $$V(r) = {-G Mm \over r}$$ The Attempt at a Solution...
  33. I

    I Does spacetime have potential energy?

    Does spacetime have potential energy, and does an object with more potential energy have more mass? (E=mc^2)
  34. NiendorfPhysics

    Radius of Half Electric Potential Energy

    Homework Statement There is a solid cylinder of radius a and then empty space then a shell cylinder of radius b. Show that half of the stored potential energy lies within a cylinder of radius $$\sqrt{ab}$$ Homework Equations In the attempt The Attempt at a Solution I'm not sure what they...
  35. D

    Time average of the potential energy of a planet

    Homework Statement (a) Prove that the time average of the potential energy of a planet in an elliptical orbit about the sun is -k/a. (b) Calculate the time average of the kinetic energy of the planet. Homework Equations F = \frac {-dV} {dr} = - \frac {k} {r} The Attempt at a Solution [/B]...
  36. C

    Work of external forces and electrostatic potential energy

    Homework Statement Two metal spheres of equal radius ##R## are placed at big distance one from the other. Sphere 1 has total charge ##q## and sphere 2 has no charge. The two speheres are moved one towards the other until they touch, then they are moved again far away one from the other. What is...
  37. J

    What is the electrostatic potential energy of a sphere?

    Hello! I'm Steven, and I'm currently working on the following problem: The Earth can be seen as a conducting sphere with an electric field: E= -(150V/m)r (on its surface) and where r is the unit vector . The Earth has a radius 6371 km. So, I am asked to calculate the electrostatic potential...
  38. L

    Gravitational potential energy

    Homework Statement A teeter toy is composed of a massless central stick of length L and two massless sticks of length l attached at angles α, each with a mass m at the end (see the figure). We imagine tilting the toy by an angle θ from the upright position. a) Find an expression for the...
  39. MattNguyen

    Potential energy equation to force equation?

    Homework Statement The binding potential energy in a diatomic molecule (N2 for example) is often approximated by the Morse potential energy which has the form U(r) = De (1-e^[-a(r-re)])2 where De is a constant that reflects the well depth (dissociation energy), a is a constant that reflects the...
  40. Automata-Theory

    A Particle Moving Along a Ring with Variable Potential

    Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...
  41. 1

    Find the potential energy of the particle

    Homework Statement A small bead of mass m is constrained to move on a helix: r (θ) = (R cos(θ), R sin(θ), q θ) where R and q are constants, and θ=θ(t) describes the position of the bead along the helix at time t. The bead is also subjected to a gravitational acceleration g downward (-z...
  42. Cocoleia

    How to find trajectory as a function of time with energy

    Homework Statement I am given that an object of mass m has an attractive force F=-A/x^2 acting on it, where A is a constant and x>0. I need to find the potential energy. After i need to suppose initial conditions (x0, v0) such that total energy=0. I need to find the trajectory x(t) with v>0...
  43. J

    Reading a Potential Energy Graph

    Homework Statement A conservative force F(x) acts on a 2.0 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is graphed in the figure. When the particle is at x = 2.0 m, its velocity is –1.2 m/s. (a) What isF(x) at this position, including sign? Between what...
  44. N

    B Is dark/vacuum potential energy infinite?

    And virtual particles potential energy is infinite too? As more and more dark energy is created does this mean that the potential energy of dark energy is infinite? Does that happen for virtual particles in vacuum and vacuum energy too?
  45. F

    Question about electrical potential energy

    Homework Statement Two charged plate hold a charge of 3 coulombs with the upper plate being positively charged and the lower plate being negatively charged. They have a pd of 6 volts. There is a spacing of 20 cm between them. A positive charge q with a charge 0.4 coulomb is located at midpoint...
  46. FallenApple

    No Potential Energy due to Sphere of Mass?

    So we all know that it takes work to build up a sphere of charge by taking charge from infinity and piling it up into a sphere. Since the sphere wants to break apart under repulsion, its like a spring. It has intrinsic potential energy.However it doesn't seem the case with a sphere of mass, with...
  47. Summer95

    Figuring Out if A Force Field is Conservative or Not

    Homework Statement There is a collection of different force fields, for example: $$F_{x}=ln z$$ $$F_{y}=-ze^{-y}$$ $$F_{z}=e^{-y}+\frac{x}{z}$$ We are supposed to indicate whether they are conservative and find the potential energy function. Homework Equations See Above The Attempt at a...
  48. FallenApple

    Exploring the Conservation of Angular Momentum in Rotating Objects

    So masses on springs store potential energy. Height in a gravational field store potential energy for the mass there.So why isn't there a potential energy stored inside rotating objects? Surely there are ways to translate the rotational energy to kinetic. Its kinda like a spring. If a set down a...
  49. ChloeYip

    What is the relationship between force and potential energy?

    Homework Statement Picture: https://drive.google.com/open?id=0B39n6QfDU8f3bWY3OWxyaGZBYU0 [Moderator: Image inserted to make problem statement visible] Homework Equations F=-dU/dx The Attempt at a Solution I have no idea in this question... The slope is always the same for the graph...
  50. J

    Why is change in potential energy is always negative?

    I'm studying relation between conservative force and potential energy,and getting a big question on change in potential energy is always negative. For gravitational PE ,when an object is lifting up, it's work done is negative(opposite direction). so the change in work done is negative. On the...
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