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. I

    Doubts about potential energy, bonding and chemical reactions

    Hello everybody, First, sorry for the bad english, it is not my language. I have a few theoretical problems and I would be very thankful if you helped me. 1º: I see the graphic about covalent bonds and potential energy a lot of times and they always say that potential energy...
  2. E

    A confusion in work and potential energy

    This is an abstract of my book " Potential energy is always defined relative to some reference point where U=0. Therefore U represents the work that would be on the test charge q0 by the field of q if q0 moved from an initial distance r to infinity. If q and q0 have the same sign, the...
  3. S

    Kinetic and Potential Energy Question

    Homework Statement A skier starts skiing from the very top of a frictionless sphere of ice with very little initial speed. At what angle from the the vertical will the skier leave the sphere of ice? Homework Equations This question was in the Kinetic and Potential Energy chapter, so I guess...
  4. A

    Calculating Work Done by Electrical Force on a Moving Charge

    Homework Statement Two positive charges of q=3*10^-6 C are a distance 1 m apart. What will be the work done by the electrical force in bringing one of the charges to a distance of 0.5 m from the other charge (which is fixed at its position through the whole process)?Homework Equations The...
  5. M

    Electrostatic Potential Energy of an ion

    Working from Krane's Modern Physics 11.5 Calculate the first 3 contributions to the electrostatic potential energy of an ion in the CsCl lattice. I believe the formula I'm supposed to use is U_{c}\,=\,-\alpha\frac{e^{2}}{4\pi\epsilon_{0}R} Just from looking in the chapter I can...
  6. B

    Can Potential Energy Convert Directly into Matter?

    Hello all . We know matter has momentum and because of this creation of pair production occur by photons , because photons have momentum . Or kinetic energy of collide two objects can create matter because objects in moving have momentum . But can potential energy directly convert to...
  7. Sneakatone

    Need help finding potential energy formula

    I took the integral of the equation but its wrong, the program does not have a fraction input to put 1/4 properly. I ended up with -x^-1/4(x^4). For part b I plugged in 4.5 and turned the number positive to get the answer. Did I do something wrong for part a?
  8. M

    Gravitational potential energy of a sphere of non-uniform density

    Homework Statement Find the total gravitational potential energy stored in a sphere with a 1/r2 density distribution if the total mass is 6.7 solar mass and the radius is 1.3 solar radius. Express you answer in units of 1041 Joules. The Attempt at a Solution To derive the equation, i...
  9. V

    Directional Derivative of Potential energy

    I'm facing some problem in understanding few basic concepts of classical physics. http://www.fotoshack.us/fotos/67357p0020-sel.jpg I cannot understand what does "ij" indicate in "Vij" and how does F=-∇iVij. Why ∇i, why not only ∇. Please help anybody. I'm practically getting frustrated...
  10. E

    Potential Energy in two springs system problem

    Homework Statement A particle of mass m= 1.18kg is attached between two identical springs on a frictionless, horizontal tabletop. Both springs have spring constant k and are initially unstressed, and the particle is at x=0. a) The particle is pulled a distance x along a direction perpendicular...
  11. H

    The form of gravitational potential energy

    http://www.scholarpedia.org/article/Celestial_mechanics#Newton.E2.80.99s_Celestial_Mechanics In this source, the gravitational potential energy is given as \frac{-MmG}{r}-\frac{mmG}{r}, seeming to imply that the \frac{MmG}{r} result only applies to a body, mass m, in a gravitational potential...
  12. E

    Change in potential energy of elastic strip under deformation

    A linear elastic strip of natural length a and stiffness k lies between x = 0 and x = a. Each point on the strip is transformed by a differentiable, monotone increasing function f. a) Characterise the change in potential energy. b) Given the boundary conditions f(0) = 0 and f(a) = b, choose f...
  13. T

    Electrons velocity and Potential energy

    hello all... i have a question: In an electric circuit the velocity of electrons are very small than how they will pass through all the elements of a circuit and gain or/and loss potential energy? for example let's take a basic circuit : An EMF and a resistor. How the electron in a resistor will...
  14. J

    Calculating Gravitational Potential Energy Increase: 3.0kg Object

    Homework Statement A 3.0 kg object travels vertically at a constant speed of 2.0m/s. What is the increase in gravitational potential energy after 4.0 sec? Homework Equations Ep=Mgh The Attempt at a Solution I know i need to find the height but, with constant velocity i don't know...
  15. L

    Parallel Axis Theorem | Kinetic and Potential Energy

    Homework Statement A rigid body is made of three identical rods, each with length L = 0.525 m, fastened together in the form of a letter H, as in Figure 10-56 below. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H. The body is allowed...
  16. D

    Potential Energy of a Spring Contradiction?

    Hi everyone, I'm a bit confused about the concept of the potential energy. Let's say we have the following scenarios here: https://dl.dropbox.com/u/29312856/Springs.jpg In the first scenario, we have two identical springs with spring constant 5000 N/cm angled at 20 degrees below the...
  17. L

    How can potential energy functions be used to model a system's motion?

    Homework Statement Homework Equations dU/dx=-Fx Conservation of energyThe Attempt at a Solution Here are my solutions. Please feel free to correct me. Any help will be appreciated. (a) I think that the particle is moving in the negative direction because the potential energy decreases (?)...
  18. S

    Difference between Electric Potential energy and Potential energy

    Homework Statement A proton is released from rest in a uniform electric field of magnitude 8x10^4 V/m. After the proton has moved 0.5 meters a) What is the change in electric potential? b) What is the change in potential energy? c) What is the speed of the proton? Homework Equations...
  19. P

    Variations of electrostatic potential energy

    Hello, (this isn't homework but I thought it wasn't worthy of the main forums) I'm looking to clarify some thoughts about the various forms of electrostatic potential energy. As I understand, the expression \displaystyle \frac{\epsilon_{o}}{2} \int \textbf{E} \cdot \textbf{E} \; dV over all...
  20. D

    MHB Re: How do I find the potential for this unusual pendulum?

    An unusual pendulum is made by fixing a string to a horizontal cylinder of radius $R$, wrapping the string several times around the cylinder, and then tying a mass $m$ to the loose end. In equilibrium the mass hangs a distance $l_0$ vertically below the edge of the cylinder. Find the potential...
  21. F

    Calculating the Potential Energy of Quarks in the Quark Model of the Neutron

    Quark Model of the Neutron According to the quark model of fundamental particles, neutrons-the neutral particles in an atom's nucleus-are composed of three quarks. Two of these quarks are "down" quarks, each with a charge of ; the third quark is an "up" quark, with a charge of . This gives the...
  22. K

    Potential Energy in a Vessel

    Hi, I have a project which I am working on which is trying to work out the Potential Energy from a Vessel filled with compressed air. I have found a few different equations for this and was wondering if anyone has any experience on this to guide me a little. To first size the receiver I...
  23. W

    Potential energy( electron moving away form proton)

    An electron is initially 2cm from a proton and is then give an initial velocity away from the proton. If v is 31m/s how far to the right does the electron move before it momentarily stops? is this right? http://i1341.photobucket.com/albums/o745/nebula-314/IMAG0112_zps5361921d.jpg
  24. F

    Hessian matrix of potential energy in electrostatic system

    Hi everyone: I am rookie in classical physics and first-time PF user so please forgive me if I am making mistakes here. My current project needs some guidance from physics and I am describing the problem, my understanding and question as below. I have an independent electrostatic system...
  25. Pruddy

    Determine the potential energy of the configuration

    . Homework Statement Diagram: Please check the attachment. It has a diagram that will help solve the problem #6)Point charges Q1 and Q2 are located at two vertices of an equilateral triangle. Point P is the third vertex.The length of each side of the triangle is 28.0 cm. Q1 = +26e, and Q2...
  26. Ackbach

    MHB Solve Sign Issues in Elec. Potential, Energy, Force, Field, Work

    I had some trouble reconciling signs while attempting to teach electricity to my students here. The topic is electric potential, potential energy, electric force, electric field, and work. After much thought - several hours - I have finally come up with a presentation that solves the issues...
  27. B

    Difference In Potential Energy

    Hello, Whenever I read about potential energy, whether its in the case of gravitational, spring, or electric, I invariably come across the phrase, "...only differences in potential energy matter," and, "...the initial potential energy is arbitrarily chosen to be zero," or phrases to that...
  28. M

    Gravitational Potential Energy Problem

    Homework Statement A simple pendulum is swinging. Its mass is m and its length is L. What is its gravitational potential energy if it is oriented at 30° with respect to the vertical? (Let gravitational potential energy be zero if it is in the vertical orientation). Homework Equations U =...
  29. C

    Pendulum Potential energy equation

    hello every one i have this pendulum: i need to stabilize the pendulum in the inverted position , i need to know the potential energy for the pendulum , i read several articles in each one i have a different equation : V=mgl_{p}cos\alpha V=-mgl_{p}cos\alpha V=mgl_{p}(1-cos\alpha)...
  30. P

    Kinetic and gravitational potential energy and velocity

    Homework Statement A watermelon with a mass of 2.0kg falls out of a tree house that is 5.4m above the ground. What is the speed of the watermelon just before it hits the ground? Homework Equations Δh = (vi^2 - vf^2)/2g Eg = mgΔh Ek = 1/2mv^2 The Attempt at a Solution I tried two...
  31. P

    Kinetic and gravitational potential energy

    Homework Statement Explain why the kinetic energy of the skier at the bottom of the hill is not equal to the gravitational potential energy of the skier at the top of the hill. Homework Equations n/a The Attempt at a Solution I think the answer is because the bottom of the hill is...
  32. J

    Does negative potential energy reduce the effect of gravity?

    Hello, my question is in the context of modeling static neutron stars via the TOV equation. This is for a 20 week research project for my undergraduate degree. I am creating different equations of state to relate energy density to pressure, I have already used ideal fermi gas models, and now...
  33. D

    Pile driver question kinetic energy and potential energy

    [b]1. a pile driver of mass 250kg is allowed to fall from rest through a distance of 2m on to a 400kg steel pile to drive it into the ground. Each impact drives the pile into the ground by 150mm. assuming that the pile driver remains in contact with the pile after impact and that momentum is...
  34. E

    Determine if angular momentum is conserved given potential energy funtions?

    Homework Statement For each of the following potential energy functions in three dimensions, what quantities are conserved (energy, momentum, angular momentum)?Homework Equations U = k/2(x^2 + y^2) U = α/r U = β(z(hat) dotted with r)^2 U = α/r + β(z(hat) dotted with r)^2 Where z(hat) is the...
  35. R

    Electric Potential Energy and Work

    Hello. I need help clearing up who's gaining potential energy and who's losing potential energy from an particular object perspective. And, from that object perspective, whether the object doing positive work or negative work. W = \int \vec F \cdot d\vec x \Delta U = -W Question 1...
  36. Saxby

    Differentiating force to find potential energy

    A particle of mass m is moving along the x-axis and experiences a force F(x), also along the x-axis, given by F(x) = -kx. Deduce an expression for the potiential energy of the particle. I tried intergrating both side (just to see if it gave me anything helpful). I got ∫F(x)dx=mv for the...
  37. N

    Total gravitational potential energy of four objects

    Homework Statement Four masses m are arranged at the vertices of a tetrahedron of side length a. What is the gravitational potential energy of this arrangement? (answer is -6Gmm/a) Homework Equations gravitational potential energy = -Gmm/r The Attempt at a Solution One mass is "a"...
  38. N

    Kinetic energy, Potential energy and change in water pressure

    Homework Statement I'm not particularly confident with my calculations and I would appreciate any feed back. A) What is the kinetic energy of an object with: mass = 5lbm velocity = 200 ft/sec B) What is the potential energy of an object with: mass = 5lbm height = 200ft g = 32.2...
  39. C

    Calculating Kinetic and Potential Energy of a Falling Object

    If a stone sits at the edge of a 155m cliff and falls 43.6m with the velocity at that point of 29.2m/s , what is the kinetic and potential energy? Are they the same or diff?
  40. H

    Potential Energy during Constant Velocity Motion

    Homework Statement Could you please clarify the confusion I have about potential energy? Consider an object being raised from the Earth's surface upwards at a constant velocity. Is the potential energy increasing while it is moving upwards at a constant velocity?Homework Equations The Attempt...
  41. S

    Potential Energy of a System of charged particles

    Homework Statement Homework Equations V = kQ/r PE = Vq The Attempt at a Solution Tried a lot of ways... get an order of magnitude less than the answer and also off by a bit too. Please help. I think you are supposed to take V at each location then multiply by q since this is PE. I carry...
  42. M

    Calculating Kinetic & Potential Energy of Rama's Impact

    Homework Statement -- This is out of Rendezvous With Rama by Arthur C. Clarke You know it is 907184 kg and is going 50,000 m/s So how much energy does it have right before it hits the earth? Homework Equations Do I use Fg= Gm1m2/r^2 ? Ek=1/2mv^2? I have ΔE=1/2mv^2 written down as an equation...
  43. shounakbhatta

    How does the formula for gravitation potential energy work?

    Hello, Can anybody please explain me: While going through gravitation potential energy, I came across: F=G.m1.m2/r^2 From there it follows: g=-GM/r^2.r How does it follow? Specially the -G case? -- Shounak
  44. shounakbhatta

    Potential Energy and gravitation

    Hello, Can someone please explain me: F=G m1xm2/R^2 In potential energy U=mgh Generally it is also written that: U=-Gxm1xM2/r+K. How -G comes into play? Also Newton's above law of Gravitation in vector form is written as: F_12=-Gm1m2/r12^2 r12 Here also how -G comes into...
  45. B

    Potential Energy vs. Position Graph

    I attached a graph of a potential energy vs. position graph. My question is, the relative minimum is characterized as a equilibrium point, but what is, specifically, is this type of equilibrium point--a stable, unstable, or neutral one?
  46. R

    Equation of Virtual Work VS Potential Energy

    For linear elastic materials (3D General)... The virtual work equation looks exactly like the equation for potential energy except that in the potential energy equation, the internal work term has a (1/2) coefficient. Why are these different?
  47. R

    Help with Potential Energy vs Kinetic Energy and finding final velocity

    Ok before we get to number 3, I need to show you what I did for number 2 because this is kind of a two-part problem: PEinitial + KEinitial = PEfinal + KEfinal mgy + (1/2)mvi2 = (1/2)mvf2 gy + (1/2)vi2 = (1/2)vf2 (9.81)(10) + (1/2)(102) = vf2/2 98.1 + 50 = vf2/2 148.1 = vf2/2 2(148.1) = vf2...
  48. T

    Potential difference vs Potential energy

    G'day! I was looking over my notes about gravitational potential energy and I came across the graphs that I drew in class of the gravitational potential energy of a mass with reference point at infinity compared with the potential energy of a mass with reference point at the surface of the...
  49. T

    How to derive the formula for Gravitational Potential Energy?

    How did scientists derive the formula -GMm/r=Ep in order to calculate the amount of work required to move an object from an infinitely large point (or an extremely large distance as my textbook says) ?
  50. T

    Gravitational Potential Energy with reference point at infinity?

    So, the gravitational potential energy of a mass "X" from the sun is, let's say, 100joules. Why is it that when we take the gravitational potential energy of the mass from the reference point of infinity that the gravitational potential energy is -100joules? I understand the negative...
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