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. MacLaddy

    Potential energy, and use of datum line

    Homework Statement The mechanism in the attached photo contains two masses, each treated as particles. When released from rest, the 4-kg block falls and the 6-kg sphere rises. Initially, the angle between the two rigid, massless linkages is θ = 60° What is the velocity of the sphere when θ =...
  2. Z

    Elastic Potential Energy to Aid Electromagnetic Induction

    Matter can neither be created nor destroyed...but potential energy can be converted into a different kind of energy. Let's say we have a spring with a mass connected to it. This mass is a magnet, and the apparatus is inside a copper coil. It's a horizontal magnet with friction minimized at the...
  3. Y

    Potential energy. What is the spring constant?

    Homework Statement Figure 8-36 shows an 8.00 kg stone at rest on a spring. The spring is compressed 10.0 cm by the stone. (a) What is the spring constant? 2. Relevant formula Mechanical energy is conserved The Attempt at a Solution The decrease in gravitational potential energy that occurs...
  4. X

    Does the potential energy of a spring do work on the both

    Suppose we have two boxes, A and B with different masses, the spring is fixed to block A. Then we take block B and press it against block A so that the spring compresses. Afterwards, we let go of both boxes. If we were to model this using the conservation of energy, then it is known that...
  5. **Mariam**

    Hooke's law vs. Elastic potential energy

    Homework Statement I am currently learning about elastic potential energy and this is a question that was given to us by my teacher: When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the force constant of the spring. Homework EquationsThe Attempt...
  6. KayDe

    Electric Potential Energy Problem

    Homework Statement Two Charged Objects (Q1= -9.0nC & Q2= 15nC) are fixed in place on the +x-axis. The first charge is 12 cm to the left from the origin the other is 12 cm to the right from the origin. A proton is moved from the origin to a position on the +y-axis 9.0 cm from the origin. a)...
  7. H

    Relationships between potential energy and distance

    Why is gravitational potential energy directly related to the distance of between two objects (mgh, so as distance increases, potential energy increases) while electric potential energy is inversely related (kq1q2/r,distance increases, electric potential energy decreases)?
  8. 8008jsmith

    Electric Potential Energy and micro-joules

    Homework Statement A uniform electric field of 16.9 N/C is directed in the positive x direction. If a charge of -2 micro-coulombs moves 2.2 meters in the negative x direction, how much does the electric potential energy change in micro-joules? Homework Equations ΔEPE = qEd The Attempt at a...
  9. J

    Understanding Work, Energy, and Displacement in a Spring System

    Homework Statement In the pictures. Homework Equations KE = 1/2mv^2. PE = 1/2kx^2 Work external = Delta KE + Delta PE W = F* dThe Attempt at a Solution In the pictures.Comments: On Problem 3 ai, I am not sure whether I have identified the correct horizontal forces. The hint gave two, but I...
  10. R

    Exploring Potential Energy in Oscillating Systems

    1. With respect to any oscillating system, what is the difference between ΔPE, PE, and PEaverage?Homework Equations ---- The Attempt at a Solution Hi all. I want to preface this by saying that we have been discussing the Lennard-Jones potential and particle theory in class recently, after...
  11. A

    Validity of application of Coulomb's Law with moving charge?

    Hi there, I'm trying to brush up on some of my E&M and am comparing treatments of Coulomb's Law in introductory calculus-based texts with higher level material. My understanding was that Coulomb's Law (and by extension, calculation of the electrostatic force on a charged particle using F = qE)...
  12. O

    Potential Energy Homework: Solving F(r) = -k(r-a)

    Homework Statement The net force on the mass is the central force F(r) = -k(r-a). Find the potential energy U(r). a is the spring of natural length and k is spring constant k. Homework Equations -dU/dx = F(x) The Attempt at a Solution F(r) = - \frac{ dU }{ dr } implies -k(r-a) = - \frac{ dU...
  13. Scott Davies

    Easy way to find the potential energy in compressed air

    I have a .81 Cu. Ft. cylinder which is at a static pressure of 80 Psi. What is the easiest way to calculate the Potential Energy of the compressed air?
  14. acdurbin953

    Potential energy of an arrangement of point charges

    Homework Statement What is the potential energy of the system composed of the three charges q1, q3, and q4, when q1 is at point R? Define the potential energy to be zero at infinity. Charges are arranged in a triangle, with q3 and q4 located up and down 2.2 cm from the origin, and q1 on the...
  15. K

    Confusion over potential energy equation.

    Hi, I am confused over the potential energy equation. I have been taught that potential energy is MGH M=mass, G=gravity on surface, and H=height from earth. However being on the internet and learning more i have noticed people use GmM/r^2 and i am very confused why it is switched. please help me...
  16. K

    Understanding the Difference Between PE=MGH and PE=GmM/r^2 in Online Discussions

    I am from New York, and a physics student. ( not trying to give to much info on the internet.) but i was curious in why people on the internet use PE equation as GmM/r^2 when i was taught that it was PE=MGH? please help me with me confusion? thank you.
  17. S

    How does potential energy increase, if height increases?

    (constants're ommitted) 1-) M=50, m=5, h=5 then Potential Energy = (50*5)/5 = 50 After increasing height 2-) M=50, m=5, h=10 then Potential Energy = (50*5)/10 = 25 Field strength decreases amount of h^2 so according to formulas potential energy decreases as h increases. But that mustn't be...
  18. D

    How to understand potential energy in Lagrangian

    Hi guys, So I'm trying to understand why the potential energy of a Lagrangian is the way it is. The system I'm considering is a closed necklace of N beads, each of mass m. Each bead interacts only with its nearest neighbour. First let me make some comments: 1) Each bead is labeled with a...
  19. M

    Gravitational potential energy: derive expression for energy

    Homework Statement Part A: Derive an expression for the energy needed to launch an object from the surface of Earth to a height h above the surface. Part B: Ignoring Earth's rotation, how much energy is needed to get the same object into orbit at height h? Express your answer in terms of...
  20. R

    Two charges, Electrical Potential

    Homework Statement Two charges q = 9.0μ C are fixed in space a distance d = 1.5 cm apart, as shown in the figure. a) With V = 0 at infinity, what is the electric potential at point C? b) You bring a third charge q = 9.0μC from infinity to C. How much work must you do? c) What is the...
  21. I

    Clarifying Electric potential energy

    I read somewhere online that according to Coulomb's law, in the context of an atom, the potential energy of an electron is proportional to the distance (squared) between the positive and negative charges, this however doesn't show up in the actual eq F = kq1q2/r^2 I thought about it in terms of...
  22. L

    Electrostatic potential energy of a cubical configuration

    Homework Statement Find the Electrostatic potential energy of a cubical configuration of point charges as shown in the figure. Each of the charges is 5.00e and the edge of the cube is 2 cm. (The image is simply a cube with one of the points labeled q) Homework Equations U=kQq/r The Attempt at...
  23. 2

    Sending a satellite to Jupiter?

    Homework Statement "In order to launch a space probe out of the solar system, it is decided to send it close to Jupiter. Why does this reduce the amount of fuel needed?" Homework EquationsThe Attempt at a Solution I can't think of anything at all. I am trying to think in terms of it gaining...
  24. K

    Higgs Potential Energy: Definition, Scale & Coleman-Weinberg

    When we discuss higgs potential energy in textbook, we mean it takes the form ## V(h)= m^2 h^2 + \lambda h^4/4##. My question is: is potential energy always defined at some specific energy scale? since the parameters depend on energy. For instance, if I am interested in the form of higgs...
  25. L

    Effective potential energy minimum

    Effective potential energy is defined by U^*(\rho)=\frac{L^2}{2m\rho^2}+U(\rho) in many problems I found that particle will have stable circular orbit if U^*(\rho) has minimum. 1. Why is that a case? Why circle? Why not ellipse for example? 2. Is this condition equivalent with...
  26. D

    Gravitational potential energy problem

    Homework Statement A broken spaceship is located h=10 km above the center of a large circular thin sheet of unknown dust. The sheet has a radius of R=106 km and a density of σ = 7*1011 kg/m2. The spaceship and the dust attract each other due to the gravitational force. a) Find the initial...
  27. julianwitkowski

    Gravitational Potential Energy of a fall

    In this case the height of the fall is far to high above Earth to be use PE=mgh. So I'm trying to integrate the inverse square gravitational force over distance. ##\int \frac{GmM_e}{r^2}dr## So I'm confused with respect to another object, specifically the moon, if the max height of the fall...
  28. oreo

    Is the Work Done in Rolling a Stone Less Than Lifting It?

    Is less work done in rolling the stone than lifting it? I think so that as gravity is conservative field therefore work done should be equal. But rolling could mean rotational kinetic energy so please clarify this?
  29. I

    Zero Potential Energy: Does an Absolute Zero Exist?

    I was thinking about the concept of the ground being the arbitrary zero potential point for gravitational potential energy and considered that since gravity is the attractive force between two objects that there would be no potential energy if an object's center of mass were somehow situated...
  30. P

    Understanding Shared Potential Energy in a Gravitational System

    Given two point masses, ##m_1## and ##m_2##, we define the gravitational potential energy of this system as: $$U_{grav} = -G \frac{m_1m_2}{r}$$ Where ##r## is the separation between ##m_1## and ##m_2##. When we analyze the motion of a single component, say ##m_1## in this system, we usually...
  31. J

    Gravitational Potential Energy Sign

    I understand that GPE is negative, but it does not come out this way when i try to derive it. I took the change in potential energy in bringing a particle from an infinite distance to a distance of b from another particle. ## \Delta U = - \int \vec F \cdot d \vec r ##. Since the...
  32. A

    Calculating Potential Energy of Iron Slab in Ferro/Anti-Ferro Magnetic States

    Hello, I am calculating the potential energy surface of an iron slab, once with a ferro magnetic behavior and later anti ferromagnetic behavior, I know for ferromagnetic I multiply the number of atoms by its magnetic moment (I use 3 that must be a little higher than its real value), my...
  33. ELB27

    How Is the Potential Energy of a Dipole Derived in Different Contexts?

    Homework Statement The problem is to show that the potential energy of a dipole (whether electric or magnetic) is given by ##U = -\vec{m}\cdot\vec{B}## in the magnetic case and ##U = -\vec{p}\cdot\vec{E}## in the electric case assuming the respective magnitudes of the dipole moment remain...
  34. P

    Understanding the Potential Energy Principle

    Homework Statement how to prove the potential energy principle? how do you make sense of the potential energy principle ie -dU/dX = F(x). What does the principle really mean? Homework Equations -dU/dX = F(x) where U is the potential energy and F the force. The Attempt at a Solution Not...
  35. B

    Effective potential energy of a charge in a magnetic field

    Hi, I'm studying the Lagrangian and its applications in electromagnetism. I stumbled across this inconsistency: The force of a charge moving through a magnetic field is ## F_b = q v \times B ## If we define B to be in the ## \hat{z} ## direction, this equation can be written as ## F_b = q (...
  36. gracy

    Potential energy of an electron

    .(1)Electron's potential energy decreases when it moves from lower to higher potential,right?And i also want to verify few more things on which i am doubtful .(2)Why when electron passes through resistance it's potential energy decreases?I think because it require energy to pass or cross...
  37. H

    Total electric potential energy of equilateral triangle

    Three charged objects, (+4 micro coulomb, -4 micro coulomb and +2 micro coulomb) are placed at the corners of an equilateral triangle with side length 2m. Calculate the total electric potential energy of the system... Guys Can you help me achieve a solution to this question? Thanks In Advance!
  38. H

    Conceptual Question about electric potential

    Guys, i really need help on answering this question... Can a charged particle ever move from a low electric potential to a high electric potential and yet have its electric potential energy decrease? Explain. What i think is that, no it is not possible for a charged particle to move to a...
  39. P

    Figuring out the potential energy

    Homework Statement A cylinder with mass M and radius R and moment of inertia I is standing on a rough surface (the left part of the triangle). A box with mass m is standing on a smooth surface (right part of the triangle). The cylinger and box is connected by a massless rope over a massless...
  40. T

    Classical Mechanics - Potential Energy Function

    Homework Statement The potential energy function of a particle of mass m is V(x) = cx/(x2+a2), where c and a are positive constants. Qualitatively sketch V as a function of x. Find two equilibrium points: identify which is a position of stable equilibrium, and find the period of small...
  41. K

    What is KE of the system using F = ma ?

    Homework Statement Three particles of mass all = 3 kg are located at the vertices of an equilateral triangle and are spinning about their center of mass in an empty space. The sides are length d = 2 m which doesn't change with time. Homework Equations What is the PE of the system? What is the...
  42. S

    When does work equal negative electric potential energy

    Homework Statement Let EPE be change in electric potential energy so if a positive charge is moving towards the negative terminal with the electric field it would mean that it is losing PE therefore work = - EPE, and if a negative charge is moving against the electric field towards the...
  43. Prof. 27

    Net Electron Acceleration and Potential Energy

    Homework Statement I was watching a Khan Academy video (here) on electric potential energy (not Voltage.) Here was the problem: There is an infinitely extending positively charged plane (uniform.) The charged plane has a positive electric field with 5 N/C (Newtons per Coulomb.) Electric...
  44. N

    Gravitational potential energy of a retaining wall

    Homework Statement Forty 2.0kg blocks 20.0cm thick are used to make a retaining wall in the backyard. Each row of the wall will contain 10 blocks. You may assume that the first block is placed at the reference level. How much gravitational potential energy is stored in the wall when the blocks...
  45. AdityaDev

    Redistribution of charges in capacitor

    Homework Statement A capacitor of capacity C is charged with potential difference V. Another capacitor of capacity 2C is charged to 4V.they are connected with reverse polarity after removing batteries. The heat produced during redistribution of charges is... Homework Equations ##Q = CV## ##U...
  46. M

    Electric Potential Energy Question

    1. Homework Statement Two electrons start at rest with a separation of 5.0*10-12m. Once released, the electrons accelerate away from each other. Calculate the speed of each electron when they are a very large distance apart. Homework Equations ΔEK+ΔEE=0 The Attempt at a Solution Okay so I...
  47. T

    How Do You Calculate Force from a Two-Dimensional Potential Energy Function?

    Homework Statement A potential energy function for a two-dimensional force is of the form U = 3x3 * y - 7x. Find the force that acts at the point (x, y).[/B] Homework Equations In a 1-dimensional case: ΔU = -∫Fx dx dU = -Fx dx Fx = -dU/dx The Attempt at a Solution I know how to find the...
  48. S

    Lagrange mechanics: Pendulum attached to a massless support

    Homework Statement A simple pendulum of length ##b## and bob with mass ##m## is attached to a massless support moving vertically upward with constant acceleration ##a##. Determine (a) the equations of motion and (b) the period for small oscillations. 2. Formulas ##U = mgh## ##T = (1/2)mv^2...
  49. S

    Gravitional Potential Energy Question

    Homework Statement Planet 1 has mass 3M and radius R, while Planet 2 has mass 4Mand radius 2R. They are separated by center-to-center distance 8R. A rock is placed halfway between their centers at point O. It is released from rest. Ignore any motion of the planets. The rock is released from...
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