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. Oannes

    Finding the Value of Gravity Given Height and Velocity

    Homework Statement If a ball is dropped from a height (H) its velocity will increase until it hits the ground (assuming that aerodynamic drag due to the air is negligible). During its fall, its initial potential energy is converted into kinetic energy. If the ball is dropped from a height of...
  2. thecourtholio

    Energy for Linear 1D Systems - 1D potential

    Homework Statement A particle of mass m moves along the x–axis under the influence of force ##F_x=-ax+bx^3## , where a and b are known positive constants. (a) Find, and sketch, the particle's potential energy, taking U(0) = 0 (b) Identify and classify all equilibrium points (c) Find the...
  3. victorhugo

    Gravitational Potential Energy & L.C.E. Questions

    1. A comet that passes by Earth has GPE, which will be all lost if it begins to fall towards Earth. If it's shot back up, it will now start with Ek and finish with a higher GPE. Now, what exactly is this GPE? if energy cannot be created or destroyed, but transformed, where does it get stored at...
  4. KT KIM

    Effective Potential Energy from Central Force Motion

    Hi, I'm studying undergrad mechanics, Central force motion, Marion's book in specific, Here, the Potential Energy is defined weird way (in my opinion though) (μ is reduced mass) So potential Energy becomes Called "Effective Potential Energy" But, I can't agree with calling it potential just...
  5. W

    Can someone explain this derivation?

    Homework Statement I've been looking at examples of motion derivations for my class, and it's honestly just very confusing. I heard Dynamics should prep you for this but I must have had a very poor course because we never had to understand geometry and physics to this degree... Homework...
  6. Amru123

    Work done and potential energy

    When work done is positive How does potential energy decrease? Work done and energy cannot have different direction can they? Can someone help me out in understanding this properly ?
  7. W

    Identifying the Potential Energy of a Spring Pulley System

    Homework Statement Homework Equations U = 1/2 kx2 The Attempt at a Solution So, I took dynamics off campus and needless to say, we didn't really do very much deriving so that aspect of physics really bogs me down and I'm trying to learn it now in another class. So if anyone wants to also...
  8. Clara Chung

    Calculating Total Energy of an Electron Orbiting a Hydrogen Nucleus

    Homework Statement Prove that the total energy of an electron orbiting a hydrogen nucleus is Etotal = -e^2/ 8ε0 π r where e is the magnitude of charge of an electron and r is the orbital radius. Homework Equations Knowledge The Attempt at a Solution Here is my attempt: For KE, mv^2/r =...
  9. A

    Relationship between potential energy and force

    Hi, I wonder which steps of my following deduce are wrong dU=-dW dU=mg dh dW=Fdx thus, mgdh=-Fdx (dx=dh) then, F=-mg which is a constant in most of situation However, F does change in some situation. I am confused about this.
  10. donaldparida

    Does Potential Energy Depend on Reference Point or Force Nature?

    Does the value of the potential energy of a system of objects depend on the reference point or the nature of force existing between them (attractive or repulsive)?
  11. M

    Is Potential Energy Infinite at Any Point for Point Masses?

    Hi everyone, first post here. Today i crushed into a question. I was going to write it down here, then i crushed into another one. Lets say we want to know the potential energy of a body relative to a center of gravity. I will refer to gravitys acceleration as "g" and to mass as "m". "k" will...
  12. K

    Why Does Moving a Negative Charge to a Higher Potential Increase Its Energy?

    Homework Statement When a -2C is moved from point A to B, the potential energy of the system increases by 10J. What is the voltage V(ab)? Homework Equations U=qV The Attempt at a Solution 10=(-2)V, I thought the voltage was -5V but the correct answer is +5V. Could someone explain why this is?
  13. donaldparida

    B Difference between W=-(ΔU) and negative U.

    Is there any difference between the meaning of the equation W=-ΔU and the meaning of the statement that potential energy of system is always negative when the reference point(zero point) is taken to be located at infinity or do they both convey the same message?
  14. N

    Water wheels and mathematical equation

    Hello everyone, currently working on a physics project. I was very curios about waterwheels and actually have an overshot waterwheel setup. I was testing how the efficiency of a waterwheel would be effected by the drop height of water onto the waterwheel. Do any of you have any idea how I can...
  15. RoboNerd

    Question on problem solving approach involving work done

    Homework Statement Homework Equations I know that U = q * V, so my attempted approach will rely on that method The Attempt at a Solution I was wondering if people could help me solve the problem and help me figure out why B is the correct answer and what the pitfall in my problem solving...
  16. haushofer

    Hamilton's principle and minimum potential energy

    Dear all, I was wondering what exactly the correspondence/relation is between Hamilton's principle (extremizing the action gives the allowed configurations) and the fact that a system wants to configurate such as to minimize its potential energy. Is there any? Somehow I can't find a decent...
  17. donaldparida

    Gravitational potential energy conflict

    I know that when an object A a does positive work on another object B, object A loses energy and object B gains energy(there is transfer of energy from object A to object B) and when object A does negative work on object B, it gains energy and object B loses energy(there is transfer of energy...
  18. Biker

    B Do galvanic cells depend on distance?

    I have seen some sites say that it doesn't and other says the opposite. So let's see Source of the pic: Chemguide Lets look at the hydrogen (Oxidation) half cell. If we assume that it contributes x volts until the electron reachs the copper, then no matter how big is the distance the voltage...
  19. t_r_theta_phi

    I Gravitational Potential Energy: 1/2 Factor Explained

    I am currently reading Gravitational Curvature by Theodore Frankel. In the derivation of Einstein's equations in chapter 3, he states that the gravitational potential energy of a blob of fluid is ∫B½p0U√gVdx where the integral is a volume integral, p0 is the rest energy density and √gvdx is...
  20. T

    Gravitational Potential Energy

    Homework Statement A body of mass m is taken at a constant speed from the surface of the Earth (radius = Re) to infinity. (a) What is the work W1 done on the body in the process? (b) If m is taken from a distance r > Re to infinity, how much work W2 is required? (c)Which quantity is larger, W1...
  21. O

    Potential Energy: Dependence on Position, Not Velocity

    The form of the Lagrangian is: L = K - U When cast in terms of generalized coordinates, the kinetic energy (K) can be a function of the rates of generalized coordinates AND the coordinates themselves (velocity and position); a case would be a double pendulum. However, the potential energy (U)...
  22. zohaibtarar

    Change in potential energy of the particle

    Homework Statement A particle with a charge of 2e moves between two points which have a potential difference of 75V. What is the change in potential energy of the particle? Homework Equations U = (75 V)(2e) The Attempt at a Solution [/B] When a particle with charge e moves through a...
  23. Andreas C

    Determining the potential energy

    I have found that even though knowing the potential energy is vital for classical mechanics, most of the times what you know is actually the force, so you have to determine the potential energy based on that. So, here's the issue: The relationship between the force and the potential energy is...
  24. E

    Is Gibbs free energy just potential energy reduction?

    So I know that things in the Universe tend to move toward a state of least potential energy. This is why forces point in the direction of decreasing potential energy, as everything is trying to minimize its potential energy. So my main question is: does Gibb's free energy basically just...
  25. G

    I Total Energy of Particle in Potential: SR Explanation

    Hi. What is the total energy of a particle in a potential? Is it $$E=\gamma m_0 c^2+E_pot$$ or is it still $$E=\gamma m_0 c^2$$ where ##m_0## is a bigger mass than the particle would have in absence of the potential?
  26. TiernanW

    Calculating the loss of Potential Energy of water in turbine

    Homework Statement Homework Equations Power = Work Done / Time Work Done = Force * Displacement PE = mass * gravity * height The Attempt at a Solution I got the first part (i) right, so the mass of the sea water is 1.32 x 10^12 kg. Part (ii) is the bit I am stuck on. My thoughts were that...
  27. X

    Question about potential energy

    Let's say we have a mass M at the ground of the Earth with speed U going upwards so its energy is E= kinetic. The speed is enough to surpass Earth's gravitational field so now it has a speed U2<U and its energy now is E= kinetic+potential. So my question now is: Is this potential energy lost? I...
  28. F

    Spring transferring half its energy to each mass?

    My question is: Does a spring between two differing masses, each with an initial momentum of zero, transfer half of its stored elastic potential energy to each? My intuition says yes. But it seems to not be the case. If you apply the conservation of energy and momentum, the answer you get is...
  29. J

    Motion with elastic potential energy and other forces

    Homework Statement A 15.0 kg stone slides down a snow-covered hill leaving point A (at the top of the hill) with a speed of 10.0 m/s. There is no friction on he hill between point A and point B (at the foot of the hill). There is friction on the level ground at the bottom of the hill between...
  30. Curieuse

    Potential Energy for dipole in Electric Field

    Homework Statement To derive Potential Energy for dipole p in Electric Field E. 2. Homework Equations Potential Energy is the work done by the external agent in turning the angle of the dipole from the U=0 position to another position against the influence of the electric field applied...
  31. G

    Electrical potential energy question

    Why does the potential energy of a system of two charged particles decrease as the distance between them increases? It seems that the PE should increase, as in U=mgh; as h increases, the PE increases. Why does this not occur in electrical potential energy, and in the gravitational potential...
  32. e2m2a

    I Gravitational potential energy and rest mass

    Does the rest mass of an object increase when it acquires gravitational potential energy, and if so, is this the reason why Einstein believed that the inertia of a mass increases in the presence of other masses?
  33. S

    Kinetic energy and Gravitational Potential Energy

    Hi Guys,When we are finding the wasted energy when something is dropped a tower, we do this: mgH-0.5mv^2 My question is, does the velocity of the kinetic energy have to be vertical component, or can it be the impact velocity when it hits the ground? Thanks
  34. A

    Gravitation energy of a spherical shell

    I am asked to find the total gravitational energy of a hollow sphere using the fact that the field energy density is given by ##u_g = \frac{-1}{8\pi G}g^2##. Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give...
  35. RoboNerd

    Potential energy in stretched spring

    Homework Statement Five identical masses of mass M are suspended by a spring stretched a distance of L. If three of the masses are removed, what is the potential energy stored in the spring? 1) (4 / 25) * M * g * L 2) (2 / 5) M * g * L^2 3) (5 / 2) * M g * L 4) (4 / 25 ) * M * g L^2 5) 5 * M *...
  36. A

    Gravitational Potential Energy

    Hello, I do not quite get this. Can anyone provide examples? " We may feel that it takes a force greater than the weight of the object being raised to lift it upwards, but it is not so. Provided the force is equal to the weight, the object will move upwards at a steady speed. "
  37. C

    Distance in Electric versus Gravitational potential energy

    Homework Statement Consider the equations for electric potential energy: and gravitational potential energy: GPE=m*g*h In the case of GPE, the potential energy increases as the distance between the two objects increases. This makes sense (to me), as the greater distance between the Earth...
  38. It's me

    Potential energy of moving charge in field

    Homework Statement 1. Homework Statement [/B] Prove the potential energy of interaction between an electric charge ##q## moving with velocity ##\vec{v}## and an electromagnetic field with potentials ##V## and ##\vec{A}## is given by ##U = qV-q \vec{v} \cdot \vec{A}## Homework Equations...
  39. ramialsaiad

    How to calculate the potential energy of a spring?

    Hi I want to calculate the potential energy of the following figure in function of x Here is my attempt : mgx + 1/2*k*(sqrt(x^2+L^2)-L)=1/2*m*v^2 Is that correct ? thanks
  40. kq6up

    A Potential Energy Curve for Ammonia Inversion?

    For my Quantum II class I am working on a paper about masers. I am using a naive model (a coupled pair of infinite potential wells), and I would like to find out where I can find a graph of the inversion potential energy curve. This would be a simple one dimensional curve of the potential...
  41. A

    Gravitational potential energy

    Suppose the mass of planet is" M" and there is body in its surface whose mass is "m" and the field strength is "g" . If the body is thrown 1800 m then Gravitational Potential energy = mg(1800). My question is why can't we use formula GPE= GMm/x ? This is also the formula for gpe but why...
  42. R

    Gravitational Potential Energy of a Sphere

    Homework Statement Homework Equations ΔPE = G × M₁ × M₂ (1/Ri - 1/Rf) where G = gravitational constant M₁ = mass of one object M₂ = mass of the other object Ri = initial distance Rf = final distance ΔPE = -ΔKE The Attempt at a Solution My solution is v = 2√(GM/d). I am making sure it is...
  43. D

    Find the minimum kinetic energy of two electrons in a 1D box

    Homework Statement Problem: Consider a "crystal" consisting of two nuclei and two electrons arranged like this: q1 q2 q1 q2 with a distance d betweem each. (q1=e, q2=-e) a) Find the potential energy as a function of d. b) Assuming the electrons to be restricted to a one-dimensional...
  44. E

    I Built-in potential in pn junction

    Hello! The (potential) energy of an electron in a solid structure is always negative; also the E_c and E_v levels (conduction band and valence band limits) are negative, in the band diagram of a pn junction. When the junction is built and thermal equilibrium is reached, the depletion region...
  45. R

    Solving for Kinetic & Potential Energy: Help Needed

    Homework Statement Homework Equations The Attempt at a Solution Kinetic Energy + Potential energy=0 1/2mv^2 = mgcos(20) 100v^2 = 1.96cos(20) v^2 = .0184 v = .136 m/s No idea if this is correct or if I should proceed with energy considerations. Please advise.
  46. eefje

    Potential energy -- child sleds down a slope and comes to a stop....

    Homework Statement A child starts from rest and slides on a sled first slope down over a distance of 25 m . Then, the child slides further over a horizontal plane. The angle of inclination is 35 ° and the kinetic coefficient of friction between the sled and the snow is 0.100. The mass of the...
  47. S

    Spring stretch - Do I use Force or Potential Energy

    I have read posts about this but still don't have a good handle on it. I am confused about something that I know is simple. If a mass is attached to a spring, the spring will stretch according to Hooke,s law, correct? So won't the weight, (mg) balance out the spring force of -kx? So in other...
  48. S

    Doubts on Work-Energy theorem for a system

    While studying energy conservation on Morin I found this explanation about the work-energy theorem for a system. Using Koenig theorem $$\Delta K_\textrm{system}=\Delta K +\Delta K_\textrm{internal}$$ so we have I've got two main question on that: Why are only external forces considered for...
  49. S

    Partial derivative of potential energy and work

    For a conservative force \vec{F}=-\vec{\nabla} U \implies dW=-\vec{\nabla}U \cdot d\vec{s} Where d\vec{s} is the infinitesimal vector displacement. Does the following hold? -\frac{\partial U}{\partial \vec{s}}=-\vec{\nabla} U \cdot d\vec{s}=d W, i.e. the infinitesimal work is minus the...
  50. A

    Potential energy stored in a dipole

    1- Potential energy stored in a dipole placed in an electric field E is maximum when a- E is perpendicular to the dipole moment b- E is parallel to the dipole moment c- E is anti-parallel to the dipole moment
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