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. M

    Distance traveled by a particle using Potential energy function

    Homework Statement A 1kg particle is in a potential given in joules by U(x)=3x2+4x-5, where x is in metres. The particle is initially at position x=1m and moving with velocity v=4m/s in the +x direction. Find the position when the particle first comes to rest. Homework Equations dKe = Kf-Ki...
  2. blair chiasson

    Conservation of energy, potential energy function

    Homework Statement The potential energy for a mss m = 1.0 kg moving in one dimension is given by U(x) = (2.5J) sin πx. The mass starts at x = 0 with an initial velocity v = 0.71m/s. (The plus sign means the motion is in the positive x-direction.) Describe the subsequent motion of the mass...
  3. Jonathan Scott

    An observation on potential energy in GR

    There are various different ways to try to add up the effective total mass of a configuration of masses in GR in such a way that it comes out to be equal to the total of the source mass as measured locally minus the gravitational binding energy. One of these is for example the Komar mass, which...
  4. S

    Calculate Potential Energy of Electron at a Parallel Plate Capacitor

    Homework Statement An electron with a speed of 5.0x10^6 m/s is injected into a parallel plate apparatus, in a vacuum, through a hole in the positive plate. The electron collides with the negative plate at 1.0x10^6 m/s. What is the potential difference between the plates? Vi= 5.0x10^6...
  5. E

    Frank-Condon Principle - Potential Energy Surfaces

    Theory and my Understanding: So I understand how the frank condon principle let's us effect electronic transitions instantaneously, since the motion of nuclei (on the timescale of such electronic transitions) is quite slow. Consequently, when a photon of light is absorbed you can have an...
  6. neomahakala108

    Potential Energy -- What are the different ways it can be stored?

    Potential energy is energy contained in certain system, for example in physical body mass in gravitational field of Earth. Potential energy at initial position has value equal to work necessary to move mass from initial position to new position. But also, i read that potential energy can also...
  7. T

    Kinetic and potential energy in firing a cannon

    Homework Statement A 20.0 kg cannonball is fired from a cannon with a muzzle speed of 1000 m/s at an angle of 37.0° with the horizontal. A second ball is fired at an angle of 90.0°. (a) Use the isolated system model to find the maximum height reached by each ball. (b) What is the total...
  8. J

    Potential Energy/ dipole moment curves

    Hi, I wasn't sure if this is more Physics/Astro or chemistry because its actually all 3. i've got some conceptual issues with some tasks at hands, and was wondering if anyone could clear that up for me. (These questions are all regarding molecules) 1) How do you create a potential energy...
  9. A

    Potential Energy of 2 Spherical Shells

    Homework Statement Find the energy required to assemble two uniform hollow spheres of charge q between radii a and b with a volume charge density roh-v. The shells are separated by a distance c. *description of picture* - two identical spherical shells with inner radius a and outer radius b...
  10. A

    What quantities are used to measure potential energy and forces?

    If two bodies A (m = 1kg) and B (M = 2kg) are at height h from the earth, when they fall and reach the ground A will have KE = 1*gh and B = 2*gh, That means double energy. Is the force FA = m*a that acted on A equal to the force FB = M*a that acted on B since a = 9.8 in both cases? FB should be...
  11. G

    Solving Physics Homework: Spring Length & Work Done

    Homework Statement A vertical spring is 10.0 cm long when supporting a 20.0 kg mass, and it is 12.0 cm long when supporting a 32.0 kg mass. Assume the stretch is linear with the load. a) What is the length of the spring with zero load? (0.06666667) b) How much work would be done in...
  12. S

    One dimension conservative force and potential energy

    Homework Statement Given a conservative force, how can we obtain the change in potential energy? Given a potential energy function, how can we determine the associated conservative force? One dimensional.Homework Equations Fx = -du/dx ΔU = -∫ F dx The Attempt at a Solution I know I can...
  13. J

    Conceptual Question on Work and Negative Work

    I'm confused by classic description of work and negative work. If someone pulls (slowly) on a rope to lift a bucket in a well, I understand that the person is doing work on the bucket and gravity is doing negative work on the bucket. So, the net work is zero. But if the net work is zero...
  14. L

    Stable Equilibrium of Two Hemispheres: a<3b/5

    Homework Statement A solid hemisphere with radius b has its flat surface glued to a horizontal table. Another solid hemisphere with radius a rests on top of the hemisphere of radius b so that the curved surfaces in contact. The surfaces of hemispheres are rough, meaning no slipping occurs...
  15. D

    Electrical potential involving a spacecraft

    Homework Statement Been stuck on this problem. Any help will be greatly appreciated 1. The (actual) spacecraft Deep Space 1 tested an ion drive engine in which Xenon atoms were accelerated (maximum voltage of 1,300 volts), neutralized and used to provide thrust. The probe carried 74 kg of...
  16. L

    Work & Energy: When to Use PE vs KE?

    I have been studying the Work and Energy chapter of physics and am currently confused on when to make work equal potential energy and when to make it equal to change in kinetic energy. Some of the problems have the work equal to change in KE and some have it equal to PE. For example, why is...
  17. D

    How to Solve a Potential Energy Problem with Given Force Components?

    Homework Statement The potential energy function associated with the force F= 4xyicap + 2x^2jcap is Homework Equations F= -dU/dx The Attempt at a Solution i treid to find the magnitude of force n then put in eq bt failed plese help
  18. M

    Density at the centre of the sun

    Hello, here is the question I have to answer; I am aware that the gravitational energy of one layer of thickness dr is dU=-\frac{GM(r)dm}{r} and that ultimately I will have to integrate this over all radii but I am unclear about the expression for \rho_{center}. The only thing that springs to...
  19. C

    Gravitational Potential Energy - Kinetic Energy

    Homework Statement An asteroid of mass m = 2.6 × 10^6 kg approaches the Earth. When it is exactly 3 Earth radii away from the Earth's centre its speed relative to the Earth's centre is u = 8.7 × 10^3 m s–1. The asteroid subsequently falls down to the Earth's surface. You may assume that the...
  20. C

    Potential Energy Gravitation Kinetic Energy

    Homework Statement An asteroid of mass m = 2.6 × 10^6 kg approaches the Earth. When it is exactly 3 Earth radii away from the Earth's centre its speed relative to the Earth's centre is u = 8.7 × 10^3 m s–1. The asteroid subsequently falls down to the Earth's surface. You may assume that the...
  21. sweet springs

    Smoothness of potential energy and powers of momentum

    Hi. In case potential energy V(x) in one dimensional stationary Shrodinger equation does not have smoothness of C-infinity, I assume that some power n of momentum for an energy eigenstate, <p^n>, diverge. Finite square well potential gives infinite <p^n> for n=6,8,10,.. for example. <p^4> also...
  22. C

    Potential energy of a particle in a system

    1. A single conservative force acting on a particle within a system varies as = (− Ax + Bx6)ihat N, where A and B are constants, is in Newtons, and x is in meters. (a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (b) Find the change in...
  23. C

    Conservative force and potential energy

    Problem: A conservative force F is acting on a particle that moves vertically. F can be expressed as (3y-6) j head N, y is in m and j head is a unit vector along vertical direction. a) Calculate the potential energy associated with F, with the potential energy set to zero at y=0. b) At what...
  24. G

    Finding electrostatic potential

    Homework Statement Find the energy stored in a solid sphere by integrating ##\frac{\epsilon_0}{2} \int E^2d^3r## given that ##E=k\frac{r^2}{4 \epsilon_0}## for ##0<r\le R## and ##E=k\frac{R^4}{4r^2 \epsilon_0}## for ##r>R## Homework Equations ##U=\frac{\epsilon_0}{2} \int E^2d^3r##The Attempt...
  25. H

    Electrostatic Potential Energy with Constant Electric Field vs NonConstant Field

    When determining potential energy we have the relationship: PE = V*q = E*q*d But depending on the scenario we can't use them interchangeable right? If you want to calculate the work needed to be done by a particle going from a distance Y to right next to another particle of the same charge...
  26. J

    Gravitational potential energy experiment

    Homework Statement To explain the forces at work when a marble is released from a height and then eventually comes to rest. We did this experiment where two lengths of hose pipe were taped together. The hosepipe was then bent into a semicircular shape (forming a track) and secured onto a clamp...
  27. ahoback

    Aaron's Gravitational Potential Energy to Launch Projectile Science Competition

    Hello my name is Aaron! I am a high school senior from northeastern Kentucky designing a pneumatic system of sorts for a science competition and need some help. I will be building a device that converts gravitational potential energy, from a falling mass, into air pressure (or possibly the...
  28. T

    Confusion with the centrifugal foce and potential energy

    When we release a suspended object, we recover the potential energy due to gravity as the object travels back through the height raised. When we release an extended spring, we recover the potential energy as the object travels back through the distance stretched. But when we release a rotating...
  29. W

    Electric Potential Energy concepts

    Homework Statement What does the following equation mean and how is it analogous to the relationship between the electric field and the the electrostatic force? V ( ~r ) = U ( ~r ) / q In general, confused about concepts, meanings and vocabulary. The naming of different terms in this...
  30. M

    Deriving gravitational potential energy (by bringing mass from infinity to r)

    I understand the derivation of gravitational potential energy when an object is moved away from Earth but when I try to derive the formula for gpe by considering a test mass moving from infinity to r then I end up with a positive gravitational potential energy. Because integrating F.dr from...
  31. C

    Potential energy turned into kinetic

    Homework Statement We have an object with much smaller mass than compared to the sun. This object is at rest when released at 1AU from the sun. After a week how far is the mass from the sun. The Attempt at a Solution So I look at the gravitational potential energy and set it equal to...
  32. Ward_edojawa

    Potential energy for a spring law

    Hi guys! Thanks for this great forum. I have a question I need explanation about please... I just started 11th grade and it's my first time taking springs. In the book, they said : Ep= 1/2 k x^2 I already understand all the previous laws like [w= -1/2 k (x2^2 _ x1^2)] and know where thay came...
  33. S

    Lagrangian Dynamics: Potential Energy formulation with spring and gra

    Hi, I have a conceptual question regarding Lagrangian dynamics. It has to do with the potential energy formulation. My instructor today mentioned something in class that does not make much sense to me. Here is he most basic example that illustrates my confusion: Take a simple 1dof...
  34. davidbenari

    Potential energy stored in a system of point charges

    The basic equation is as follows: U=∑kqiqj/Rj with (i≠j) My question is how is this definition useful? What makes you want to say that is the potential energy of the system? For example, I thought that it is useful because if all particles change in position then you could evaluate that...
  35. S

    What is the Change in Potential Energy of a Displaced Meter Scale?

    A meter scale of mass m initially vertical is displaced at 45 degrees keeping the upper end fixed. . find out the change in potential energy.
  36. W

    Does an electron with negative electrostatic potential energy fall up?

    In a vacuum under standard gravity, an anchored spherical metal electrode is brought to +1,000,000 volts relative to the distant walls of a much larger chamber. (I'm a new user; hopefully this will display as attachment 1) Therefore, electrons that fall through a small gap in the electrode...
  37. K

    Potential energy in a falling tree?

    Hi, My first post here, hope it goes well. I wonder if someone of you skilled persons could help me and my friend calculate the energy in a falling tree. I´m no good at maths neither good in english but I will try to explain what I´m after. If you cut down a tree that is 25m heigh and weighs...
  38. M

    What is gravitational potential energy?

    is GPE at a point the work we must do against the gravitational force to bring an object from infinity to the point? Or is it the work done by the gravitational force?
  39. M

    Gravitational Potential Energy And Work Done

    This question may sound weird but when we lift an object with a force equal to the weight of the object up to a certain height the Earth is doing negative work on the object as well. So shouldn't the net work be zero?
  40. A

    Electric potential energy and its applications

    Hi guys I just want to make sure that my understanding of potential difference is right or wrong I just want someone to tell me whether my understanding is right or wrong. I know that when we move a charge if it's attracted to another charge it gain potential energy and when we leave it it lose...
  41. S

    Potential Energy Approach to Derive Spring Element Equations

    Good day! I am a beginner in Finite Element Analysis and Structural Mechanics. I have problem in understanding the insight of potential energy approach to derive spring element equations. I have already search for similar post and I found this, and agree with the example raise...
  42. G

    Does potential energy have measurable corresponding mass?

    When a rubber band is stretched, or a battery is charged, or two massive objects are separated, the potential energy of all these systems increases in each situation. Now say that any of these systems were suspended in space. If we were to measure the gravitational field of the uncharged...
  43. H

    Change in Electric potential, potential energy, and work problem.

    Homework Statement Imagine a lithium atom where the two electrons in the first orbital are at exact opposite sides of the nucleus and the electron in the second orbital is in line with the other electrons so that the three electrons and the nucleus all lie on a straight line. How much work...
  44. T

    Potential energy difference related qs

    in bringing a test charge (+q ) from a postion to another in an electric field of another charge +Q an external force , F is applied which is just as same as the electric force, F[SIZE="1"](electric) how is this possible? doesnt an unbalanced force be required to...bring about this...
  45. K

    Potential energy of some mass

    Homework Statement A mass of 3kg is 1m above the floor. the zero of the potential energy is chosen to be on the floor. I understand that the 30j potential energy belongs to both the Earth and the mass, so, why don't i take into account also the distance to the center of the earth? Why don't...
  46. N

    (What is) Schwarzschild Radius and Potential Energy

    I was thinking a bit earlier: What if you created a particle at infinity (ignore the normal particle rules for simplicity), and allowed it to fall towards a massive body? Ignoring other effects such as the other forces, would the particle ever gain enough energy to surpass the energy...
  47. Greg Bernhardt

    What is Potential Energy? A 5 Minute Introduction

    Continue reading...
  48. J

    Function describing Potential Energy

    Hi, can someone please help me on this problem. I'm not sure what to do with the equation given. I tried taking the derivative, partial, and anti and nothing seems to be working. Can someone please give me a hint on how to start this problem. Thanks in advance. Suppose the following...
  49. kartikwat

    Potential Energy of dipole in external electric field

    Why do we take Θ=90° for calculation of potential energy
  50. C

    Potential Energy of a Charge Configuration

    Is there a quick way to figure out the total potential energy between more than 2 charges without having to find the potential at each point and the. Multiplying it by the charge at that point and adding it all up? For example - a 2D square with a charges Q, 2Q, -3Q, and another Q at each...
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