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. gracy

    Potential energy in an external field

    External field means field does not belong to or is not of the charges present in it,right?So,if there is a system of two point charges and these charges are present in an external field ,it means this external field is not produced by any of the charges present,right? Then there is a derivation...
  2. gracy

    Questions based on derivation of electrical potential energy

    Consider a system of two charges ## q_1## and ##q_2## separated by distance ##r_1##.This configuration is associated with a potential energy ##U_1##.When the separation is increased to ##r_2##.Potential energy becomes ##U_2## ##dW_E##=##\vec{F}##.##\vec{dr}##...
  3. gracy

    Kinetic energy and potential energy relationship

    I know,kinetic energy=##\frac{1}{2}####mv^2## But I saw one other equation it is kinetic energy=##\frac{1}{2}####|P.E|## Then I started looking for in which specific condition is it true?Because I know it is not always applicable .But I could not find that particular condition when it is true.So...
  4. CivilSigma

    Potential energy negative, force & displacement co-linear?

    Homework Statement In the following question, in the solution, why is it that when they calculate the gravitational potential energy at point 2 (impact with spring), it is negative? I know that if both the force and displacement act in the same direction, then the work done should be positive...
  5. F

    Potential Energy and Conservation of Energy

    Homework Statement A 700g block is released from rest at height Ho(initial) above a vertical spring with spring constant k=400 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 19.0 cm. How much work is done A) by the block on the spring...
  6. W

    Approximate Values of Kinetic Energy and Potential Energy

    Homework Statement https://s2.lite.msu.edu/res/msu/perl_author/MI3/CH7/IMAGES/MI3_7P32.png The figure shows a potential energy curve for the interaction of two neutral atoms. The two-atom system is in a vibrational state (i.e., a total energy state) indicated by the heavy solid horizontal line...
  7. M

    Is energy conserved in an object sliding down an inclined plane on ice?

    1. A ball falls to the ground through the air. Is the energy of the air conserved?2. None3. When a ball falls to the ground a transformation of energy occurs. The previously stored potential energy gradually becomes kinetic energy during its fall. The energy conserved in the air is the slight...
  8. K

    Spring potential energy and mass

    Homework Statement One end of a vertical spring of spring constant k = 1900 N/m is attached to the floor. You compress the spring so that it is 2.50 m shorter than its relaxed length, place a 1.00-kg ball on top of the free end, and then release the system att = 0. (All values are measured in...
  9. B

    Potential Energy and Loop-de-Loops

    Homework Statement A bead slides without friction around a loop–the–loop (see figure below). The bead is released from rest at a heighth = 3.60R. (a) What is its speed at point ? (Use the following as necessary: the acceleration due to gravity g, and R.) v = _________________ (b) How large...
  10. RMM

    How much energy can be generated by a swinging pendulum 60 kg

    I would like to make a pendulum go on moving by a permanent magnet that pushes the pendulum back with a force that is big enough to make it swing back with the same height. Can anyone tell me how much energy could be generated by a pendulum with height is 2 meter and 60 kg, swinging 90 degrees...
  11. davidbenari

    What exactly is meant by potential energy in the Lagrangian?

    I was solving the double pendulum problem via Lagrangian methods but something bothered me quite a lot. (Consider the two bobs are of equal mass and the pendula are of equal length). Then the potential energies are conveniently written as ##V_1=-mgl\cos\theta## and...
  12. kostoglotov

    Is negative potential energy actually meaningful?

    Disclaimer: not sure if this is actually the most appropriate forum, but it is a question inspired by my work on a homework question...I'm happy for a moderator to move this to a different forum. (But General Physics states: NO HOMEWORK/COURSEWORK QUESTIONS HERE) 1. Homework Statement Ok...
  13. K

    Stable Equilibrium of Stacked Hemispheres

    Homework Statement A solid hemisphere of radius b has its flat surface glued to a horizontal table. A second solid hemisphere of different radius a rests on top of the first one so that the curved surfaces are in contact. The surfaces of the hemispheres are rough (meaning that no slipping occurs...
  14. Calpalned

    Work is positive/negative potential energy

    I understand that ##\Delta U = -W## and that ##\Delta V = \frac {\Delta U}{q}## I don't understand why the example below has "set the change in potential energy equal to the (positive of the) work ...
  15. D

    Vacuum: Potential Energy & Universe Expansion?

    If I induce vacuum in a glass tube and then I open the lid of the glass tube, air rushes into fill in the vacuum. Can vacuum be regarded as a sort of potential energy, able to exert a force? Can a vacuum tube be considered as a potential storage device for energy, just like a container filled...
  16. Calpalned

    Potential energy of electricity

    Homework Statement I don't understand the answer to part b Homework Equations n/a The Attempt at a Solution The solution guide skipped too many steps. How was this derived? If the 5th charge is in the middle, it will be equidistant (about ##\frac {b\sqrt {2}}{2}##) from each of the...
  17. Calpalned

    Time-Averaging the Potential Energy

    Homework Statement Homework Equations Gravitational potential energy The Attempt at a Solution Isn't this the solution? So Is <U> = U(r) where a = r? How do I incorporate the ##\frac {1}{\tau}## and the given "useful definite integral" from zero to 2π? Thanks
  18. I

    Skater Ramp Simulation: Potential Energy vs. Position

    Hello, In this simulation (link is below) the graph of the potential energy with respect to position U(x) when there is no friction on the ramp looks like the graph of potential energy of Hooke's Law spring U(x)=(1/2)KX^2). For the spring, the negative of the derivative is equal to the...
  19. H

    How much work, speed and distance

    Homework Statement A child wants to go ride on her sleigh, and she decides to walk up the Big Hill, of height 100 m relative to where she starts. There are two ways up; the steep way, where the slope is 30.0 degrees, and the not-so steep way, where the slope is 15.0 degrees. The...
  20. T

    Force and Potential Energy Coordinates

    Homework Statement Evaluate the force corresponding to the potential energy function ##V (r) = \frac{cz}{r^3}##, where ##c## is a constant. Write your answer in vector notation, and also in spherical polars, and verify that it satisfies ##∇∧F = 0##. Homework Equations ##F(x)=-\frac{dU}{dx}##...
  21. xSpartanCx

    Conservation of electric potential energy

    Homework Statement An alpha particle is a nucleus of helium. It has twice the charge and four times the mass of the proton. When they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 3.6×10−3c, where c is the...
  22. K

    Charged Particles (Potential Energy)

    Homework Statement Figure 24-21 shows four pairs of charged particles with identical separations. (a) Rank the pairs according to their electric potential energy (that is, the energy of the two-particle system), greatest (most positive) first. (b) For each pair, if the separation between the...
  23. gracy

    Form taken by potential energy

    I have come across the following paragraph from my book "The gravitational force is always attractive .Whereas the electric force is attractive or repulsive acording to whether q0 is negative or positive.Each of the above forces is conservative,so a potential energy is associated with each of...
  24. gracy

    Definition of potential energy

    In my book definition of potential energy difference between two points as the work required to be done by an external force in moving without accelerating charge q from one point to another in electric field of any arbitrary charge configuration.I want to know why without accelerating ?
  25. P

    Electrical Potential Energy of three quark system

    Homework Statement A proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 3×10-15 m and calculate the potential energy of the subsystem of...
  26. P

    Calculating electrostatic potential energy

    Homework Statement Consider potential field V(ρ, φ, z) = V_0/ρ in free space and cylindrical coordinates. Calculate electrostatic potential energy stored in half cylindrical shell defined by a≤ρ≤b, 0≤φ≤π and 0≤z≤h. Homework Equations W_E=½∫∫∫ρ_vVdV The Attempt at a Solution I have no idea...
  27. M

    Potential Energy and Kinetic Energy

    Homework Statement Two blocks are hung by a string draped over a pulley, a 1.5-kg block on the left and a 3.0-kg block on the right. The two blocks start out at rest and at the same height. A. What is the change in the gravitational potential energy of the system of blocks and Earth when the...
  28. S

    Approximate spring potential energy U(x) for small oscillations

    Homework Statement "Take a PE function U(x), which has an equilibrium point at x=0, and provides a restoring force in that region, and show that a Taylor expansion around that area can be approximated by a SHO PE function for small x." Homework Equations U=.5kx^2...x =...
  29. Quadrat

    Potential energy in a physical pendulum

    Hey PF! 1. Homework Statement If I have a pendulum; a vertically hanging rod with (length ##L## and mass ##m##) which can rotate freely about a point ##p## on the upper edge of the rod. Now I fire a bullet (also with mass ##m##) into it (strictly horizontal on the lower end of the rod). I...
  30. UMath1

    Significance of negative potential energy

    Using the potential energy formula -GMm/R^2 I understand that the maximum potential energy is 0. But what is the significance of the potential energy as it approaches negative infinity? I am not sure how exactly to word this, but I cannot seem to grasp the what negative potential energy tells us...
  31. P

    A problem with Gravitational and Elastic Potential Energy

    I am calculating the energy transfer in two different formulas and they are giving different results. What could be the reason of this difference? I would be grateful if someone tell me what i am missing here. http://s18.postimg.org/o4tknn77d/potential.jpg
  32. P

    Electric potential energy and work

    Homework Statement Positive point charge (Q = 8 μC, mass m = 19 g) is fixed at point (9 cm,0). A second identical charge q is constrained to slide on a frictionless wire along the y-axis. Assume: the only force on q is the electrostatic force. If q starts at (0,7 cm) and is released from...
  33. N

    Source of potential energy of body made in space falling

    Hey all, question about gravitational potential energy. If an object begins on ground then gains height when it falls then energy it consumes to fall down was the potential created by moving upwards, if an object was created in space, then moves gravitationally towards a celestial body where...
  34. M

    Electrostatic Potential Energy

    Homework Statement As an electron moved through a region of space, its speed changed from an initial velocity of vi=8114.3 km/s to the final velocity vf=2233.7 km/s. The electric force was the only force acting on the electron. Across what potential difference did the electron travel...
  35. flm

    Potential energy in 2 gravity fields

    Hi everyone, First, sorry if the question is stupid, I do not have any background in Physics. Just very curious. Potential energy due to gravity is: m * g * h Joules Now, suppose I lift a weight on Moon at a given height. I will have: 1.6 * m * h Joules I maintain it at that height and go to...
  36. Antonius

    Why it's (1/2)? [Electric Potential Energy]

    My question is, why it's 1/2 [qiVi]? Shouldn't it just be qiVi? Thank you ...
  37. M

    Electrostatic Potential Energy

    Two charges, q1=-9.4 μC and q2=1.2 nC with masses m1=13.4 gram and m2=2.7 gram were located 8.5 cm from each other. Charge q1 is held in place. We wish to push the 2nd charge q2 as far from the 1st charge as possible. With what initial velocity should charge q2 be pushed to send it all the...
  38. S

    Potential energy of a non-uniform density sphere

    Homework Statement Perform potential energy W of a non-uniform density sphere by density d=d(r) and o(r)=dW/dm. Homework Equations The answer is W=1/2.integral(from 0 to R)(4x3.14xd(r)xo(r)xr^2xdr). The Attempt at a Solution I have solved this by this way: o(r)=-GM(r)/r...
  39. K

    Why is the same equation used for both particles in the initial state?

    I'm trying to solve an exercise that asks what is the final speed of two positive particles after they are very distants each other. Then I've used the conservation of energy to solve it. The initial energy of the system is the potential energy = Q².k/d The final energy is the 2 knetic energy of...
  40. B

    Gravitational potential energy

    Homework Statement Why is the gravitational potential energy of a ball a distance r from the center of the Earth negative? Homework Equations U_\text{grav}(r) = - GMm/r [/B] (To me, this makes sense because gravity is an attractive force and bodies will want to minimize the distance between...
  41. Titan97

    Different cases of work done done by 3 conservative forces

    Homework Statement Homework Equations W=-ΔU for conservative force. The Attempt at a Solution Let all three forces be conservative. Since particle comes back to where it was, ΔU=0. Hence ΔUAB+ΔUBC+ΔUCA=0 Hence WCA=-WAB-WBC For case A, if both WAB, WBC>0, then WCA<0. Else its greater than...
  42. G

    Finding Min. Potential Energy: Variation Calculus Method

    I was solving for a shape on Earth which has minimum potential energy. i used method of variation calculus. I assumed a function f(x) and rotated it around Y axis. sorry for uploading the problem in word.
  43. DavideGenoa

    Understanding the Potential Energy of a Dipole in an Electric Field

    Hi, friends! I read that the torque exerced by a uniform electric field ##\mathbf{E}## on a dipole with moment ##\mathbf{p}## is ##\boldsymbol{\tau}=\mathbf{p}\times\mathbf{E}##. Then the book, Gettys' Physics 2, explain that the work made to rotate the dipole around a fixed point is...
  44. SquidgyGuff

    Potential Energy of a 2D Crystal Lattice

    Homework Statement Use a computer to calculate numerically the potential energy, per ion, for an ifinite 2D square, ionic crystal with separation a; that is, a plane of equally spaced charges of magnitude e and alternating sign. Homework EquationsThe Attempt at a Solution The closest I can...
  45. K

    Hydrostatic pressure and Gravitational Potential Energy

    So say I had a glass of water on a table ,with the glass filled to the top. The bottom of the glass, the water would have a higher pressure than the top of the glass. This is the concept of hydrostatic pressure etc. But how does GPE fit into all of this? Does the water at the top of the glass...
  46. Meera.sheeda

    To calculate potential energy of paraelectric crystal

    I understand that to calculate the potential energy of a paramagnet you use U=2μBBS but is there an equation to calculate the energy of a para-electric crystal. Also, if this equation required S, would that always be N/2 (is a para-electric crystal always completely polarised?)
  47. D

    How to differentiate this potential energy function?

    Homework Statement Given the potential energy function V(x,y)=V(ax-by) where a,b is an arbitrary constants differentiate with respect to x and y. Homework Equations Multivariavle differentiation The Attempt at a Solution The answer yields (d/dt)p1=-aV'(ax-by) (d/dt)p2=+bV'(ax-by). The right...
  48. D

    Does Space Expansion Add Potential Energy?

    Space is expanding, which separates objects from each other in space. Won't this add potential energy? Doesn't this violate the law of conservation of energy? But if it does not, how can space be added without adding potential energy?
  49. rogerk8

    What is the equation for gravitational and electrical potential energy?

    Hi! I just wish you to help me derive two types of potential energy. A) Gravitational Potential Energy B) Electrical Potential Energy A useful equation is W=\int Fdr Which I consider is the work that has to be done to the particle to move it a certain distance from the attractive centre of...
  50. J

    Potential Energy of Nearly Hovering Rocket

    I have a question concerning gravitation potential energy and rockets under an unusual situation. Let a rocket be in a gravity well of a massive object such as a planet. For simplicity, assume that the rocket is in a vacuum. (we can add air effects later). The rocket engine thrust is dynamically...
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