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. A

    USAPhO F=ma 2010 exam # 17 (Gravitational potential energy)

    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? Homework Equations U = -Gm2 / r The Attempt at a Solution The potential energy is the negative of the work done by gravity in...
  2. M

    Deriving potential energy of an electron inside a nucleus

    Homework Statement Derive equation below. It is the potential energy of an electron inside a nucleus assumed to be a uniformly charged sphere of R. Homework Equations V'(r) =( -Ze2/4∏ε0R)(3/2 - (1/2)(r/R)^2) The Attempt at a Solution So I understand that I need to find the ∫ from infinity...
  3. Q

    Annihilation and potential energy?

    Sorry, brand new here and this may be in the wrong place or very obvious. When matter and antimatter annihilate is the energy released the sum of all their potential energy? does E=MC2 only work because of the specifics of our universe, and if the universe were to contain more matter (and...
  4. H

    Electric Potential Vs. Electric Potential Energy Concepts

    Homework Statement A charge moves towards a positively charged sphere, as it does, it's electric potential (V) increases. Give an instance on when the Electric Potential Energy (Ee) will decrease. Homework Equations V= Ee/q The Attempt at a Solution Alright, This is basically a theory...
  5. V

    Potential energy and mass/energy equivalence

    How does potential energy fit into mass-energy equivalence in SR? As with all forms of energy, a potential energy of ##E## added to static system ought to increase the system's mass by ##E/c^2##. This is often illustrated by saying that a compressed spring has slightly more mass than an...
  6. Ascendant78

    Potential energy vs position graph w/ total mech. energy?

    Ok, I've been trying to soak up the MIT physics material, but I am stuck on something and it is driving me crazy. They have several questions about graphs of potential energy vs. position, which also includes the total mechanical energy. I just can't fully wrap my mind around these graphs and...
  7. J

    Resonance Structures Chemistry: What is Potential Energy?

    I was reading this article from Wikipedia on resonance structures: http://en.wikipedia.org/wiki/Resonance_(chemistry ) What I do not understand is, what is meant by potential energy in terms of chemistry? In physics, potential energy is defined by location in a force field. What is it that...
  8. D

    Sign of potential energy of SHO

    Suppose the particle is at distance x from mean position and moving away . The standard formula for calculating potential U is U=-w here wis the work w=kxdx when the particle is moving away .On integration U=1/2Kx^2 . When the particle is moving towards mean position w=-kxdx on integration...
  9. S

    Thermodynamics - (polymer) caluclate the average potential energy

    Homework Statement A polymer of ##10^{20}## molecules each 2nm long is hanged from the ceiling. The other end of the polymer is attached to a ##m=4\cdot 10^{-10} g## load. Calculate the average potential energy! Temperature is 300 K. Homework Equations ##<E>=<E_p>=\frac{\mathrm{d} (\beta...
  10. omarMihilmy

    Potential Energy: Differentiating to Find Force

    To find the force we will differentiate the function with respect to x (dx) My problem is with the solution If we differentiate: dU/dx = 9x^2 - 7 From where does the negative come from also the j component?
  11. O

    Gravitational Potential Energy and Gravitational Field and Gravitation

    I don't get the difference between these equations: U = \dfrac{-Gm_1m_2}{r} F_g = \dfrac{-Gm_1m_2}{r^2} g = \dfrac{F_g}{m} = \dfrac{GM}{r^2} Also, why are the first two negative? Here's my thinking: The first equation is like U=mgh. Except it's when two masses are very far apart. It...
  12. N

    Potential energy: where is the error in my logic?

    1) For gravitational potential energy: ##F(r)=-\frac{\gamma M m}{r^2}##. 2) For potential energy of a conservative force-field: ##-\nabla E_p = F##. So the gradient of the potential energy is always equal to the force in that direction, just with the opposite sign. So when you move in the...
  13. M

    What is the Meaning of 0 V or 0 Potential Between Two Charges?

    What does it mean by 0 V or 0 potential between two charges? If there are two point charges A and B. And if there is a point between them that has 0 V then why is: Va + Vb = 0?
  14. Crazymechanic

    Water , gravitational potential energy

    Hello , I was thinking about dams and hydroelectrostations , the turbines can turn because the water before the dam is higher than after it so there is stored potential energy waiting bto be released, Now I wonder if we were to take two places one at the water surface level in the dam reservoir...
  15. R

    Gravitational potential energy of a system

    Homework Statement What is the gravitational potential energy of a system of 8 masses of 10 kg each placed at the corners of a cube of length 0.25 meter apart. Homework Equations U=-G*m1*m2/r The Attempt at a Solution I have actually taken one particle pair at a time and sum all...
  16. F

    How is - (gravitational) potential energy and free fall compatible?

    I was having a few problems with Negative gravitational potential energy, I wasn't able to put my finger on why because it worked so well with everything else I had learned. I tried to say it made sense because in space you don't free fall, but that's not actually true, though the...
  17. S

    Can this method turn potential energy into kinetic energy?

    I am wondering if this method is in use already somewhere, or if its possible to be used. For example, using the equation of gravitational potential energy a 100kg weight that freefalls 100 meters has 98,000 J of energy, which equals 24,000 watts after approx 4 seconds of freefall. Assuming I...
  18. F

    Gravitational potential energy between Earth and Moon

    Homework Statement Consider the Earth's radius to be 6.40x103km, its mass to be 6.00x1024kg, the Moon's mass to be 7.36x1022kg, and the Moon's radius to be 1.74x103km. The average value for the Earth-Moon distance is 3.84x105kg. Neglect friction and rotation. a. Sketch the potential...
  19. I

    Potential energy and kinetic energy

    So today in class we were talking about gravity and my professor said that generally KE = -.5PE And so TME = .5PE I don't understand how that works.
  20. R

    Potential energy of spring and mass system

    Homework Statement O^^^^^^O^^^^^^O |------------------------------------------→ There are 3 equal masses connected by springs with length a and spring constant k. The system can only move in the x axis. x1,x2,x3 is the position of each massWhat is the...
  21. M

    Potential energy and conservation of energy problem

    Homework Statement An outfielder throws a baseball with an initial speed of 79.0 mi/h. Just before an infielder catches the ball at the same level, its speed is 65 ft/s. How much of the ball's mechanical energy is dissipated by air drag? (The weight of a baseball is 9 oz.) Homework Equations...
  22. T

    Getting the Potential Energy from a Conservative Force

    Homework Statement The problem basically asked me to check if a given force was conservative and if it was conservative, also find the potential energy. F = k(x,2y,3z) Homework Equations (\nabla X F) = Curl of F U = Integral of F 3. attempt So the force is clearly conservative as the curl...
  23. L

    Understanding Potential Energy in QM

    Hi all, I'm having conceptual troubles understanding the significance of the potential energy term in Schrodinger's equation. More specifically, the physical meaning of the potential "wells" is not clicking with me; my textbook is not making this very clear. For clarity, consider an...
  24. S

    Gravitational potential energy confusion

    Hi, I've managed to get myself confused over the simplest thing. Intuitively I'd think that gravitational potential energy is proportional to distance as described by the near-body equation GPE=-mgh. The alternative for farther bodies (-G*M*m/R) has me confused because it is inversely...
  25. D

    What Does the Potential Energy Equation U(x) Tell Us About Motion and Forces?

    [solved] graph of potential energy Homework Statement A mass of 5 kg follows the potential energy shown by the equation: U(x) = .333(x-4)^3 - \dfrac{x^2}{4} + 5 1. Find the force on the mass at x=2 2. Describe the motion qualitatively if the mass is placed at x=4 m and released 3...
  26. P

    Potential energy of gravitation

    I was writing a script to help me calculate gravitation and various other things when i noticed i don't know how to calculate this I need to calculate the kinetic energy of an object being pulled towards a second object until they meet knowing only the weight of the objects, the distance of the...
  27. 1

    When a ball hits the ground, where in the ball is potential energy = 0

    This is a question that me and a friend have been wondering. He says that when the ball hits the ground and is at rest for a very brief moment, potential energy will be 0 in the center of the ball, while I thought that it doesn't matter as the entire ball's potential energy is at 0. Which answer...
  28. M

    Question about potential energy in capacitors

    Hello, I'm studying capacitors in my freshman physics class and I'm not quite following my book here. My book states that we can calculate the potential energy U stored within a capacitor by calculating the work done to charge it. Let q and v be the charge and the potential difference...
  29. H

    Why is potential energy negative?

    Total energy is \frac{1}{2}mv^{2}-mgh=C for a classical non-rotating object right? C can be determined based on an arbitrary initial condition that suits the problem, right? How come it's not \frac{1}{2}mv^{2}+mgh=C? This seems like a more suitable definition of "total" energy. I'm sure there's...
  30. G

    Calculating Force Components for Conservative Potential Energy Function

    Homework Statement A particle of mass m = 10 kg moves in space under the action of a conservative force. Its potential energy is given by PE = 2xyz + 3z2 + 4yx + 16 where PE is in Joules and x, y, and z are in meters. Calculate the x-, y-, and z-components of the force on the particle...
  31. B

    What Is the Distance at Which There Is No Net Force Between Two Atoms?

    Homework Statement The potential energy of two atoms separated by a distance r may be written as: U(r) = 4Uatomic * [(r0/r)12 - (r0/r)6] >Given r0 = 4.0 Ao and Uatomic = -0.012795 eV, what is the distance at which there is no net force between the atoms? Express your answer in terms of...
  32. Z

    Work and Potential Energy: To the Moon physics problem

    Homework Statement Part 1(complete and correct. I'm including this for context's sake) You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the Earth with enough speed to make it to the moon. You leave the surface of the...
  33. G

    Gravitational Potential Energy of an Ideal Gas

    I'm trying to find the avarage enerrgy of an ideal gas when it's under a gravitational potential. I know how to obtain the kinectic avarage energy but the potential energy depends upon the position of each molecule. There is a avarage height lo look for in order to determine this potential term?
  34. E

    Finding the Potential Energy Function

    Homework Statement Which of the following forces is conservative? (a) F = k(x,2y,3z), (b) F=k(y,x,0), and (c) F=k(-y,x,0). For those which are conservative, find the corresponding potential energy U, and verify by direct substitution that \vec{F} = - \nabla UHomework Equations The Attempt at...
  35. adjacent

    How can objects have negative potential energy at 0 height?

    As we all know,Potential energy =mgh.If someone digs a hole and place a ball at 0 height,the potential energy should be zero but it falls somehow.How is this possible?
  36. L

    Greater electric potential but less electric potential energy?

    Greater electric potential but less electric potential energy?? The picture in my book looks like this: 1. The electric potential at pt. B in the parallel-plate capacitor shown here is less than the electric potential at pt. A by 4.50V. The separation between pts. A and B is .120cm, and the...
  37. S

    Potential energy of a capacitor

    Homework Statement What happens to the potential energy of a capacitor with length d when said length d is doubled? Use the formula for the potential energy of a capacitor [U = 1/(2C) * Q]. After that, refer to the work done by moving the capacitor the distance d. These two approaches should...
  38. A

    Checkpoint: Conservative Forces And Potential Energy

    Homework Statement Consider two identical objects released from rest high above the surface of the Earth (neglect air resistance for this question). In Case 1 we release an object from a height above the surface of the Earth equal to 1 Earth radius, and we measure its kinetic energy just...
  39. H

    Where is the Equilibrium Position of a Bead on a Rotating Circular Wire?

    Homework Statement A particle is constrained to move without friction on a circular wire rotating with constant speed ω about a vertical diameter. Find the equilibrium position of the particle, and calculate the frequency of small oscillations around this position. Find and interpret...
  40. D

    Potential Energy using effective potential

    Homework Statement For a given angular momentum L, find the potential energy function U(r) that leads to a spiral path of the form r=r0θk. Choose the total energy E to be zero. Hint: obtain an expression for r' that is only a function of r, not θ, and then use the energy equation with...
  41. N

    Relating to potential energy of a spring and mass on inclined plane

    Homework Statement Here is an illustration to ease understanding: Angle inclined plane: θ = 20.0° spring of force constant k = 525 N/m block: m = 2.71 kg distance of block from spring: d = 0.330 m speed of block: v = 0.750 m/s By what distance is the spring compressed when the block...
  42. pratikaman

    Does Potential Energy Always Decrease with Conservative Force?

    is it true that potential energy of a particle always decreases in the direction of conservative force acting on it.
  43. C

    How to Calculate the Potential Energy of Two Protons?

    Homework Statement Consider the electric field of two protons b meters apart. The potential energy of the system is equal to: U = \frac{\epsilon_0}{2}\int {\bf E}^2dv = \int({\bf E}_1+ {\bf E}_2)^2dv = \frac{\epsilon_0}{2}\int {\bf E}_1^2dv + \frac{\epsilon_0}{2}\int {\bf E}_2^2dv +...
  44. H

    How Does the Integral of Force Relate to Potential Energy?

    In my physics class, my teacher has been referring to Potential Energy in a 1D force field as the negative integral of the force with respect to position. AKA: U(x)=-\int{F(x)dx} where U is the potential energy at x and F is the force at x. Can someone please explain this to me in...
  45. R

    Classical mechanics ~ Potential energy and periodic movement

    Hey all, suppose there's a particle with Potential Energy : U(x) = A*[ x^(-2) - x^(-1) ] , where A is a constant. I'm supposed to find the energy required to make the particle go from periodic movement to unlimited movement. First thing I did was U '(x) = 0 to find the balance points, now...
  46. L

    What is the maximum potential energy of an oscillating mass?

    1. Homework Statement A 2-kg mass attached to a spring oscillates in simple harmonic motion and has a speed of 5 m/s at the equilibrium point. What is the maximum potential energy of this oscillating mass? 2. Homework Equations I know that the potential energy is: Ep = 1/2 kx2 k = mω2
  47. V

    Why is Equal and Opposite Force Necessary for Work Against a Field?

    Hello everyone! When we do work against a field on an object, why must the force we apply on it be equal and opposite to that of the field? If the object is initially at rest, then shouldn't we be applying a force greater and opposite to that of the field to first set it into motion? We could...
  48. C

    Difference in Potential Energy between two Reservoirs

    Homework Statement 3. Water is pumped from one reservoir to another 100m away. The water level in the second reservoir is 20m above the water level of the first reservoir. What is the increase in specific potential energy of the water in J/kg? Homework Equations The relevant equation I've...
  49. M

    Partition between kinetic and potential energy?

    Hi, If I have a body which is freely vibrating with kinetic energy given by, say, Ekin=(1-1/10sin(ωt))cos2(ωt) what can be said about the potential energy? Of course the total energy should be constant but how big is it, in other words what is the potential energy? Thanks!
  50. B

    What is the Relationship Between Electrostatic Force and Potential Energy?

    hi, please can anyone analyze the following sentence in terms of the formulas of electrostatic forces or Potential energy (assuming electrostatic force is directly proportional to potential energy) statement: "When the force between two objects is attractive and decreases with distance, the...
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