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. F

    Something I don't understand. [Kinetic & potential energy]

    I really don't understand this example: A feather or spring or whatever it's called got the stiffness 29.5 N/m. It is lying inside a horizontal tube (feather cannon). The feather /spring is connected in the very end of the tube. The feather / pring is as "long" as the tube if it's not being...
  2. S

    Question about gravitational potential energy

    I am wondering how this all works and am hoping to get some guidance. If a 1000 lb weight freefalls vertically from 660 ft the energy is 894,289 joules. If the fall is down a 30 degree slope that is 1300 ft long, then it takes 17 seconds and the potential energy can be said to be 53 KW. If...
  3. Z

    About potential energy and matter-antimatter creation

    Hi, I'm not sure if this is the correct section to post this. As far as I know, it is widely accepted that antimatter has "normal" gravity, and that for creating a matter-antimatter pair, you need to input the rest mass of the particle in energy (Einstein's equation). But as potential...
  4. G

    Calculating electrical potential energy

    Homework Statement Three equal point charges, each with charge 1.60μC , are placed at the vertices of an equilateral triangle whose sides are of length 0.600m . What is the electric potential energy U of the system? (Take as zero the potential energy of the three charges when they are...
  5. PsychonautQQ

    Potential energy per unit length in a string (sin wave)

    Homework Statement Given that the stretched length of a string is Δx(1+1/2(dy/dx)^2) show that the potential energy per unit length is equal to 1/2F(dy(x,t)/dx)^2 Homework Equations potential energy = kx^2 cos(kx-wt) idk really... The Attempt at a Solution The fact that the...
  6. SamRoss

    Why does the Lagrangian have negative potential energy?

    I am watching Susskind's derivation of Newton's F=ma from the Euler-Lagrange equations (53 minutes in) here for which he uses the Lagrangian of kinetic energy minus potential energy. I have seen this done elsewhere as well. As far as I can tell, and please correct me if I'm wrong, the only...
  7. snoopies622

    Potential energy in the Dirac equation

    Why does the Dirac equation not have a potential energy term? The Schrödinger equation does, and the Dirac equation is supposed to be the special relativity version of the Schrödinger equation, no?
  8. E

    Why do objects always move to a state of lower potential energy?

    Is there no answer given by QM till now?... Also, on a related note, when objects move through space we consider it as a point mass for the purpose of interactions. Why this simplification? Is it due to the distribution of potential energy throughout the object when a force(contact/non-contact)...
  9. O

    Why Does Hooke's Law Involve Potential Energy? Explanation Needed!

    Hello, I am self studying physics and am a bit confused with Hooke's law. Using the conservation of energy equation: (PE+KE)_i = (PE+KE)_f I don't see why the springs potential energy (½ kx^2) goes in the final part. Could someone please explain? EDIT: Also, (I'm a new user) can you...
  10. Jalo

    Finite square well potential energy

    Homework Statement Hello. Imagine a particle bound in a square well potential of potential energy V0 if |x| > a 0 if |x| < a The wave function of the particle is: (ignoring the time dependency) -A*exp(kx) if x<-a B*sin(3*pi*x/4a) if |x|<a A*exp(-kx) if x>a where k =...
  11. A

    Derivation of Potential Energy for Multi-Particle Systems

    I am reading 'Classical Dynamics: A Contemporary Approach' by J. Jose, and I am confused about a step in the author's development of potential energy for a system of many particles. He begins by writing down a term equivalent to the total change in kinetic energy of the system: \sum_i...
  12. S

    Gravitational Potential Energy question

    Hello! I'm having some problems with a question that my professor has given me. Below is the question. I have already figured out the planet's orbital and angular-orbital velocities, but included that part due to the fact that some information was included. PICA-9 and PIC-10 are planets...
  13. andyrk

    Relation between Change in Potential Energy and Work Done

    Why is dU=-\vec{F}.d\vec{r} Integrating with putting the limits on we get: ΔU=-W Why is this? Here \vec{F} is a conservative force/Force field.
  14. O

    Real gravitational potential energy to kinetic energy

    This isn't a homework problem, but something that has being buzzing in my head. I've been thinking about it cause at huge distances from Earth g changes and also in what happens for really dense objected and small things could change too. The real equation for gravity no matter which body...
  15. L

    Explaining which one has more potential energy.

    Explain which has more potential energy in each pair: water/glucose I think the answer is glucose since it's a bigger molecule and thus can store more energy than water. Am I right in thinking this?
  16. G

    Potential energy of water from electrolysis

    Could I please have help with something: If I generated hydrogen via electrolysis from water, sent it high up a long tube then converted it back to water (via a cell or motor to reclaim energy) then, taking into account inefficiencies (or assume no energy loss), where does the energy come from...
  17. Saitama

    Electrostatic potential energy - dielectric between concentric spheres

    Homework Statement A conducting sphere of radius ##a## carries an initial charge ##q_o##. It is surrounded by another concentric sphere of radius ##b##. The space between the two spheres is filled with a dielectric of permittivity ##\epsilon## and conductivity ##\sigma##. Find the electrostatic...
  18. M

    What is the Velocity of the Last Piece of a Chain Falling on a Quarter Circle?

    Homework Statement Consider a circle with radius r diagrammed as the unit circle, but take only the second quadrant. On this quarter of the circle lies a chain with mass per unit length \rho (the length of the chain is \pi r/2). If \theta is the angle made with the vertical axis at any point on...
  19. P

    Potential Energy and Work done to lift object distance h

    Potential Energy and Work done to lift object distance "h" The amount of energy needed to power a 0.10 kW bulb for 12 minutes would be sufficient to lift a 1 kg object how high? Power = work/time PE = mgh First I converted kw to watts which is 100 watts. Then converted minutes to seconds...
  20. W

    How Are Potential Energy and Work Related in Physics?

    1. When taking an object and the Earth as a system, its change in potential energy is given by a. m*g*change in height b. (-m)g*change in height c. either a or b d. there is not potential energy due to gravity 3. I think it is c because the sign of energy does not matter?
  21. P

    Vector B in Magnetic Potential Energy

    U = -m x B Is B the total magnetic field of the whole system? If there is two objects X,Z and they all have a magnetic field. But different strengths, I want to calculate the U for Z, B should be the total magnetic field of BOTH fields or only X's field strength? Since X is the...
  22. J

    Spring Potential Energy problem: Where did I go wrong?

    A spring with k= 53 N/m hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with ruler marks? According to the book, the final reading will be 61 cm...
  23. S

    Gravitational potential energy from ∞ to r

    Hello, I'm a high school student studying for the AP Physics test tomorrow. I've been having trouble proving the negative value of gravitational potential energy through working out the work integral. I will greatly appreciate any help and clarification. Homework Statement Find the change...
  24. D

    Strain potential energy and efficiency question

    Homework Statement A sphere of mass 0.1 kg is pushed against a rubber band catapult with a force of 80N, and released upwards. Calculate: A) The strain potential energy when stretched by 0.3m B) The work done by the applied force C) The speed of the sphere when released D) The...
  25. kira506

    Why does the kinetic theory of gases neglect potential energy ?

    My textbook says that the forces of intermolecular attraction between gas molecules are very weak due to large intermolecular spaces between them , that's why they're negligible , Does this have a relation with "force is inversely proportional to the square of distance " (again , I don't know...
  26. M

    Gravitational Potential Energy of a rocket

    Homework Statement A rocket is launched straight up from the Earth's surface at a speed of 1.80×104m/s . What is its speed when it is very far away from the earth? Answer in m/s Homework Equations K1+U1=K2+U2 The Attempt at a Solution .5mV1^2-(G*m*Me)/r= .5mV2^2-(G*m*Me)/r *** THe mass of...
  27. B

    Spring Constant & Potential Energy

    Homework Statement Problem - Find the following: a. Potential energy in a fully compressed plastic spring. b. Spring constant This was a lab and we're supposed to do it at home, here are the variables I have measured: spring height when not compressed: 0.115 metres. spring height when...
  28. I

    Relationship between Potential Energy and Force

    Hello Everyone, I am having a very difficult time intuitively understanding the formula -dU/dx = Force(x). I don't want help deriving it, I'm simply looking for an intuitive understanding about why this might be true. An example with gravity would really help. My thoughts so far: I find...
  29. P

    Water and copper heat capacity difference due to potential energy?

    I was looking at this page and it explains the heat capacity difference between copper and water in terms of a difference in potential energy change as the molecules are heated. What does that mean? I know water has polar bonding so is it due to the water molecules having much stronger...
  30. 9

    How Does Gravitational Potential Energy Convert into Kinetic Energy?

    Hi everybody, I'm reviewing for the MCAT (it's been a while), and I'm having a lot of trouble understanding potential energy. In my review book (and a whole bunch of other googled sources), it defines energy as the capability to do work. It also says work is something along the lines of, the...
  31. X

    How come potential energy is negative when charges attract

    and positive when they repel? It doesn't make any sense to me at all. To what are they referring to? The way I see it, if you're got... +...- The closer they are, the less electrical potential energy they have. So it should still be positive. And if you've got two like charges C...C The...
  32. K

    Work and Energy (Kinetic Energy/Grav. Potential Energy)

    NOTE: I know this seems like quite a bit, but it's really not! Most of the questions involve simple 1-line equations, so please don't be discouraged by the amount of text - any assistance is greatly appreciated :) Homework Statement A 6kg steel ball moving at 4m/s hits a 6kg putty ball...
  33. G

    Expectation value of potential energy of Ideal gas

    Homework Statement Say you have a large column of gas with insulating walls standing on the Earth's surface, which is L high and at room temperature (25degC) at the interface of the surface and column. Assuming the potential energy on the gas is only duel to gravity, U = mgx where x is the...
  34. T

    IPA Potential Energy Approximation

    Homework Statement The IPA potential-energy function ##U(r)## is the potential energy "felt" by an atomic electron in the average field of the other ##Z-1## electrons plus the nucleus. If one knew the average charge distribution ##p(r)## of the ##Z-1## electrons, it would be a fairly simple...
  35. S

    Potential Energy to bring in sphere from infinity

    Homework Statement Given a uniform sphere of mass M and radius R. Use integral calculus and start with a mass dm in the sphere. Calculate the work done to bring in the remainder of the mass from infinity. By this technique show that the self-potential energy of the mass is: P =...
  36. U

    Plucked string, potential energy

    Hello, I don't understand the second question, i don't know what I have to do: Homework Statement A string of length L, which is clamped at both ends and has a tension T, is pulled aside a distance h at its center and released. (a) What is the energy of the subsequent oscillations? (b)...
  37. R

    Force and Potential Energy Graphs: Mastering Physics HW 11.39

    Homework Statement The figure below shows the force exerted on a particle that moves along the x-axis. Draw a graph of the particle's potential energy as a function of position from x=0 to x=1.1 . Let U be zero at x=0.Homework Equations F=-dU/dxThe Attempt at a Solution I decided to divide the...
  38. R

    What is the change in the proton's electric potential energy?

    Homework Statement A proton moves in a constant electric field E from point A to point B. the magnitude of the electric field is 6.4x10^4 N/C. The direction of electric field is opposite to the motion of the proton. If the distance from point A to point B is 0.50m, what is the change in the...
  39. C

    How Does Electric Potential Affect Proton Movement?

    Homework Statement Suppose that a metal plate is held at an electric potential of 1.8 Volts. A proton is placed on the plate where it is repelled by the plate. What is the electric potential energy of the proton measured in Joules? __ x 10-19 Joules After the proton has moved away from the...
  40. N

    Kinetic and Potential Energy on a roller coaster

    Homework Statement A roller coaster starts at the top of hill that is 10 m high. If it is to barely make it to the top of a second hill that is 20 m high, how fast must the initial speed of the roller coaster be? Assume that the roller coaster is frictionless. Homework Equations KE =...
  41. C

    Schrodinger equation, potential energy function

    A particle of mass m is in the state \Psi (x,t) = A e^{-a[(mx^2 / \hbar ) + it]}Find A For what potential energy function V(x) does \Psi satisfy the Schrodinger equation? Do I just re-arrange for A? (Sorry if I seem really dumb). I'm not really getting this.
  42. I

    Potential Energy of water in a wedge

    Homework Statement A symmetric wedge of depth h and width A is filled to the brim with water of mass m, where acceleraton due to gravity is g. What is the potential energy of the water with respect to the base of the wedge? Homework Equations E = mgh The Attempt at a Solution E =...
  43. A

    Average Potential Energy/ Oscillator

    Hi, i regard a single harmonic oszillator: $$H_{1}=\frac{p^{2}}{2m} + \frac{m \omega^{2}}{2} x^{2}$$ I know the partition function of the oszillator is: $$Z=\frac{kT}{\hbar \omega}$$ so the probability function is: $$F_{1}(x,p)=\frac{1}{Z}\exp{\frac{-H_{1}(x,p)}{kT}}$$ Now I want to...
  44. L

    QM: Potential Energy & Particle Free Fall

    In classical mechanics is defined potential and kinetical energy for particular particle. For example, in case of free fall potential energy of the particle is ##mgh## and kinetic energy is ##\frac{m\upsilon^2}{2}##. In QM there isn't potential of the particle, but potential of part of the...
  45. B

    Electric Potential and Potential Energy Due to Charged Particles

    Two charged particles of equal magnitude are located along the y-axis equal distances above and below the x-axis. Plot a graph of the electric potential at points along the x-axis over the interval -3a<x<3a. You should plot the potential in units of (KeQ)/a Let the charge of the particle...
  46. A

    Canonical Ensemble and potential energy

    Hi guys :cry:, I regard an ideal diatomic gas which is in a Volume x,z and got a angular \phi: 0 \le x \le L, ~~~~~~~~~~~~ 0 \le z \le \infty, ~~~~~~~~~~~~0 \le \phi \le 2 \pi The hamiltonian for the single particle is: ~~~~~~H= \frac{p^{2}_{z} + p^{2}_{x} }{2M} +...
  47. J

    Potential energy and magnetic torque

    i'm having a hard time understanding why potential energy is 0 when u(mu) is perpendicular to B(mag field). Isn't the torque at max when the angle between u and B is 90? and there for has potential to do work all the way until the angle is 0. The way my mind sees it is, since there is a torque...
  48. E

    Confusion in electric potential energy

    This is an extract from my book ... " We define the potential V at any point in an electric field as the potential energy per unit charge associate with a test charge q0 at that point: V=U/q0." I don't know why did the book bring the test charge q0 now in the frame. Shouldn't the potential be...
  49. N

    Potential energy of pendulum in terms of displacement.

    Hi guys, I'm having troubles finding how to write the potential energy of a 1D pendulum down. In terms of displacement however. This should be easy and it is, but my professor had this nice "clean" solution whereas mine is really dreadfull, any help? :) edit: Ok nvm guys. I was thinking I went...
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