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. S

    Why do conservative forces try to reduce potential energy?

    I do not understand the reason why a conservative force always "tries" to reduce the potential energy of a system at its minimum (forgive me if I said it in a wrong way). The explanation I gave me is: since for a conservative force, from the definition of potential energy, W=-\Delta U that...
  2. S

    Simple gravitational potential energy

    Homework Statement A 400-N child is in a swing that is attached to a pair of ropes 2.00 m long. Find the gravitational potential energy of the child-Earth system relative to the child’s lowest position when (b) the ropes make a 30.0° angle with the vertical Homework Equations Ug=mgy The...
  3. R

    How Many 100W Bulbs Can Be Powered by Converting Water's Potential Energy?

    Could anyone help me with this sum - To generate electricity, 180000 kg water is dropped from a height of 50 m (let g = 10 m/s^2). If half the gravitational potential energy is converted to electric energy, how many 100 W bulbs can be lit ? Formula - Ep = mgh I calculated the potential energy...
  4. Anthony Santelices

    Finding energy in a 4 object charge system

    Homework Statement An object with charge +2.0×10−5 C is moved from position C to position D in the figure (Figure 1) . q1 = q3 = +10.0×10−5 C and q2 = −20.0×10−5 C. All four charged objects are the system. Here's a picture to the problem Homework Equations $$ F = \frac {kq_1 q_2}{r^2} $$ $$...
  5. H

    Orbital stability and fictitious potential energy with a change of convention

    The condition for a stable orbit is given by (3.42), where ##V'## is the fictitious potential energy (potential energy of the corresponding fictitious one-dimensional problem) and ##r_0## is the radius of the circular orbit. The result ##n>-3## is obtained by using the convention that positive...
  6. i_hate_math

    A really confusing question on potential energy,

    Homework Statement A 975 g block is released from rest at height h0 above a vertical spring with spring constant k = 410 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 24.2 cm. How much work is done (a) by the block on the spring and...
  7. A

    Max speed and tension of bungee jump?

    Just signed up, hi everyone! 1. Homework Statement A man weighs 150 lb, and attaches a bungee cord having a stiffness of k = 500 lb/ft, to his feet. If he jumps from rest off the side of a bridge, determine the required unstretched length of the cord so that he can just touch the surface of...
  8. J

    Conservation of energy - elastic potential energy and k.e.

    1. Homework Statement For part (iii) , I used the principle of conservation of energy, K.E of the 2 kg particle after collision + E.P.E = K.E of the 2 kg particle at the furthest distance away from A + E.PE, But the solution for this question did not include the E.P.E of the string...
  9. P

    Electric Potential Homework: Proton vs Alpha Particle

    Homework Statement A proton is in a place where the electric potential is V, and as a result it has a potential energy E. If you replace the proton with an alpha particle (twice the charge of the proton and four times the mass) in the same place, it will experience an electric potential...
  10. iamazombie911

    Gravitational Potential Energy

    Homework Statement Two neutron stars are separated by a distance of 4.80 E 10 m. They each have a mass of 3.60 E 30 kg and a radius of 1.30 E 5 m. If they are initially at rest... How fast is each star moving when their separation has decreased to half its initial value? How fast is each star...
  11. U

    Gravitational Potential Energy in orbit

    This pertains to a homework question but I get the concept of PE or U = -GmM/a for an elliptical orbit. I also understand the derivation of the total energy of an object in an elliptical orbit as E = -GmM/2a. However, I have a homework question that asks for the ratio of an object's kinetic...
  12. R

    Potential energy and conservation of energy

    When a particle (or any objects) accelerates when acted upon by fundamental forces, what is happening to the amount of energy in that particle? A large example would be an asteroid in space caught by Earth's gravity and accelerates toward Earth as a result. The fundamental forces here can be...
  13. R

    Particle potential energy - acceleration?

    Homework Statement Homework Equations ΔU = Uf - Ui The Attempt at a Solution Would I have to make the left side of the equation equal to m*a*x? Is the x on the left side equal to -100 m?
  14. M

    Finding Force from Potential Energy Function

    Homework Statement The potential energy function for a system of particles is given by U(x) = −4x^3 + 3x^2 + 8x, where x is the position of one particle in the system. (a) Determine the force Fx on the particle as a function of x. Homework Equations du/dx[U(x)] = Fx The Attempt at a Solution...
  15. hackhard

    B How to check if force is conservative?

    given a force F = f(x) i^ + g(y) j^ + h(z) k^ (x,y,z,are coordinates of body) how can i prove or disprove that the force is conservative ?
  16. M

    Why can we add/subtract constants to potential function?

    I have 3 questions regarding the topic: 1-Why is that we are allowed to add or subtract a constant to a potential energy function V(x) to set it to zero where it is constant? 2-What does adding/subtracting a constant physically correspond to if anything at all? 3- Do we do it simply for...
  17. blee22

    Electrostatic, Electric Field,Electrostatic potential energy

    Homework Statement In the figure below, a right triangle, determine the magnitudes of the a. Net e-field at p (assume a proton is placed at p) b. Net electrostatic force at P c. Net electrostatic potential at P let q = 1.70 x 10^-8, R = 78cm and P is halfway between Q1 and Q3 Red dot is P A^2...
  18. Danny Boy

    I Why is reflection coefficient defined this way

    In Griffith's "Introduction to Quantum Mechanics, second edition" he states: For the delta-function potential, when considering the scattered states (with E > 0), we have the general solutions for the time-independent Schrodinger equation: $$\psi(x) = Ae^{ikx} + Be^{-ikx}~~~~\text{for }x<0$$ and...
  19. F

    Electric Potential Energy Problem. Intuition needed

    There's this problem that was given in my physics class.. "Three identical, negatively charged particles are situated at rest in a straight line, as shown below. All three are released simultaneously, and are free to move. Find the maximum velocities attained by particles A, B, and C. They have...
  20. J

    Understanding Electric Potential Energy Calculations: Addressing Sign Confusion

    I am confused about the signs in calculating the potential energy change from the electrostatic force. Suppose there was a point charge +q1 and I moved a second point charge +q2 from a distance of b from q1 to a distance of c from q1. c is smaller than b. So the potential energy change is - ∫...
  21. S

    Potential Energy in a molecule

    Homework Statement Potential energy in a molecule[/B] (b) The figure below shows all of the quantized energies (bound states) for one of these molecules. The energy for each state is given on the graph, in electron-volts (1 eV = 1.6 ✕ 10-19 J). What is the minimum amount of energy required to...
  22. K

    How is potential energy is derived from work here?

    Since capacitors can store electrical energy in the form of a electrostatic field between its plates, one can derive that potential energy by looking at the work it takes to "push" the charges around to create the voltage. Therefore Work = integral from 0 to Q of V(q) dq = integral from 0 to Q...
  23. P

    Integrals and potential energy

    Does the equation http://m.imgur.com/2KAADas Accurately describe the potential energy gained by an object falling by 100,000 units? I asked my physics teacher and he said he didn't know enough about integrals to answer it. I asked my math teacher and she just asked "Are you trying to find the...
  24. N

    What is the gravitational potential energy of the box relative to the floor?

    Homework Statement An 18.5kg box is slid up a 5.6m long ramp that makes an angle of 33 degrees with the floor. What is the gravitational potential energy of the box relative to the floor? Homework Equations Ek = 1/2mv2 The Attempt at a Solution My teacher gave me an answer of 550J, but I'm...
  25. neilson18

    What is the potential energy of this group of charges?

    Homework Statement Three electrons form an equilateral triangle 0.800 nm on each side. A proton is at the center of the triangle. Homework Equations U = k[(q_1*q_2)/r] The Attempt at a Solution I tried to use the following equation: k*[(3e^2)/(0.8*10^-9) - (3e^2)/(0.4*10^-9)] I plugged in...
  26. K

    Circular Motion and Energy Calculations

    Homework Statement A) An object moving along the x-axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m? B) A 50-kg child riding a Ferris wheel (radius of wheel R = 10 m) travels in a vertical...
  27. T

    Does internal potential energy affects temperature?

    Hello If I take an extreme case, where a body has only an internal potential energy with zero internal kinetic energy, does this body have a temperature? Another question related to it: if two objects A and B having different temperature: A: having only internal potential energy and B having...
  28. A

    Find the interaction potential energy

    Homework Statement 2 concentric shells are placed with inner shell having charge q and outer charge -q, with radii a and b respectively. Homework Equations don't know The Attempt at a Solution the question asked me to find self energy of the 2 shells and interaction potential energy,i found...
  29. FruitNinja

    Potential Energy function for this system

    Homework Statement Find the potential energy function for the three mass, earth, and pulley system as shown. The potential energy will be as a function of the vertical position downward as shown in the diagram. Also, find the equilibrium position of this system. The two outside masses are...
  30. J

    Potential energy in solids,liquids and gases

    Homework Statement Is the potential energy between atoms in solids, liquids and gases, elastic or electrical? I've read in some sources that for solids, p.e. > k.e. because it has the strongest intermolecular forces among the three states of matter. So I'm assuming it is elastic potential...
  31. AntoineCompagnie

    Potential energy variation = work of -(conservative forces)

    Homework Statement Why is potential energy variation between two points equals to the work of the opposite of conservative forces between these two points? Homework Equations If we call these forces $$\vec F_ext^C$$ \begin{equation} \Delta E_p=E_p(B)-E_p(A)=-\sum W_{A\rightarrow B}(\vec...
  32. Rmehtany

    Gravitational Self Potential Energy

    Note: I know this question has been asked before, but I wasn't allowed to ask my question on that thread 1. Homework Statement The gravitational self potential energy of a solid ball of mass density ρ and radius R is E. What is the gravitational self potential energy of a ball of mass density...
  33. Liz Hoyt

    Can Calculating a Horse's Leg Spring Constant Predict Jump Heights?

    Science fair help needed! Horses use the energy stored in their tendons to help propel them over a jump- much like a spring. By determining the spring constant for the leg, the student wants to then calculate the potential energy stored in that leg. Would this work? From her research...
  34. Q

    Tannor Quantum Mechanics derivative of variance of position

    0http://stackoverflow.com/questions/34833391/tannor-quantum-mechanics-derivative-of-variance-of-position# In the Tannor textbook Introduction to Quantum Mechanics, there is a second derivative of chi on p37. It looks like this: χ"(t) = d/dt ( (1/m) * (<qp + pq> - 2<p><q> ) (Equation...
  35. gracy

    Potential energy in concentric shells

    Homework Statement There are two concentric shells of radii a and b respectively ,inner shell has charge Q and outer shell is neutral what will be potential energy of outer shell due to inner shell Homework Equations ##V##=##\frac{KQ}{R}## PE=Charge .V The Attempt at a Solution I know what...
  36. V

    Non-Zero Potential Energy in SHM: Is Spring Stretched in Mean Position?

    in shm,if minimum potential energy of an shm is not zero,does that mean that in mean position ,spring is stretched. eg mass attached to a vertical spring.
  37. Buzz Bloom

    Question regarding GR wrt potential energy

    The motivation for this post comes from a discussion on another thread https://www.physicsforums.com/threads/questions-regarding-mass-volume-x-density.851172/ It seems worthwhile to me to try a simplification in this post to hopefully avoid the complications raised in the cited thread. Assume...
  38. Gian Lukmana

    Gravitational potential energy of a cylinder to a particle

    Hi everyone I'm kinda new here, your support will really be appreciated ! :D 1. Homework Statement Let's say the cylinder has radius R, and height T. Homework Equations U = ∫GmdM/x The Attempt at a Solution My attempt is shown in the picture, I took a tiny element of the cylinder with...
  39. Physicscookie

    What is the change in potential energy of two blocks in a physics problem?

    I present the following problem to my AP and have received a variety of answers, being a new physics teacher I am not sure that my answer is correct. I would love to see the solution and justification. Thanks One attempt based on the inference that one block is gaining U (A) and the...
  40. T

    Can potential energy be greater than total energy?

    I'm working on a homework problem which states: "Some object, starting from far down the negative x-axis and moving in the positive x direction, experiences a force, the potential energy U of which is modeled by the function U = 2e^(-x^2), where x is in meters and U is in Joules. The total...
  41. lucphysics

    Kinetic and potential energy (satellite low orbit)

    Hello, I have this problem statement : "Due to air drag, the radius of a satellite’s circular orbit decreases from r to r - △r, where the positive quantity △r is much less than r. The mass of the satellite is m. Show that the increase in orbital speed is △v = +(△r/2)[(GM/r^3)^1/2]; that the...
  42. B

    Amplitude vs Location when KE=PE?

    Homework Statement A 0.50-kg object is attached to an ideal massless spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration? (b) At...
  43. S

    LaTeX Potential Energy Stored in latex rubber

    I am looking for a simple number which is the potential energy that can be stored in rubber. ( Joules per gram or something similar ) I know there are a number of forms of rubber and I keep reading numerous articles on how to calculate the energy content of a rubber band. Can anyone just tell...
  44. B

    Solving for potential energy after time t.

    Homework Statement A stone of mass 0.2kg is dropped from the top of a building 80m high. After t seconds it has fallen x meters and has a velocity of v. What is the potential energy of the stone t seconds later Homework Equations The answer is 2(80 - x) = 160 - 10t^2 Using suvat: s = ut +...
  45. E

    Potential Energy of an Electron in a Battery

    Homework Statement An electron moves from the positive to the negative terminal of a battery (9V). How much potential energy did it gain or lose? Homework EquationsThe Attempt at a Solution Solving for the amount is basic. That's just qV = 14.4 * 10^-19 J I'm not sure whether it will gain the...
  46. R

    At what angle does the normal force go to zero?

    Homework Statement An ice cube is placed on top of an overturned spherical bowl of radius r, as indicated in the figure. If the ice cube slides downward from rest at the top of the bowl, at what angle θdoes it separate from the bowl? In other words, at what angle does the normal force between...
  47. H

    Why is the work in this question = to the potential energy?

    Homework Statement A mass of 235kg is lifted by a winch and an electric motor. The motor does 1800J of work on the mass to raise it to an upper floor. The electric energy needed to complete this task is 160,000J Homework Equations I know the solution but I don't why it is the solution...
  48. N

    Is potential energy only acquired in a *Conservative Field*?

    Is potential energy gained or lost only in a conservative field, or when work is done against or by conservative forces?
  49. B

    Total electric potential energy

    Homework Statement My textbook states that for point charges ##q_1, q_2, ... ,## where distance between ##q_i## and ##q_j## is ##r_{ij},## the total potential energy U is the sum ## U = \dfrac{1}{4\pi\epsilon_0} \sum_{i<j} \dfrac{q_iq_j}{r_{ij}} ## and specifically mentions not to count them...
  50. 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...
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