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. T

    Confused by capacitors and potential energy

    HiI was reading about capacitors and potential energy. But the equation seems counter to how i thought. For potential energy you have: U = Q^2 / 2C or U = CV^2 / 2 But doesn't this suggest you lose potential energy the more capacitance you have? Since in the first equation as C increases U...
  2. Benjamin Fogiel

    A rocket burns out at an altitude h above the Earth's surface

    Homework Statement A rocket burns out at an altitude h above the Earth's surface. Its speed v0 at burnout exceeds the escape speed vesc appropriate to the burnout altitude. Show that the speed v of the rocket very far from the Earth is given by v=(v02-v2esc)1/2 Homework Equations KEf-KEi=Ui-Uf...
  3. rpthomps

    Comparing 100J and -100J of Electric Potential Energy

    Is the 100 J of electric potential energy actually greater than -100 J of electric potential energy?
  4. S

    Graphing Kinetic Energy of a Toy Car Released from a Compressed Spring

    Homework Statement A toy car is held at rest against a compressed spring, as shown in the figure. When released, the car slides across the room. Let x=0 be the initial position of the car. Assume that friction is negligible. Sketch a graph of the car's kinetic energy from the moment it is...
  5. S

    Potential energy of ball thrown upwards

    Homework Statement A 1.00 kg ball is thrown directly upward with an initial speed of 16.0 m/s. A graph of the ball's gravitational potential energy vs. height, Ug(h), for an arbitrary initial velocity is given in Part A. The zero point of gravitational potential energy is located at the height...
  6. cianfa72

    Potential Energy for "stone + field" physical system

    Consider the classical scenario a stone falling in the Earth gravitational field. Classically we attach a Potential Energy to the stone and using the law of conservation of (mechanical) energy we are able to evaluate the dynamic of the falling stone. This model assume a stone in a "external"...
  7. J

    Moving Down a Ramp: Answers & Explanations

    Homework Statement Please look at the problem attached as a screenshot. Homework Equations Assuming frictionless, Ei = Ef, which means objects that are the same will end up in the same heights (so we can group A&C, B&D, and E&F). For A&C and E&F, mgh = KE_rot + KE_trans For B&D, it is mgh...
  8. J

    Do A and C have same or different KE at the end?

    Homework Statement Please look at the attached screenshot. Homework Equations Assuming the ramp is frictionless, Ei = Ef and thus mgh = KE ( = 1/2mv^2, which isn't really necessary here) The Attempt at a Solution I'm okay with all other examples except for A and C. From the answer template...
  9. L

    Confused on potential energy losses and regain.

    Homework Statement A 3.20kg rubber ball drops from a height of 4.80m to the ground a bounces back to a height of 2.70m a) how much potential energy does the ball lose on the trip down? b) how much energy does the ball regain on the trip back up? c) what is the net loss of potential energy...
  10. shk

    Gravitational Potential Energy questions near the surface of a planet

    Homework Statement The change in gravitational potential energy of a mass m as it moves from the surface to a height h above the surface of a planet of mass M and radius R is given by: ΔPE= GMmh/R(R+h) a) show that when h is very small compared to R , this approximates to the more familiar...
  11. J

    Speed or turning point using energy

    Homework Statement Please look at the attached screenshot. This problem is really confusing for me and I can't seem to make much sense out of it. Homework Equations Ei = Ef The Attempt at a Solution As you can see, I did get (a). (The other checkmarks, I guessed — there were only two...
  12. Hawkingo

    B Calculating the P.E. of a system

    Let, we want to calculate the P.E(potential energy) of a system containing 3particles p1,p2,p3.the point of observation is P.so now we should add up the P.E at P due to p1,p2,p3 to get the net potential energy of the system,but why we take the P.E of particles due to each other into count...
  13. Arman777

    Potential energy and Conservative Force

    Homework Statement I have a force ##\vec{F} = a_x\vec{i}+2a_y\vec{j}+3a_z\vec{k}##. Find the potential Homework EquationsThe Attempt at a Solution Lets suppose And we know that ##\vec {F} = ∇U## In this case I said that ##U_x=-\int F_xdx## ##U_y=-\int F_ydy## ##U_z=-\int F_zdz## and then I...
  14. sal1234

    Electrostatic potential energy

    [Note from mentor: this was originally posted in a non-homework forum, so it does not use the homework template.] There is a general relation between the work U required to assemble a charge distribution ρ and the potential φ(r) of that distribution: U = 1/2 ∫ ρ...
  15. YMMMA

    Elliptical orbit/ determine speed & potential energy

    Homework Statement True statements about Jupiter as it moves in its elliptical orbit around the Sun include which o the following? I. It has its greatest speed when closest to the Sun. II. It has its greatest potential energy when farthest from the Sun. III. The magnitude of its...
  16. A

    Work Required to Move a Piano Onto a Truck

    Homework Statement Movers must push a piano onto a truck, the bed of which is a height 1.35 m above the ground. To do this they will use a frictionless ramp. If the piano has a mass of 1806.0 kg and the movers push it up the slope at a constant velocity, how much work do they need to do on it...
  17. YMMMA

    Potential energy of a block moving up and down an incline.

    Homework Statement Which graphy represents the potential energy of the block as a function of time? Homework Equations PE=mgh The Attempt at a Solution First, the potential energy is zero until it reache the top of the incline where the potential energy is maximum. Moving down, the potential...
  18. J

    Variation of potential energy with height

    Homework Statement Show that the variation of gravity with height can be accounted for approximately by the following potential function V = mgz(1+z/re) in which re is the radius of the Earth. find the force given by the above potential function. Homework Equations V = GM/r The Attempt at a...
  19. PaulCam

    B Space Curvature & Potential Energy

    So I'm an Software Engineer, not a physicist, nor a mathematician. So I like to work in the qualitative, not the quantitative. Today I hit on a problem. I've been trying to remove the concept of "down" or "inward" from my thinking of gravity and GR. When people show the concept of space/time...
  20. L

    Are the answer choices wrong? (electric potential energy)

    Homework Statement Homework Equations U=kq1q2/r The Attempt at a Solution W = changeU = Uf-Uo Uf = k(7*(-5) + 7(-4) + (-5)*(-4))/0.1 = -4.3*10^-4 Ui= k((7*(-4))/0.1= -2.8*10^-4 Uf-Ui = -1.5*10^-4k J
  21. P

    Electric potential energy between charge and moving magnet

    The setup for one magnet Introduce a magnet: Inertial Frame 1 (or lab frame) A frame where a magnet is seen to move with uniform velocity v and carries a uniform polarization P while a point charge Q is seen to be stationary at time t=0. Inertial Frame 2 (or material frame) A frame where a...
  22. DracoMalfoy

    Spring Potential Energy: Horizontal Spring Problem

    Homework Statement A horizontal spring with a constant of 700N/m is compressed 2cm. A ball of mass 200g is placed in front of the spring. The spring is released. The ball slides along a horizontal track for 10cm while experiencing a frictional force of 0.75N. What is the velocity of the ball at...
  23. cookiemnstr510510

    Potential energy and work relationship

    Homework Statement Taking my Electricity and Magnitism course right now and we are in the section in the book of the electric potential. I have some basic questions regarding work and potential energy. Lets say we are holding a ball 10m above the ground and release it. I am defining the ground...
  24. L

    Derivation of the Potential Energy of an Electric Charge System

    Hi, I learned about how PE = U=kq1q2/r is the electrical potential energy for the system. It is found by taking the integral of electrical force and dr from infinity to the point of location we are interested in. So that is the intregral(F*dr) from r=inf to r=ro. My question is that do I...
  25. cookiemnstr510510

    Understand Electric Potential Energy, Difference & Potential

    Homework Statement My textbook is no help, my teacher is no help, so I've found myself here. I am having a difficult time understanding the differences in 1.Electric Potential energy 2. Potential Difference 3. Electric potential Im sure this question has been asked tons of times but I need...
  26. N

    Elastic potential energy (spring) problem

    Homework Statement A 0.200 kg object is attached to a horizontal spring with a spring constant of 77.0 N/m. The other end of the spring is attached to a wall in such a way that it rests on a frictionless horizontal surface. A 10.0 N force is exerted on the spring, causing it to compress a)...
  27. zachx

    2 Different Ways to Write Potential Energy of a Pendulum

    I have been doing pendulum problems lately, and I have found 2 different formulations for potential energy of a pendulum. U=mgl(1-cos(Θ)) and U=-mglcos(Θ) The first says U=0 when Θ=0 (at the bottom). The second has U=0 when Θ=π/2 (halfway to the top). Both give the same equation of motion...
  28. V

    Problem in understaning potential energy

    Homework Statement If we lift a block with constant velocity, by applying a force mg upwards, is the work done zero?Homework EquationsThe Attempt at a Solution The work done must be zero as the resultant force is zero, what I don't understand is how does the block get potential energy if no...
  29. P

    Does the gravitational potential energy affect the burning of two logs?

    Homework Statement Let's consider two wooden logs. We burn the first one at the base of the mountain and the second one on the peak. Which one is releasing more energy? Do they release the same amount of energy? Does the potential energy affect the burning Homework Equations ## \Delta H =##...
  30. pintu935

    I What does complex potential energy mean for a particle?

    Griffith says in problem 1.15 the potential energy has an imaginary part. my question is that any real case exists where the part of the potential energy is imaginary?
  31. Jonathan Scott

    A Explore Potential Energy, Pressure & Newtonian Gravity

    I've now found a different way to look at potential energy and its location in the Newtonian approximation to relativistic gravity which may perhaps shed some light on how the corresponding terms work in GR. This is related to a previous thread of mine on "Pressure and Newtonian potential...
  32. zonde

    I Problem with classical electrostatic potential energy

    In classical physics electrostatic potential energy is: ##U=k_e\frac{q_1q_2}{r}## So amount of potential energy is not limited as ##r\rightarrow 0## But obviously potential energy (= binding energy) is limited by masses of charge carrying particles. Say when electron and positron annihilates...
  33. D

    Two separate "gravitational potential energy" equations?

    I am hoping to get a deeper understanding of the difference between two different gravitational potential energy equations, the first of which is given by U = mgh and the second given by U = (Gm1m2)/r I first assumed that in a system consisting of the Earth and, say, a tennis ball, these...
  34. A

    Do electromagnetic waves have potential and kinetic energy

    Do electromagnetic waves have potential and kinetic energy like springs, strings, etc. If so how are they calculated, inter-related? What is the total energy? Are the energies fluctuating over time? I am a physics hobbyist so generally the first answers should come with the least mathematics...
  35. G

    Energy Confusion (Conservation of Energy?)

    Anyone know if the following statement is true (and why)? "Getting to higher ground would increase his gravitational potential energy, decreasing the effects of non-conservative forces, which would allow him to move easier." CLARIFICATION: "move easier" refers to a lack of friction and not the...
  36. I

    Relationship between force and potential energy

    I am aware that the negative derivative of potential energy is equal to force. Why is the max force found when the negative derivative of potential energy is equal to zero?
  37. D

    Can we transfer 100% Potential energy to electricity?

    I read somewhere PE=KE, how? It mean we can get transfer 100% PE to KE and KE to Joule Please anyone can explain? If I throw mass of 1000kg from 50 meters height can I get energy equal to Pe=mgh = 1000*9.81*50=490500 Joule? It mean 490500Kn = 490500watt= 490.50Kw. Is it possible to to get this...
  38. J

    Potential energy loss related to force applied?

    How can I calculate the loss of potential energy when forces are applied but no motion in the system occurs? Here's an example: Let's say I build a battery operated car that is set to drive forward, but I put it right in front of a wall. It attempts to drive forward, but instead it just pushes...
  39. Jackson Smith

    B Creation of PE - WHEN is it created?

    Generally, a change in altitude within a gravitational field is said to increase or decrease PE. I posit that the change in PE never occurs UNTIL there is a change in KE. Thus, in the case of an object with a constant velocity UP, there is no gain in PE until the instant that the thrust no...
  40. M

    Gravitational Potential Energy Project Thor

    Homework Statement Project Thor is a proposed (and terrifying) weapon system where a cylindrical tungsten rod (19600 kg m3 ) about the size of a telephone pole (6.10 m long and 0.300 m in diameter) is dropped from Earth orbit. Imagine you dropped one of these from an orbit 10,000 km above the...
  41. J

    Mechanical energy for planet in elliptical orbit around star

    Homework Statement A planet is in an elliptical orbit around a star. Which of the following best represents the mechanical energy E_planet of just the planet and the mechanical energy Es_tar-planet of the star-planet system as functions of time for one complete orbit? Homework Equations...
  42. A

    Potential ##V## and potential energy ##E_{pot}##?

    Hi, I know that in an elecric field the potential energy ##E_{pot}## is equal to the potential ##V## times the charge ##E_{pot}=q V##. Here my problem: I know that the potential energy of a spring is ##E_{pot}= \frac{1}{2}kx^2##. In my theoretical physics book i read also that the potential is...
  43. isukatphysics69

    Using potential energy graph, find particle turning point

    Homework Statement Homework Equations Emec - PE = KE The Attempt at a Solution When particle starts at x = 4 KE = .5(.25)(225) = 28.125 Energy of system = 28.125 I don't have anything with position here so i am unsure how to find what position that the energy will be equal to the Emec and...
  44. Murphy.T

    Potential Energy of an Electron near a negative source charge

    If an electron starts from rest 85.0 cm from a negative fixed source charge of -0.135 micro coulombs we use the equation ke final - ke intial + pe final - pe intial. In solving you use ke = pe which appears to cancel out the inital kinetic and potential energy but how can the initial potential...
  45. F

    The electrostatic potential energy of two spheres

    Homework Statement Homework Equations The Attempt at a Solution Is my answer correct ?
  46. A

    B Mass-Energy Equivalence: Matter as Potential Energy?

    I think mass as a form of potential energy and am always told that this is wrong. According to wiki: "In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors." Why do this...
  47. F

    Find the electric potential energy

    Homework Statement Homework Equations ##V= \frac {kq}{r}## ##V= \frac {U}{q}## The Attempt at a Solution ##V= \frac {kq}{r}## = 9*109*-5*10-9 /0.1= -450 V ##U= \frac {V}{q}## = -450 * -2*10-9 = 900nJ Is my answer correct ?
  48. A

    How close will body approach fixed point charge?

    Homework Statement Charged sphere with a mass of 15 mg and charge 2 nC moves with a speed of 15 cm/s towards a fixed point charge of 3 nC. How close will sphere approach charge? Homework Equations K=(1/2)*mv2 U=k*(Q1Q2/r) The Attempt at a Solution So I am not sure I approached correctly but...
  49. J

    Deriving gravitational potential energy -- mistake

    Homework Statement Hi I'm attempting to derive the gravitational potential energy of a point mass (##m##) that's moving from infinity to a point r' inside a gravitational field produced by a another mass ##M##. For simplicity I treated it as a one dimensional case. The problem I get is that the...
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