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

    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...
  2. 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 ?
  3. 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...
  4. 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...
  5. Wes Turner

    Change in electric potential energy

    Homework Statement As an electron (q2) moves from point A to point B, it moves farther from a positive charge (q1). Does the electric potential energy increase, decrease, or stay the same. Homework Equations U=-kq1q2/r The Attempt at a Solution The electric potential energy decreases in...
  6. K

    What does a negative potential energy mean?

    A consequence of Coulomb's law is that oppositely charged particles have a negative potential energy. I'm having trouble undsrstanding how anything can have a negative potential energy and what consequences that has. Does it just mean the change in potential energy is negative or is it a matter...
  7. Sultan Abdullah

    Does the Earth have potential energy?

    well, we say that an object on Earth has a potential energy that is dependent on its position, i.e height. In this case we take Earth as reference point, similarly if we take sun as reference point, the Earth should have some sort of potential energy.
  8. J

    Time period from potential energy expression

    Homework Statement Homework EquationsThe Attempt at a Solution U = 5x2 - 20x F = -dU/dx F = -10x + 20 The expression for force doesn't look like motion is SHM . How should I deal with this ?
  9. T

    Kinetic & Potential Energy of 0° Ice/Water: Examined

    Hi. In all of my question, I mean degrees celsius when I say degree. Think we have a 0 degree ice. we give some energy to it (by a heater) and all of it get into a 0 degree water. How does the kinetic and potential energy of the molecules change? In the book in which I saw this question, it...
  10. D

    Potential energy and internuclear distance

    What exactly is this potential energy? I was searching and its looks like electric potential energy (U = K*Q*q/d - K*Q*q /d0), because the two atoms attract each other that means that the product of Q*q = negative, so, a negative energy. Ok, that's make sense, but why when the repulsive forces...
  11. A

    What is the relationship between voltage and charge in a battery?

    I'm trying to understand what exactly it means in terms of the voltage of a battery. I know that the voltage in a battery is just the potential difference between the two terminals. But, is the negative terminal used as a relative point and seen as 0? If that's the case does 12V mean that the...
  12. A

    Electric Potential vs Electric Potential Energy

    So in my physics textbook a problem is stated. We are given an external electric field directed downwards of 150N/C. We are then told that an electron is released in the electric field and it moves upwards 520m. Finally we are asked to calculate the change in electric potential energy of the...
  13. Y

    Uniform Electrical potential energy

    Can someone explain the math of how potential energy travels from higher potential energy to lower potential energy (PE) along a uniform electric field? I understand that in order for the point charge to move, gaining kinetic energy, it will lose potential energy. But using the equation...
  14. A

    Confusion regarding Electric Potential Energy and Work

    Hi everyone. I've been doing a lot of reading regarding electric potential and electric potential energy. Unfortunately, I have a lot of confusion regarding this topic, as I keep receiving different information. My main confusion is regarding the signs, positive or negative, of work and it's...
  15. H

    How do you calculate Electric Potential Energy in a Square?

    Four identical particles, each having charge q and mass m, are accelerated from rest at the vertices of a square of side L. How fast is each particle moving when their distance from the center of the square doubles? I used the Conservation of Energy => Kf= -deltaU = Ui-Uf 4(mv^2 /2) = kq^2...
  16. How to Find the Potential Energy of a Particle # 9 - YouTube

    How to Find the Potential Energy of a Particle # 9 - YouTube

    How can one find the potential energy of a particle. The derivation of PE can be done by the fact that change in PE of a particle is equal to negative of work done by a force on the particle. This combined with Kinetic energy work theorem gives us an equation on conservation of mechanical energy.
  17. G

    Calculating Potential Energy Change for a Mountain Climber

    Homework Statement A 95-kg mountain climber hikes up a mountain to an elevation of 5000 m. What is the change in the climber's potential energy? Homework Equations I might be missing something but here's everything that might be relevant: w=fx p=w/t p=f*v KE=1/2mv^2 PEg=mgh PEe=1/2kx^2 Wnet=E...
  18. Alexanddros81

    Calculate the contact force between the skis and the track

    Homework Statement 14.37 A 75-kg ski jumper starts his run in the position shown on the parabolic track. The equation of the parabola is ##y = (12/225)x^2##, where x and y are in meters. Neglecting friction, calculate the contact force between the skis and the track at O. Homework...
  19. Alexanddros81

    Determine the smallest possible speed of the bob at A

    Homework Statement 14.34 The 0.5-kg bob of the pendulum travels a complete circle about the pivot point O. Determine the smallest possible speed of the bob in position A if it is suspended from (a) a rigid rod of negligible mass; and (b) a string Homework EquationsThe Attempt at a Solution...
  20. rocky4920

    How to find Potential Energy without distance

    Homework Statement [/B] A small cube, with a mass of 2 kg, slides along a frictionless horizontal surface at a constant speed of 20 m/s until it collides with, and sticks to, a large wooden 5 kg block. The large block is attached to the left end of a spring with a spring constant of 75 N/m as...
  21. A

    Setting Up an Experiment: Force vs. Displacement

    Homework Statement I'm trying to figure out the setup of an experiment I have to complete. The experiment calls for a rubber band to be secured by rods on the sides, and for a clothespin to be attached to the rubber band. I have to figure out how far back the clothespin needs to be pulled down...
  22. Alexanddros81

    The 2.5-kg wieght is released from rest -- Determine the spring constant k

    Homework Statement 14.27 The 2.5-kg weight is released from rest in position A, where the two springs of stiffness k each are undeformed. Determine the largest k for which the weight would reach position B Homework EquationsThe Attempt at a Solution Hi. Can you check if I am going at...
  23. B

    Gravitational potential energy of a coupled pendulum

    Homework Statement I'm trying to solve problem a problem of complete energy of doubled pendulum (2 mathematical pendulums connected by a string). For a kinetic energy I would get (1/2) J(w_1)ˆ2 + (1/2) J(w_2)ˆ2 and for a potential energy of a spring (1/2) k (ϕ_1-ϕ_1) What about gravitational...
  24. Alexanddros81

    A ball is placed on the spring and launched vertically, Find k

    Homework Statement 14.28 The spring of stiffness k is undeformed in the position shown. The 30-g ball is placed on the spring and launched vertically by compressing the spring 150mm and releasing it. If the ball reaches an elevation of 14.25m above A, determine the value of k. Homework...
  25. K

    Calculate the rate of potential energy loss of water in a pipe

    Homework Statement Question: what rate does the water lose gravitational potential energy? Data: I have a pipe that water is flowing through and the pipe has 2 sections. In section 1: - the pipe is 11.9m above section 2 so, h = 11.9m - the velocity of water is $$v_1 = 0.3240ms^{-1}$$...
  26. G

    Potential energy and annihilation

    Let's assume an electron and an anti-electron are in a gravitational field so they both have potential energy. What will become of this energy if they annihilate? Will the momentum of the photons after the annihilation will increase so the total energy will be conserved? Thanks for answering!
  27. Pushoam

    Change in the potential energy of a star after explosion

    Homework Statement Homework EquationsThe Attempt at a Solution I think : the question means that almost all of the potential energy gets used into the explosion. If this is true then the potential energy gets reduced by ## \frac { GM^2} R ## or if the star just gets transformed into a...
  28. J

    Calculating Potential Energy in a Rotary Mousetrap Spring System

    Homework Statement Calculate the potential energy created by the spring in the mousetrap as a function of the angle the spring is pulled back. Homework Equations PE = ∫Fdx = ∫ kxdx = ∫k rΘ rdΘ ?? The Attempt at a Solution Is this a linear spring? we can use x = rΘ, and dx = rdΘ, so PE =...
  29. K

    B What is the ΔEp = ΔEk + W equation used for in thermodynamics?

    What is ΔEp = ΔEk + W I have come across this formula, but i haven't seen it before. What is it used for?
  30. B

    Where is the gravitational potential energy?

    I am confused on where the gravitational potential energy is in this solution. Thank you
  31. B

    Adding a constant to potential energy doesn't change action?

    Hello. I've been watching Susskind's online Stanford lectures on classical mechanics to review the subject, and I believe he said that adding a constant to the potential energy does not change the action of a system. I see how it doesn't change the Euler-Lagrange equations and therefore...
  32. Leah12

    What is the Elastic Potential Energy of a Toy Car's Spring?

    The force constant of the spring in a child’s toy car is 550 N/m. How much elastic potential energy is stored in the spring if the spring is compressed a distance of 0.012m? The formula for spring force is F =kx When I do 550 x 0.012m I get 6.6 but I am supposed to round my answer four decimal...
  33. Leah12

    Potential Energy Problem -- GPE of a person at 5334m above sea level

    1. With an elevation of 5334 m above sea level, the village of Aucanquilca, Chile, is the highest inhabited town in the world. What would be the gravitational potential energy associated with a 64.0 kg person in Aucanquilca? Assume that the free-fall acceleration at Aucanquilca is equal to that...
  34. M

    Finding the speed of the block for one and two springs

    Homework Statement The spring in the figure (Figure 1) is compressed by length Δx. It launches the block across a frictionless surface with speed v0. The two springs in the figure (Figure 2) are identical to the spring of figure 1. They are compressed by the same length Δx and used to launch...
  35. M

    Integration of an interaction force to find potential energy

    Homework Statement A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x) N where x is in m. Find an expression for the system's potential energy. Express your answer in terms of the variables x and the constant of integration C, where C is in joules. Homework...
  36. A

    Accelerated Electron and its Potential Energy

    Homework Statement An electron acquires 3.16*10^-16 J of kinetic energy when it is accelerated by an electric field from plate A to plate B. What is the potential difference between the plates, and which plate is at the higher potential. Homework Equations w =Δv * q The Attempt at a Solution...
  37. A

    Negative work and electric potential energy

    I am confused how a charge could have negative work done. To clarify, I was doing a problem earlier in which a positive charge and negative charge are moving towards each other. I used the equation work = Δv * q And when I was doing this, the change in electric potential, Δv, was negative, and...
  38. K

    Potential and kinetic force of an arrow shot at space.

    Assume a person is at space, and assume there's no friction or gravitational force in that space. The person has a bow and arrow. He stretches the arrow on the bow, and then shots the arrow out in the space. Since there are no friction and gravitational force in that space, the arrow will have...
  39. C

    Using Conservation of Energy to Analyze a Potential Energy Graph

    Homework Statement I'm trying to figure out how to do D) and relate time to this potential energy graph. Homework Equations All I really know is that F = -dU/dx The Attempt at a Solution I tried to do something with F = ma and a = d2x/ dt2 and then set the - derivative of U(x) equal to the...
  40. B

    Non-conservative work energy theorem and potential energy

    Here is problem I quickly made up: Suppose there is a ramp with a height of 6 meters and length of 12 meters. A block of 5 kg is pushed up to the top of the ramp with a constant velocity. The force of friction is 15 N. Here's the confusion: By using the non-conservative force work energy...
  41. B

    Gravitational potential energy and continuous matter

    The gravitational potential energy of two massic points ##P_1## and ##P_2## with respective masses ##m_1## and ##m_2## is given by $$U = -G \frac{m_1 m_2}{|| P_2 - P_1 ||}$$ Now I was wondering how this formula could be applied to continuous matter. Let us imagine a very simple case where we...
  42. zonde

    I GR: Mass of Potential Energy in Weak Field Limit

    There is something that has been bothering me for some time about binding energy (and respective mass difference) but I was not sure how to formulate the question. Now it feels like I can ask it meaningfully enough. In GR energy produces gravity just like mass. But how potential energy is...
  43. V

    Potential energy of a ball on top of a vertical rod

    Homework Statement The problem is to take a small ball of mass m on a uniform rod of mass m which is hung on a hinge vertically downward, they're asking to find the velocity to be imparted for it undergo a complete rotation. I have the kinetic energy bit worked out but I'm getting the wrong...
  44. D

    Finding the decrease in potential energy of atwood machine

    Homework Statement In the system below, m1<m2. When the object of mass m2 has descended a distance h, the potential energy of the system has decreased by: Homework Equations the answer is (m2-m1)gh The Attempt at a Solution I used ΔU= Uf-Ui m1gh-m2gh=ΔU (I think that the decrease in...
  45. A

    Elastic potential energy problem

    Homework Statement A 1.00kg mass and 2.00kg mass are set gently on a platform mounted on an ideal spring of force constant 40.0 N/m. The 2.00 kg mass is suddenly removed. How high above its starting position does the 1.00 kg mass reach? Related to it... An 87 g box is attached to a spring with...
  46. C

    Finding the potential energy of a gravitational force?

    Sorry if something is wrong... this is my first ever post 1. Homework Statement The Question: In one dimension, the magnitude of the gravitational force of attraction between a particle of mass M1, and one of mass M2 is given by: F(r)=GM1M2/r^2 Where G is a constant and x is the distance...
  47. Jonathan Scott

    A Pressure and Newtonian potential energy

    Recent discussions on pressure as a source of gravity and the related Tolman paradox have reminded me that few people seem to be aware that even in Newtonian gravity the pressure is related to the potential energy, which I've mentioned a few times on these forums before. This is easy to show...
  48. G

    Electric Potential Energy - Final Velocity

    Homework Statement Four protons (each with mass 1.7 10-27 kg and charge 1.6 10-19 C) are initially held at the corners of a square that is 7.1 10-9 m on a side. They are then released from rest. What is the speed of each proton when the protons are very far apart? (You may assume that the...
  49. Ahmed Abdalla

    Why do we use Taylor expansion expressing potential energy

    My textbook doesn’t go into it, can someone tell me why Taylor expansion is used to express spring potential energy? A lot of the questions I do I think I can just use F=-Kx and relate it to U(x) being F=-Gradiant U(x) but I see most answers using the Taylor expansion instead to get 1/2 kx^2...
  50. Pushoam

    Mean thermal energy of a system with given potential energy

    Homework Statement Homework EquationsThe Attempt at a Solution ## V(r) = \frac 1{r^3} \left( A - Br^2 \right )## At the bottom of the well, r is verry small. So, ## V(r) = \frac A{r^3}## Assuming the validation of Equipartition of energy theorem, since the degrees of freedom is 1, the...
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