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. D

    Does Space Expansion Add Potential Energy?

    Space is expanding, which separates objects from each other in space. Won't this add potential energy? Doesn't this violate the law of conservation of energy? But if it does not, how can space be added without adding potential energy?
  2. rogerk8

    What is the equation for gravitational and electrical potential energy?

    Hi! I just wish you to help me derive two types of potential energy. A) Gravitational Potential Energy B) Electrical Potential Energy A useful equation is W=\int Fdr Which I consider is the work that has to be done to the particle to move it a certain distance from the attractive centre of...
  3. J

    Potential Energy of Nearly Hovering Rocket

    I have a question concerning gravitation potential energy and rockets under an unusual situation. Let a rocket be in a gravity well of a massive object such as a planet. For simplicity, assume that the rocket is in a vacuum. (we can add air effects later). The rocket engine thrust is dynamically...
  4. S

    I with Potential Energy compared to energy used.

    your going up hill in a big truck ,18 wheeler at a (*10 % Grade) or (* 5.7106 DEGREES) your fully loaded at (*80,000 lbs) or (*36287kg) or (*40 short tons) your traveling at (*30 mph) or (*13.41120m/s) you travel for about (*10 miles) or (*1609.344 Meters) the actual distance traveled would be...
  5. M

    What is the motion of a test charge in a non-uniform electric field?

    Homework Statement Describe the motion of a test charge in a non-uniform electric field.By considering the electric forces acting and Newton’s second law, explain the type of motion occurring in a non-uniform electric field. Homework EquationsThe Attempt at a Solution I wrote that the...
  6. S

    Change of state and potential energy

    A book said that the PE of molecules increase during melting of ice but shouldn't it be decrease since the distance between molecules increase ?Isnt the force between the molecules determine the PE?
  7. R

    Voltage drop and potential energy

    Hi! What is the potential energy of electrons converted to, in a circuit? I'm asking this question because I don't really understand the concept of voltage drop across some element. If I have a series circuit with a 10V battery and two equal-in-magnitude resistors, then the potential...
  8. R

    Electric Potential Energy Concept

    I'm unsure if the following is true or not in the absence of external forces: Electric potential is a scalar quantity. This I know is true because there is no direction associated with potential energy. It is always possible to assign a value of zero to the electric potential at the...
  9. J-dizzal

    Potential energy curve, turning points

    Homework Statement The figure shows a plot of potential energy U versus position x of a 0.220 kg particle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9 J, UC = 20 J and UD = 24 J. The particle is released at the point where...
  10. C

    Question: Gravitational Potential Energy in a Ball-Earth-Moon system?

    Hello, here's a questions I was wondering if any of you could solve. I don't have the exact numbers, but the scenario is this: a guy standing on the Earth throws a ball upwards and catches it a few seconds later. How does would affect the potential energy and/or mechanical energy of the...
  11. S

    Conservation of Mechanical Energy

    Homework Statement This is my first time posting here guys so correct me if I am wrong. This question was on my test and I wanted to know if I did it right. There is a block of mass m and it is moving at a certain velocity before pressing against a spring which compresses distance x. Find...
  12. olgerm

    Potential energy in strong- and weak- nuclear interaction

    Schrödinger equation for N-particles is: U_{System Potential Energy}(r_1,r_2,r_3,...,r_n,t)-\sum_{n=1}^{n_{max}}(\sum_{d=0}^{d_{max}}(\frac{d^2Ψ(r_1,r_2,r_3,...,r_n,t)}{dx_n^2})*\frac{ħ^2}{m_n})=i*ħ \frac{dΨ(r_1,r_2,r_3,...,r_n,t)}{dt} Where \sum_{d=0}^{d_{max}} is summation over dimensions...
  13. Drakkith

    Potential Energy and Velocity of a Spaceship

    Homework Statement 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. Some information that will help during this problem:mearth = 5.9742 x 1024 kg rearth = 6.3781 x 106 m...
  14. olgerm

    Schrödinger equation for 2 particles

    U(x,y,z,t)*ψ(x,y,z,t)-(ħ/(2*m))*(d2ψ(x,y,z,t)/dx2+d2ψ(x,y,z,t)/dy2+d2ψ(x,y,z,t)/dz2)=ħ*i*dψ(x,y,z,t)/dt qproton=-qe Schrödinger equation for electron in hydrogen atom (if we consider proton as point charge which is moving at a constant speed vproton→=(vp;x;vp;y;vp;z).) is...
  15. F

    Human Energy, Work Done and Declining results

    Hi I am having trouble locating resources for a topic as I do not know exactly what it is called, and I am looking for assistance. If you wanted to look at human performance and calculate the various ways a human could perform a task and how this would affect outcome by including "work done"...
  16. T

    Changes in electrostatic potential energy of a moving object

    Homework Statement "An object is moving in a straight line from a positively charged area (A) to a negatively charged area (B). Explain how the electrical force and electrostatic potential energy experienced by the object will vary when it is neutral (has no charge)." Homework Equations N/A as...
  17. D

    Double Pendulum Potential Energy

    Hello, everybody. This website and many others define the potential energy of a double pendulum as: V=-(m_1+m_2) g l_1 cos\theta_1-m_2 g l_2 cos\theta_2 However, I came up with the following equation: V= (m_1+m_2) g l_1 (1-cos\theta_1)+m_2 g l_2 (1-cos\theta_2) I started from the position...
  18. S

    2 Types Of Magnetic Potential Energy

    There are 2 types of magnetic potential energy equations: 1. ##U = -\vec \mu \cdot \vec B## 2. ##U = \frac{1}{2} \int \mathbf{A} \cdot \mathbf{J} \, \mathrm{d}V## - I have searched for the second equation, only can find some information in one web site. Do you know what their names are and...
  19. S

    Dot product in the Gravitational Potential Energy formula

    This is the gravitational potential energy formula $$U = -\int_\infty^r\vec{F}_\text{field}\cdot d\vec{r}$$ If r vector's direction is form infinity to r, then it means it has same direction as Gravitational Force. So cos0=1 But after multiplication there is a negative sign here: "-GMm" $$U =...
  20. toforfiltum

    Exploring the Effects of Equal Water Depths on Gravitational Potential Energy

    Homework Statement Homework Equations GPE=mgh The Attempt at a Solution I don't understand why the answer is B. My approach is assigning h a random value, say 10m. When the depths of water in both vessels are equal, the height is 5m. Therefore, since the mass of water in both vessels are...
  21. B

    Electric charge and potential energy

    Homework Statement A particle with charge q experiences a force F when placed a distance d from a point charge. At a distance d, the electric field has a strength E and a potential V. Which of the following represents the potential energy of the charge? (A) Fd (B) Eqd (C) Vq (D) Ed Homework...
  22. N

    Angular momentum & Energy using Yukawa's potential

    Hello there! I was doing my Gravitation problems and I found this problem that I'm unable to solve. Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force produced by a proton and a neutron is: U(r) = \frac{k}{r}e^{-\alpha r},\ k<0,\ \alpha > 0...
  23. I

    Potential energy term in Schrodinger's equation?

    consider a 1-D problem where a charged particle travels along +x with a bound state energy. the vertical potential energy axis is displaying information about the force that is parallel to the particle's axis of motion. is this correct? so then this would be an accurate representation? where...
  24. L

    The Change in Elastic Potential Energy with Different Spring Stretches

    Homework Statement A spring constant of ##3200 N/m## is initially streched until the elastic potential energy is ##1.44## J (##U=0## for no stretch). What is the change in elastic potential energy if the initial stretch is changed to (a) a stretch of ##2.0## cm, (b) a compression of ##2.0## cm...
  25. Glenboro

    How High Will the Ball Bearing Rise When Released from a Compressed Spring?

    Homework Statement A ball bearing of mass m = 50.0 g, is sitting on a vertical spring whose force constant is 120.0 N/m. The initial position of the spring is at y = 0 m[/B] a) The spring is compressed downward a distance x = 0.200 m. From the compressed position, how high will the ball...
  26. S

    Finding the frequency of small oscillations given potential energy U

    Homework Statement The potential energy of a particle of mass m near the position of equilibrium is given by U=U0sin2(αx) where U0 and α are constants. Find the frequency of the small oscillations about the position of equilibrium. Homework Equations Work energy equation...
  27. R

    Condition for stable equlibrium

    Homework Statement A homogeneous wooden bar of length 10 cm, thickness 4 cm and weight 1 Kg is balanced on the top of a semicircular cylinder of radius R as shown below. Calculate the minimum radius of the semicircular cylinder if the wooden bar is at stable...
  28. Sampad Saha

    How does Potential Energy converted into Kinetic Energy? ?

    As we know that every object that has kinetic energy could also have potential energy. Now suppose an object is in rest at a distance of h meter from ground so it has some potential energy and no kinetic energy, now if it starts to fall towards the ground can we say that its total potential...
  29. S

    Potential energy of an electric dipole in electric field

    Homework Statement Show that the energy of an ideal dipole p in an electric field E is given by U = -p ⋅ E Homework Equations Work = θτ where τ is torque τ = p × E The Attempt at a Solution U = ∫(p × E) dθ' (from θ to 0, since the dipole will eventually align itself with the magnetic...
  30. M

    Graphing Oscillating Objects: Can You Find the Spring Constant?

    How could you graph a potential energy vs. time graph only knowing the position vs. time graph and the velocity vs time graph for a hanging object oscillating up and down on a string?
  31. L

    Need to sketch the potential energy of the spring system

    https://scontent-sjc.xx.fbcdn.net/hphotos-xpt1/v/t34.0-12/11160576_1059930500703784_4106088481400641257_n.jpg?oh=2e1906c36fc3e407fc8e2b8eb544bbba&oe=55401DBB 1. Well the entirety of the question along with the variables is given within the picture ^.2. I can't figure out how to make the graph...
  32. Y

    Electric Potential Energy Inside a Charged Sphere

    Homework Statement A point charge q<0 lies just outside a uniformly and positively (non-conducting) charged ball. Assume the charge can pass through the ball freely. Describe the motion of the charge. Homework Equations Coulomb's force law, energy equation. The Attempt at a Solution Obviously...
  33. Mr Davis 97

    Where Does the Non-Zero Potential Energy Come From?

    I have a question about the conservation of energy. Imagine that there is an object on a level plane with zero kinetic energy and zero gravitational potential energy. Now imagine moving this object at some constant velocity in the y-direction for a few meters. Since it was moved at a constant...
  34. M

    Spring with weight question / Potential energy of the spring

    Homework Statement The spring of a dynamo-meter grows 20cm when one suspends a 4N on weight. What is the potential energy of the spring when one suspends a weight of 12N? Homework Equations Ue = 1/2*k*r2 Ug= m*g*h The Attempt at a Solution so to find k I do this step. 1/2*k*0.22 = 4*0.2...
  35. SnakeDoc

    Gravitational Potential energy Problem

    Homework Statement A projectile is fired vertically from Earth's surface with an initial speed of 3.1 km/s. Neglecting air drag, how far above the surface of Earth will it go? Homework Equations KF+UF=KI+UF U=-G(M1m2)/r2 K=1/2mv2 mass of Earth = 5.972E24 radius of Earth = 6371km G=6.673E-11...
  36. S

    Electric Potential Energy & Electric Potential

    Two frictionless pucks are placed on a level surface, as shown, at an initial distance of 20 m. The mass of puck 1 is 0.80 kg and it has a charge of +3.0 x 10^-4 C, while puck 2 is 0.40 kg with a charge of +3.0 x 10^-4 C. The initial velocity of puck 1 is 12 m/s [E] and the initial velocity of...
  37. H

    Sign on change in electric potential energy

    Homework Statement I'm trying to figure out why potential energy decreases in this situation http://imgur.com/9PfjRVE Homework Equations ΔU = FΔy The Attempt at a Solution If I define up to be positive, and ΔU = FΔy. In this picture, force is pointing down (so it is negative) and the height...
  38. B

    Comparing force of mass at rest vs falling mass

    What equations can be used to compare the force of a resting X mass to the force of a smaller Y mass falling Z distance. Specifically, how much resting mass would equal the force of 300 pounds being dropped from 10 feet up?
  39. D

    Why doesn't electrode potential depend on amount of metal?

    When a metal (electrode) is in contact with water, an equilibrium forms: Mg ⇔Mg2++e- Adding more of the metal Mg should convert some of it into more electrons so that the ratio of Mg to Mg2+ remains the same (as the equilibrium requires). Therefore twice the amount of metal in contact with water...
  40. K

    Calculating Energy Conservation in a Spring-Mass System on an Incline

    Homework Statement A 2kg block is pushed against a spring of force constant k=400 N/m, compressing it .22m. When the block is released, it moves along a frictionless, horizontal surface and then up a frictionless incline with a slope of 37 degrees. a.) what is the speed of the block as it...
  41. Calpalned

    Gravitational potential energy

    Homework Statement For a satellite of mass ##m_s## in a circular orbit of radius ##r_s## around the Earth, determine its kinetic energy K. Homework Equations ## K = \frac {1}{2}mv^2 ## Gravitational potential energy ## U(r) = - \frac {GmM_E}{r}## The Attempt at a Solution My answer is ## K...
  42. Calpalned

    Find the potential energy function

    Homework Statement A particle is constrained to move in one dimension along the x-axis and is acted upon by a force given by ##\vec F (x) = \frac{-k}{x^3} \vec i ## where ##k ## is a constant with units appropriate to the SI system. Find the potential energy function ##U(x)##, if U is...
  43. F

    Electric Potential Energy Conversion

    Hello everyone, Imagine two points that have a Electric Potential Difference of 10V and they are connected through a conductor wire. Let's call these points A and B: Now imagine we have a charge on A of 1C. To move the charge to B, we need to make a work of 10J, right? So, now, imagine the...
  44. Last-cloud

    Obtain Equation Using Hamilton's Principle

    I want to obtain equation using Hamilton principle but I just couldn't figure it out; i have The kinetic energy : \begin{equation} E_{k}=\dfrac{1}{2}m_{z} \displaystyle\int\limits_{0}^{L}\ \left[ \left( \dfrac{\partial w(x,t)}{\partial t}\right)^{2}+\left( \dfrac{\partial v(x,t)}{\partial...
  45. H

    Determine the total electrostatic potential energy

    Homework Statement Determine the total electrostatic potential energy of a nonconducting sphere of radius r_0 carrying a total charge Q distributed uniformly thorughout its volume. Homework Equations U = qV The Attempt at a Solution \rho = \frac{Q}{4/3\pi r_0^3} = \frac{dq}{4\pi r^2dr}...
  46. W

    Gravitational Potential Energy Question

    Homework Statement [/B] Calculate the gravitational potential energy of the interacting pair of the Earth and a 23kg block sitting on the surface of the Earth. You would need to supply the absolute value of this result to move the block to a location very far from the Earth (actually, you...
  47. K

    Inf. Parallel Plate Capacitors and Potential Energy

    Hopefully no one minds that I post a couple questions in a row as long as I'm following the rules: 1. Homework Statement Two infinite parallel plates labelled W and X are separated by 5.2 cm. The electric potential between the plates is 150 V. An electron starts from rest at time tW and...
  48. A

    Electric Potential Energy and Sign

    There is a negative point charge with a positively charged plate above it and a negatively charged plate below it. Define up as positive and down as negative. When the point charge moves towards the positively charged plate it does negative work. Why? The force the charge experiences is upward...
  49. S

    Is the ball's height the same on Earth and Mars?

    Hi, I understand that if a ball is dropped on Earth and dropped on mars, the ball will reach the same height on both planets thanks the law of conservation of energy. Can anyone prove this mathematically? Thanks in advance
  50. H

    A spring and two blocks with kinetic energy

    1. I have two blocks, one that is 1.6 kg moving left at 3.00 m/s and the other is 2.1 kg moving right at -1.74 m/s, and they are compressing a block with a spring constant of k=600 N/m. I'm supposed to be finding the distance that the spring is compressed at that instant, and I know that...
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