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.

View More On Wikipedia.org
Recent contents Top users
  1. N

    A 2.8-kg block slides over the smooth icy hill -- Find the minimum speed to clear the pit

  2. R

    Expression for magnitude of the constant friction force

    I approached the problem using the work done by force equation (W=F*d) In my understanding all potential energy would have been converted into kinetic energy (KE) by point P (no friciton) We know d= L ; W= Wf ; f = Ff height = (H+h) So the Energy at point P is entirely kinetic: Which translates...
  3. Z

    Is the line integral of tangential force in pendulum equal to the negative of change in potential energy?

    Consider a simple pendulum as depicted below Consider the integral $$\int \vec{F_g}\cdot d\vec{r}$$ My question is if we can equate this to the negative of a change in a potential energy function, ie ##-\Delta U##? Since ##F_g## is conservative, by the 2nd fundamental theorem of calculus...
  4. A

    B How does an object gain potential energy?

    When we are acting with some force ##F = mg## on an object of mass ##m## vertically in the positive ##y## direction, we are doing work that is equal to the work done by gravity on the same object, but of course opposite in sign. It means that net work is equal to zero, hence no change in kinetic...
  5. D

    B Conceptually understanding change in potential energy with 0 net work

    Suppose somehow an object is moving upwards with a speed ##v##, at this point I start applying a force ##F## that is equal to its weight, so the net force on the object is zero. So it will continue moving upwards with its initial speed. Suppose after the height difference is ##h##, I stop...
  6. Leureka

    I Does potential energy curve spacetime?

    Hi there, I looked around on the net but I didn't quite find the answer to my question. I preface that I don't have training in GR, even though I know about the basics (like what tensors are, geodesics, a bit about topology and differential geometry...). So I wasn't sure if to put this question...
  7. G

    Force components for mass attached to two springs

    So at first I tried to express the potential energy as a function of x, y and z, but since I'm not quite sure about the geometry of the situation, I decided to separate out the potential energy into three components: ##V_x, V_y, V_z## (I'm pretty sure this is valid because in the partial...
  8. l4teLearner

    Potential of particles moving on a circle attracted by elastic force

    I use ##l-1## lagrangian coordinates ##\alpha_1,...,\alpha_{l-1}## . ##\alpha_i## is the angle between ##OP_{i-1}## and ##OP_{i}##. As the length of a chord between two rays with angle ##\alpha## is ##d=2Rsin(\alpha/2)##, I write the potential energy of the system as...
  9. Z

    Is potential energy defined only for internal conservative forces?

    Is gravitational potential energy defined only for internal conservative forces? For reference, this is the chapter. Suppose we have two objects: object 1 and also object 2. If we consider the system to be both objects, then we can compute the work done by the pair of internal conservative...
  10. V

    How Much Explosive Force is Needed to Overcome Drag and Elevate a Car?

    Hello! Apologies if I'm missing some information but here is my thinking so far. Had the drag force not been there, the potential energy would equal the amount of energy the explosives have to disipate to get the car to that height. However, since drag force is included it makes it more...
  11. hongseok

    B Is Comparing Binding Energy and Mass to Kinetic and Potential Energy Valid?

    Can I understand the relationship between binding energy and mass by comparing it to the relationship between kinetic energy and potential energy? When an object falls, its gravitational potential, a scalar value, decreases, and its energy is converted into kinetic energy. Even when a nuclear...
  12. Lotto

    Why can we move the spring with constant speed when we apply a force?

    One solution is that if we move with the same velocity as the spring does, the initial velocity of the block will be ##v## and the final will be zero, so its kinetic energy will transform into a potential energy of the spring. I would also say that we can say that if we pull the spring, we...
  13. P

    Challenging problem about an impact with a smooth frictionless surface

    The system of two material points of identical mass connected by a rigid rod of negligible mass and length ##L## is an example of a conservation of energy problem. The initial energy of the system is the sum of the kinetic energy of the two points and the potential energy of the rod, which is...
  14. T

    Graphing Elastic Potential Energy

    Good afternoon, I have a question on graphing this problem. There seems to be something weird going on. In Excel, I set up the potential energy function (kx²/2) and plotted it from x = -0.300m to 0.300m, which looks like the following: The overall shape of the graph looks like what's...
  15. JMAMA

    Hooke's Law using Potential Energy

    Max speed occurs when all energy has been translated from spring into box. E (Potential) = 1/2kx^2 E (Potential) = (1/2)(42 N/m)(0.280 m)^2 = 1.6464 N m Ep = Ek =1/2mv^2 1.6464 N m= 1/2 (1.2 kg) v^2 v = 1.6565 m/s
  16. G

    I Different Equations of Motion for different frames

    I might be getting hooked up on this subject, but this is the last question I'm gonna ask about this. When potential energy on earth is given by ##mgy##, we know space is said to be homogeneous. If you're standing on the ground and in one case, ball is dropped from some height and then another...
  17. Lil123

    Can a sudden blow truly change potential energy?

    Why there will be no change in potential energy due to this sharp blow ? Potential energy is a function of position , so won't this position get changed due to this sharp blow?Please help!
  18. S

    I Dark energy contributing to, or modifying, mass estimates?

    I have found some papers (like this one: https://www.aanda.org/articles/aa/full_html/2009/45/aa12762-09/aa12762-09.html) which say that dark energy increases the potential energy in a system of a quasi-stationary gravitationally bound many-body system. It also says that because of this, the...
  19. P

    Filmmaker and inventor fascinated by Physics

    Hi, my question is about electricity, hydrostatic pressure, potential energy and friction. Using an electrically powered compressor (such as compressors used to fill diving bottles) if I fill a tank of volume 10 cubic meters to a pressure of 100psi, 1. what is the potential energy stored in that...
  20. AyushNaman

    I Work-Energy Theorem for Moving Block and Spring System?

    In the chapter of center of mass and linear momentum, there are multiple problems involving two block systems connected by a string, with both blocks given certain initial velocities. The goal is to calculate the maximum elongation or compression in the spring. For example, consider this...
  21. TonyCross

    Kinetic-Potential energy of moving Ice

    Hi, Am i correct in thinking that if we take a block of ice, moving at a constant velocity, it's then exposed to a heat source which melts the ice and turns it into water vapour, that we have simply removed any Kinetic energy, by Sublimation or converting it into heat. My question is does the...
  22. HighFlyer

    B Springboard physics questions for diving coach at YMCA

    I'm a diving coach at the local YMCA and I want to give a lesson regarding the physics of diving off the board with maximum efficiency. This is the type of diving board with an adjustable fulcrum, basically a lever with one end fixed with bolts. Its been almost 15 years since I've taken a...
  23. S

    I Potential energy of spin anti-alignment

    Hello everybody, I consider two electrons that have enough kinetic energy to reach their respective classical electron radius. This would be: 2.0514016772310431402e-13 J The corresponding speed is v = 287336682 m/s. The electric field is E = \frac{k_{e}}{R_e^2} = 1.8133774657059088443 ×...
  24. S

    Rate of loss of potential energy

    I got answer for (a), which is 0.51 m For (b), loss of potential energy = 35 x 9.81 x 0.51 = 175 J Rate of loss of potential energy = 175 J / 1 s = 175 W But the answer key is 80 W. Where is my mistake? Thanks
  25. Darmstadtium

    B Conversion of Potential Energy: Sound or Heat?

    When a coin is dropped from a certain height and collides with a glass surface, is the majority of the potential energy converted to sound or heat? And how would one determine this as I only hear the sound and cannot measure the significant change in temperature?
  26. Muu9

    Kinetic Energy / Potential Energy / Total Energy question

    W_ext is the external work done on B and C, which is 12 J Delta K_tot is the internal work, which is the work done by A on B plus the work done by A on C Delta K_tot = 5 Solving for \Delta U, we find that the change in potential energy is 7 J This answer says otherwise...
  27. S

    Why is the elastic potential energy in position 2 zero?

    Hello, so we have two potitions right, if we take ##\theta = 90## as the first position (i.e. both rods are flat) and then the second position at ##\theta = 0##. I totally understand the exercise, not difficult. The only issue I am having is the torsional spring... it says that it is uncoiled...
  28. mathbrain9

    Link between increase in Potential energy and the thermal energy lost

    "Heat is the transfer of kinetic energy between molecules. If the velocity is more, the kinetic energy will be more so that the heat is more." "As an object's speed increases, the drag force from the fluid increases exponentially. For example, when you drive at high speeds, the frictional force...
  29. L

    Two charged spheres hitting each other

    Since the forces involved (gravity and electric force) are conservative we can use conservation of energy. The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get...
  30. J

    Why is the height of the table not necessary to solve this problem?

    Ki + Ui = Kf + Uf 1/2)kx2 = (1/2)mvf2, but W = (1/2)mvf2 = F∆d, so 1/2)kx^2 = F∆d. The solution says that I should just substitute v as d/t. But could anyone explain why my reasoning is wrong? Thanks.
  31. S

    I Water powered funicular with equal masses?

    I found a paper (https://www.researchgate.net/publication/312123871_Introducing_a_Modified_Water_Powered_Funicular_Technology_and_its_Prospective_In_Nepal) where the authors design a funicular system powered by water but with a modification from traditional systems where apparently the funicular...
  32. M

    I Principle of Physics: Derivation of -dU/dx=F

    Hi, Everyone! This is the page(first image) from Principle of physics by resnik. I want to ask the definition of work(##W=F(x) \Delta x##) by variable force here is somewhat different from the usual integral version. I don't understand how is this valid definition? Secondly, how did they reach...
  33. A

    B Gravitational Potential Energy & Mass Change: Andrew's Question

    If I start with two, otherwise isolated, masses M and m initially together and do work to separate them then the work done, I assume, goes into the gravitational binding energy between them. Will the system of mass M and m have increased in mass due to this in accordance with e=mc^2? I...
  34. maxolina

    I Potential energy of a pressurized gas canister in space

    Suppose there is a pressurized gas canister in space, at rest. With a mass "m" of gas inside of it at a pressure "P". Next the valve of the canister is opened. The canister will accelerate in the opposite direction to the valve opening. When all the gas has left the canister, it will be moving...
  35. S

    I "A system tries to minimize total potential energy"

    While reading this thread on Stack Exchange... https://physics.stackexchange.com/questions/113092/why-does-a-system-try-to-minimize-potential-energy ... a question came to mind : - Say an object is launched away from Earth at a velocity greater than the escape velocity. This system will not end...
  36. C

    I Gravitational potential energy

    Hello everyone! I noticed in the derivation of potential energy, Mr Lewin defined the gravitational potential energy of a mass m at point P relative to a much larger mass M. He says the potential energy of m at point P is equal to the work he would have to do to move the mass m from infinity to...
  37. Delta2

    Potential energy of a sphere in the field of itself

    My attempt was to consider spherical shells of radius ##r## (##r\leq R##))and thickness ##dr## and then the potential energy of this shell would be in the field only of the "residual" sphere of radius ##r## (a result also known as shell theorem) $$U_{dr}=G\frac{\rho\frac{4}{3}\pi r^3 \rho 4\pi...
  38. warhammer

    B Difference Between Potential and Potential Energy

    In generic terms and expressions without going into specificity or nature of fields/forces in order to highlight the same, how exactly could we characterise the distinction between 'Potential' & 'Potential Energy'?
  39. Haorong Wu

    I Potential Energy in Wormholes: Charged Particles & Electric Fields

    Suppose a charged particle is in an electric field and feels an electric potential. Then the particle travels through a wormhole to another electric field and the particle feels a different electric potential. The potential energy of the particle will change. So what will that part of potential...
  40. R

    Relationship between diameter and elastic potential energy of a wire

    I think the answer is that the elastic potential energy will be a 1/16th of the original value. This is my reasoning: 1) If the diameter doubles, the cross sectional area is 4 times the original value. (from A= πr2). 2) F= stress/area. Force (load is the same). If cross sectional area...
  41. S

    I Hamilton’s principle maximises potential energy?

    Hamilton’s principle minimises kinetic energy minus potential energy, that is, with a fixed kinetic energy, Hamilton's principle maximises potential energy. What if we consider the limit that the kinetic energy or the mass/the inertia can be ignored then the lagrangian is solely the negative of...
  42. N

    The connection between potential energy and force

    Hi, if the force is the derivative of potential energy, does it mean that the force is equal to mg and with a constant gravity, it will be the same at any height? But in real life, F (or mg) would be different on the Earth's surface and 400 km above it (~8 m/s^2). So, this formula is used to...
  43. T

    I What is the relationship between force and potential in particle interactions?

    Suppose I have some interaction potential, u(r), between two repelling particles. We will name them particles 1 and 2. I want to find the force vectors F_12 and F_21. Would I be correct in saying that the x-component of F_12 would be given by -du/dx, y-component -du/dy etc? And to find the...
  44. C

    B Potential energy and lifting an object vertically

    So the potential energy of an object in a gravitational field is pe=hmg where h is the height of the object in the gravitational field in meters m is the mass in kilograms and g is the acceleration in meters per second per second I read on an answer to a question that the force to lift an...
  45. MarkTheQuark

    Spring-mass system with a pendulum using Lagrangian dynamics

    I'm stuck in a problem of a spring mass system with a pendulum attached to it as showed in the figure below: My goal is to find the movement equation for the mass, using Lagrangian dynamics. If the spring moves, the wire will move the same amount. Therefore, we can write the x and y position...
  46. C

    A rocket on a spring, related to potential/kinetic energy

    Part A) So from a force diagram we can see that the only two forces acting in our system are the spring force(positive y axis) and the weight of the rocket(negative y axis), which means the spring force is equal and opposite to the weight force. The weight is simple enough ##12* 9.8=117.6N##...
  47. C

    Power required to climb a 20-m-tall building in 55s

    Summary:: A 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying 40kg of gear. How much power does he need to reach the top of the building in 55s. So first the total mass of our system is 130 kg. Using this mass, I found the potential energy the firefighter would...
  48. V

    B How is capacitor energy the same as electrostatic potential energy?

    The energy stored in a capacitor is derived by integrated the work needed to move charge dQ from one plate to another. I'm confused on how this energy is the same as electrostatic potential energy, the energy needed to assemble this configuration from infinity. In the case of capacitor energy...
  49. J

    Find largest potential energy difference between 2 loop orientations

    I thought the largest PE difference would be when the loop's area vector is in the same direction as the magnetic field, hence cos(0) =1, minus when the loop's area vector in perpendicular to the field, cos(pi/2) = 0. Just plug in the variables and you get 0.126 joules. Did I make a mistake?
  50. J

    Find the Potential energy of a system of charges

    There are six pairs. three turn out to be negative and three turn out to be positive (3q^2 - 3q^2) which nets zero when you add them together with the equation. But zero was the incorrect answer. Did I do something wrong? Thank you
Back
Top