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

    What Materials Cannot Use the Electric Potential Energy Law?

    my professor has explained Electric potential energy Law U=∫D*E above all the space. he said you can not use for some kind of materials. l can 't remember if they are Ferroelectricity or piezoelectric materials. then can you say to me the reason too? thank you
  2. B

    Find the potential energy function

    Homework Statement 1. Given F = -2 N/m^3 ( (2xyz - z^3)i + x^2z j + (x^2y - 3xz^2)k ). a. Find the potential energy function for this force, taking (i + 2 j + k) m as reference point. b. Find the work done by this force on a 4-kg block moved from the reference point to the origin. c...
  3. B

    When to Use Kinetic vs. Potential Energy: Explained

    Can someone explain to me when you use 1/2mv^2-mgh as opposed to 1/2mv^2 or mgh
  4. G

    Definition of potential energy

    Why is change in potential energy is defined as PE1 - PE0 = -W I mean I could see it for example for gravity if we took PE0 to be zero at ground and we integerated -mgy(y^) we get -mg(y0 - y1) -> -mgh,but is their a proof somewhere where it shows it will be always negative work ? Thank you.
  5. B

    Potential Energy Functional - Timoshenko Shear Locking

    Folks, The total potential energy functional for an isolated finite element timoshenko beam is given as ## \displaystyle \Pi_e(w, \Psi)=\int_{x_e}^{x_{e+1}} \left[ \frac{EI}{2} \left (\frac{d \Psi}{dx}\right )^2 + \frac{ G A K_s}{2} \left ( \frac {dw}{dx} + \Psi \right )^2 +...\right]dx...
  6. S

    What is magnetic potential energy?

    We know that a Magnetic field does no work. Then how does an inductor store energy (1/2 LI2)? When that stored energy is needed, it can be retrieved back and clearly it can be used to do some work. In a fix here.
  7. L

    Gravitational potential energy, orbital speed, binding energy.

    Homework Statement a satellite having a mass of 1800 kg orbits the Earth at a distance of 6.3 x 10^5 m above the surface find the gravitational potential energy of the satellite while in orbit, the orbital speed and the binding satellite. The Attempt at a Solution gravitational potential...
  8. L

    Change in gravitation potential energy in space

    Homework Statement an object of mass 750 kg is lifted from the Earth's surface to a height of 6.8 x 10^6 m above its surface. Calculate the change in gravitational potential energy for the object. The Attempt at a Solution I used this formula ΔEg = Eg2 - Eg1 ΔEg = -(GMm/r2) -...
  9. J

    Quick question regarding kinetic energy, potential energy and velocity.

    Ok so I have got the right answer to my calculation however I do not understand part of it, here is the question... Q2: The rollercoaster car from Task 1 Q2 above is initially traveling at 6.5m/s at point A in the diagram below. Assuming negligible frictional forces as previously, what will...
  10. L

    Gravtational Potential Energy

    Homework Statement 9. What is the total energy needed to place a 2.0 x 10^3-kg satellite into circular Earth orbit at an altitude of 5.0 x10^2 km? 10. How much additional energy would have to be supplied to the satellite in question 9 once it was in orbit, to allow it to escape from...
  11. C

    Gravitaional Potential Energy help, please

    Homework Statement Four uniform spheres, with masses mA = 350 kg, mB = 600 kg, mC = 1500 kg, and mD = 300 kg, have (x, y) coordinates of (0, 50 cm), (0, 0), (-80 cm, 0), and (40 cm, 0), respectively. Sphere A is then removed. (a) Calculate the gravitational potential energy of the remaining...
  12. D

    Question about vibrational kinetic energy and potential energy.

    Homework Statement You hold up an object that consists of two blocks at rest, each of mass M = 3 kg, connected by a low-mass spring. Then you suddenly start applying a larger upward force, of constant magnitude F = 94 N (which is greater than 2Mg). Some time later, the blocks have moved...
  13. L

    Calculating Energy Transfer and Work Done by a Crane

    Homework Statement A creane lifts a 1500 kg car straight 20 m [up] How much potential energy does the car gain? How much energy does the crane transfer to the car? How much work does the crane do? The Attempt at a Solution How much potential energy does the car gain? Eg = mgh Eg =...
  14. A

    Work done by a spring & its potential energy

    According to work - mechanical energy theorem , W = K(final) - K(initial) + U(final) - U(initial) . . . . (1) as we define Potential energy as negative of work done by conservative force and assuming that the only force in this situation is Spring force then , W(spring) = K(final) -...
  15. J

    Finding Force from the Potential Energy

    Homework Statement Click to make larger Homework Equations -du/dx = F (in x direction) The Attempt at a Solution Would I have to use system equations to estimate a cubic equation, and just take the negative derivative of it? Cause it turns out to be a mess and I end up getting a...
  16. Seydlitz

    Potential Energy of an electron in a parallel plate capacitor

    Homework Statement What is the potential energy of an electron in a parallel plate capacitor if kept on the negative plate before being released? Homework Equations 1/2mv^2 = qV = PE Capacitor Energy = 1/2QV The Attempt at a Solution 1/2mv^2 = qV = PE However if I'm not mistaken there's...
  17. N

    Potential & Kinetic Energy of Revolving Object (e.g. Moon)

    So let's consider the moon its rotating around the Earth in a fixed orbit, its moving at a velocity say v so it possesses a kinetic energy 1/2 mv2 . the gravitational force between the Earth and the moon is also present which attracts the moon towards the Earth . My question is does the moon has...
  18. B

    How Do You Solve Potential Energy When No Height is Given?

    Homework Statement how do you solve potential energy when no height was given? Do I just do gravity times the mass to get it? Homework Equations The Attempt at a Solution
  19. E

    Work Energy Theorem and Potential Energy violation?

    I came across a rather confusing topic about Work Energy Theorem and Potential Energy applied in lifting a particle.I will be glad if anyone clears it for me. Consider a particle at a height =0.Potential Energy is considered as zero at height=0.Now it is lifted to a position where height is h...
  20. N

    Energy of H Atom in 1st Excited State - 23.8 eV

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  21. L

    Find Max Potential Energy per Unit Length of Wire

    Homework Statement A wire is fixed at both ends vibrating fundamentally. For what value of x (x position on the wire, with 0 being one edge and L being the other) is the potential energy per unit length has the maximum value? Known: Length of wire (L), Tension in wire (T), Mass of wire (m)...
  22. S

    Need help with graphs of potential energy and force

    Hi everyone! Homework Statement The potential energy U of a point mass is U(x)= Uoxo x/(x2 + xo2) where Uo and xo are positive contants, Uo in joule and x,xo in meters. Draw the graphs of U(x) and F(x). Homework Equations F(x) = -dU/dx The Attempt at a Solution I found the F(x) function...
  23. I

    Elastic potential energy - springs

    I know this problem has been asked before but i am trying to understand. Homework Statement A 2.00-kg block is pushed against a spring with negligible mass and force constant k = 400 N/m, compressing it 0.220 m. When the block is released, it moves along a frictionless, horizontal surface and...
  24. K

    Potential Energy in a vertical spring mass system

    Homework Statement A mass of 0.5 kg hangs motionless from a vertical spring whose length is 0.90 m and whose unstretched length is 0.45 m. Next the mass is pulled down to where the spring has a length of 1.15 m and given an initial speed upwards of 1.4 m/s. What is the maximum length of the...
  25. A

    Calculate the change in gravitational potential energy

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  26. D

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  27. F

    Potential energy and electric potential

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  28. R

    Why why why is Potential Energy equal to Kinetic Energy in this problem?

    Why why why is Potential Energy equal to Kinetic Energy in this problem?? A 31.0 kg child on a 3.00 m long swing is released from rest? when the ropes of the the swing make an angle of 28.0° with the vertical (a) Neglecting friction, find the child's speed at the lowest position.____m/s...
  29. U

    Find potential energy function and show that it is proportional to displacement

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  30. N

    Gravitational Potential Energy - Orbits

    Homework Statement A satellite is in a circular orbit 655km above Earth's surface. Determine the magnitude of the gravitational acceleration at this height. Homework Equations Eg=mgh Eg=-GMm/r The Attempt at a Solution Would I just set the aforementioned eqations equal to each...
  31. E

    Electrostatic potential energy of a nonconducting sphere

    Homework Statement Determine the total electrostatic potential energy of a nonconducting sphere of radius r0 carrying a total charge Q distributed uniformly throughout its volume. Express your answer in terms of the variables Q, r0, and appropriate constants. Homework Equations V = kQ/r...
  32. J

    Potential energy in nuclear energy

    Where does the potential energy go if you carry uranium to a nuclear power plant on the top of a mountain and part of its mass becomes energy?
  33. H

    Potential energy of a dipole point and point charge

    Homework Statement A point dipole p is at the origin of coordinates, while a point charge q is at position r. Calculate the potential energy U of this system in two ways (a) by treating the dipole as a source and q as a test charge in the dipole field (b) by treating the dipole as a...
  34. N

    Sketching this function for potential energy of two atoms in a molecule

    Homework Statement The potential energy of two atoms in a molecule can sometimes be approximated by the Morse function, where r is the distance between the two atoms and A, R, And positive constants with S<<R. Sketch this function for 0<r<∞... ##U(r) = A ( (e^{(R-r)/(S)}-1)^2 - 1) ## This is...
  35. L

    Potential Energy problem help

    If I have a mass m1 sitting on an incline plane attached by a rope and a pulley to another mass m2 hanging off the incline plane, what would be the potential energy? I was thinking that m1 only plays a role on the potential energy.
  36. S

    Kinetic and Potential Energy with acceleration

    Homework Statement A 4-kg mass is launched with zero initial velocity on a frictionless circular track. The speed of the mass at point 1 is 20 m/s (base of the curve). The mass then travels along a rough horizontal surface between points 1 and 2 (L-4m, μk=0.3). It then travels up a...
  37. A

    Potential Energy - Work Done etc

    Please help me to solve the following question... I am really stuck. 1. Two children of mass 40 kg and 50 kg are holding on to the ends of a rope which passes over a thick horizontal branch of a tree. The parts of the rope on either side of the branch are vertical and the heavier child is...
  38. C

    Finding Force Given Potential Energy

    Now let me start off by saying that I, along with over 100 students in my class are having issues with this concept, thanks to our "amazing" professor, while our midterm exam is a few days away. I don't want to sound like I am complaining, but I am frustrated with the fact that the professor...
  39. D

    What Differentiates Work Done by a Spring vs Work Required to Stretch It?

    Homework Statement What is the difference between "the work required to stretch a spring" and "the work done by a spring"? Homework Equations Fdx = dW F (from the spring)= -kx so, F (from me) = kx The Attempt at a Solution I have tried and I found out the work required to stretch a...
  40. C

    Taylor series expansion for gravitational potential energy. GMm/r=mgh near the earth

    Using taylor series expansion to prove gravitational potential energy equation, GMm/r=mgh at distances close to the earth. R= radius of the Earth h= height above surface of the Earth m= mass of object M= Mass of the earth U = - GmM/(R + h) = - GmM/R(1+ h/R) = - (GmM/R)(1+ h/R)^-1 do a...
  41. M

    Does everything have potential energy?

    Do all physical objects at rest or in motion have PE?
  42. M

    Potential energy, Is energy a constant scalar value?

    Hello everyone, Does everything in the universe have potential energy? I know there are two main form's of energy that are showen every day... Motion KE and potential energy and I believe all physical object's have PE and some are in KE even if they lose that motion they will return back to PE...
  43. S

    Potential vs. Potential energy

    I was reading electrostatic and found out that the electric field is just the negetive divergence of potential . My questions are why are we taking the negetive divergence ? Electric field is a conservative field and so it can be written as divergence of a scaler function but why we ar taking...
  44. D

    Gravitational potential energy near the earth

    I am a bit confused about gravitational potential energy near the earth, namely the formula given by mgh. I know that potential energy is defined as U(x) = -W(x0 to x) where x0 is our chosen reference point. Let's take the Earth's surface as the zero point and let's travel upwards to a point...
  45. B

    Force and potential energy function

    Homework Statement A single conservative force acting on a particle within a system varies as = (− Ax + Bx5) N, where A and B are constants, is in Newtons, and x is in meters. (a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (Use any...
  46. V

    Elastic potential energy of vertical spring

    help is urgently needed please and thank u. 1. When a 13.2-kg mass is placed on top of a vertical spring, the spring compresses 5.93 cm. Find the force constant of the spring. 2. If a spring has a spring constant of 400 N/m, how much work is required to compress the spring 25.0 cm from...
  47. P

    Question regarding electrical potential energy required to assemble a system

    Homework Statement Four charges, q1=+q, q2=-q, q3=+q and q4=*q are at the corners of a square with the side a=7.5 cm. (In such way that if one travels along the perimeter of the square, the charge signs are alternating.) If q=3.0 μC, what is the total energy required to assemble this system of...
  48. M

    Finding force from electric potential energy using gradients.

    Homework Statement In a certain region, a charge distribution exists that is spherically symmetric but non-uniform. When a positive point charge q is located at (r,θ,φ) near this charge distribution, there is a resulting electric potential energy for the system given by: U(r,θ,φ) =...
  49. C

    Potential Energy, Springs, and Friction

    Homework Statement A block of mass m rests on a plane inclined at an angle θ with the horizontal. A spring with force constant k is attached to the block. The coefficient of static friction between the block and plane is μs. The spring is pulled upward along the plane very slowly. What is the...
  50. S

    How Can Nuclear Energy Be Modulated in Reactors?

    Electric charge is an example of a form of energy whose energy potential we can readily and conveniently manipulate, to modulate its state, to make it go up and down cyclically. What is the most dense form of energy whose energy potential we can quickly manipulate or modulate? I'm talking...
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