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Questions tagged [potential-energy]

Potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system.

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Why are there no potential operators that are non-diagonal in position basis?

The potential energy operator in the Hamilton operator can be expressed in the following way $$ \begin{aligned} \hat V &=\int dx\int dx'|x \rangle\langle x|\hat V|x'\rangle \langle x'| \\ &=\...
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The Lagrangian for gravitational potential energy in a double pendulum

For a double pendulum what would be the gravitational energy. I am trying to work out the Lagrangian for the double pendulum. I got the kinetic energy but I am struggling on the gravitational ...
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Elastic potential energy

Elastic potential energy derivation For a string ...
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Electric potential in circuits

From what I understand from my notes, an e.m.f or electromotive force provided by a battery is the electrical energy per unit charge converted from other forms of energy required to drive a unit ...
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Simplified computation of matrices for normal modes?

In normal modes, we often refer the total potential energy of the system to be: $$V = q^T B q$$ where $V$ is the total potential energy, $q$ is the coordinates of the system and $B$ is just some ...
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In the tunnel through the Earth thought experiment, how does total energy of a particle vary when it goes from surface of the Earth to its center?

In the typical tunnel through the center of the Earth thought experiment, a particle at the surface would oscillate between the two diametrically opposite points ignoring the rotation of the Earth. ...
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What is the relativistic energy of a bounded static particle?

Premise: The speed of light is set $c = 1$. Let's consider an electron in an external electromagnetic field. Its four-momentum will be $$p^{\mu} = (E, \bar p) = (\gamma m_e, \gamma m_e \bar v),$$ ...
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Clarification on electric potential energy

From what I understand from my notes (correct me if I'm wrong), electric potential energy is the work done in bringing the charge from infinity to a certain point from the source charge. Let this ...
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Conservation of mechanical energy proof (Kleppner Kolenkow)

On page 168 of Kleppner and Kolenkow's mechanics they give a proof of the conservation of mechanical energy theorem which starts roughly as follows: The work done by a conservative force depends only ...
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What is the resultant force acting upward on the point of contact under an elastic deformation?

The situation here is you have an elastic string (or a rubber band) fixed at two ends A and B. A•-------------------------------------------------•B An object is ...
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Charged Particle in Magnetic Field

For a charged particle in circular motion in a magnetic field, is there any potential energy involved? If yes, how do we calculate it? If no, i.e. the entire energy is kinetic, how do we know when ...
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Is this understanding of potential energy correct?

I am studying basic mechanics and have reached the chapter on potential energy. However I am a bit confused about the difference between potential energy and the formula for the potential energy due ...
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What does the external work done signify?

When a point charge is moved from one point say A to another point B in an electric field, then the work done by the field is stored as potential energy but what about the external work done? ...
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Why electric potential requires absence of acceleration?

As of 28/05/2019, Electric Potential is defined in Wikipedia in the article with the same name as: The amount of work needed to move a unit of positive charge from a reference point to a specific ...
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Why the work done by system not stored as potential energy?

Now choose a spring mass system now work done by external agent in slowly moving from equilibrium position is stored as potential energy but where is work done by spring force gone.For genralization ...
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How do conservative forces conserve mechanical energy?

A force that conserves mechanical energy is known as a conservative force. Question: How do conservative forces conserve mechanical energy?
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Why there is a negative sign in the formula of calculating work done in electrostatics?

$$W = - \int _ { a } ^ { b } \vec { F } \cdot d \vec { r }$$ ( from The Feynman lectures on physics vol. 2, new millennium edition, page 4-4) In this formula why there is a negative sign in the ...
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Self-energy of conducting shell

While calculating self energy of a conducting shell we integrate $Vdq$,where $V=\frac{q}{4π\epsilon r}$, but when the $dq$ charge is bought close to the shell it changes the charge distribution on the ...
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Can someone explain how magnetic potential energy can exist even though the field is non-conservative?

$U=-B\cdot \mu$ is defined to be the magnetic potential energy, I saw this in my lecture notes, but we had already talked about the fact that since the work done to move a charge there is path ...
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$\Delta K=\Delta U$ vs $\Delta K = -\Delta U$

While doing physics homework, I noticed that in some problems, the change in kinetic energy(KE) is equal to the change in potential energy(PE), even though I learned that conservation of energy shows ...
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Is the total mechanical energy conserved in a system that's a simplifying approximation of an actual roller coaster?

Suppose you have a 2-dimensional Euclidean space where one dimension goes left and right and the other dimension goes up and down where one of the units of length is the meter. Furthermore, suppose ...
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Meaning of “a force that derives from potential energy”

In mechanics course, when the idea of equilibrium was introduced they included the idea of a force that derives from potential energy which is the force $F$ which is related to the potential energy $...
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Branching ratios for alpha decay into a rotational band

I want to understand the $\alpha$-decay of $242$-Curium to different excited states of $238$-Plutonium (image taken from Introduction to Nuclear Physics page 258; Author: Krane): I'm interested in ...
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Work done by battery?

Why the work done by a battery is Q*V where V is emf of battery and Q is charge that is made to flow in circuit?please explain detail? explain and write the formulas
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How can differentiating a scalar like potential energy functions give a vector like field strength functions?

Just wondering if anyone had a good explanation of how differentiating a scalar can give rise to a vector quantity.
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The work due to friction given an influential force

Statement: I am trying to work through Chapter 8, Problem #70 of OpenStax University Physics Volume 1 and I cannot figure out what I'm doing wrong. The problem statement is as follows: A particle of ...
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Energy density in electrostatics - definition [closed]

Background: It can be shown that the potential energy of charge distribution can be calculated by $U = \frac{1}{2}\int_V \rho(r')\Phi(r') d^3r' $ by means of integration by parts and the poisson ...
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How to calculate the gravitational binding energy of a uniform cube of length $L$ and mass $M$?

The functional form is known already (as attached). But what is the solution for this integral?
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Work done and change in mechanical energy

I have a hard time understanding the equation $W_{Driving} +W_{Friction} = \Delta E_{mechanical}$ Is there any derivation of it?
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Work and energy - explanation of definition [duplicate]

I have a question about the definition of energy. the definition is "ability to do work". what does it mean? what is the ability that the definition talks about? what is the meaning of ability in ...
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What is the error in the potential energy calculation of an elongated rod (if any)?

When we calculate the energy stored in the rod after elongation by an external force, we only consider longitudinal expansion. My question is that according to Poisson, there is also a sideways/...
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Electric Potential: Building system of point charges

How can we prove that the amount of work we have to do to build a system of point charges is same , whether we place the point charges one by one or all at once
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Why is force 0 either side of an inflexion point in neutral equilibrium?

In Tipler & Mosca 5th edition p173 it defines neutral equilibrium as a point in a U-x curve where $\frac{dU}{dx}=0$ and also $\frac{dU}{dx}=0$ for a small displacement either side of the point. ...
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How is voltage (potential difference) like gravitational potential energy? [closed]

How is voltage (potential difference) like gravitational potential energy? What are their similarities
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Can all fields contribute to the potential energy that appears in QM Hamiltonian?

Most importantly: can that potential energy in the QM Hamiltonian able to describe the motion of a single particle in an external electromagnetic field? Background: In non-relativistic QM using the ...
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Direction of $d\mathbf{l}$

A solid sphere has charge $q$ and radius $R$. Find the potential at a point a distance $r$ from the center of the sphere where $r>R$, using infinity as the reference point. My attempt: From Gauss'...
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Sign in $\Delta U= -\int\vec{F}\cdot d\vec{l}$

So I have been trying to understand why there is a negative sign in the following$\Delta U= -\int\vec{F}\cdot d\vec{l}$ I wanted to try to understand it by trying to derive the gravitational ...
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Increased mass of compressed springs [closed]

Based on the idea that mass is an emergent property of fundamental particles with potential energy bound in a restricted space, I want to make a macroscopic analogy. I want to put compressed springs ...
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Infinite field but finite potential Is it possible?

I calculated the electric potential at any point (assuming zero potential at infinity) on the circumference of a uniformly charged ring (non conducting) and after evaluating that integral it turns out ...
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Two different solutions for the expression of potential energy of a uniformly charged solid sphere [closed]

I am a bit confused because I did some rigorous derivation of potential energy of a uniformly charged solid sphere and got two different solutions.(Sorry for the long exercise) Now have a look at my ...
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Change in Energy when placing an object on the ground

It seems like a simple question but I was wondering where does the energy go when I place an object from a height on the floor. Initially it's all stored as potential energy, and as I'm moving the ...
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Is external force equal to restoring force [duplicate]

I have reached a confusion. We know $$F=-kx$$ in a spring. If an external mass $m$ is suspended to a spring and the spring extends by a length $x$ and the mass comes to rest, external force, $~mg = \...
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At infinite separation do charges get kinetic energy?

When charges are infinitely separated, the potential energy is reduced to zero. As we know that loss in potential energy is nothing but the gain in kinetic energy . So do charges start flowing at ...
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How Do I Calculate the Potential of System?

I was doing my homework when I came across this question: Three equal point charges, each with charge $1.40 \, \rm\mu C$ , are placed at the vertices of an equilateral triangle whose sides are of ...
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Gravitational potential energy of an isothermal sphere

I am trying to calculate the gravitational potential energy, W, defined as: $W = -\frac{1}{2}\int\rho(r)\Phi(r)d^{3}r$ for an isothermal sphere. I am given that the density profile varies with r as:...
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Gravitational potential of an infinite plane

In this link http://www.feynmanlectures.caltech.edu/I_13.html#Ch13-S4 , Feynman first computes the gravitational field generated by an infinite plane of constant density, and then he computes the ...
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Nonlinear GPE of a solid block seems wrong

I am trying to calculate the gravitational potential of a solid block, and I have a nonlinear answer which strikes me as wrong. A block with horizontal surface area $A [m^{-2}]$ and uniform density $\...
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Why is there no negative sign in the formula of work against electric field?

Why is there no negative sign in the first formula of work done against electric field where as second formula below has it?
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Vector calculus simplification in calculation of generalized force

Consider a system of $N$ particles subject to forces $\vec F_i\ (i=1\dots N)$ that derive from a potential $V$. My lecture notes propose a simple proof that $$Q_j = -\frac{\partial V}{\partial q_j}$$ ...
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What exactly makes negative energy negative?

Antimatter is the opposite of matter since it has opposite electric charge (e.g. proton -> positive whilst anti-proton -> negative). So what exactly makes negative energy negative? What property does ...