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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On the connection between forces and the principle of stationary action

Feynman tries to account for the relation between the principle of stationary action, which is a statement about the whole path of a particle, and Newton's second law, which is a statement about the ...
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25 views

Slingshot Energy into traveled distance [on hold]

If I have a slingshot and I am told that when pulled it has about $E$ joules of energy, how do I compute the height at which an object of mass $m$ would travel if the slingshot is released in the ...
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Of the two variables (Q and V) in the equation of capacitor energy, which is better to take the average of?

$U_c = \frac{1}{2}QV$ I understand from the graph which it should be one half but not quarter, or taking the average of both. But it doesn't really matter to me which variable is on y or x axis? ...
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What is the definition of potential energy? [duplicate]

I have problems with this equation: $$U_G ~=~ G\frac{m_1m_2}{r}.$$ It's for potential energy of say something placed on Earth. But it intrigues me. $r$ is the distance from the very center of the ...
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56 views

Why is the equation for electric potential energy so counter-intuitive?

The equation: $U_E = Vq$ or $(Eq)d$. This works the same way as the equation for gravitational potential energy: $mgh$ But to me, for charges of different signs, the potential energy also varies. ...
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Approximate Electric Potential $V$ so that it is of the form $V(r) + V(\phi) + V(z)$

I'm trying to simulate the conductivity of a nanowire that is modeled by a cylindrical shell of infinite potential with benzene rings in the core of the wire. (This is based on a coiled-coil protein ...
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Can the electric potential corresponding to the negative plate ever be equal to anything bigger than zero?

I am doing my homework. I read my textbook. It says that the negatively charged plate is the low potential plate. It also shows a example of lower plate equal to 0V, I guess for simplicity. But what ...
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31 views

Potential Energy of two rolling cylinders [closed]

I want to get the Lagrangian of a System of two cylinders, the smaller (mass $m$ and radius $r$) rolling on the bigger one (radius $R$). There is a solution, which tells me, that ...
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71 views

A little confusion in the derivation of potential energy of a shell

This is a paragraph and a figure from The Feynman Lectures, He's trying to prove the Shell theorem for gravity: If we rearrange $dm=2\pi y \mu ds$ we obtain $\dfrac{dm}{2\pi yds}=\mu$. In this ...
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How does The work done in going around any path in a gravitational field is zero implies conservation of energy?

In The Feynman Lectures, Feynman states: The work done in going around any path in a gravitational field is zero. This is a very remarkable result. It tells us something we did not previously ...
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If systems minimize their potential energy, why do people climb mountains?

A person climbs a mountain. They convert the stored chemical energy of food in their body and back pack into heat energy on the mountain, and gravitational potential energy as they move towards the ...
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A confusion regarding an example in The Feynman Lectures

In The Feynman Lectures, In the chapter entitled Work and potential energy, Feynman states: The work done in going around any path in a gravitational field is zero. This is a very remarkable ...
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does $Q_AV_{AB}=Q_BV_{BA}$ in this case

Sorry fo unclear title but I can't find any suitable on for this question. Here is what my text book says about how to find out the energy of a system of charge of n particle. What I don't know is ...
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What is an effective potential in classical mechanics?

What is an effective potential in classical mechanics? I have read the wikipedia article and David Tong's lectures notes, but I didn't understand how an effective potential simplifies a situation or ...
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237 views

Why is $F=-\nabla V$?

I came across this equation $$F=-\nabla V$$ where $V$ is potential energy. I do understand that $$F(r)=-\frac{dV}{dr}.$$ Hence does this mean the nabla operator in this case means derivative? Because ...
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Derive frequency given potential using Newton's laws

A mass with mass $m$ has a potential energy function $U(x)$ and I'm wondering how you would find the frequency of small oscillations about equilibrium points using Newton's laws. I started by finding ...
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68 views

Deriving gravitational potential energy using vectors

Here is my attempt at derivation: First you must find a vector function for the gravitational force. By the inverse square law, the magnitude of gravitational force between two bodies of mass $m$ ...
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What is the meaning of this definition of potential energy?

The isolated system of particles is being observed. In the coursebook, $\vec F_\mu$ is by definition the vector sum of forces of all other particles acting on $\mu$-th particle. Usually, potential ...
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66 views

Hooke's Law Problem [closed]

This question assumes that the spring obeys Hooke's law. Say we have a spring Length $L$. The energy of said spring when extended will be $E=(kx^2)/2$. The extension $x_1$ of said string would be ...
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What is the binding energy in General Relativity?

In general relativity, the potential energy is given by $$V(r)=\frac{h^{2}}{2r^{2}}\left(1-\frac{2M}{r}\right)-\frac{M}{r}.$$ Solving $V^{\prime}(r)=0$, there are two points where circular orbits ...
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Feynman Lectures: Why a non-reversible weight lifting machine cannot lift higher that a reversible one?

Consider weight-lifting machines—machines which have the property that they lift one weight by lowering another. Let us also make a hypothesis: that there is no such thing as perpetual motion ...
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Definition for potential energy

I came across this definition for potential energy: If we let $T$ be the Kinetic energy, we have that: $$T = \frac{1}{2}mv^2 \implies T = \frac{1}{2}m{x'}^2$$ $$T'= mx'x'' = F(x)x' \implies \\T = ...
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Differential form of the law of gravitation potential

I have problem understanding transaction (operations and methods applied) for one equation to other equation. It is about gravitational potential. $${\vec F_{grav}=\frac{GMm_{obj}\vec R}{R^3}}$$ If we ...
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Is the Einstein Energy-Momentum equation $E^2 = p^2c^2 + m_0^2c^4$ valid only for Free Particles?

Is the energy -momentum relation $$E^2 = p^2c^2 + m_0^2c^4$$ satisfied only by free particles or even bound particles? Does the Energy refer to total Energy(including potential) or only (kinetic ...
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Electrostatic potential due to two charge system

When we calculate electric potential energy of a two particle system, say first I bring $+q_1$ and then I bring $+q_2$ against $q_1$'s electric field. Say I get that $q_2$ charge to a point $r$ ...
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Why is a conservative force defined as the negative gradient of a potential?

I'm learning about work in my dynamics class right now. We have defined the work on a particle due to the force field from point A to point B as the curve Integral over the force field from point A to ...
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Resistance and potential difference across it

I have this question that has baffled me for hours now. My question is what really happens when charge passes from one point to another in a circuit for eg what happens when it passes over a ...
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Sign of an electric field in electric potential energy problem

I was wondering why the electric field E in this problem is negative. Is it because the earth is negative? We can assume that near the Earth’s surface, a uniform electric field is set up thanks to ...
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Turning points of particle

A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential: $$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$ Determine the ...
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Why is intermolecular potential energy given in 'per mole'?

I was just wondering that if intermolecular potential is the interaction potential energy of two atoms/molecules, then why do we give its value in J/mole? I don't understand why 'per mole' ...
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Proof that oscillations in 1d potential well occur between certain points

In >>this<< situation, a particle with energy $E$ will oscillate between the positions $x_1$ and $x_2$ indicated on the diagram. This simple fact is taught in many introductory courses however I ...
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Change in Potential energy moving toward line of charge

I'm analyzing the energy involved with charges moving in an electric field and I'm getting caught up here and I must be missing something. So given that an infinitely long line of charge produces a ...
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Can KE and PE of a small element of a transverse progressive wave be maximum simultaneously?

Maybe a string can be taken as an example to produce the transverse progressive wave.
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A captious work problem: same paths but same forces?

A man jumps onto a chair. A man climbs onto a chair by putting a leg first and then the other. In both cases, the work has been the same. TRUE or FALSE...? Spoiler!: The path is the same, so the ...
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What makes an orbit stable or unstable?

I have an assignement, where I have a given central potential $V(x)=-\frac{K}{6r^6}$ and object with an angular momentum $L$. I've calculate the radius of a circular orbit, which I've done by ...
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How to calculate the period of the movement from a potential?

I have an assignment, where I have an object moving in 1-D with a given mass and energy, and the potential V(x), and I'm supposed to calculate the period of the movement as a function of the energy ...
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Gravitational potential difference

in my revision guide it defines gravitational potential difference as: The gravitational potential difference is work done in moving a unit mass. It then goes on to explain the gravitational ...
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Positions and corresponding terminology of “acoustics energy”?

From limited knowledge, decades ago, dating back to the nineteenth century: Ohm's law of specific acoustic energies was the first biological application of Fourier's theorem. Actually, it was ...
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Gravitational field strength and potential different signs

In my revision guide the gravitational field strength is given as $g=GM/r^2$ whereas gravitational potential is $V=-GM/r$. Why does potential have a minus sign but field strength doesn't?
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Graph of electric potential

In my AP physics guide the graph for electric potential (for a radial field, i.e. point charge) and gravitational potential (for radial field, i.e. point mass) slightly differ from each other and I ...
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Potential Energy of a Molecule

A generic problem asks that we find the total potential energy of a water molecule. Potential energy is given by $\Sigma \ kQ_{1}Q_{2}/r$ where $Q_{1}$ and $Q_{2}$ are the charges of any one bond ...
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The amount of potential energy at the height of h [duplicate]

When we lift an object upwards with a constant velocity for a distance of $ h $ the work that we've done is $mgh$ and the work done by the force of gravity is $-mgh$. So the net work on the object is ...
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Total Energy of Inverted Pendulum

I have to find the total energy $V$ of an inverted pendulum (rod). The following parameters and their values are given: Mass $m$ and length $l$ of the pendulum $\theta$ as the angle of the ...
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Derivation of Interaction energy of Dipole - Induced Dipole Interaction

I see that the formula giving the potential (interaction) energy of a dipole and an induced dipole is $$V=-\frac{C}{r^6}$$ where $$C=\frac{\mu_1^2 \alpha'_2}{4 \pi \epsilon_0}$$ and that the formula ...
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What is the difference between the potential $V$ and the effective potential $V_{eff}$?

What is the difference between the potential $V$ and the effective potential $V_{eff}$? Some times when solving problems, an effective potential $V_{eff}$ is defined and its usually equal to the ...
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How did Feynman prove that energy cannot be extracted from electric field?

In the Feynman Lectures, vol. II, chapter 4, Feynman discusses electric potential and says: If we carry a charge from point $a \to b$, $$W = -\int_{a}^{b} \mathbf{F} \cdot ds.$$ Now, in general, ...
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Is potential energy an energy exists or potentiality of energy? [closed]

I want to ask whether Potential Energy is truly existing Energy - though i know the energy concept is abstract and we do not know what is energy truly as Feynman said - or it is the potentiality that ...
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Susceptibilities and response functions

It is often confusing whether a susceptibility is the same as a response function, specially that often they are used interchangeably, in the context of statistical mechanics and thermodynamics. Very ...
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79 views

Are black holes an infinite source of energy? [duplicate]

Black holes are considered particularities because in a determined point in time they are pointless, as consequence there are some mass in a null space so the density become infinite. Finally if ...
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Why should Conservative forces have their curl equal to zero?(intuition)

There are several conditions that must be met in order for a force to be conservative. One of them is that the curl of that force must be equal to zero? What is the physical intuition behind this? If ...