# 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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### Energy stored in an object in spring

Suppose we have a vertical spring of spring constant $k$ and an object of mass $m$ is tied to it. If we stretch the object by a distance $x$,the work done by the restoring force is $\frac{kx^2}{2}$ ...
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### Discrete Spectrum vs Continuous Spectrum and Bounded, Scattering States

Apolgies in advance if this is a confusing ramble and multitude of questions, I'm not quite sure how to articulate myself. I am currently reading up on quantum mechanics and seem to have confused ...
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### Proof of principle of stationary action when the Lagrangian is not $L=T-V$

The principle of stationary action claims that the action $S$ takes a stationary value in a real system, where: $$S = \int_{t_1}^{t_2} L dt\tag{1}$$ and $L$ is the Lagrangian of the system. It can be ...
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### Velocity- and time-dependent forces can not be conservative [duplicate]

I have already seen many posts about this specific question but in only a few of those mathematically rigorous answers were given. Unfortunately none of them are accessible at my level (first year ...
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### Lagrange equation of motions for a particle moving in a surface in the presence of gravity

I have to model the dynamic behaviour of a particle solid in a gravitational field.It is for a control theory course. And my background in dynamics is not the greatest. The particle can move left and ...
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### Does electric current flow from higher potential to lower potential or from higher potential energy to lower potential energy?

Here, $O$ is a field charge with a $+T$ charge. $A$ and $B$ are test charges with $+T_1$ and $+T_2$ charge, and they are fixed in place. Suppose the points at which $A$ and $B$ are situated are $P_1$ ...
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### Is the mass of two vertically stacked blocks greater than when they're placed side by side?

At the end of this video on mass-energy equivalence, it's states that two blocks stacked vertically have more mass than when placed side by side because they have more gravitational potential energy. ...
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### Why kinetic energy is called kinetic energy and not potential even though it has a potential to do work?

I lift a block of mass $m$ by a height $h$ in gravitational field. I have done a work of $mgh$ on the block. This energy is stored in the block when it is at height $h$. At height $h$, the block has ...
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When a load P is applied gradually on an object, the work done on it is the average of the initial and final loads, which is generally P/2 multiplied by the deflection Δ1. In the case of impact load, ...
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### In general relativity, assuming a spherical uniform mass distribution, what is the total energy value of the gravitational field inside the sphere?

In Newtonian mechanics, assuming a spherical uniform mass distribution, the total gravitational potential energy (gravitational self-energy) inside the sphere is $$U_{gs}=-\frac35\frac{GM^2}R.$$ In ...
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### What would be the outcomes in this arrangement? would potential varies along a conducting wire? [closed]

Two conducting solid sphere,one with charge Q1 and radius R1 and the other with charge Q2 and radius R2 are kept far away $$Q_1=5Q_2 \text{ and } R_1=5R_2$$ If these spheres are connected with ...
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### Is energy infinite in an electric field?

Energy is defined as the capacity to do work. Work in turn is defined as force x displacement. An electric field exerts the field in all directions infinitely (even though the strength of that force ...
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### Using Variation of Energy for a Dielectric to define the Electric Field

I have been reading through Zangwill's Modern Electrodynamics on my own, and I am confused about something in section 6.7.1, concerning the variation of total energy $U$ of a dielectric in the ...
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### Work done on a probe

When moving a probe from the radius of a planet to a new orbit of radius 2R, do we find the work done by subtracting the final potential energy from the initial potential energy? That would give GMm/...
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### How to Derive Potential Momentum?

The only derivation/definition of potential momentum I've seen is using the fact that: $$E^2-p^2c^2=m^2c^4$$ And if you add a potential, you must subtract something else from the momentum called the ...
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### Where should I apply the harmonic spring function in the case of polymer simulation?

I need to simulate the off-lattice movement of a polymer chain in a 3D space using Monte Carlo simulation. Note this is not a simulation of polymer growth; rather this is about polymer movement/motion....
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### Spring attached to a block [closed]

CONCEPTUAL DOUBT: Consider an ideal spring of length $l$, one end of which is fastened to a wall and the other attached to a block. Take the spring as the system. Now as the block is elongated by a ...
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### A block starts from rest at the top frictionless slide at a height $h_1$ above the ground and leaves the slide perfectly horizontally

A block starts from rest at the top of a frictionless slide at a height h1 above the ground. The block leaves the side moving perfectly horizontally at a height h2 above the ground. The block ...
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### Why gravitational potential away from a planet increases?

textbooks---- "potential increases towards infinity and is maximum at infinity" But that is true only when we are seeing potential w.r.t Earth EXPLANATION--------- So , as we know that ...
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Define $V=V(\mathbf{r})$ as the potential function, $\hat{A}$ is some differential operator, then for an arbitrary function $\psi$ $$\hat{A} \hat{V} \psi \iff \partial (V\psi)$$ whereas $$\hat{A} V\... 0 votes 1 answer 34 views ### Potential energy in Schrodinger eq In the Schrodinger eq what does potential energy V mean? In harmonic oscillation, it is the potential energy of the particle itself. However, At potential well, it looks like the potential is an ... 0 votes 1 answer 41 views ### Convert horizontal wind movement of a swaying tree into vertical movement under the tree How to efficiently convert the horizontal wind movement of a swaying tree into vertical movement under the tree? One way I can imagine is by tying a rope to a point in the ground some distance from ... 0 votes 0 answers 39 views ### Why didn't we account for kinetic energy of two stars in conservation of mechanical energy Two stars of masses 3×10^31kg each, and at distance 2×10^11m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In ... 0 votes 0 answers 9 views ### Decrease in average kinetic energy at Lennard-Jones phase transition I have written a molecular dynamics simulation to model argon using the Lennard-Jones potential. I am investigating the behaviour of the system near it's melting point for a specific pressure and ... 1 vote 2 answers 78 views ### Intuition behind gravitational potential Gravitational potential at a point is equal to work done in bringing a unit mass from infinity to a particular point That was the text book definition$$V_{p} = -\frac{GM}{r}$$If we calculate V_p ... 1 vote 2 answers 36 views ### Change in gravitational potential energy when the work is zero I may be misunderstanding the whole concept , but my doubt is this. Let us say there is an isolated system comprising of a rock and the Earth. If I was to lift the rock up with a force equal to the ... 4 votes 2 answers 153 views ### Coulomb potential vs Coulomb potential energy I know that the Coulomb potential in a hydrogen atom is V(x)=\frac{-e^2}{4 \pi \epsilon_{0} r}. Usually the potential is given by the potential energy divided by the charge, so I would expect V(r)=\... 0 votes 0 answers 12 views ### Nearest Neighbor Entropy Estimate Differentiation I am interested in differentiating an effective potential based on the following nearest neighbor estimate from .$$H_n = \frac{1}{n}\sum_{i=1}^n \ln(n\rho_{n,i})$$where,$$\rho_{n,i} = min_{j \...
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We learned that $$-Work = \Delta U = q(Va-Vb).$$ However, we write that $$W = q(Va-Vb)$$ in this question. Why don't we write the minus sign in the equation? How does external work affect the minus ...