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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Hamiltonian function for classical hard-sphere elastic collision

I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at $x = 0$. Everything I've read on the topic (e.g. this ...
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56 views

Binding energy of a galaxy?

I'm a novice in physics and new to the forms, so please forgive me if this is a dumb question or if this is in the wrong section to be posted, but how would one find the gravitational binding energy ...
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20 views

How to efficiently cool down simulated gas by time-dependent potential?

I'm trying to simulate condensation of a highly diluted gas (a model gas, not any real one). For simplicity I restrict the simulation to 2 dimensions. To setup the simulation I take some interparticle ...
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921 views

Shape of a string/chain/cable/rope/wire?

The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall) and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc ...
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51 views

Deriving the formula for energy stored in a spring without using geometry (determining the area under a curve)?

Using Hooke's Law, we know that the force applied is proportional to the extension of the spring. Therefore by plotting a graph of force against extension, through the area under the curve we are able ...
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42 views

Transform QM radial equation to spherical Bessel equation

I'm currently learning about spherical potentials (ex. hydrogen and hydrogen-like systems) and am trying to work through the problem of a generic spherical potential well such as: $$V(r) = ...
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124 views

Lagrange: when a potential force, when a generalized force?

Consider the following case of a drum unrolling a mass that is on a massless string wrapped around the drum: According to my professor, here we must consider the mass $m$ being in a gravitational ...
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79 views

Question about defining potential energy of a magnetic dipole placed in a magnetic field

We know that magnetic field is a non-conservative field, since it exists in closed loops. Then how can we define the potential energy of a magnetic dipole placed in a magnetic field ?
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Modelling gravitational potential of a galaxy

I am interested in modelling the gravitational potential of a disc-shaped galaxy with radius $R$, i.e. solving the 2D Poisson equation numerically by Gauss-Seidel relaxation: $$\nabla^2 \phi = 4\pi G ...
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850 views

What is the minimum physical distance between two electrons?

If electrons repel, then it seems to me that energy is required to decrease the distance between two electrons. Since energy and mass are equivalent, adding energy to a system also adds some mass. ...
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1k views

Differences between time-independent and time-dependent Schrödinger equation for potential generation

Suppose I wanted to develop a potential describing the interaction between two lithium atoms. One way to do this is to calculate the energy between the two lithium atoms for various distances and ...
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39 views

Interpretation of a case of the double square well

Consider a 'double square well' potential (where $E < 0$) defined as: $$V(x) :=\begin{cases} -V_0~~~~~~~~~~~~~\text{for }\frac{b}{2} < x < \frac{b}{2} + a \text{ and } -a - \frac{b}{2} < ...
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Wave function for step potential

Given the step potential $$V(x)=\begin{cases} 0~~~~~~~~\text{if }~~x \leq 0 \\ V_0~~~~~~\text{if }~~x > 0 \end{cases}$$ Consider the case where $E < V_0$. In this region $x \leq 0$ we have ...
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27 views

Does a potential of interaction produce also torque?

I have a system of particles (spheres with masses and radii), with $6$ degree of freedom (they are free to move and rotate as they wish). Between each couple there is an interaction potential $V(d)$, ...
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30 views

Effective potential kerr solution

In Newtons mechanic we obtain $E=V_{eff}(r)+\frac{1}{2}mv²$ with $V_{eff}(r)=V(r)+\frac{1}{2} \frac{L²}{mr²}$ for the effectiv potential. The first equation is easy to interpret the total energy ...
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72 views

Potential Energy of two masses

If two particles with masses $m_1$ and $m_2$ interact and are located at $\vec{s_1}$ and $\vec{s_2}$ have their potential energy $U$ defined by the modulus of their position vectors, how would I ...
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40 views

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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199 views

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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21 views

Energy density in electrostatics

Imagine two hollow spheres with radius $R$ with charges $q$ and $-q$. $L>2R$ is distance between them. Potential energy of the each sphere is \begin{equation*} W_1=\frac 1{8\pi \epsilon_0}\frac ...
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110 views

Generalization of Feynman's derivation of the formula for gravitational potential energy in FLP volume I

In the Feynman Lectures on Physics, Feynman derives the formula for gravitational potential energy by applying a line of reasoning he borrowed from Carnot on reversible weight lifting machines (FLP I, ...
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39 views

Can anyone give me a simple proof for the sign change of electronic wavefunction when taken around a loop containing a conical intersection?

How and why does the sign of the electronic wavefunction changes when it is taken around a contour? For example, suppose the initial wavefunction is $f(s;S_0)$ at nuclear configuration $S_0$ and now ...
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82 views

Does a pulled rubber band contain as much energy as a twisted rubber band?

lets say I take two similar rubber bands. One of them I pull until it almost reaches its breaking point. The other I twist until it almost reached its breaking point. Do both of these rubber bands ...
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451 views

Gravitational potential energy and Center of Mass

I've been reading about the Nordtvedt effect, and how Gravitational Binding Energy (GBE) affects total mass. According to the WP article, experimental evidence rules out the existence of this effect. ...
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481 views

Infinite chain of alternating charge

The problem There is an infinite chain (1d) of alternating charges that are in a distance a from each other. That is there is one charge +q and next to it -q and so on. Now calculate how much work it ...
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148 views

Deriving the curve of a cantilever

Essentially, there is a beam of length L and negligible mass sticking out of a wall with a mass Mg hanging at the end of it. We are given an equation for elastic energy (which I don't think needs to ...
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261 views

Potential energy of a spring

I have a little problem with the potential energy of a spring... I hope you can help me! I have two coupled pendula, given by two masses $m$ fixed to two rigid bars (that haven't any mass) and with ...
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16 views

What is the physical meaning of potential energy in a band diagram of a semiconductor?

According to this slide (from this website), the potential energy of an electron in a semiconductor is defined by the difference between the Energy level of the conduction band and the fermi level. ...
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32 views

When should gravitational potential energy be included in the law of conservation of energy

I have a problem that says: A block of mass 0.249 kg is placed on top of a light, vertical spring of force constant 4 975 N/m and pushed downward so that the spring is compressed by 0.090 m. ...
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10 views

Potential energy of a shell & point system

Consider the system of a point particle with charge $q$ and a spherical shell with uniform charge $Q$ and radius $R$ whose center is a distance $r > R$ away from the point particle. I'm trying to ...
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57 views

Why is the longitudinal term removed to form the Lorentz force equation?

Beginning with the expression for interaction energy, and deriving the potentials form for the force on a test charge moving at velocity $\vec v$ yields: $$\vec F = q(-\nabla\phi - {D\vec A \over ...
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23 views

Energy potential of a cold sink inside the sun

An answer in this question discusses using a fusion engine in a theoretical spaceship within a star. ...
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Relation between gravitational field and gravitational potential

gravitational field is the negative differential of gravitational potential . now gravitational potential due to a particle at a distance r is -Gm/r where m is the mass of the particle . If i take the ...
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Mechanical energy of a body

What is the total mechanical energy of an air-plane flying in the sky? Does it possess both kinetic energy and potential energy,taking the zero potential energy at ground? As it is moving it will ...
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Electrical energy in a piezoelectric material

How do we define the electrical energy stored in a piezoelectric material? I'm confused about both the naming and the meaning. Are "electrostatic energy density", "dielectric energy density" and ...
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51 views

Infinite square well physical interpretation

In quantum mechanics, the description of the infinite square well is given with the potential energy defined as $$V(x) = \begin{cases} 0 & \text{if } 0 \leq x \leq a,\\ \infty & ...
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55 views

Deriving Kepler's First Law from Newton's Law of Universal Gravitation: Interpretation of the $u = 1/r$ change of variable

I'm working through a somewhat unsatisfying derivation of Kepler's First Law from Newton's Law of Universal Gravitation. The key to obtaining the equation of motion that you can solve lies in making ...
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81 views

Potential vs Potential Difference for a line charge

How would I calculate potential for an infinite line of charge a distance 'r' away from it? What does the reference point for potential difference mean? I know delta v = Q/(2pi*epsilon0*L)*ln(r2/r1) ...
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34 views

Strain energy density (potential energy of elastic continua)

This question has to do with writing down the potential energy of an elastic body, which obeys a generalized Hooke's law [; \sigma_{ik} = \sum_{klm} \lambda_{iklm} u_{lm} ;] Where $\sigma$ is the ...
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184 views

Work done by flow of a fluid

I'm looking at the power a flow of steam in a turbine. I originally assumed that the kinetic energy of a moving section of steam was equal to (let $V$ be volume, $\rho$ be density, and $v$ be velocity ...
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70 views

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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110 views

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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35 views

What kind of potential profile that an electron live in provides bound state energy levels?

Given the electron Hamiltonian $$H=T+V(r)$$ where $T$ is the kinetic energy, $V$ is the potential energy and it is not necessarily isotropic. If $$V \sim -\frac1{|r|},$$ we have hydrogen-like bound ...
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60 views

Rest masses, binding energy - mechanism for negative mass

Let us have an two objects (in a box) both of mass $m_0$ far from each other. They attract each other and at some moment their distance is close and they have substantial kinetic energy. Something ...
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59 views

How can energy be partitioned equally when energy is relative?

According to the Equipartition theorem in a system at equilibrium the energy should be on average be divided equally between the available degrees of freedom. The most common examples are the three ...
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32 views

Obtaining angular velocity of a general orbit

Provided you are given a effective potential function i.e. $$ V_{eff}=\dfrac{J^2}{2ml^2sin^2(\theta)} + mgl(1-cos(\theta))$$ how do you obtain the angular velocity for different types of orbits; i.e. ...
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357 views

Is there a way to measure the energy stored in a twisted rubber band?

I am building an energy storage device using rubber bands. It contains 24 bands which are twisted by a set of gears. I would like to measure (or predict) the amount of energy that the device can ...
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Questions regarding rubbing catfur on glass

I have certain questions regarding the electrostatic charge developed by this rubbing effects: 1-what is the threshold for electrostatic charges by this process? 2-can we define potential energy ...
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379 views

Saddle point and transition state of a molecule

During a transition of a molecule from one state to another, it pass through a transition state. This transition state, mathematically speaking, is a saddle point. That means, the second derivative ...
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85 views

Active and passive transformations and the change in potential energy

Under active transformation, the particle moves. On the other hand, for a passive one, the coordinate is just relabel. I've read that the passive one will not affect the potential energy and the ...
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111 views

Interpretation of contribution of gravitational potential energy to the gravitational field

In terms of General relativity we have as a matter of principle that anything that has inertial mass contributes to gravity. All forms of potential energy have inertial mass, it follows that the ...