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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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How is rest mass $m_0$ in $E=m_0c^2$ related to mass $m$ in $F=ma$?

A particle at rest has energy given by $$E=m_0c^2$$ where $m_0$ is defined as its rest mass. So rest mass is essentially a measurement of a particle's intrinsic amount of potential energy. How is ...
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Total potential energy and equilibrium

Suppose a deformable body is under an external load. If there is no inclusion of gravity. When the body reach an equilibrium state, will the total potential energy be equal to zero? The total ...
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Optical trapping: factor 1/2 in definition of gradient force and potential energy?

If one consider the original deduction of the gradient forces that is applied to the trapped particle we can find the following: $$F_{grad}=\frac{1}{4} \alpha \nabla E_0^2(r),$$ where $E_0(r)$ is an ...
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How looks the “overarching” wavefunction of a number of electrons in an insulating sphere?

I changed my question after reading the comment of Anna. If we put a huge number of electrons inside a non-conducting sphere, what will the total wavefunction describing all electrons look like? I ...
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Is there any physical scalar potential where $U$ is also depends on $\dot q_i$s?

In the book of Classical Mechanics by Goldstein, at page 21, while deriving the Lagrange's equation, when the external forces are derivable from a scalar potential $U$, the author implicitly assumes ...
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To consider or not to consider potential energy of a mass attached to a spring in oscillation? [closed]

For the above system I have the following expressions for kinetic and potential energy: $$ V = \frac{1}{2}\,k\,x^{2}+m\,g\,l\,(1-cos\,\theta)-m\,g\,x\\ T = \frac{1}{2}\,m\,\dot{x}^{2}+\frac{1}{2}\,m\,...
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Potential must be real for Hamiltonian to be Hermitian?

I have seen a few proofs specify for finite wells, step functions, and harmonic oscillators, that $V$ must be real for $H$ to be Hermitian. Why is that? If we're solving the Schrodinger equation, we ...
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Relationship between potential and electric field

There are a number of ways to solve this problem but was interested in doing it via the formula: $$ ∇V = -E$$ However the potential on the line due to -q is $$ \frac{-q}{4\pi\epsilon_0((0.5d)^2+y^...
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How to reach $U = mgh$ Using Newton's Law of Universal Gravitation? [duplicate]

today i was curious about the potential energy, so, i started studying the Newton's Law of Universal Gravitation which its equation is \begin{eqnarray} U= -\frac{GMm}{r}.\end{eqnarray} Well, since i ...
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What would a universe which follows an inverse force law look like?

If the gravitational force obeyed an inverse law $f_\text{g} \propto \frac{1}{r}$ rather than an inverse square law $f_\text{g} \propto \frac{1}{r^2} ,$ the amount of work needed to separate two ...
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Proving that gravitational potential is work done by the object against gravity while KE increases and PE reduces

There's a person in my class who thinks that the formula for gravitational potential (-GM/r) represents the work done by gravity to move an object from infinity to any point in the gravitational field....
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Is a *difference* of potential energy relative to a frame of reference?

If we consider an electrical field, or a gravitational field, and two points in this field, is the difference of potential between this two points depending of a frame of reference ? It seems to me ...
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Why don't we avoid self-interaction terms when we measure energy of a continuous charge distribution as we do for point charge distribution? [duplicate]

When we calculate the electrostatic potential energy for discrete point charges we make sure that while adding potential energy for individual charges we don't take the same charge and square it up by ...
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Why does the potential energy of the system decreases when two charged particles are attracted to each other?

I've been reading about lattice energy, it says that during the formation of ionic compound the ions formed due to electrostatic force are attracted to each other and libration of energy takes place ...
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Why would Low Voltage produce HIGH current with the same resistance? Transformers

We always see in Ohm's law that $v=IR $. So if $R$ is fixed for a wire, how can the electrons with High P.D have low current. Isn't it the electrons bumping into the resistor that creates the heat? ...
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Does an object at the center of the Earth have potential energy?

"Potential energy: The energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors." in other words, I think that potential ...
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Why is electric power needed at all when elevator is descending?

If the ropes are doing negative work on lift, why is electric energy needed? And why is there a limit on number of passengers in a lift in this case?? Please explain in terms of energy conservation ...
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Charging two spheres by induction n times

There is a conducting sphere $S_1$ of radius 'r' mounted on an insulating handle. The sphere is given a charge Q. Another uncharged conducting sphere $S_2$ of radius R mounted on an insulating handle ...
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Gravitational potential energy of a rod, attached by its end to an axis

Situation: We suppose a rod is attached by its end to some pivot, and is allowed to fall from a horizontal position. As this occurs, the rod loses gravitational potential energy ($∆U_G$), say 10J, ...
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Mass of potential gravity energy?

Assume a system where there only two 1 kg solid iron balls floating in space. The two balls are touching each other, so the potential gravitational energy between them is 0. Now I move them 1000 m ...
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What is the derivation of potential energy of an object?

I want to know why we use the gravitional force to compute the potential energy. Assume we have a ball, and we lift it up by a distance $h$. Then, as I understand, the force $F_l$, must have been ...
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Meaning of the term $V(x)$ in the Schrodinger equation [closed]

I'm new to quantum mechanics and I am currently trying to understand finite potential well (although my question is not specific to finite potential well ). In the Schrodinger equation, many texts ...
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Question about the general potential operator

The Hamiltonian operator is given by $$\hat{H} = \frac{\hat{\textbf{p}}^2}{2m} + \hat{V}.$$ For this reason it's of interest to know how to find $\hat{V}$ in any representation. Is the potential ...
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Why is Coulomb's force law a $1/r^2$ dependence, while the Coulomb potential has a $1/r$ potential?

My source of confusion comes from reading the following except from my general chemistry textbook, "The energy of interaction between a pair of ions can be calculated using Coulomb's law" $$V = \...
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Is the potential term in a Lagrangian velocity-dependent?

I know that the Lagrangian of a system has to be dependent on the coordinate (as the type of potential in it is dependent on the coordinate) and on velocity and time (per KE and PE, respectively). ...
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Approximating the time it takes for a particle with a potential $-Ax^4$ to approach the origin [closed]

Here's the problem I'm solving: A particle of mass $m$ can only move along the $x$-axis and is subject to an interaction described by the potential energy function $U\left(x\right) = -Ax^4$, where $...
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How can an object with zero potential and kinetic energy ever move?

I am not sure how to ask this question but I am learning about potential energy in my high school physics class. From the definition of potential energy, (energy stored in an object with the potential ...
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Can magnitude be negative?

My teacher told that magnitude is the positive value of that quantity or the modulus of that quantity. he also told that vector quantities have both magnitude and direction and scalar quantities have ...
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Potential Energy of Conservative Forces [closed]

For a conservative force, its associated potential energy at position $\mathbf{r}$ is $$U(\mathbf{r}) = - \int_{\mathbf{r}_{0}}^{\mathbf{r}} \mathbf{F}(\mathbf{r'}) \cdot \text{d} \mathbf{r'}$$ ...
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Do real electrons solve the Thomson Problem?

The question of how $N$ electrons (seen as point charges) on a conducting sphere will arrange themselves in the electrostatic final state was first posed by J.J. Thomson in 1904--hence, aka the ...
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Why does the GPE of an object always equal the work done?

I had a question that said, "If you do 100 J of work to lift an object over your head, what is the gravitational potential energy relative to its starting position? What would be its gravitational ...
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Work done in lifting a mass vs work done by mass as it falls to starting position

There are variations of this question on here but I was unable to find exactly what I was looking for so please bear with me if this is old hat. If I start with a mass m at rest at height H1 and ...
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Does potential energy get transferred from my body to a wall when I push a wall and fail to move it?

When I push a rock (and fail to move it), I do not do any work and therefore there should be no energy transfer. But my teacher says that, when one pushes a rock, energy is transferred to the rock ...
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Electrostatic potential of a point charge

From Wikipedia The electrostatic potential energy, UE, of one point charge q at position r in the presence of an electric field E is defined as the negative of the work W done by the electrostatic ...
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Gravitional Potential Energy Formula Magnitude confusion

It is pretty intuitive that increasing the height or distance of an object and also increasing the mass of it increases the gravitational potential energy (GPE). Basically the question is asking, ...
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Why isn't the work done on the spring encapsulating this idea?

We know that work done ON the spring is given by the integral $$\int kx \, dx =\frac12kx^2$$ if we start from $x=0$ .But what if I apply more force on the spring.Wouldn't I be doing more work on it? ...
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Negative Work done by gravity

When we lift an object from ground we say we did work on object . We also say that gravity has done negative work because we did work to overcome gravity . When we did work our chemical energy was ...
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Potential energy of a charge in a magnetic quadrupole field

I have a charged particle of charge $q$ that moves with velocity $\vec{V}$ from a position $\vec{r}$, inside a magnetic quadrupole field of the form: $$\vec{B}=B_{0}(x,y, -2z)$$ The Lorentz force acts ...
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Centrifugal force in effective potential

$$E = \frac { 1 } { 2 } m v _ { r } ^ { 2 } + \frac { L ^ { 2 } } { 2 m r ^ { 2 } } + U ( r )$$ This is the formula of total energy of an object with mass $m$ orbiting an assumed stationary body of ...
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Potential Energy and Work [duplicate]

My physics textbook says when a rock is lifted gravity does negative work and increases the gravitational potential energy. My understanding of negative work implies energy is being removed when an ...
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Work-Energy theorem and System

In the book Classical Mechanics by David Morin,while discussing Work Energy theorem he gives an example of importance of choosing System. As he considers lifting the book upward then by WE theorem: $...
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How are various forms of energy ability to do work? [closed]

According to various sources that i have come across, energy is the ability to do work. Can someone elaborate how diff forms of energy like potential energy and kinetic energy are ability to do work? ...
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Work done in circular expansion of a rubberband or an elastic wire

What will be the work done in radially stretching a rubberband it can't be zero as there is potential energy being stored in it All I came up with it that there would be increase in overall length so ...
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Surface Tension and Potential Energy in a Lagrangian

It seems natural to define the potential energy due to surface tension to be $U = \int \sigma dA$. But then I have the following problem. I wanted to investigate surface tension in a simple ...
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Does space expansion increase potential energy, and hence increase mass?

As space expands the gravitational potential Energy increases. So does the potential energy between Atoms and quarks and so on. I have read several times that these effects are so minuscule that they ...
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Proof for $W_{\text{total}}$

Looking upon a certain solution of a problem in Griffiths regarding the work done in arranging two concentric spheres with inner shell having charge $q$ and outer shell with charge $-q$ and I found a ...
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Can potential energy be the sum of the work done by all forces?

I often see that the total energy of a system is the sum of potential energy+ kinetic energy. Is it always like that? Could I say that the total energy of a system is the sum of the work of all force +...
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Could someone explain what is a potential?

In many part of physics, me talk about potential (electrical potential, gravitation potential, elastic potential...). All those definition looks very different, and I would like to know how all those ...
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Deriving effective potential energy from the Lagrangian of a two-body system [duplicate]

I'm having some issues understanding how the effective potential energy of a two-body system is derived from the Lagrangian of the system. Specifically my issue is with one step... Suppose we are ...
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Conducting sphere

A conducting sphere is to be charged by bringing in positive charge a little at a time until the total charge is $Q$. The total work required for this process is alleged to be proportional to $Q$ ...