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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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Explicitly verifying a scattering theory identity

I have recently studied scattering theory on a formal level and I think I understand the subject quite well by now. However what I often struggle with is to translate the abstract identities into ...
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Breaking spaghetti and conservation of energy [duplicate]

For the past few days there have been news about scientists solving the old problem of bending a piece of spaghetti and breaking it into exactly two halves. Earlier it was already determined that the ...
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3answers
103 views

Kinetic energy and conservative fields

If $W = E_1 - E_0$ for every force and a conservative field is a field such that the work on a closed path is 0, then every field should be conservative, since $W = E_0 - E_0 = 0$. I know that this ...
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Potential gravitational energy versus potential spring energy [duplicate]

My textbook points out the following predicament, and I do not know the answer, despite a lot of thinking: A spring is hanging of a ceiling and a mass is attached. As a result the spring descends to ...
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2answers
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Calculating Elastic Potential Energy of a Stretched Sheet

Essentially, I'm trying to determine the amount of elastic potential energy stored in a thin, elastic sheet that has gone under some type of stretching (ex. A flag of stretchy fabric waving in the ...
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1answer
22 views

Lost potential energy?

If there are two electrons and a positron are in an closed system (not being influenced by gravity) all these have electromagnetic potential energy amongst them . if one of the electron then touches ...
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When a balloon pops and lets a brick fall, where does the energy come from?

Let's say a scientist attaches a 1 kg brick to a large helium inflated balloon, lets the balloon go, and then it reaches an altitude of 10 000 meters before it pops, dropping the brick. The brick ...
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2answers
51 views

Is it possible to avoid a dangerous collision with the ground after free fall by converting the potential energy into rotational kinetic energy?

Is a human body able to survive if someone sabotages your parachute and you're in a free fall towards earth suddenly realizing that you have one out of two options left- either die or stand on the ...
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Is this a new form of renewable energy? (sand) [closed]

Can we make a machine that takes a mass of sand from the top of a sand dune keeps it in a box. Then moves it horizontally until it is hovering above the lowest point near the slipface of the dune. ...
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1answer
79 views

Potential energy and conservation law

I'm preparing for my masters entrance exam on pure mathematics (thought some problems are devoted to classical/lagrangian mechanics). I would be grateful to clarify some basics regarding the ...
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2answers
65 views

Work-energy theorem and Conservation of energy formula

We have $$W_{net}=\Delta K \quad(work-energy\; theorem)\tag{1}$$ And also $$W_{net}=\Delta K +\Delta U \quad(Conservation\;of \;energy \;formula)\tag{2}$$ How's that happening? In proof for bernoulli'...
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Particle in electromagnetic field Lagrangian

Given the two definitions of $\vec E$ and $\vec B$ by scalar potential $\phi$ and vector potential $\vec A$: $$\vec B=\vec \nabla \times \vec A$$ $$\vec E=-\vec \nabla \phi -\frac 1 c\frac {\partial \...
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2answers
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Relativistic energy level shift from $s$ to $d$ orbitals

I have read this question: This question is not about the energy levels, negative and kinetic, why it is lower (more negative) close to the nucleus. I understand those. I understand electrons have ...
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Angular velocity of a rod rotating under the action of constant force in the presence of gravity as a function of angle of rotation

I'm supposed to find the angular velocity of the uniform rod (mass $m$ and length $L$) when a constant, horizontal force is applied at the bottom using work-energy theorem. I tried to solve the ...
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1answer
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From where energy comes for the heat released when direction of electric field is changed with a dipole placed in the field

This is an example problem in my book. Forget about the values. Initial anf final(after heat is released) conditions in this problem are same, ie, dipole moment and electric field are in same ...
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Defining magenetic field potential energy in inductor

I have seen a bunch of URLs about this matter like here and here but none of them were asking my question. So please bear with me. As we can see in Introduction to Electrodynamics D.Griffith (Page:...
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1answer
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Electric Potential-Electric Field Relationship

In my book its given-At point A(closer to electric field) the potential is v but at point B(farther from electric field) potential is v+dv.How is it possible as we know that potential decreases if we ...
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7answers
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Does energy have a sign? [duplicate]

Quantities like position and time allow us to place our origin anywhere, but can the same be said for energy? I was thinking about the way we have defined the quantity gravitational potential, and for ...
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2answers
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What is the diffrence between Electrostatic potential (not “Potential Energy”!) And Electric potential

I have spent an hour with all I had got to figure out the diffrence between them : So What I understood is please correct me if I'm wrong (I know I will be dead wrong) That electrostatic potential ...
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2answers
32 views

Potential energy stored in lifting a body upwards

How much potential energy will be stored in the body if it is lifted upwards with acceleration greater than acceleration due to gravity?
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1answer
52 views

Does heat radiation also produce gravitational waves?

My question is as it sounds. We know that in a vacuum, materials radiate away their heat energy. To my understanding, this is the result of charged particles losing their energy to produce photons. ...
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1answer
53 views

Do force fields come from potential fields, or do potential come from forces?

Please excuse me if this question is a duplicate. I tried my best but I didn't find an existing question for this. In physics class, I was first introduced to gravity in terms of a force, ...
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Sigmoidal potentials

At first sight, elastic potentials $\sim x^2$ and gravitation-like potentials $\sim 1/x$ look quite different and yield quite different behaviours of objects exposed to such potentials. But if you ...
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How long and to what extent can tidal energy sustain a productive system?

I've been idly re-reading some articles lately on Enceladus and Europa. Regardless of the prospects for the actual existence of life in their oceans, it spurred some thinking on how systems reliant on ...
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0answers
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Why is the distance between two nucleons greater than the minimum energy point?

The potential energy associated to the interaction between nucleons has its minimum (point of equilibrium) at $r\sim 0.7 fm$, as showed in the following graph: Nevertheless, there are two facts ...
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why isn't conservation of energy just a definition? [duplicate]

I am new to theoretical physics. When I was reading the proof of conservation of energy, I found that the proof was a little bit trivial and everything seems to just be a definition. The potential ...
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2answers
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Work Energy misunderstanding

Suppose I have to displace a body to a height $h$ and I applied force more than its weight. So, there will be an acceleration on the body. Then the body will reach the height $h$. Then I let the ...
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4answers
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How do we recover units of force from units of gravitational potential?

The gravitational potential $G_\text{pot}$ has units of energy per unit mass: $$ \bigg[\rm\frac{J}{kg}\bigg] = \bigg[\rm\frac{kg\cdot m^2}{s^2\cdot kg}\bigg] = \bigg[\rm\frac{m^2 }{s^2}\bigg]. $$ ...
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1answer
95 views

Why physically do things in general tend to move toward a lower potential value in a potential field? [duplicate]

There are many answers on the site discussing motion of electrons in an electric potential field, See Why is voltage described as potential energy per charge? but also mass tends to move toward a ...
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5answers
96 views

Why is voltage described as potential energy per charge?

Voltage is often called an electromotive force since it causes a flow of charge. However, it is described in terms of Joules per Coulomb or Potential Energy per Charge. Question: How does the ...
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1answer
77 views

Can a piece of glass get higher than the height the original cup of glass fell from?

If yes, what physics concepts make this possible? This isn't for any class or anything, is just a honest doubt of mine.
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2answers
144 views

How can the total amount of energy in the universe be zero? [duplicate]

First of all, it is important to note that I'm not very savvy in neither general relativity nor any other area of expertise that answering this question may require. Therefore, I mean for the question ...
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2answers
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Multi-electron Atom

I'm reading the following text on multi-electron atoms: for a system of $n$ electrons the Hamiltonian is $$ \hat H = -\frac 1 2 \sum_{i=1}^n \nabla_i^2 - \sum_{i=1}^n \frac{Z}{R_i} + \frac{1}{2} \...
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3answers
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Springs in parallel store less energy than springs in series … but where does the excess energy go?

Two springs in parallel with a weight of 15 N will stretch a certain amount, while the same two springs arranged in series will stretch more under the same weight and so store more energy. I'm fine ...
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0answers
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Are the gradient field are the only fields which are only conservative? [duplicate]

I have found that gradient fields are always conservative. But for my knowledge I wanna ask "are the gradient fields are only fields which are conservative"? I mean is it necessary that a field which ...
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Hamiltonian formalism, polynomial of a certain rank and velocity-independent potential

In page 88 of Shankar's Principles of Quantum Mechanics, we have the following lines: $$\mathcal{H}(q,p) = \sum_{i=1}^{n}p_i \dot{q_i} - \mathcal{L}(q, \dot{q}) \tag{2.5.8 } $$ where the $\dot{q}$'...
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Proportionality of distance to work in differing conditions

Why is Work done by $F_{grav}$ and EMF proportional to distance but work done by $F_{elastic}$ proportional to the square of the distance?
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Value of Lenard-Jones Potential in case of (extensional / compressional) force application on two of its joining/neighbouring atoms?

The Lennard-Jones potential is defined as in the following equation, $$U(r)=4\epsilon\left( \left(\frac \sigma r\right)^{12}−\left( \frac \sigma r\right)^6 \right)\,,$$ where $\epsilon$ is the depth ...
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1answer
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Gravitational potential energy on a see-saw

Why is it that the total gravitational potential energy of two objects on a see-saw is always constant, no matter the angle? EDIT: The see-saw is in equilibrium, i.e. the torques on each side balance ...
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Why does gravity becomes negative when finding the negative derivative of potential? (I know $F=-dU/dx$) Why is $F$ itself negative?

By definition of the gravitational energy: $$ -\frac{dU}{dx}=-\frac{GMm}{x^2}=F $$ Then by integrating we get: $$ U(x)=\int\frac{GMm}{x^2}=-\frac{GMm}{x} $$ (I am not confused why force is ...
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1answer
56 views

Finite square well bound states

Let's suppose I have a finite potential well: $$ V(x)= \begin{cases} \infty,\quad x<0\\ 0,\quad 0<x<a\\ V_o,\quad x>a. \end{cases} $$ I solved the time-independent Schrodinger equation ...
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Electric potential energy and work done

My revision notes states that "to move the positive test charge from infinity to point P, the external force provided to that test charge must be equal to the electric force the source charge exerts ...
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1answer
54 views

Gravitational force and gravitational potential energy

When a test mass enters the gravitational field of a larger mass, the test mass is attracted towards the larger mass as a gravitational force that is dependent on the strength of the gravitational ...
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1answer
49 views

Potential energy in continuum physics: Why is this $0$ in the surface?

At the start of the continuum mechanics, we were calculating the potential energy. Here is the part that's not clear to me: Let $V$ be the potential energy and $U$ be its density function. Then: $$V=\...
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2answers
55 views

Total Energy of the ISS orbiting the Earth [duplicate]

I had a bit of confusion earlier about a discussion in astrophysics. I was reading that the ISS orbits the earth at $8 kms^{-1}$ but then when I calculated the total energy that the ISS had, I was ...
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1answer
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Why is the potential energy of spring negative while it's positive for a dipole?

Potential Energy is the work done against the conservative force As the definition suggests , for a spring $$ U= -\int F \cdot \mathrm{d}x \,.$$ But for a dipole placed in an electric field $$ U= \...
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4answers
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How does negative gravitational work result in an increase in potential energy?

I'm trying to untangle some confusion when it comes to understanding work. Suppose a rocket is moving upwards (in the opposite direction to the force of gravity), with a uniform velocity. For ...
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1answer
55 views

Work done by conservative and non-conservative forces

Work done by conservative forces changes one form of mechanical energy into another. Is it correct to assume that work done by non-conservative forces changes one form of energy to another, for e.g., ...
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1answer
69 views

Does potential energy affect the mass of an object?

Assume a space contains one black hole and two electrons $e_1$ and $e_2$ only. The distance between the black hole and electron $e_1$ is $10^6$ km, and the distance between the black hole and $e_2$ is ...
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0answers
25 views

Binding energy in Euclidean Gravity

I suppose I'm asking in the context of classical gravity, but an answer in the effective GR quantum theory would be fine too. I can't seem to find much on the attractive nature of the gravitational ...