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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Why are L4 and L5 lagrangian points stable?

This diagram from wikipedia shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the L1, L2, and L3 lagrangian points. The blue ...
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Why does a system try to minimize potential energy?

In mechanics problems, especially one-dimensional ones, we talk about how a particle goes in a direction to minimize potential energy. This is easy to see when we use cartesian coordinates: For ...
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What is potential energy truly?

I have a problematic question for which I have been unable to attain a satisfactory answer. What is potential energy truly? - I have read about how potential energy can be seen as the "highering" ...
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How is potential energy actually stored in a steel spring at the atomic level?

Elasticity is one the most intriguing phenomena, wiki gives a summary explanation of what happens in a steel spring: the atomic lattice changes size and shape when forces are applied (energy is ...
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How does a sponge “suck” up water against gravity?

If I take a sponge and place it in a shallow dish of water (i.e. water level is lower than height of sponge), it absorbs water until the sponge is wet, including a portion of the sponge above the ...
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Is it possible to prove that planets should be approximately spherical using the calculus of variations?

Is it possible to use the Lagrangian formalism involving physical terms to answer the question of why all planets are approximately spherical? Lets assume that a planet is 'born' when lots of ...
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In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence?

The Lennard-Jones potential has the form: $$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$$ The (attractive) $r^{-6}$ term describes the ...
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Mechanical Equivalent of Heat

Recently I have been looking up James Joule's experiment regarding the mechanical equivalent of heat. After viewing some drawings of the apparatus, I assumed that the lines holding the weights would ...
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Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
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How does escape velocity relate to energy and speed?

I have several confusions regarding escape velocity. I am sure I am missing something(s) obvious or maybe I am taught wrong. Lets say we throw an object of any mass at exactly escape velocity of ...
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Why does acceleration seem not to be the gradient of gravitational potential?

Consider a spherically symmetric distribution of density $\rho(r)$. We can define the mass enclosed within each radius $r$ using $\frac{dM(r)}{dr} = 4\pi r^2 \rho(r)$, with the condition that $M(r=0) ...
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Direction of rotation of proton in magnetic field--opposite to a dipole

Chatroom created by @pcr for discussing this: http://chat.stackexchange.com/rooms/2824/direction-of-rotation-of-proton-in-magnetic-field Here's a small paradoxical question I was asked a long ...
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What do we mean when we talk about Gibbs Free Energy?

Before I start, I'm aware that this question may be better suited on the Chemistry or Biology site, but it's my belief that physicists are more likely to have a clear understanding on what certain ...
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Origins of many-particle interactions

The internal potential energy of an $N$ particle system is a general function of the coordinates of the particles: $U(r_1,...,r_N)$. In some approximations and expansions - e.g. virial expansion - it ...
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What can be known about the formulas for energy only from the fact that it is conserved?

The question is to figure out how the energy can be derived knowing just one thing: There is a quantity called Energy that is conserved over time. The goal is to get an equation that somehow ...
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Why is gravitational potential energy negative, and what does that mean?

I usually think of gravitational potential energy as representing just what it sounds like: the energy that we could potentially gain, using gravity. However, the equation for it (derived by ...
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Does potential energy in gravitationall field increase mass?

I was just taught (comments) that any type of energy contributes to mass of the object. This must indeed include potential energy in gravitational field. But here, things cease to make sense, have a ...
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what is the 2D gravity potential?

In 3D, I can calculate the total force due to gravity acting on a point on the surface of the unit sphere of constant density, where I choose units so that all physical constants (as well as the ...
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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 ...
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About mass defect

Here's how my book explains mass defect: Particles inside the nucleus interact with each other - they feel attraction. The potential energy $U$ of such attraction is negative, because in absence ...
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Is quantum tunneling related to imaginary time?

I was studying for my exam and looking at the chapter which talks about Potential-energy graphs. Let's take this as an example: My book states that: "If the object is in $B$ and has a total energy ...
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Can the momentum eigenstates be non-orthogonal?

Consider the Hilbert space of a particle, whose position domain is confined to $q\in[0,1]$ (e.g. a particle in a box with unit width). Using $$ 1=\int_0 ^1 dq |q\rangle\langle q| $$ and the position ...
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Orbital mechanics and rocketry: Is it ever a good idea to intentionally lower periapsis?

tl;dr: Hohmann Transfer appears to be the optimal way to achieve a circular-to-circular orbit, but is it possible to lower the periapsis in order to achieve a more elliptical orbit with apoapsis at ...
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How does potential energy work out for floating things?

Seeing a ship canal lift in TV spawned the following thought: "Oh my, this sure is a heavy ship and it can be lifted by simply adding water. What a marvellous machinery. After all, I could lift that ...
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While holding an object, no work done but costs energy (in response to a similar question)

I read the answer to Why does holding something up cost energy while no work is being done? and wanting to know more, I asked my teacher about it without telling him what I read here. Instead of ...
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Physics of every-day life: rotating bag of tea

Whilst studying for my physics courses, I like to drink tea. Today, I noticed that if you pull a bag of tea out of a hot cup of water, it gradually starts to rotate, picking up speed as time ...
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Gravitational potential outside Lagrangian points or Lagrange points

The diagram in Why are L4 and L5 lagrangian points stable? shows that the gravitational potential decreases outside the ring of Lagrange points — this image shows it even more clearly: If I ...
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Energy Gain with capacitor?

I have a question about energy gain in capacitors. Assume the following system: As the electron gets accelerated inside the capacitor, it will have more kinetic energy coming out than going in. But ...
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Particle coming across a step potential barrier

My quantum mechanics textbook says that when a particle (in the classical case) comes across a potential-step barrier of finite height, if it has sufficient energy to surmount the barrier, it will ...
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What does energy represent in $E= mc^2$?

Due to energy-mass equivalence, any object with mass can be said to have a corresponding amount of energy. So in a 5kg object there are 450,000,000,000 joules. A joule as i understand it is the ...
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What is the energy required to create mass of m at a height of h above the Earth?

What is the energy required to create mass of m at a height of h above the Earth? Is it $E= m c ^2$ or $E = mc ^ 2 + mgh$ ? Let's reverse the process also. If you convert mass $m$ at $h = 0$ to ...
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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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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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Sign of Work and potential energy in electrostatics

Conceptual question: Suppose we have a configuration of point charges. If the potential of the energy of the system is negative, this means work is positive. I'm kind of rusty with my mechanics, ...
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Potential energy of a spring

I'm puzzled about the potential energy of a spring. A spring is a conservative system. So the potential energy should be defined only up to a constant -- can be defined to be 0 anywhere. However, ...
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What was the amount of energy released in the 9/11 terrorist attacks?

I read somewhere on the internet that the amount of energy released by the terrorist attacks on the twin towers on 9/11 should have been of the order of 100 tons of TNT. This number surprised me, ...
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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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Where do flying gas molecules get their energy from?

If you heat up water in a tank to boiling point, some of the water will turn to steam. Gas bubbles are created in the water. According to Archimedes principle, the gas bubbles will have a force equal ...
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What maintains constant voltage in a battery?

I know there's lots of questions that address similar situations, (Batteries connected in Parallel, Batteries and fields?, Naive Question About Batteries, and the oft-viewed I don't understand ...
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The “stationary potential energy” condition for static equilibrium in mechanical systems

I've often read that, for a mechanical system which can be described by $n$ generalized coordinates $q_1,...,q_n$, a point $\mathbf{Q}=(Q_1,...,Q_n)$ is a point of equilibrium if and only if the ...
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Where does energy in a field come from?

Let us consider for example Earth's gravitational field. If we put a ball somewhere in this field, the ball starts to accelerate due to the gravitational force exerted on it. I understand the ...
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Kinetic energy of the object, but Potential energy of the system: Why is it so?

Examples from Principles of Physics (by Walker,Resnick,Halliday) will say it better: Let us throw a tomato upward. . .as the tomato rises, the work $\mathbf{W_g}$ done on the tomato by the ...
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Sea surfer position displacement

Waves are means by which the energy propagates through a medium (e.g., sea water). This is not associated with a net movement of water in the direction of wave propagation. If this is the case, then ...
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What exactly is ''electric energy''?

If the two fundamental types of energy are kinetic and potential energy, is electric energy simply the kinetic energy of charge carriers? Also, is the statement "A cell converts chemical potential ...
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electrical potential energy stored in vacumm for a single point charge?

I have come to know the electrostatic potential energy in vacuum is given by $${\frac{1}{2}} \epsilon_0\int d^3x {E^2} $$ and this energy is due to the mutual electrostatic coulomb potential energy. ...
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Trying to understand Laplace's equation

I'm struggling here so please excuse if I'm writing nonsense. I understand that the gravitational potential field, a scalar field, is given by $$\phi=\frac{-Gm}{r}$$ where $\phi$ is the ...
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What is the mathematical justification for the quadratic approximation to the energy of a spring in a one-dimensional lattice?

It follows easily from this draw, the length $l$ of this spring as a function of the vertical distance $x$, as $l(x)=\sqrt{1+x^{2}}$ Now, $l$ can be expressed as a MacLaurin expansion: $$l(x) = ...
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speed of sound and the potential energy of an ideal gas; Goldstein derivation

I am looking the derivation of the speed of sound in Goldstein's Classical Mechanics (sec. 11-3, pp. 356-358, 1st ed). In order to write down the Lagrangian, he needs the kinetic and potential ...
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Rubber Band Forces

I have a question regarding the force a band places on an object. Say I have a rubber band wrapped around 2 pegs at a certain distance, and at that distance I know the pounds of force per inch it is ...
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Potential Energy Concept

Imagine a book that we lift it with a force that is exactly equal to the force of gravity so the forces cancel out and the book moves with a constant velocity. Consider the situation after the book ...