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 do I correctly express the work required to put an object with positive buoyancy down into a certain depth (of water)?

It seems to me that I can express the work required to put an object under water in the same way that I express lifting an object up against gravity. I. e., in both cases I increase the potential ...
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413 views

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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1answer
292 views

How much (usable) potential energy is stored in a compound bow?

I have done a bit of reading about the energy stored in bows, but I haven't seen anywhere a description of how much energy actually is stored. Clearly there are many factors, bow design being ...
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430 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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201 views

Why is the spring constant $W_p''(0)$?

According to my physics book, the spring constant can be calculated from knowing the potential energy, with the formula $k = W_p''(0)$. I don't really understand why, and the book doesn't explain it ...
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201 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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2answers
299 views

Measuring work done by gravity over non-constant gravitational acceleration

A question from an example from a MIT Classical Mechanics Lecture on Work. Here's the given definition for gravitational potential energy (~32:00): "The ...
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1answer
233 views

exercise concerning the inclined plane

I have an exercise to ask yourself. A ball of mass m = 5 g starts at rest and travels 50 cm along a ramp inclined at 45 ° to the horizontal. a) If we imagine frictionless motion of the ball along the ...
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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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185 views

Elastic potential

I have a doubt: elastic potential energy is given by: $U=\frac{k}{2}x^2+K$ but does elastic potential exist? (for example: potential gravitational energy is given by $U=mgz+K$ and gravitational ...
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1answer
410 views

What is the energy of interaction between a point charge and an infinite cylinder?

I don't remember enough from my electromagnetism course and I can't find any simple, full example on this subject. I know, that I can consider the cylinder as a wire with the same charge density ...
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721 views

Is there a mathematical derivation of potential energy that is *not* rooted in the conservation of energy?

For simplicity I'll consider only gravity, but in general this question only applies to conservative forces. As per my understanding, the way one gets to the equation for gravitational potential ...
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1answer
598 views

Potential Energy in General Relativity

I often hear about how general relativity is very complicated because of all forms of energy are considered, including gravitation's own gravitational binding energy. I have two questions: In ...
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1answer
551 views

Derivation of the self gravitational potential energy of a sphere

I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
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3answers
856 views

What is meant by potential energy for a particle in a field?

Potential energy is usually defined using a field and a particle that experiences the field force, as the work down in moving a unit particle from infinity to a position in that field. But some ...
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2answers
342 views

Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$

This is probably a simple question, but what does the subscript $0$ mean in the following expression? $$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
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1answer
91 views

Is more energy required to magnetize based on its distance to other objects?

I have had this question since I was in college physics, but never could figure out how to express it. Well, now I think I have it. Let's imagine two scenarios A and B. Both scenarios start with two ...
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1answer
93 views

Do field and potential energy always come together?

Is energy directly due to a field always potential energy? Is potential energy always due to a field? From the two Wikipedia links: a field is a physical quantity that has a value for each ...
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2answers
532 views

Lever Mechanics - How to formulate an ideal lever launch

Let's say I have a simple lever as shown below, and the lever is massless and the pivot is frictionless and there is no air resistance. I'm thinking the cradle for the projectile would have to have a ...
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1answer
292 views

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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3answers
500 views

What is the most efficient machine for translating gravitational potential energy of one mass into kinetic energy of a different mass?

As the question states, what is our current best machine for translating falling gravitational potential energy, such as a large weight, into launching a smaller projectile vertically? A lever? A ...
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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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249 views

Why do hydrogen atoms attract?

That is, why is the potential energy with the orbitals overlapping less than with the Hydrogen atoms 'independent'. Similarly, why is a noble gas configuration stabler than if an electron were to be ...
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1answer
181 views

In $\textbf{f} = -\boldsymbol{\nabla} u$, what is $u$?

I know that force is the negative gradient of the potential: $$\textbf{f} = -\boldsymbol{\nabla} u$$ where force $\textbf{f}$ is a vector and $u$ is a scalar. This is a relatively soft question, ...
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97 views

Can a mechanical systems on hold be switched off, in another way than just letting it do it's thing?

Can the value of the potential energy, which is responsible for driving the system, diminish in time, while the system itself is stationary during that time? Can there be dissipation in a system, ...
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1answer
507 views

why is total electron energy of an electron in metal negative?

In my textbook, it says that any electron bound in metals, modelled as some potential well $U$, has negative total electron energy, as shown below in the figure. Why is the total electron energy ...
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950 views

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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4answers
2k views

Does the mass of an object change as it moves away from the earth?

The mass of a helium nucleus is less than the mass of two isolated protons and two isolated neutrons. When the component hadrons are assembled, this mass is lost as energy ($E=mc^2$). This makes it ...
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1k views

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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1answer
219 views

Atomic weight in respect to the binding energy?

My book says that the weight of helium (with the nucleon number of 4 and proton of 2) is that of $6,6447*10^{-27}$ kg. Earlier the book stated that if the proton number is left out it means that the ...
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Electricity & Magnetism - Is an electric field infinite?

The inverse square law for an electric field is: $$ E = \frac{Q}{4\pi\varepsilon_{0}r^2} $$ Here: $$\frac{Q}{\varepsilon_{0}}$$ is the source strength of the charge. It is the point charge divided ...
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656 views

Electrostatic Potential Energy

I have read many books on Mechanics and Electrodynamics and the one thing that has confused me about electrostatic potential energy is its derivation .One of the classical derivations is : ...
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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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Still trying to understand gravitational potential and Poisson's equation?

A week or so back I asked a question about the gravitational potential field $$\phi=\frac{-Gm}{r}, \qquad r\neq 0, $$ and how to show the Laplacian of $\phi$ equals zero for $r\neq 0$? Eventually, ...
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2answers
281 views

Why no basis vector in Newtonian gravitational vector field?

In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$ which is a vector field. On the same page, it is also given as a ...
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1answer
862 views

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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1answer
203 views

Asynchronous generator run in vacuum chamber

what will be happen if we put asynchronous generator in vacuum chamber & run it above its synchronous speed. After reaching its over synchronous speed we will cut off electrical supply. Can it run ...
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411 views

storing energy (as mass)

When chemical energy is released mass is reduced, if only by a negligible amount. Presumably that's true for all energy. And presumably that works in reverse as well: storing energy involves an ...
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Differences In Potential Equations

Could someone please describe the differences between the uses each of these potential equations: Potential due to a point charge: $V = \frac{k \cdot q}{r} - \frac{k \cdot ...
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1answer
90 views

Terminology question about energy

I'm looking for the appropriate term to use for what gets "used up" as potential energy is converted to heat and work. For example, some of the the energy in solar radiation is converted by ...
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1answer
426 views

Potential energy in a gravitational field

I've seen the following formula for the potential energy of a body in a gravitational field ($\rho$ is the density, $g$ is the gravitational acceleration): $$ \rho g \int_E z dV $$ Can you please ...
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465 views

About constructing potential energy functions

There are many classical systems with different potential functions. My problem is that I do not understand how one can construct a certain potential function for a certain system. Are there any ...
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1answer
197 views

Violation of conservation of energy and potential energy between objects

I would like to clarify my question. I have numbered them to be independent questions For any conservative fields, $\vec{F} = -\nabla U$. Which means the restoring force is opposite to the ...
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226 views

What is the physical reason a $+5V$ equipotential coutour cannot intersect a $-5V$ equipotential coutour?

Now I've been told that equipotential contours with different values can never intersect. That is, if one level is 5V and one is -5V, they can't intersect. This make sense to me mathematically (one ...
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2answers
449 views

Does the potential energy of fluid rising on a string change?

Lets say I have a glass of water at rest. Then I go and hang a string above the water (vertically), such as the end of the string is immersed in the water. Over time some of the water is going to ...
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873 views

Is there really no meaning in potential energy and potential?

I have been told all my physics life that potential energy between two mass/charge has no meaning and only their difference has meaning. The same goes for electric potential, only the difference ...
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260 views

Could someone remind me what this means again? $\nabla U = \pm F$

You know that for a potential function (conservative force/fields) that $\nabla U = \pm \vec{F}$ In math, we don't have that minus sign, we have only the plus one. What does it mean if you get rid ...
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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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3answers
1k views

Potential energy of a charged ring

Consider a ring of radius $R$, and charge density $\rho$. What will be the potential energy of the ring in its self field? The best I can do: $$dq = \rho R \cdot \, d \alpha $$ $$E_p = 2 \pi R \cdot ...
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2answers
184 views

In continuum mechanics, what is work potential in the context of total potential energy?

I'm reading a book on the finite element method. Specifically I'm looking at the background material where they are discussing potential energy, equilibrium, and the Rayleigh–Ritz method. The book ...