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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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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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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2answers
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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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4answers
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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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3answers
299 views
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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4answers
418 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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1answer
80 views
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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2answers
246 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
66 views
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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4answers
667 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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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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1answer
169 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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1answer
672 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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0answers
74 views
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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6answers
334 views
Electrostatic Potential Energy Derivation
How is the boxed step , physically as well as mathematically justified and correct ?
Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy
As work done = $- \Delta U $. for Conservative ...
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3answers
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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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1answer
137 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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3answers
123 views
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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3answers
281 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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1answer
407 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
147 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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3answers
316 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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0answers
172 views
Shape of a string/chain/cable/rope?
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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5answers
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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
277 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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2answers
138 views
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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4answers
98 views
Potential energy sign conventions
Almost every book on physics that I read have some weird and non-clear explanations regarding the potential energy. Ok, I do understand that if we integrate a force over some path, we'll get a ...
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2answers
251 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
54 views
Work done by gravity on Water
Now according to me we would see change in potential energy of system and equate it to the work done by gravity.
But when we see this the first column lowers by $H/2$ and right one rises by $H/2$ ...
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2answers
272 views
Higher To Lower Electric Potential
The question I am working on is:
"An electron moving parallel to the x axis has an initial speed of $4.65 \cdot 10^6~m/s$ at the origin. Its speed is reduced to $1.27 \cdot 10^5 ~m/s$ at the point ...
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1answer
135 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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2answers
250 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
162 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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2answers
293 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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2answers
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Center of mass problem
According to the definition of potential energy, we use $U= mhg .
$
In the figure below ,
A thin uniform rod of mass m and length h is positioned vertically above an anchored frictionless pivot ...
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2answers
104 views
Negative potential energy of gravity
Does the negative potential energy in the gravitational field have to be considered in calculating the total mass of the system in question (because of $E=mc^2$)?
If so it seems to me that the ...
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2answers
464 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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3answers
398 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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1answer
62 views
Locally every force admits a potential?
I have a little doubt about a force being or not conservative. Well, as I understood, some forces cannot be expressed as exterior derivative of some scalar potential because the work done by the force ...
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3answers
252 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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2answers
160 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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2answers
52 views
Electrostatic Potential Definition
In the book, Introduction to electrodynamics by David J. Griffiths, he introduces potential separately as a function and potential energy through that function.
How can potential be defined before ...
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1answer
69 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
221 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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2answers
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Potential energy during vertical fall
Suppose I have a weightless spring connected perpendicularly to the ground, and it has on top of it some weightless surface. Now, I release some sticky object from height $h$ above the system of light ...
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1answer
153 views
Proof that flux through a surface is independent of the inner objects' arrangement
$$\Phi=\iint_{\partial V}\mathbf{g} \cdot d \mathbf{A}=-4 \pi G M$$
Essentially, why is $\Phi$ independent of the distribution of mass inside the surface $\partial V$, and the shape of surface ...
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1answer
229 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
296 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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1answer
195 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 ...
