Tagged Questions
10
votes
1answer
239 views
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 ...
2
votes
2answers
252 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?
$$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
2
votes
2answers
252 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 ...
4
votes
1answer
171 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 ...
3
votes
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, ...
3
votes
3answers
318 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 ...
0
votes
1answer
160 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 ...
