3
votes
3answers
82 views

Higher order derivatives - Equation of motion

One possible starting point to create a physical theory is the Lagrangian $L$. There we assume that the variation of the action $\delta S = \delta \int_{-\infty}^\infty dt \ L = 0$. In classical ...
1
vote
1answer
44 views

Derive force from the pair-wise potential equation [closed]

How can we calculate the force exerted on particle $i$ by particle $j$ given a general potential function $V(d)$? Let's discuss this genenal question with a concrete example below. To simulate the ...
0
votes
1answer
156 views

Electrical Potential Energy and Electric Force [closed]

Under certain circumstances, potassium ions $(K+)$ move across the $8.0 nm$ thick cell membrane from the inside to the outside. The potential inside the cell is $−70 mV$ and the potential outside is ...
3
votes
2answers
200 views

Strong Newton's third law of action and reaction: Mathematical Interpretation

According to the strong law of action and reaction for internal forces(Goldstein): "$F_{ij}=-F_{ji}$ and the forces lie along the direction joining the particles." Now consider the statement If ...
2
votes
2answers
193 views

Stable equilibrium given force

If a particle moves under the influence of a resistive force proportianal to velocity and a potential $U$, $$F(x,\dot x)=-b\dot x-\frac {\partial U}{\partial x}$$ Where b>0 and ...
3
votes
1answer
170 views

Is there any potential associated with magnetism

Can anybody please tell me if magnetism is a conservative force or if there is a field associated with it? How to reason? One thing I know is that the work done by a magnetic force is $0$.
1
vote
1answer
557 views

Force exerted on potential wall

A particle bound in an infinite potential wall at $x=0$ will apply a force on the wall. For a plane wave and imagining it as a fluid bouncing off the reflection wall at $x=0$, find the force in terms ...
3
votes
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, ...
1
vote
2answers
242 views

What does $\textbf{f} = -\boldsymbol{\nabla} u$ mean in practice and how is it computed?

In classical computer simulations such as molecular dynamics (MD) simulations, one integrates Newton's equations of motion to determine particle trajectories. If we think of Newton's Second Law as ...
6
votes
4answers
563 views

Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?

Sorry if this is a silly question but I cant get my head around it.
3
votes
3answers
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 ...
4
votes
3answers
4k views

Force as gradient of scalar potential energy

My text book reads If a particle is acted upon by the forces which are conservative; that is, if the forces are derivable from a scalar potential energy function in manner $ F=-\nabla V $. I ...