All Questions
7 questions
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Suppose for all value of $r$ expression for Effective Potential Energy $U_{eff}$ is zero, does that mean $F(r)$ is zero?
Suppose for all value of $\textbf{r}$ expression for Effective Potential Energy ($U_{eff}$) is zero, does that mean $F(\textbf{r})$ is zero?
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5
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4
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1k
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Partial derivative in Newtons Second law
Newton's second law states Force is the time derivative of momentum. But is it a total derivative or partial derivative? What is the reason behind it?
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0
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1
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60
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Goldstein's generalized forces
In Goldstein's
$$
Q_{j}=\sum_{i} \mathbf{F}_{i} \cdot \frac{\partial \mathbf{r}_{i}}{\partial q_{j}}=-\sum_{i} \nabla_{i} V \cdot \frac{\partial \mathbf{r}_{i}}{\partial q_{j}}
$$
which is exactly ...
1
vote
2
answers
146
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Work done as change of potential, how total derivative is converted to partial derivative
I am reading Goldsetein's Classic Mechanics 3rd edition in Chapter 1 it says,
If work done in moving form point 1 to 2 denoted by $W_{12}$, is independent of the path it should be possible to ...
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2
votes
3
answers
420
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Potential energy with constraints moving body
I know that for conservative forces $\vec{F}=-\nabla{U}$. Let's consider the case of gravitational potential energy, I know that $U=mgy$. Just to check: $\vec{F}=-\nabla{U}=(0,-mg)$: perfect!
Now, let'...
1
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0
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80
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How does the gradient operator pick up a minus sign when the reference frame is switched from one particle to another? [closed]
A potential between two particles, $i$ and $j$, is given as a function only of the separation distance,
$$V_{ij} = V_{ij}(|r_i − r_j|)$$
It should follow that the force by $j$ on $i$ is equal and ...
3
votes
2
answers
718
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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 ...
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