All Questions
23
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The conservative force [closed]
I read about the definition of the curl.
It's the measure of the rotation of the vector field around a specific point
I understand this, but I would like to know what does the "curl of the ...
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-1
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1
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63
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Conservative forces and Variation
I am currently studying "Classical mechanics by Goldstein" and have just started. The book introduced something simple. For a conservative force, the work done in taking a mass from one ...
- 585
1
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1
answer
56
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Conditions for a force to be conservative - Does the second condition imply the first? [duplicate]
John Taylor's Classical Mechanics says this...
I was wondering if the second condition already implies the first? I mean, are there situations where the first condition is violated even though the ...
- 97
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1
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46
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Why is the force being the differential of a potential equivalent to it being a conservative force?
I was reading Goldstein's book on mechanics and came across this theorem:
$F(r) = - \nabla V(r)$ is a necessary and sufficient condition of the force field being conservative.
So far, I have ...
- 169
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2
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96
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Is net force conservative?
From the work-energy theorem, $$\int_{C}^{}\vec{F}\cdot d\vec{r}= \frac{1}{2}mv^2_f -\frac{1}{2}mv^2_i$$
Is velocity the gradient of position, and if so, does that make this force a conservative ...
- 65
1
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1
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812
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Work done for conservative forces is path independent Proof
So I’m looking at the proof for work that is path independent.
There is a line were the integral
Partial derivative V dr from r1 to r2 becomes
Partial derivative V r’ dt from t1 to t2
I’m a bit ...
1
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2
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97
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Conservative Force in a loop
Could someone prove mathematically that why in this situation a charge could move in a loop with net work done.
Could someone explain this paragraph to me.
user286173
0
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2
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790
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Why does an exact differential mean a force is conservative?
If you can express an integrand as an expression of just one variable i.e. $xdy + ydx = d(xy) = df$ then why does that mean that a loop integral on that will equal 0? Is it because if it is just a ...
- 535
20
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3
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Conditions for a force to be conservative
Taylor's classical mechanics ,chapter 4, states:
A force is conservative,if and only if it satisfies two conditions:
$\vec{F}$ is a function of only the position. i.e $\vec{F}=\vec{F}(\vec{r})$.
The ...
- 1,295
1
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3
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Defining potential energy in Taylor's Classical Mechanics
I'm trying to understand this sentence in introducing potential energy in John Taylor's book:
If all forces on an object are conservative, then can define a quantity called potential energy, $U (\...
- 753
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2
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459
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Path independence of a conservative force
My book Halliday et al. gives a proof of the path independence (conservative force). It is said that the net work to move a particle from a to b and then from b to a is zero. Thus the work done from a ...
user248666
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2
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190
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In order for a force to be derived from the gradient of a potential energy, does the work done by such a force need to be invariant of the path?
Suppose a force $\mathbf{F} = \mathbf{F}(\mathbf{r}, t)$ where $\mathbf{r}$ is a three dimensional space vector and $t$ is time.
I understand that in order to a force be conservative two conditions ...
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3
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1
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353
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Conservative field vs conservative force
For a conservative field (e.g. electrostatic field) the circulation of the field (along a closed line) is zero.
For a conservative force (e.g. macroscopic elastic force) the work performed on a ...
- 719
2
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5
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315
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Can a conservative force not conserve mechanical energy because of explicit time dependence?
Let us define a conservative force as being a force whose work is path independent. Then, in particular, a vanishing force is conservative.
If a force acting on a particle can be written from a scalar ...
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Is this understanding of potential energy correct?
I am studying basic mechanics and have reached the chapter on potential energy. However I am a bit confused about the difference between potential energy and the formula for the potential energy due ...
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