All Questions
55
questions
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
12
votes
2
answers
7k
views
Can a force in an explicitly time dependent classical system be conservative?
If I consider equations of motion derived from the principle of least action for an explicitly time dependent Lagrangian
$$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$
under what circumstances (...
- 8,523
7
votes
1
answer
2k
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A Question about Virtual Work related to Newton's Third Law
In describing d'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as,
$$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$
where $...
- 190
5
votes
4
answers
2k
views
Work done by constraint forces -- Generalisation
Consider the above scenario: In the subsequent motion, we need to find the work done by tension on the (trolley + mass) system.
Solution: Suppose at an instant, the velocity of the trolley (and hence ...
- 1,295
4
votes
1
answer
127
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What does it mean for a force to 'produce' virtual displacement?
Book: Variational Principles of Mechanics by Lanczos, 1st edition, 1949.
Statement (page 80):
"Two systems of forces which produce the same virtual displacements are dynamically equivalent."...
- 41
3
votes
1
answer
445
views
Confusion with curl of Lorentz magnetic force
Since the magnetic force is a no work force, $dW=\vec F\cdot d\vec r=0$ for $\vec F(\vec r)=q(\vec v(\vec r) \times \vec B(\vec r))$, therefore $\oint \vec F \cdot d\vec r=0$ by Stoke's theorem. ...
- 26.8k
3
votes
4
answers
2k
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Why the total virtual work done by forces from constraints vanishes? (Perpendicularity of two or more particles)
My mechanics book claims that the total force on the $i$-th particle is
$$
F_i=K_i+Z_i \tag{2.5}
$$where $Z_i$ is the force due to constraints and $K_i$ the real, dynamic force. Then, the book states ...
- 1,335
3
votes
1
answer
358
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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
votes
5
answers
317
views
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 ...
- 17.8k
2
votes
1
answer
12k
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How to prove force is conservative?
How do I prove whether a force perpendicular to the motion is conservative and $\mathbf{F}=\mathbf{F_{0}}\sin(at)$ conservative, where $\mathbf{F_{0}}$ is a constant vector.
I knew that for a force ...
- 494
2
votes
3
answers
16k
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Why is walking up stairs harder than walking normally?
I must admit, I'm pretty new to studying physics and I know this is a simple concept but I'm having difficulty understanding it. I've tried reading the questions here but I just need a little bit of ...
- 123
2
votes
1
answer
143
views
Example of a single constraint force doing virtual work despite the sum of work done by constraints being zero
When deriving d'Alembert's Principle it must be assumed, that the total virtual work done by constraint forces vanishes.
$$\sum_{j=1}^N\mathbf{C}_j\cdot\delta \mathbf{r}_j=0.$$
In the books I've read, ...
- 72
2
votes
1
answer
2k
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Is total mechanical energy always equal to maximum potential energy?
Am I correct in stating this: When initial velocity of an object is $0$ then the total mechanical energy will always be equal to the maximum potential energy (with maximum height or displacement) (...
- 23
2
votes
2
answers
261
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Work done by static friction during rolling while slipping?
I'm a bit confused on whether, during slipping while still rotating, friction does work on the object. I know there are multiple questions on SE that address the rolling case, but this is very ...
- 1,177
2
votes
3
answers
720
views
Work done by tension on a system-generalisation
In All the Classical Mechanics problems I have come across so far, There's one thing that happens invariably: That the work done by tension is zero. Mostly, It simply happens because the (massless) ...
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