All Questions
Tagged with classical-mechanics work
214
questions
67
votes
15
answers
22k
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Why is ascending some stairs more exhausting than descending?
I have been asked this question by school kids, colleagues and family (usually less formally):
When ascending a flight of stairs, you exchange mechanical work to attain potential Energy ($W_\text{...
- 831
52
votes
4
answers
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What's the real fundamental definition of energy?
Some physical quantities like position, velocity, momentum and force, have precise definition even on basic textbooks, however energy is a little confusing for me. My point here is: using our ...
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20
votes
3
answers
4k
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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
18
votes
2
answers
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Conceptually, what is negative work?
I'm having some trouble understanding the concept of negative work. For example, my book says that if I lower a box to the ground, the box does positive work on my hands and my hands do negative work ...
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votes
5
answers
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Proof of conservation of energy?
How is it proved to be always true? It's a fundamental principle in Physics based on all of our currents observations of multiple systems in the universe. Is it always true to all systems? Because we ...
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13
votes
1
answer
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The role of the virtual work principle
Lanczos' masterpiece "The Variational Principle of Mechanics" has, on page 76, the following statement:
Postulate A (virtual work): The virtual work of the forces of reaction is always zero for any ...
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12
votes
2
answers
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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 (...
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9
votes
5
answers
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D'Alembert's principle and the work done by constraint forces in Atwood's machine
From what I understand, constraint forces do no work because they are perpendicular to the allowed virtual displacements of the system. However, if you consider an unbalanced Atwood machine, in which ...
- 483
8
votes
11
answers
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Is it more work to put more (apparent) effort to get the same outcome?
I was taking my dogs for a walk yesterday evening when this question occurred to me.
The two dogs were pretty enthusiastic about the walk and wanted to run on ahead, so the leads were taut and they ...
- 257
8
votes
4
answers
602
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Is there a fundamental reason not to define the work vice-versa
My question arises from something which has never been really clear: in continuum mechanics, why is strain energy defined as:
$$W=\int_\Omega \underline{\underline{\sigma}}:\mathrm{d}\underline{\...
- 734
8
votes
2
answers
2k
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Intuition behind Work
I have a doubt in understanding the intuition behind the concept of work. First of all, I think this isn't duplicate, I've searched on the site, and the closest thing I've found was this post which is ...
- 36.4k
7
votes
1
answer
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A Question about Virtual Work related to Newton's Third Law
In describing d'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as,
$$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$
where $...
- 190
6
votes
2
answers
1k
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What is the physical intuition behind this energy conservation theorem?
I'm reading Quantum Theory for Mathematicians, by Brian C. Hall. Although the book is about Quantum Mechanics, it's chapter 2 is actually about Classical Mechanics, in which I encountered the ...
- 163
5
votes
2
answers
2k
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Why does the work-energy theorem need to include internal forces?
Can anyone kindly explain me why work energy theorem must also include internal forces?
The proof of work energy theorem is derived from Newton's laws of motion, but Newton's laws of motion don't ...
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5
votes
3
answers
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How the definition of work is derived from Noether theorem?
I cite the following phrases from an answer to the Phys.SE question Why does a force not do any work if it's perpendicular to the motion?
...an alternative would be to treat the work-energy ...
user143115
5
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4
answers
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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
6
answers
1k
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Does work-energy theorem account for thermal energy?
Suppose a box (which I assume to be a rigid body) with an initial velocity that starts to slide on a level surface with friction. Imagine this experiment is done in vacuum, so there is no air drag or ...
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4
votes
2
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How do we justify that work is a "transfer of energy" in the general case?
By the work-energy theorem, we can justify that the work on a particle due to the net force equals the change in kinetic energy of the particle. In compact notation,
\begin{align}\tag{1}
W_{\text{net}}...
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4
votes
7
answers
634
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Why does incline on treadmill burn calories faster?
So I was at the gym today, running on the treadmill, when the question hit me:
If I run with the treadmill on incline, I burn more calories. Since I run at the same speed, kinetic energy is constant, ...
- 163
4
votes
2
answers
599
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Work done changes between reference frames?
(This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent ...
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4
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2
answers
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Why is potential energy defined for only a conservative force? [duplicate]
I want direct answer for this and some interpretation with example.
why do we need conservative force to define potential energy?
what is wrong with non-conservative force and other? I have seen many ...
- 93
4
votes
2
answers
488
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What's wrong with my derivation for the spring constant? [duplicate]
An $8.00\ \mathrm{kg}$ stone at rest on a spring. The spring is compressed $10.0\ \mathrm{cm}$ by the stone. What is the spring constant?
I used conservation of energy to solve this problem. The ...
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votes
1
answer
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Is work done by the internal forces independent of the frame of reference?
This question is about work done being dependent on the frame of reference, which is, obviously the net work done.
I ask what is the reason for the work done by internal forces to be independent of ...
- 362
4
votes
1
answer
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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
2
answers
628
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Areas with anti-parallel gravity in classical physics
I cannot indicate an error in the following reasoning if it is done in the framework of classical physics.
Let's make the imaginary setup with two wedges and the ball, when the gravity in the left ...
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3
votes
3
answers
4k
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What is the work done against a force?
Suppose a particle travels a path $\gamma : I\subset \mathbb{R}\to \mathbb{R}^3$ subject to a force $\mathbf{F}: \mathbb{R}^3\to T\mathbb{R}^3$, then we know that we define the work done by the force ...
- 36.4k
3
votes
3
answers
859
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Is there an intuitive explanation of the work formula?
Upon learning calculus, I decided it was time to derive all of classical mechanics to give myself a good understanding of physics. What I found was that, while trying to do so, I would need some ...
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3
votes
1
answer
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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
3
answers
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Where does a torque-invoking force belong in work energy theorem?
First of all, sorry for the poorly phrased question, simply couldn't figure out a better way to put it.
So, the work energy theorem states that work done on an object is equal to the change in its ...
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4
answers
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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 ...
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