All Questions
Tagged with classical-mechanics energy-conservation
30
questions with no upvoted or accepted answers
3
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Why does the law of conservation of energy not hold true when the work-function $U$ depends explicitly on $t$?
[...] the infinitesimal work $\overline{\mathrm dw}$ comes out as a linear differential form of the variables $q_i$: $$\overline{\mathrm dw}= F_1~\mathrm dq_1 +F_2~\mathrm dq_2+ \ldots + F_n~\mathrm ...
user36790
3
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0
answers
222
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Does the additivity property of Integrals of motion and Lagrangians valid in all situations?
I would like to know if the additivity property of an integral (constant) of motion valid in all situations ? It works for energy but does it work for all other integrals of motion in all kinds of ...
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2
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2
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291
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The so called "Energy Approach" vs "Force Approach", when and how should they be used?
I'm new to physics and I've been trying to solve a few high school olympiad questions. I've figured that I approach the questions by analyzing the forces acting on objects and trying to induce ...
- 657
2
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A particle constrained to always move on a surface whose equation is $\sigma (\textbf{r},t)=0$. Show that the particle energy is not conserved
In Goldstein's Classical mechanics question 2.22
Suppose a particle moves in space subject to a conservative potential $V(\textbf{r})$ but is constrained to always move on a surface whose equation is ...
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2
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0
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80
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Does $\frac{d}{dt}E=0$ always yield unambiguous equations of motion?
If you have a conservative system, one way you can derive the equations of motion is by using the fact that the total energy $E$ of the system is conserved, i.e.:
$$ \frac{d}{dt}(T+V)=0 $$
For example ...
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1
vote
2
answers
106
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Law of Conservation of Energy ambiguity in Giancoli textbook
In my version of the textbook by Giancoli: Physics for Scientists and Engineers, in chapter 8, there is a formulation of the law of conservation of energy that seems unintuitive and correctable to me. ...
1
vote
1
answer
59
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Statistical Analysis of motion under central force
My question is very simple. If we were to plot the motion of a particle inside circular walls governed by a central attractive force with perfectly elastic collisions, would the statistics of the ...
- 11
1
vote
1
answer
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Energy conservation for changes in the Hamiltionian
If the Hamiltonian represents the total energy of the system,
then how does it change?
Does a change in the Hamiltonian violate the conservation of energy?
Of course, we know from the Hamiltonian ...
- 11
1
vote
2
answers
94
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Law of conservation of energy and potential energy
I completely understand how this law goes and how energy is changed from one form to another. But there is something that I thought about, we all know how the potential energy works and when an object ...
- 11
1
vote
0
answers
73
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What's the meaning of $\Delta E-W_{nc}=0 $?
Suppose a system of particles is subject to internal forces, some of which are conservative and some of which are non-conservative. Let $\Delta E$ be the change in mechanical energy of the system as ...
- 11
1
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0
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What is the physical interpretation of a Lagrangian with $\dot{x}^4$?
Among the exercises in the first chapter of Goldstein's book "Classical Mechanics", it appears the lagrangian
$$
L\left(x,\frac{dx}{dt}\right) = \frac{m^2}{12}\left(\frac{dx}{dt}\right)^4 + m\left(\...
- 1,201
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Question about Helmholtz's paper "ON THE CONSERVATION OF FORCE"
Below follows the exact extract from Helmholtz's paper "On the conservation of force".
Let us now imagine, instead of the system $A$, a single material
point $a$, it follows from what has been just ...
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1
vote
1
answer
41
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When can I go in the reference frame of a moving object?
Two particles separated a distance r, each of mass m, are being launched at opposite directions with the same speed v. If we’re in the reference frame of the center of mass of the particles, what ...
- 131
1
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1
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108
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Lagrange Equation - Basics
The basic equation of Lagrange is given by,
$$\frac{\mathrm d}{\mathrm dt} \frac{\partial L}{\partial \dot{q_j}} - \frac{\partial L}{\partial q_j} = Q_j \tag{1}$$
where $T$ is the kinetic energy, $V$ ...
- 17
1
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1
answer
29
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How are the equations for the final velocities of objects derived here?
Assuming linear momentum is conserved in an elastic collision between 2 objects ($\Delta K= 0$) the initial equations one can set up are:
$m_{1}v_{1i} + m_{2}v_{2i} = m_{1}v_{1f} + m_{2}v_{2f} $
$\...
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