All Questions
Tagged with classical-mechanics energy-conservation
248
questions
2
votes
2
answers
780
views
How does energy stay conserved if the force is time dependent and doesn't depend on location?
While reading The Theoretical Minimum for Classical Mechanics the author said that the derivative of the potential energy is equals the force and showed this equation describing the potential energy ...
- 77
1
vote
1
answer
42
views
Elastic collision between 2 particles in 2D [closed]
A particle with mass $m_1=m$ moves along the x-axis at a velocity of $v_0$ and collides with another particle $m_2=4m$. As a result of the collision $m_1$ travels upwards at an angle of $90 ^\circ$. (...
- 111
0
votes
1
answer
70
views
Solving a problem using energy conservation doesn't work [closed]
Hello I'm trying to solve the following problem as I'm preparing for physics olympiads:
The solution they gave involves finding the forces acting on the cylinder and hence finding acceleration, which ...
- 135
0
votes
2
answers
74
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Why is the work done by moving an object up vertically not greater than mgh
Watching Walter Lewin's classical mechanics. In lecture 11 he says when moving object up vertically distance h, the work done by gravity is -mgh, which makes sense. But then he said the work done by ...
2
votes
3
answers
199
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Describe the characteristics of a Hamiltonian System to a non-scientist
A Hamiltonian system is a dynamical system driven by a Hamiltonian $H$, i.e.
$$ \dot{q}=\nabla_p H,~~~~ \dot{p}=-\nabla_q H. $$
These systems have nice properties like being symplectic as well as the ...
- 265
8
votes
1
answer
2k
views
If the Lagrangian depends explicitly on time then the Hamiltonian is not conserved?
Why is the Hamiltonian not conserved when the Lagrangian has an explicit time dependence? What I mean is that it is very obvious to argue that if the Lagrangian has no an explicit time dependence $L=L(...
- 227
1
vote
2
answers
184
views
Time varying potentials and conservation of total energy
When a potential explicitly depends on time, energy is not conserved. However, if we take into account what is causing this potential (for example, a machine moving some object(s)), would the total ...
- 167
1
vote
0
answers
57
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Why is the conserved Lagrangian energy $E$ equal to the total energy in this example but not in a similar example? [duplicate]
I am aware that there exists duplicates to the title and have gone through the answers but it still doesn't answer my issue with a statement in the last image.
These two similar situations with slight ...
1
vote
0
answers
52
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Intuition behind energy not being conserved in Rheonomous mechanical system [closed]
firstly, this is what Rheonomous System means. So, in such a system, the kinetic energy is not exactly just a quadratic function of generalized velocities because one of the generalized coordinates ...
- 301
-1
votes
2
answers
92
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Can someone explain what did Feynman wanted to explain in his lectures (Vol 1, Chapter 4.2.)?
This is the text from Feynman lectures - Vol. 1 - Chapter 4-2 Gravitational potential energy:
Consider weight-lifting machines—machines which have the property that they lift one weight by lowering ...
-1
votes
3
answers
118
views
How can mechanical energy be preserved if the potential energy is negative? [closed]
If I set the upwards direction as positive, the gravitational acceleration $g$ will be negative (and thus, $mgh$ will be negative if $h$ is positive). Thus, the potential energy will be negative, but ...
- 248
1
vote
1
answer
49
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Potential energy with Taylor series for particle
I have been doing the following problem:
Imagine we got a particle in $U(x)$ field and we need to consider the motion of the particle near $x=a$. It says to use Taylor series for $U(x)$
$U(x) = U(a) + ...
- 525
15
votes
5
answers
3k
views
Why does time-translational symmetry imply that energy (and not something else) is conserved?
I'm trying to understand Noether's theorem from an intuitive perspective. I know that time-translational symmetry implies the conservation of energy. Is it possible to convince oneself that time-...
- 253
1
vote
1
answer
46
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Angular velocity - from inclined to horizontal plane [closed]
Assume a uniform ball ($m,\ R,\ I=\frac25mR^2$), experiencing pure rolling on both horizontal and inclined planes.
If we imagine a point $A$ at the very start of the inclined plane, we can show that ...
- 11
13
votes
6
answers
1k
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(A modification to) Jon Pérez Laraudogoita’s "Beautiful Supertask" — What assumptions of Noether's theorem fail?
I am curious about the following (physically unrealizable) scenario involving a supertask described here: https://plato.stanford.edu/entries/spacetime-supertasks/#ClasMechSupe. The original paper is ...
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