New answers tagged energy-conservation
0
votes
Closest distance of approach
Rewrite the total energy as:
$$
H = C + \frac{1}{2}\mu v^2 + \frac{kq_1q_0}{r}\;, \qquad(1)
$$
where $r$ is the relative distance, $v$ is the relative velocity, $\mu$ is the reduced mass, and $C$ is a ...
1
vote
Closest distance of approach
Identical velocities implies zero relative velocity, meaning the objects are not moving with respect to each other - they are not getting any closer or farther from one another. Since the objects were ...
0
votes
Closest distance of approach
Say the two objects are moving to the right. As long as the one on the left is moving faster it gaining on the other and the the distance between them is decreasing. Once the one on the right is ...
1
vote
Accepted
Total rotational energy of oval-shaped object
As requested, I’ll try to make my comment more accessible. For a rigid body rotating about a point, you can associate two vector quantities: angular velocity $\vec \Omega$ and angular momentum $\vec L$...
1
vote
How did Noether use the total time derivation to get her conservation of energy?
You have to use the Euler -Lagrange equation also $\left( \frac{\partial L}{\partial x}-\frac{d}{dt}\frac {\partial L}{\partial \dot x}= 0 \right)$
1
vote
How did Noether use the total time derivation to get her conservation of energy?
There are two ways of seeing that the two equations can be combined to yield the desired result...
The first one is simply to substitute
$$\frac{d}{dt}\bigg(\frac{\partial L}{\partial \dot{x}}\dot{x}\...
1
vote
Understanding conservation of energy in a pulley problem
I think you can argue as follows. We have a tension T acting on both masses. The variation of kinetic energy for $m_1$ is
$$
KE^1_{f} - KE^1_{i} = \int_0^h (- m_1 g + T) \ dx,
$$
while for $m_2$ we ...
2
votes
Accepted
Yet another perpetual motion machine: does this imply large selective membranes are not possible?
Many devices that seemingly constitute perpetual motion machines contain two parallel paths that clearly provide excess energy each way.
One example is a capillary wick that lifts water to be ...
1
vote
Does a water heater consume more energy if constantly kept on than if it is made to heat the water on demand?
Yes, your reasoning is correct.
Let's consider a cylinder:
Diameter 0.5m
Length 0.8m
Internal volume 157l
It has a total area of $ 1.65 m^2 $.
Suppose it is insulated with PIR foam, thickness 5cm, ...
6
votes
Accepted
Where does the excess energy go in this problem?
By postulating the collision is an inelastic collision, you postulate it to not conserve mechanical energy (that's what inelastic means). As this is your postulate and you haven't set a place for the ...
-1
votes
How conservation of energy looks like in the moving frame?
Let' say there are two earths, on one of those earths a car is accelerating.
Now the car says that the kinetic energy of the earth that the car is not pushing increases by a huge amount, and the ...
-1
votes
How conservation of energy looks like in the moving frame?
Energy is not invariant across reference frames. From the car's frame you would correctly calculate the car's kinetic energy to be 0. The earth, on the other hand, would have massive kinetic energy.
...
2
votes
How conservation of energy looks like in the moving frame?
From the car's point of view, there is a fictitious force, which does work. Therefore, the car sees extra potential energy. You can think of the fictitious force as weak constant gravity. Similar to ...
1
vote
Why did Noether use the Lagrangian for her conservation of energy theorem?
The very starting point of Noether's theorem (NT) is an action formulation (and hence a Lagrangian), and quasisymmetries thereof.
Noether did not formulate her theorem with only energy conservation ...
2
votes
Why did Noether use the Lagrangian for her conservation of energy theorem?
However, I know that the Lagrangian doesn't always equal energy.
The Lagrangian never equals the energy, unless there is no potential $U$ so the problem is trivial.
In many cases, we can show that ...
0
votes
Microscopically, are all collisions really elastic collisions?
Even at a grade-12 level, the answer is "no." It's perfectly reasonable to construct a collision where energy is conserved, but kinetic energy is not conserved.
For an example you could ...

rob♦
- 74.3k
0
votes
Microscopically, are all collisions really elastic collisions?
In practice, ordinary materials have a mesoscopic structure (fibers, connections between supra-atomic structures, arrangement of atomic planes). The inelasticity observed in macroscopic bodies, like ...
0
votes
How is a motorcycle whip possible?
To me, this looks like it can be explained by the classic experiment of standing on a round table and holding a spinning bicycle wheel.
If you stand on a turntable, take a bicycle wheel, hold it ...
2
votes
Accepted
Why do we give so much importance to energy, i.e., the conserved quantity under time symmetry?
As a complement to Nickolas's great answer, note that throughout physics, conservation laws are so useful that even approximate conservation laws can be of enormous interest. Conservation laws let you ...
1
vote
Is the total gravitational energy in the sun greater than the energy that is produced by the sum total of the nuclear fusion contained therein?
I will address the title:
Is the total gravitational energy in the sun greater than the energy that is produced by the sum total of the nuclear fusion contained therein?
Two concepts are confused in ...
1
vote
Is the total gravitational energy in the sun greater than the energy that is produced by the sum total of the nuclear fusion contained therein?
Unlike a chemical chain reaction or a fission chain reaction I believe fusion cannot sustain inself.
Fusion reactions in the sun proceed very similarly to how regular exothermic chemical reactions ...
4
votes
Is the total gravitational energy in the sun greater than the energy that is produced by the sum total of the nuclear fusion contained therein?
To sum up: energy is conserved, fusion converts some mass into energy, this is exothermic, and the gravitational binding energy doesn't contribute much to the heat of the sun.
The total gravitational ...
1
vote
Is the total gravitational energy in the sun greater than the energy that is produced by the sum total of the nuclear fusion contained therein?
Stars sustain fusion for millions or billions of years. The density and temperature in the core of a star is high enough to sustain fusion at a rate that replenishes the outgoing energy. The energy to ...
0
votes
Statistical Analysis of motion under central force
i'd recommend reading this, the motion really depneds on the initial conditions of the particle:
https://en.wikipedia.org/wiki/Classical_central-force_problem
10
votes
Why do we give so much importance to energy, i.e., the conserved quantity under time symmetry?
At the end of the day, physics is an experimental science. If your experiment can't measure some effects, you might just as well ignore them. That is quite often the case with cosmological effects.
If ...
1
vote
Accepted
Are one-dimensional bifurcations dissipative or conservative?
In general, a dynamical system $\dot{x} = f(x)$ is conservative if and only if $∇·f = \mathrm{div} f = 0$ (in the entire phase-space volume of interest).
This works irrespective of the dimension of ...
0
votes
Energy conservation in a system of two bodies
You choose the system.
Once this is done then internal and external forces need to be identified.
An internal force will always have a Newton's third law pair and an external force will not have a ...
2
votes
Piano on the moon
both the strings on the piano and the structure of the piano itself will vibrate without radiating away any sound energy, but since they both possess internal friction, the vibrational energy will ...
4
votes
Piano on the moon
The strings making up the chord and the body of piano will vibrate for a longer period of time since none of that energy will be used to create pressure waves in 1 atm of air.
0
votes
Conserving energy in newtonian mechanics
But we know energy is always conserved
For mechanical systems, a more general statement is that the work of the net force is equal to the change of the kinetic energy. For example, if the object is ...
1
vote
Energy conservation in a system of two bodies
Total mechanical energy (KE+PE) of a system is conserved if the sum of external forces acting on the system is zero. Consider the following systems:
$m_1$ plus Earth
$m_2$ plus Earth
$m_1$ + $m_2$ + ...
0
votes
Energy conservation in a system of two bodies
Generally, only the total energy of an isolated system is conserved.
You write
No external force us acting on that system.
meaning the system of earth and one of the masses... But it is not true: ...
2
votes
Accepted
Where is the excess energy going to when a solar inverter is operating a photovoltaic (PV) panel away from the maximum power point (MPP)?
The answer is easier if you only consider a single cell, and apart from some details the same answer holds for an entire string of cells and then for an entire panel that consists of several strings.
...
6
votes
Is David Tong incorrect in this remark about classical mechanics in his QM lectures?
Well, in Tong's defense he did insert the phrase roughly speaking to indicate that the remark is not precise.
Concerning that the Lorentz force is not a conservative force according to the ...
14
votes
Accepted
Is David Tong incorrect in this remark about classical mechanics in his QM lectures?
Indeed, I think that the statement in Tong's book is quite ambiguous (though it is not definitely false as I discuss below). In principle there is no relation between the possibility of a Hamiltonian ...
1
vote
Conserving energy in newtonian mechanics
Energy is NOT always conserved.
Energy is conserved ONLY in closed systems.
If you take up a stone in your hand, the stone is not a closed system.
If you put energy into a stone by accelerating it, it ...
1
vote
Conserving energy in newtonian mechanics
So, right now, you are considering the ball as a part of the system, which obviously will lead to contradictions in the conservation of energy in a similar, but not the same way as you have told.
See, ...
Top 50 recent answers are included
Related Tags
energy-conservation × 2964newtonian-mechanics × 907
energy × 569
homework-and-exercises × 454
potential-energy × 296
work × 282
thermodynamics × 243
conservation-laws × 227
momentum × 216
classical-mechanics × 215
electromagnetism × 195
newtonian-gravity × 193
forces × 149
collision × 144
cosmology × 114
quantum-mechanics × 105
general-relativity × 105
perpetual-motion × 101
spring × 100
dissipation × 98
mass-energy × 91
rotational-dynamics × 90
special-relativity × 88
kinematics × 82
friction × 82