The law of conservation of energy, which states that the amount of energy in a system is constant. For questions about Earth's environment, see the climate-science tag instead.

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Prove energy conservation using Noether's theorem

I wonder how you prove that energy is conserved under a time translation using Noether's theorem. I've tried myself but without success. What I've come up with so far is that I start by inducing the ...
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0answers
13 views

How to Detrmine mass of the ball that is being hit by another ball on the pendulum [on hold]

I know mass of ball on the pendulum M, initial height of that ball h+H, height of the table on which pendulum is and I know how far away from the table the ball mass m falls. I have the following ...
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1answer
248 views

Lorentz invariance, energy-momentum conservation & the locality of interactions

I have been reading these notes ("Minkowski Spacetime: A Hundred Years Later", by Vesselin Petkov) 1, in which the author states (in the middle of the text on page 137) that "The only Lorentz ...
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2answers
59 views

Work done according to Newton's Principia

Actually I was going through the principia, reading Newton's derivations of the properties of ellipses. Suddenly I had this question which got stuck in my mind - Throughout Principia Newton uses the ...
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2answers
70 views

Newton's Cradle: why does it stay symmetric? [duplicate]

How is it that always the same number of balls leave at the other end in Newton's cradle. I understand that the momentum needs to be conserved, but as momentum is defined as p=m*v couldn't you have a ...
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3answers
156 views

Are mechanical energy of an element of a rope and energy density constant in the case of mechanical waves?

I'm confused about energy driven by a wave. Consider a sinousoidal wave moving in a rope. In my view each element $dm$ of the rope follows a simple harmonic motion in time. That means that the ...
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2answers
106 views

Do conservation laws contradict quantum mechanics? [on hold]

Take for example the double-slit experiment interpreted in the Copenhagen sense. The particle leaves as an object with mass, yet passes through the slits as a massless wave, only to collapse again as ...
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1answer
115 views

Quantum field theory with constraint: energy-momentum conservation?

Suppose I have a 2-form field $B$ and a Lagrange multiplier field $\lambda$, then the Lagrangian $S = \int (B \wedge \delta B + \lambda \delta B \wedge \delta B)$ with a Lie derivative operator ...
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0answers
32 views

Feynman's paradox : “conservation of angular momentum or Lenz's law ?” [duplicate]

When I was in high school, out of my interest I read electro-magnetism topic from Feynman's lecture on physics. There was a Paradox question in that topic, answer of which i am seeking here... Below ...
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4answers
17k views

Why can't energy be created or destroyed?

My physics instructor told the class, when lecturing about energy, that it can't be created or destroyed. Why is that? Is there a theory or scientific evidence that proves his statement true or ...
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2answers
7k views

Why can't we destroy energy?

From a wikipedia article: In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither ...
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1answer
398 views

Conservation of energy when focusing black body radiation on another black body

This question about whether or not it is possible to focus black-body radiation to make something hotter than the radiation's source was answered mostly negative: the second law of thermodynamics ...
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4answers
681 views

Optimal speed for the water wheel

The hydroelectricity plants extract the potential energy of highly deployed massive object (water) as it falls down. Without turbine, all that energy would be converted into speed (kinetic energy) at ...
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1answer
137 views

Work done by friction on a body?

I know that when a body slides over a surface, the work done by friction is not stored as potential energy in the body. It is dissipated in the form of heat. But why is it not stored as potential ...
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1answer
27 views

Conservation of energy in a sound wave

I have two ultrasonic transducers, an emitter and a receiver, and I'd like to know how the energy of the spherical wave is conserved. I guess the energy is proportional to its amplitude and it ...
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1answer
40 views

Velocity Related To Gravitation [closed]

Which Equation is correct $v^2=\large{\frac{2GM}r}$ OR $v^2=\large{\frac{GM}r}$? I am getting confused here.
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3answers
58 views

Is conservation of energy only for isolated systems?

I am thinking in the mechanical context. Everywhere I research (e.g. Wikipedia) the law of conservation of energy is stated only for the special case of an isolated system. I am wondering if ...
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1answer
377 views

first law of thermodynamics and conservation of energy

The first law of thermodynamics is referred to as a reformulation of the law of conservation of energy. I am not sure to fully understand this relationship. My way of picturing it is the following. ...
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2answers
228 views

Current on both sides of a capacitor

When a capacitor is connected to a DC circuit, what ensures that the current on both sides of the capacitor is the same? When charges arrive at one end of the capacitor they stop moving; presumably ...
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3answers
37 views

Finding an object's final velocity with distance dependant force [duplicate]

I am (just for fun) trying to calculate the velocity with which the moon would impact the earth if it stopped orbiting and simply headed towards earth. I know the force is $\frac{G m_1 m_2}{r^2}$. ...
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1answer
44 views

Can we produce energy from pure substance having considerable mass? [closed]

According to Einstein's formula, $E=mc^2$. Any substance which has mass can be converted into energy or energy is also existing in the form of mass. So I am very much interested to build a machine ...
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4answers
2k views

Do virtual particles actually physically exist?

I have heard virtual particles pop in and out of existence all the time, most notable being the pairs that pop out beside black holes and while one gets pulled away. But wouldn't this actually violate ...
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4answers
246 views

How is energy converted when massless spring is attached to a rigid support

Say a massless spring of length $l$ is attached to a rigid support. It is extended to length $l + x$. Now at this position, the force extending it is removed. How will its potential energy be ...
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3answers
49 views

Change in linear momentum [closed]

Let A and B be to rigid blocks. A is stationary while B is moving with a velocity $u$. So if B collides with A. (These blocks are on a frictionless surface.) What would happen after B collides with ...
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3answers
939 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
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2answers
117 views

Why is the object's maximum speed at $x=0$ for spring?

My book derives velocity of the hanging object of a horizontal spring (on frictionless surface) as a function position: $$v=\pm \sqrt{\frac{k}{m}(A^2-x^2)}$$ and shows the maximum speed is at when x ...
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1answer
35 views

In this energy conservation problem, why are the answers different with different units? [closed]

Really basic question, but basically I'm given a change in height in centimeters (that's how I measured it). From that, I'm supposed to find the initial kinetic energy. $KE_i = PE_f$ After doing ...
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1answer
55 views

Understanding potential energy

I am self-studying the classical mechanics using the book by Taylor, and I have a question about the potential energy. The book (pg 111) says: If all forces on an object are conservative, we can ...
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2answers
237 views

Changing momentum of moving trolley

Consider a trolley of mass $m$ moving at a velocity $v$ along a smooth horizontal plane. It is full of water, and water is leaking at a constant rate out of the bottom of the trolley, i.e ...
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2answers
769 views

In wave motion of a string both kinetic energy and potential energy are minimum at $y=y_\text{max}$ then why does the string comes down again?

In wave motion of a string both kinetic energy and potential energy are minimum at $y=y_\text{max}$ then why does the string comes down again? As everything in tries to attain lowest energy possible ...
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2answers
169 views

Do all forms of energy fall under kinetic and potential energy?

I know that energy is recognized through motion. Even in the mass-energy equivalence a velocity is present even though it is a rest-energy (Not really sure if this would count as a potential energy ...
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0answers
40 views

What are the conditions for the string of a pendulum to become slack? [closed]

Suppose the bob of a stationary pendulum is given a sharp hit to impart it some horizontal speed. Now what are the conditions for the string to become slack after rotating a particular angle? ...
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2answers
37 views

Why do people say that 'power flows' into or out of a component in an electric circuit?

Currently, I am learning about electric circuits, and how to apply the basic concepts of physics, like work and energy. But I keep running into the same phrase--on Wikipedia, my textbooks, ...
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1answer
35 views

Are all heaters exactly as energy efficient as each other?

I many applications, efficiency is measured in terms of how much of the input energy is wasted generating heat instead of the actual type of energy you want. For example, lightbulbs generating heat ...
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1answer
44 views

Free fall in non-uniform field

Imagine I'm a space-diver, with mass $m_1 $, 500 miles above the Earth's surface at $x_i$. I want to calculate my position, velocity, and acceleration as a function of time, accounting for the Earth's ...
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1answer
47 views

Energy conservation around a black hole

In the Schwarzschild black hole, the Killing vector "time translation" $k^a$, so that the following quantity is conserved along a geodesic: $$E = -g_{ab}k^au^b = (1 - ...
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1answer
101 views

Is Phone-Charging Plant Product Even Possible?

Bioo, a new company making the rounds in the press, claims to produce "electricity from plants' photosynthesis." Specifically, their website claims that a single potted plant with their integrated ...
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14 views

Derivation of Poynting theorem in matter

In most textbooks I have read they derive the Poynting theorem using the Maxwell's Equation in vacuum and the fact that the force density $f=\pmb{E} \cdot \pmb{J}$. Then they just generalize it ...
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1answer
43 views

What are the assumptions behind the Lagrangian derivation of energy?

What are the assumptions behind the Lagrangian derivation of energy? I understand that we're searching for a function $L$ that describes a set of physics so that solving the energy minimization ...
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34 views

Is expectation value of the Hamiltonian always the energy? [duplicate]

There are time dependent & space dependent systems (magnetic fields) and time independent (particle in a box or harmonic oscillator). In the latter the expectation value is the 'average' energy ...
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1answer
67 views

Do you know the principle which says that connecting two sources of similar kind produces a waste and destruction? [closed]

There is a great article, called commutation cells, which states that you cannot transfer kinetic energy from one container to another immediately, bypassing the potential energy storage. Otherwise, ...
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2answers
178 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
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1answer
40 views

Conservation of energy and realm of possibility

The law of conservation of energy states that energy cannot be created or destroyed. Based on this principle, you can safely conclude that any effect resulting from a cause must somehow keep all ...
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3answers
505 views

Poynting's theorem - energy conservation

Poynting's theorem: $$\int_V\left(\vec{E}\cdot\vec{J}\right)\,\mathrm dV = -\dfrac{\partial}{\partial t}\int_V\dfrac{1}{2}\left(\epsilon_0 E^2 + \dfrac{1}{\mu_0}B^2\right)\,\mathrm dV - ...
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1answer
36 views

Expansion of the Universe and Conservation of Energy [duplicate]

How the expansion of the universe doesn't violate the principle of the conservation of energy? If we would put a spring between two objects, the distance would get bigger between them, so would the ...
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0answers
26 views

Collision time of two particles [duplicate]

The question I am trying to answer is the following. Consider two particles of mass $m_1,m_2$, initially at rest at a distance $2a$ apart. They are attracted to each other via Newton's law with ...
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1answer
79 views

How does the uncertainty principle relate to quantum fluctuations?

I found a webpage that just kind of mentions the uncertainty principle lightly but doesn't really go into detail as to why we need it in the first place when considering quantum fluctuations and ...
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3answers
141 views

Where does the energy go when engine braking?

If you're in gear in a car and not accelerating, the car slows down faster than it would from just air resistance and tire deformation. In normal braking, the energy is turned into heat from the brake ...
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76 views

Where does the energy of a photon trying to escape a black hole go?

I've heard "light cannot escape a black hole" explained several ways. One is that if a photon inside the event horizon tries to escape a black hole it loses energy to gravity. As it loses energy its ...
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Why does positive work done by internal conservative forces $\implies$ decrease of potential energy?

Potential energy can be thought as the amount of work that the force can potentially do on the point because of its position. $$W=-\Delta U=U_{initial}-U_{final}$$ A positive work done by a force ...