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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In an elastic collision, can we choose between cons. of energy and cons. of momentum?

Suppose we have two solid spheres with masses $m$ and $M$, respectively, and that m is significantly smaller than M. The lighter sphere is placed directly on top of the heavier one, and the two are ...
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1answer
7 views

Approximating energy loss caused by drag force

We know the usual aerodynamic drag equation is given by: $$F_d = -bv^2$$ Where $b$ here is just some constants combination related to the property of the fluid and the material passing through. My ...
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+200

Can a car get better mileage driving over hills?

Two towns are at the same elevation and are connected by two roads of the same length. One road is flat, the other road goes up and down some hills. Will an automobile always get the best mileage ...
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3answers
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Conservation of momentum but not kinetic energy in inelastic collisions

In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is. Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: ...
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18 views

Fluid approximation for inflaton?

In cosmology there is a widely used fluid approximation which applies when the mean free path is very small compared to the scale of observation and then all the properties of stress energy tensor can ...
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2answers
66 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $?

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
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1answer
41 views

Difference between speed of light and of bullet after passing through a barrier [duplicate]

I just read that, when a ray of light traveling in vacuum at $c$ strikes a glass slab, its speed decreases and then when it re-emerges it gets back to its original speed i.e $c$. If I draw a ...
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3answers
116 views

Example of law of conservation of energy

Law of conservation of energy states that "Energy of the universe remains constant. Energy can neither be created nor be destroyed, but it can be transformed from one form to another". So I ...
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1answer
113 views

Changing momentum of moving trolley

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

Is potential energy an energy exists or potentiality of energy? [closed]

I want to ask whether Potential Energy is truly existing Energy - though i know the energy concept is abstract and we do not know what is energy truly as Feynman said - or it is the potentiality that ...
0
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0answers
32 views

How to convert rotational energy into electricity [closed]

Could someone explain how to convert rotational energy (of a motor) into electricity by means of electro-induction (at least that’s what I think it's called) using magnets? please, can you break it ...
0
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1answer
44 views

Doesn't the Big Bang negate the law of conservation of matter? [duplicate]

I was watching Hawking (2004 film) and in the movie, Hawking has a sudden insight that all the matter and energy observed in the known universe may, in fact, have sprung out from nothing (singularity) ...
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1answer
39 views

Ideally black plates

Let's consider $m$ ideally black, thin, infinite plates. Let $T_i$ be the temperature of the $i$-th plate. For given $T_1 > T_m$, why is the radiant flux between any two adjacent plates the same ...
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1answer
173 views

Proof of the conservation of the energy functional for the Gross-Pitaevskii equation?

From the Gross-Pitaevskii equation \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation ...
2
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1answer
39 views

How does energy get transfered from destructive interference point to constructive one?

If there are two pressure waves (like sound waves) that travel in opposite directions and have the same amplitude then destructive interference occurs: one wave will compress the air particle (here ...
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2answers
72 views

Blackbody radiation and emissive power

According to blackbody radiation theory, and thanks to Planck, we now know that there is a energy density, $u(\lambda,T)$ [$J/m^3$], associated with a certain wavelength at a particular temperature. ...
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0answers
39 views

How can electron move and yet have zero total energy?

Imagine an electron positioned at a zero electric potential plate with zero kinetic energy. The zero electric potential plate is combined in series with another plate with positive electric potential ...
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0answers
22 views

Why is the total energy of current universe conserved? [duplicate]

I began to think about this problem a long time ago and also asked some classmates as well, but none of them can give me a creative solution. I actually developed an original theory that our ...
0
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2answers
33 views

Find max height [closed]

I have stucked with finding max height of an $m$, given only $m, M$ and initial velocity of $m$ - $\vec{V}$. There is no friction in the system. As I understood I need to find $\vec{V_0}$ - velocity ...
2
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3answers
418 views

Two dimensional elastic collisions with varying angle of incident

If in an elastic collision I know all initial values and that mass for each object remains constant throughout the collision (but different from one another) how can I determine their final velocity ...
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1answer
143 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 ...
4
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3answers
275 views

Do photons lose energy due to gravitational redshift? If so, where does the lost energy go? [duplicate]

In the gravitational redshift, the frequency of photons radiated from some source is reduced. As the energy of a photon is given by $\hbar\omega$, if the frequency is reduced where is the lost energy? ...
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2answers
42 views

How does Ohm's law relate to transferring energy?

Potential difference = Current x Resistance where Resistance is a constant. Walking through a circuit I have 1 battery, a wire and 2 components. I start of with 6 volts at the battery and after the ...
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2answers
36 views

Why does this capillary action generator not work?

So I was doing a bit of reading. Apparently the the obstacle to generating energy from the forces driving capillary action is breaking the surface tension at the top of a capillary tube. It is just ...
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3answers
123 views

Does energy conservation not hold in fission and fusion processes?

I have read that during fission and fusion processes, there is some kind of equilibrium between the single nucleus and the disintegration products, so they are constantly being converted into each ...
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1answer
24 views

What is the source of energy in this system? (resonance realated)

This is curiosity question, sorry if description is too vague. Suppose we have a string attached to some small frame on both sides Then we apply a force by plucking it with a finger, lets say 5.0 N ...
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3answers
596 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 ...
2
votes
1answer
41 views

Ball rolling on half-pipe

It is well-known that a ball rolling down a half-pipe where the side it starts on has enough friction for the ball to roll without slipping and on the side other to be frictionless, that the ball will ...
4
votes
1answer
349 views

Sufficient conditions for the energy to be not conserved?

I'm almost embarrased to ask this question because I thought I was by now very confident with classical mechanics. Someone has stated that given a mechanical system with a Lagrangian $L$ s.t. ...
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1answer
139 views

Why isn't jumping against a wall an elastic collision?

According to this calculator http://www.abecedarical.com/javascript/script_collision1d.html when low mass object hits high mass object it is reflected gaining opposite velocity almost the same as ...
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0answers
23 views

beta minus decay: expression for maximum electron energy

I'm having some trouble finding an expression for the maximum electron energy in beta minus decay. In the frame where the neutron is initially at rest, conservation of momentum reads: ...
0
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1answer
48 views

Where does mass go when energy is converted in to photons?

If matter and anti-matter annihilate each other they emit a photon with the energy that corresponds to the mass, right? This is the best example I could think of matter/energy being converted directly ...
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0answers
18 views

Why must the deviations from equilibrium be small for zero difference in energy in this solenoid?

A long solenoid with a square cross-section is partially immersed in a magnetic, non-conductive liquid of permeability $\mu$. The solenoid's axis is parallel to the liquid's surface. ...
4
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1answer
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How much power would it take to stop a bullet with a magnet?

If a 7.5 gram copper-jacketed lead bullet (say, a 9x19mm Parabellum) was travelling at 360 m/s, how much power would it take to diamagnetically stop it in the space of one meter? This question comes ...
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6answers
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Total energy of the Universe

In popular science books and articles, I keep running into the claim that the total energy of the Universe is zero, "because the positive energy of matter is cancelled out by the negative energy of ...
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1answer
88 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, ...
2
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1answer
26 views

Comparing Brachistochrone curve with a Hypocycloid curve

I want to compare the time that it takes to slide a particle in a frictionless hypocycloid curve, so time would be given by the arclength divided by the velocity So I need first compute the ...
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4answers
309 views

Is any energy required to deflect an asteroid, with force always perpendicular to its trajectory?

Let's assume there is an asteroid traveling on a straight line (far from any gravitational source), and we need to deflect it from its actual trajectory, so we build a rocket motor on the surface and ...
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1answer
14 views

Energy lost is a percentage or flat rate?

If I drop a ball onto the floor, there are a few possible outcomes. Firstly, that the collision is perfectly elastic, and no energy is lost from the ball into the surroundings (ie it bounces to the ...
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1answer
50 views

Showing time-invariance of Lagrangian with time-displacement operator

I am trying to show that the time-invariance of the Lagrangian of a simple one-particle system implies energy conservation for that system. The first step is, well, to show that the Lagrangian is ...
2
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1answer
109 views

Insight into Torricelli's Equation ($v^2=u^2+2as$) [closed]

Torricelli's Equation ($v^2=u^2+2as$) is usually presented as the particular formulation of the SUVAT system which doesn't involve t. It is derived from the others using some (perhaps well-motivated) ...
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3answers
321 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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0answers
49 views

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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0answers
91 views

Why 'Force x displacement', and not momentum to measure energy? [closed]

[I have changed the title and also edited the question in other ways to make it clearer what I am asking. I hope it no more reads like a duplicate. Nor it remains any more a history question.] I have ...
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3answers
81 views

Finding the angular velocity of a rod hit at a distance from its pivot [closed]

A 1m long, 2kg stick is nailed to the wall with a single nail, allowing it to pivot and freely rotate at the end. A 1kg ball, with speed 3m/s makes contact with the stick at some distance x (unknown) ...
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2answers
51 views

Auto spinning turbine generator

This might be dumb question but I'm so curious to know if this actually works or is impossible. I was researching how you could generate electricity from magnets and copper wire and also have read how ...
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1answer
122 views

Heat Equation with In-Depth Radiation Exact Solution

I am looking to solve the heat conduction equation in a semi-infinite solid with in-depth radiation on the domain $-\infty < x < 0$. The governing equation of this problem is: $$\rho c ...
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4answers
2k views

Escape velocity from Earth

We know the escape velocity from the Earth is 11.2km/s. Isn't it the velocity required to escape from earth if we go normal to the surface of earth? i.e while we derive the formula for the escape ...
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1answer
78 views

Falling rope problem (disagreement with solution found at Problem Set)

On a frictionless table there is a homogeneous rope of length $L$ and mass. We push the rope such that it immediately starts falling due to gravity. Find the velocity when the rope has fallen of ...
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2answers
68 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 ...