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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Lagrangian and conservation of energy

If Lagrangian of the motion is $$\mathcal{L}=\frac{1}{2}m\left(a^2\dot\phi^2+a^2\dot\theta^2\sin^2\phi\right)+mga\cos\phi,$$ how can I show that total mechanical energy is conserved? I've read ...
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2answers
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Elastic collision and spring

Bodies $A$ and $B$ are moving in the same direction in a straight line with a constant velocities on a frictionless surface. The mass and the velocity of $A$ are $2 \text{kg}$ and $10 \text{m/s}$. ...
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2answers
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Are information conservation and energy conservation related?

as evident from the title, are both, conservation of energy and conservation of information two sides of the same coin?? Is there something more to the hypothesis of hawking's radiation other than ...
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2answers
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curvature tensor component capable of doing work on $T_{\mu \nu}$

I'm wondering what part of the curvature tensor is able to do work (and hence transfer energy) in matter. I'm wondering if this tensor: http://en.wikipedia.org/wiki/Stress-energy-momentum_pseudotensor ...
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1answer
393 views

Speed of a falling pencil [closed]

If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground? (Assume the pencil is a uniform one ...
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3answers
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Where does the electricity, generated by a solar panel, go if you don't use the electricity?

I'm sorry if this question is too trivial for this Q&A forum. I am a layman when it comes to physics (though I did cover the high-school physics courses). I was wondering what happens to the ...
9
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1answer
143 views

How can a planet gravitationally capture objects?

I would expect that any asteroid or other object originating far away but passing near a planet would pick up speed and energy as it approaches, but unless it comes into contact with the atmosphere ...
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1answer
251 views

Numerical schemes, time integration algorithms and energy conservation

What does it mean when someone says a numerical scheme or a time integration algorithm is "energy conserving". How can a numerical scheme "gain" or "lose" or "conserve" energy apart from the numerical ...
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5answers
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Can I take heat from the air and convert it to electricity?

Its a summer day and the air in my house has been heated up. I could switch on my air conditioning, but then I'd be using energy from the grid in order to reduce the amount of energy in my house. ...
6
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2answers
385 views

What is changing in latest light bulb technologies?

I'm confused with the latest home lightning bulbs. Understanding filament bulbs was easy. For example take 220V, 100W filament bulb: Power = $V^2/R$ Filament gets heated and emits energy in the form ...
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4answers
996 views

How to tell if the collision is elastic or inelastic?

I'm a programmer and a game developer, not a mathematician or a physicist. So please go easy on the math :) I know two things: How to find the new velocities of two objects after an elastic ...
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3answers
230 views

Is energy conserved in general relativity? Does $\nabla_aT^{ab}=0$ represent the conservation of energy and momentum?

For example, the radiation dominated cosmology, the energy density of radiation is propotional to $a^{-4}$ and the volume is propotional to $a^3$, where $a$ is the scale factor. So the total energy ...
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2answers
266 views

Total Energy of the Universe? [duplicate]

I've heard the total energy is zero, but I've also heard it cannot be said to be zero since there's so much unknown stuff in the universe. Is that true?
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3answers
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If empty space has energy, and space is expanding, is this energy equally distributed as space expands?

The cosmological constant (dark energy) is often described in terms of empty space having a non 0 energy value and this energy being the source of the accelerated expansion of the universe. If space ...
3
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3answers
194 views

computer vs heater coil comparison

If I have a computer and a heater coil that consume exactly the same amount of energy, which would be more efficient at heating my room? This is assuming that they both have the same fans and heat ...
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2answers
2k views

First integral of an equation of motion: $\mu\ddot r=-\frac{k}{r^2}$

I've got an equation of motion (EOM), which is $ \mu\ddot r=-\frac{k}{r^2} $ How do I find the first integral of this EOM? I'd appreciate it if someone could show me the steps involved. I should ...
2
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2answers
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Extra energy in quantum tunneling

In quantum tunneling, the probability of finding an electron inside the potential barrier is non zero (http://i.stack.imgur.com/v8Kr1.gif). So we can actually find an electron which had an energy E in ...
2
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1answer
317 views

The relation between Hamiltonian and Energy

I know Hamiltonian can be energy and be a constant of motion if and only if: Lagrangian be time-independent, potential be independent of velocity, coordinate be time independent. Otherwise ...
2
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3answers
223 views

Redshifted photons

When a photon is emitted from a far away source and then measured by an observer, there is a loss of energy or redshift which takes place. Why does this happen? I have read this similar post, however ...
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1answer
2k views

How to calculate calorie expidenture from lifting a weight?

Am I correct to say that when a human lifts a dumbbell from, say, 2 feet off the ground to 6 feet off the ground, he will have increased the potential energy of the weight and thus will have burned ...
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1answer
49 views

Is change in kinetic energy invariant?

Consider the inelastic collision between two bodies. This question follows on from this: Is the coefficient of restitution frame independent and energy conservation?. One of the answers to this ...
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1answer
325 views

How do I recover the 1D wave equation from the Lagrangian?

Consider small displacements, $y(x,t)$, of an element of a string (circled in red and shown below) from equilibrium. The force balance in the vertical direction yields: $$+\uparrow \Sigma F: ...
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1answer
925 views

How is quantum tunneling possible?

How is quantum tunneling possible? According to quantum mechanics, each particle is represented by a probability density function. This function must be continuous, and therefore when we look at a ...
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3answers
572 views

The “binding energy” of bonded particles adds mass?

This is a follow-up my previous question. Several of the answers indicated that the mass of a particle (atom, proton, etc.) increase with the "binding energy" of it's component particles - the energy ...
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1answer
47 views

What happens to the energy of photons when two light waves with plane wavefront interferes destructively? [duplicate]

When I began learning about optical interference, I came to know about destructive interference in which light waves cancel each other. How the energy is still conserved ? I found that the ...
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6answers
446 views

Why is kinetic energy stored as potential energy in a body during its motion against gravity?

Everyone knows kinetic energy is converted to potential energy in the body when it moves up against the earth's opposing gravitational force. But I am facing some problem with this. What I learnt ...
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0answers
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Conservation of kinetic energy on a moving inertial frame

The velocity of an object differs from the point of views of two different inertial observers standing at two different frame of reference. Assuming no gravity and acceleration = 0 for the object and ...
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2answers
133 views

Conservative Forces & Conservation of Energy?

I'm trying to relate them, I'm trying to find the key relation that would show how the conservative forces serve conservation of energy. How would they relate? Also, how are non-conservative forces ...
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2answers
196 views

Energy Analysis of Niagara Falls in Linus Pauling's “General Chemistry”

I just started reading Linus Pauling's "General Chemistry" and the first example confuses me. He writes: Example 1-1. Niagara Falls (Horseshoe) is 160 feet high. How much warmer is the water at ...
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1answer
63 views

Integrating for speed [closed]

Trying to determine the speed of a falling body with respect to traveled distance and initial speed. I've been provided with the following equation for acceleration as a function of distance and the ...
0
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0answers
62 views

Adiabatic Expansion with expanding control volume

I have a tube with a length $L$ and diameter $d$ that is open on 1 side. At a certain point (say $x$) from the closed end of the tube, I have a gas with a high pressure. At this point, $x$, there is ...
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2answers
117 views

Perspective and changes in kinetic energy

Say you have two planes flying next to each other at the same speed and one decides to pick up speed by burning a tank of rocket fuel. If someone on the ground wanted to know that plane's new speed ...
0
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2answers
311 views

Energy of quarks and the mass of the proton

We know that energy of quarks inside the proton can not be exactly fixed because if it,the 'proton decay' must not be exist. My question is if the energy of quarks inside the proton is not exactly ...
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0answers
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Determining impact velocity over long distances [duplicate]

Everything I have found concerning impact velocity from a given height deals with constant acceleration due to gravity. I would like to know how to work in varying acceleration into the equation. So, ...
0
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4answers
395 views

Does car lose kinetic energy when turning?

I am writing simple car simulation. Assume non friction, then in straight line the car doesn't lose speed. But what if the car is turning, there should be some kinetic energy loses to change the ...
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3answers
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Finding Distance an Object Travels Up an Incline After Launch

I've been doing a review for an introductory physics course final. I have a question on one problem though. Here is the problem: A mass (M=2kg) is placed in front of a spring with k=900N/m, ...
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2answers
900 views

How did the inflaton field “add” energy to the universe?

How did inflation add energy to the universe? What mechanism did this occur by? In other words, where did that energy come from? Was it due to the quantum fluctuation (or that scalar field rolling ...
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2answers
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Work done by spring over distance

I'm working through a problem involving energy conservation. Unfortunately, I cannot calculate the work done by a spring. ...
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2answers
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How exactly, or whats the process, rather, of energy changing into matter?

$E=mc^2$ this is the equation by Einstein claiming energy can change from energy to mass. this would happened at the big bang I assume, when electrons and protons were made to create hydrogen and some ...