Questions tagged [mass-energy]

The special-relativistic relation connecting energy with mass, $ E^2 - (m c^2)^2= (pc)^2 $. May be used to provide accounting constraints in energy and momentum, both conserved in total, even in reactions where $m$ is not.

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Does the electric field of a charged particle really contribute to its mass? [duplicate]

An electron at rest creates a static distribution of an electric field around it. Wherever the particle moves, it carries or drags the field with itself. Does this electric field contribute to the ...
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What is the mass of photon? [duplicate]

I'm sorry if this question is asked before, but I searched through the site and none satisfied me. In most of the books I've come across, they just write "rest mass of photon is zero." But never talk ...
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How am I supposed to get this answer? [closed]

This question is from the Oxford Physics book, and I didn't understand how to get the answer. I'm assuming that the equation that I'm supposed to use E=mc^2 to solve the equation.
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Is there any known experimental violation of Einstein's $E=mc^2$?

Note that I am not talking about $E_0= m_0c^2$ but $E=mc^2$, where m is the relativistic mass. I know that one holds for stationary particles, moving particles, even light, I read that it even holds ...
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Released energy in a reaction

I'm having some trouble in understanding how the released energy in a nuclear reaction is actually calculated. I think I understand the general approach if we are dealing with a reaction like $$\rm ^{...
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Why does a particle, e.g. a proton, at rest have $v=0$?

Given the formula $E=mc^2$, the mass is equivalent to energy through the speed of light. This equation is also the special case of $E^2=(mc^2)^2+(pc)^2$ when $p=0$. Thus, it is at rest respectively ...
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Calculating binding energy from mass defect

I am trying to wrap my head around the relationship between binding energy and mass defect. I have read that the difference between the binding energies of the products and reactants of a nuclear ...
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186 views

Why is the equation $E=mc^2$?

The equation $E=mc^2$ never made any sense to me. c is a constant (speed of light), therefore c squared is also a constant. We're not specifying any units so surely the equation should be reduced to ...
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How to express the $Q$-value for alpha decay in terms of binding energy of the relevant species?

I have 2 questions regarding the solution to the following question: The solution states that: Mathematically, I understand how the end result $$Q=BE\left({}^{A-4}_{Z-2}\mathrm{Y}\right)+...
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Do Quarks decay into Photons at high enough temperatures?

At high enough energy, particles lose coherence and are ripped apart into a Quark-gluon plasma where the individual quarks can break free of the atomic nucleus and fly around unencumbered. A black ...
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Why Didn't the Energy-Momentum Relation Work?

I am currently studying for the GRE Physics subject test by working through published past tests. My question is about problem 20 from the test GR8677: A positive kaon ($K^{{}+{}}$) has a rest ...
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Lavoisier law of mass conservation vs. conservation of energy

Lavoisier law states that for any isolated system, mass must be conserved over time. Also, Einstein's equation $E = mc²$ shows energy-mass equivalency. So, since mass must be conserved and energy ...
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In special relativity is mass just a measure of all other energy than kinetic?

The energy momentum equation in special relativity is: $$E^2=(pc)^2+(mc^2)^2.$$ and it holds for a moving but not accelerating object. One special case is the massless photon: $$E=pc.$$ And another ...
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How to understand $E=mc^2$?

I am trying to understand Einstein's mass-energy equation $E=mc^2$. Knowing about the atomic bomb I am inclined to believe that $E$ is proportional to the mass: $E=Cm$. For this equation to be ...
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Question about $E=mc^2$

When a nuclear reaction happens, the amount of mass disappeared satisfies $E=mc^2$. However, the reaction will stop at a certain point, there is no way to make the whole thing disappear into energy. ...
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4answers
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Is there a limit to the amount of mass we can concentrate in a region of space?

Black holes are solutions to Einstein's Field Equations. Black holes contain a singularity hidden from the outer universe. As I understand, these singularities are infinitesimal and contain a very ...
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Is fission/fusion to iron the most efficient way to convert mass to energy?

Is fission/fusion of any element to iron-56 (or nickel-62?) the best way to convert mass to energy, that doesn't involve black holes? In other words, will we be always limited to convert only about 1%...
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Effects of Relativistic/Inertial Mass

What would happen to a ball of ice in a remote region of space if spun in a circle accelerating toward the speed of light? As the ball of ice approaches the speed of light, does it melt/sublimate as ...
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A spacecraft orbiting the sun charges a battery which becomes a tiny bit more massive. How does this effect the velocity of the spacecraft?

According to $E=mc²$ the spacecraft which stores the Energy from the sun becomes a tiny bit more massive. how does this effect the impulse of this spacecraft. Would it grow because P = (m + extra mass)...
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What is the relativistic energy of a bounded static particle?

Premise: The speed of light is set $c = 1$. Let's consider an electron in an external electromagnetic field. Its four-momentum will be $$p^{\mu} = (E, \bar p) = (\gamma m_e, \gamma m_e \bar v),$$ ...
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Is there a known mechanism for mass-energy distorting spacetime?

I’ve been really interested in learning about the mechanisms behind physical phenomena that go beyond just learning to manipulate the equations and give a physical intuition about HOW something ...
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Does a black hole singularity compress mass back into energy? [duplicate]

I was watching this PBS spacetime video which made the case that mass is just a form of bound energy. Essentially massless particles are confined in a small space giving particles the illusion of mass....
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Is spacetime volume preserved in presence of a mass in General Theory of Relativity (GTR)?

In many publications about the warping of spacetime in presence of a mass the metric of spacetime is stretched, expanded : http://discovermagazine.com/~/media/Images/Issues/2015/april/relativity.jpg ...
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Do photons bend spacetime or not?

I have read this question: Electromagnetic gravity where Safesphere says in a comment: Actually, photons themselves don't bend spacetime. Intuitively, this is because photons can't emit ...
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Binding energy and strong force

If binding energy is responsible for holding nucleons together than what is meaning of strong force?
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1answer
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Reaction energy $Q$

Really simple question, but I'm confused with it because of contradictions between sources (absence of clarity online vs lecture notes (says nuclear) and practise questions provided (uses atomic) ) ...
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Will the mass of a stick of dynamite be conserved when it is exploded?

If a stick of dynamite is blown up in a hermetically sealed chamber, the mass of the chamber and fragments, the heat, sound, and light would still be equal to the original mass of the chamber and ...
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1answer
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Is there a general relativistic mass in general relativity?

In general relativity the energy of a test-body moving in a spherically symmetric gravitational field can be written as: $$E=mc^2\left(\frac{\sqrt{1-\frac{2GM}{rc^2}}}{\sqrt{1-\frac{v^2}{c^2\left((1-\...
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Does kinetic energy warp spacetime?

My interpretation of GR leads me to think that energy (namely kinetic) also adds to the curvature of space-time. Which, has raised a thought experiment. If a $10000$ kg ship closely passed a $1$ kg ...
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Does gravity follow law of conservation of energy? [duplicate]

Law of conservation of energy states that energy cant be created nor destroyed.I dont understand how it is applicable for a object moving under influence of gravity.If some force has been applied on ...
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Scope of $E=mc^2$ [closed]

As far as I can see, Einstein's $E=mc^2$ is most often mentioned in the context of nuclear physics, even though it is more generally applicable. I understand that this is due to the large nuclear ...
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1answer
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Calculating the speed of a proton in the LHC at 7TeV without a calculator

There are several threads on this forum regarding the LHS at CERN however I am interested in a non-calc solution. I recently stumbled upon a multiple choice question about it while studying for a ...
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$E = mc^2$ and Binding Energy Confusion [closed]

I have been introduced to $E =mc^2$ and binding energy recently while studying nuclear physics and I have a hard time understanding the following: Mass-Energy what does $E=mc^2$ really mean, as I ...
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What is the maximum energy that can be released by thermonuclear device?

Forgive me by posing this somewhat scary question, but it's just out of curiosity I'm asking it. In this video we're witnessing the beautiful and at the same time horrific blast of the tsar bomba, ...
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2answers
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Increased mass of compressed springs [closed]

Based on the idea that mass is an emergent property of fundamental particles with potential energy bound in a restricted space, I want to make a macroscopic analogy. I want to put compressed springs ...
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1answer
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How to get the mass squared for the Green-Schwarz string?

Im following the GSW book. Specifically equations (5.2.39), (5.2.40) $$H=\frac{1}{2p^-}((p^i)^2+2N)$$ $$N=\sum_{m=1}^\infty(\alpha_{-m}^i\alpha_m^i+mS_{-m}^aS_{m}^a)$$ are not clear for me. I know, ...
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1answer
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For which kind of nuclear reactions is the nuclear binding energy per nucleon appropriate?

The nuclear binding energy curve is often presented as a reason why iron is abundant in planet cores. However, to me it is not entirely evident why binding energy per nucleon, E/A, is chosen to assess ...
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Why does gravitational pull increase when black holes spin?

I was reading "the science behind interstellar", and found that Kip Thorne purposefully used a SMBH in his simulation which had its maximum attainable spin around its own axis. He argued that this was ...
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Bare Critical Masses of $^{241}$Am, $^{242m}$Am, $^{238}$Pu and $^{242}$Pu

$^{238}$Pu has 144 neutrons, and it has 2.8$\times$10$^{3}$ g$^{-1}$.s$^{-1}$ spontaneous fission neutrons and bare critical mass in 10 kg. $^{242}$Pu has 148 neutrons, and it has 1.7$\times$10$^{3}$ ...
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Is the potential energy of falling into a black hole already included into $E=mc^2$?

Each object in the Universe has a huge potential energy, because you can drop it into a black hole, accelerating it to nearly the speed of light. Is this potential energy already included into ...
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How to derive: $\frac{E^2}{c^4} = \frac{p^2}{c^2} + m_0^2$?

My teacher wrote the following equation on the board a few days ago: $$\frac{E^2}{c^4} = \frac{p^2}{c^2} + m_0^2$$ And I got no idea how this is derived especially since we already derived that: $$m^...
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Why is the actual KE value smaller than what I calculated?

Problem The nuclear equation for the decay of calcium-47 into scandium-47 is given by: The following data are available: Mass of calcium-47 nucleus = 46.95455 u Mass of scandium-47 nucleus = 46....
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Fusion Kinetic Energy

In fusion, the mass of the reactants is greater than the mass of the products. Thus, mass is lost in fusion. My thinking was that this mass defect is converted into binding energy that is then used to ...
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Composite objects, mass, and internal energy in relativity

Why do we define the free Hamiltonian of composite particles as $$H_0 = \sqrt{M(t)^2c^4 + P^2c^2}$$ with $M(t)\neq\sum_im_i$ instead $$H_0 = \sqrt{M^2c^4 + P^2c^2} + U(t)$$ with $M=\sum_im_i$ and $...
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Why does stability come from binding energy and not mass

The mass of a nucleus is given by: $$ Mc^2=n M_n c^2+zM_pc^2-B(z,n) $$ And we were told that nuclei want to maximise the binding energy per nucleon. However, I don't see why they don't want to ...
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Basic Question on Black Holes and the Potential Loss of Conservation of Energy/Mass [duplicate]

I am reading Kip Thorne's "Black Holes and Time Warps" and I have a basic question on a topic he is discussing while talking about Einstein and Eddington's disbelief in black holes. So the general ...
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How we can prove that photons have no mass? [duplicate]

I am thinking nowadays that how its possible that a particle without mass, actually exists? in the case of light its used to say that photons have no mass no weight but they have momentum. can any ...
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2answers
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Is this relativistic mass?

I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc. But I've also seen people saying that a ...
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1answer
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Is there an example of two elementary particles colliding to result in a single elementary particle?

Apologies for the novice question, but I don't know enough particle physics to immediately answer my own questions. I have the following questions. Is there an example of an inelastic collision ...
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2answers
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Why is energy released during fission reactions?

If the energy released during a fission reaction is the binding energy then what energy is left to bind the nucleons together? I'm very confused if there's a better explanation on fission I'd ...