I was always taught that mass was how much matter something is made of, but I recently read that it is how resistant an object is to acceleration; as such, you could add mass to an object by increasing its energy, even though you aren't really adding any matter. Which is correct?
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Read Francis Bacon's words from the wiki "experiment", and understand that mass to be an axiom obtained from an experience, you can see Newton (in his pricipia) explaining the term by providing an experiment... – Sensebe Oct 06 '15 at 17:48
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Related: http://physics.stackexchange.com/q/8610/2451 and links therein. – Qmechanic Oct 06 '15 at 22:10
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Mass is a constant that relates how momentum and energy are balanced.
In prerelativistic physics, energy is $mc^2+p^2/2m$ and in relativistic physics energy satisfies $E=\sqrt{(cp)^2+(mc^2)^2}$ and the former is approximately equal to the latter when $|pc|\ll mc^2.$
Timaeus
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Mass is not the amount of matter present in a body (this is what most books say).
It is actually the measure of inertia of a body.
Therefore, by increasing its energy, you increase inertia. So, mass is also increased, even though there is no exchange of matter.
Hope I helped you.
PCM
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good point; I object to downvotes without reasons - apologies for not doing it earlier. Inertia is not the "intermediary" between energy and mass: E=mc^2, where the mass is the relativistic mass comprising what used to be called "rest mass" + the mass equivalent of energy left over. NB but on it's own I'd just not have up or downvoted: mass as measure of inertial is correct see e.g. https://en.wikipedia.org/wiki/Inertia but I doubt that simple statement provided would help the OP at all since that was more or less what he was seeking an explanation of. – Julian Moore Sep 09 '21 at 10:51
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