# Changing Mass

#### Fusilli_Jerry89

I've heard that when an object is accelerated at huge huge speeds they actually gain mass. Is there a formula to see how much mass an object would gain will going a certain velocity.

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#### Hootenanny

Staff Emeritus
Gold Member
I quote RandallB, since this topic was somewhat discussed in https://www.physicsforums.com/showthread.php?t=149350"recently.
The problem you will continue to have with ones like this, is thinking of mass as actually changing with speed. That is a very old idea to think of the mass “as if it increases” with speed. Which works ok in a limited way, such as getting to E=mc^2. But modern science accepts the idea is incorrect in application and mass should be understood as intrinsic and unchanging with speed. Only momentum “p” or ‘mv’ is factored to increase with speed, and not mass.
But for any real mass, while it remains the same at mo; as the speed increases it must create a momentum "mv" that if factored by relativistic "gamma" to a larger number than expected by classical thinking.
Thus momentum as v approaches c would approach infinity and creating it would require an impossible amount of energy to reach it.
The important concept to note here is that it is the momentum which increases, not the 'mass'. In my opinion, in special relativity only invariant mass should be considered and the whole notion of 'relativistic' mass should be abandoned in special relativity (the situation in general relativity is somewhat more complex). As Randall says above, the notion that mass increases is usually introduced when explaining the 'basics' of relativity in a general context, but leads to misunderstandings when it comes to formally learning relativity. Below are some links which you may wish to peruse;

http://en.wikipedia.org/wiki/Rest_mass" [Broken]
http://en.wikipedia.org/wiki/Relativistic_mass" [Broken]
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c3"

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#### Littlepig

mass has 2 situations:

invariant mass, that, independent from the observer, it has a defined value.
relativistic mass, that depends on observer.

relativistic mass is "transformed" by lorentz factor.

invaritant mass, isn't "tranformed", and it is normally the mass that we use in classical mecanics, in expressions like: density=m/V, kinectic E=1/2mv^2, potential E=mgh and so1.

relativistic mass, is used in modern mecanics, and is too "named" as energy, by the E=mcc.

both masses can be used in momentum expression(p=mv)

in case of photon, it has no invariant mass, but as it have energy, we must assume it as relativistic mass

Regards, littlepig

#### Janus

Staff Emeritus
Gold Member
relativistic mass, is used in modern mecanics, and is too "named" as energy, by the E=mcc.

Regards, littlepig
$E = mc^2$ gives the energy equivalence of the invarient mass.

#### Littlepig

$E = mc^2$ gives the energy equivalence of the invarient mass.
so that's why, in my post, https://www.physicsforums.com/showthread.php?t=149350"

i couldn't say the energy released by hidrogen in man "B" couldn't be greater than in man "A". The invariant mass doesn't varies, because velocity doesn't take efect on invariant mass....humm....getting it...:tongue2: