Extra mass due to near light like speeds

Question

Why does mass seem to increase as you near the speed of light?

Answer 1

Actually the relativistic mass $E/c^2$ changes while the intrinsic mass (rest mass) stays the same. We use relativistic mass when the mass is moving and the instrinsic mass when the body is at rest.

Relativistic mass

Main article: Mass in special relativity After Einstein first made his proposal, it became clear that the word mass can have two different meanings. Some denote the relativistic mass with an explicit index:

$m_{\mathrm{rel}} = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$ .

This mass is the ratio of momentum to velocity, and it is also the relativistic energy divided by $c^2$ (it is not Lorentz-invariant, in contrast to $m_0$). The equation $E = m_{rel}c^2$ holds for moving objects. When the velocity is small, the relativistic mass and the rest mass are almost exactly the same.

$E = mc^2$ either means $E = m_0c^2$ for an object at rest, or $E = m_{rel}c^2$ when the object is moving.

The two interpretations of what “mass” means. The first (in green) is that mass is something that does not change with speed — often called “invariant mass” or “rest mass”, it is used by particle physicists. The other, “relativistic mass”, is just energy divided by c-squared, and grows with speed. Note the two are almost identical at small velocities, and so are usually equal in daily life.

So the intrinsic mass, $m_0$, that we associate with the object at rest stays constant while the relativistic mass, $m_{rel}$, goes to infinity as the velocity increases to the speed of light.