It has been shown here that the measured
mass of a body depends on the velocity of the body relative to the
observer making the measurement. 

From this it was concluded that momentum also must be a relative
concept (as momentum is the product of mass and velocity). 

We find that the "relativistic" momentum of
body can be found by simply using the Newtonian equation for
momentum but with the appropriate (velocity dependent) mass. 



This is not the case when calculating the
kinetic energy possessed by a body. 



Suppose we have a body of rest mass, m_{o} which we
cause to accelerate away from observer A. 

During the period of acceleration, work is
being done by the force. 

As in Newtonian mechanics, we will
define the kinetic energy of the body to be equal to the
work done accelerating it. 



It can be shown that if
the speed of the body relative to A is such that its mass (as
measured by A) is m, then 



Here we are seeing the
equivalence of mass and energy. 

Some of the work done by the force is
converted into mass and if we define the total energy, E,
possessed by a body to be the sum of its rest energy (m_{o}c^{2})
and its K.E. we arrive at the most famous equation in physics 



It is easy to show that if the velocity of
the body relative to the observer is small compared with the
velocity of light, then the relativistic formula reduces to the
Newtonian expression (½mv^{2}) 



If the velocity of the body relative to the
observer is very close to the velocity of light, virtually
all the work done by the force is converted to mass. In
other words... no matter how long you keep pushing the body, it
doesn't go any faster! 



Experiments involving high speed protons,
electrons etc in particle accelerators, confirm these predictions of
special relativity. 



Units of Mass and Energy 

The S.I. unit for mass is the kilogram. 

The S.I. unit for energy is the Joule. 

We now see that mass and energy can be
considered to be two manifestations of one underlying phenomenon
(let's call it mass/energy or maybe massergy or perhaps enermass...
ok, maybe not!) 

As discussed here, when referring to
the quantities of energy possessed by subatomic particles, we often
use the electronVolt (eV) where 1eV
= 1.6×10^{19}J 

Perhaps a little perversely, having invented
this nice small unit, we then often
go back the other way and use MegaelectronVolts (MeV), where 

1MeV = 1.6×10^{13}J 

So, when working with subatomic particles,
the unit for the quantity mc^{2}, a quantity of energy, is
the MeV 

This then leads us to
alternative unit for mass (on the small sale): 

If mc^{2} corresponds to energy then
mc^{2}/c^{2} corresponds to mass. 

For example, the energy equivalent to the
rest mass of an electron (9.1×10^{31}kg),
from E = mc^{2}, turns out to be about 511MeV. 

Thus we can say that an electron has a
rest energy of 511MeV
and/or a rest mass of 511MeV/c^{2} 
