## Tuesday, November 4, 2014

### Understanding Relativistic Mass

Do you know that the mass of a body increases with increase in its speed. From Einstein's Special Theory of Relativity we get

where M = mass of a body moving with velocity v.
Mo= mass of the body at rest(ie v=0)
c   = velocity of light in vacuum

Now we do not observe it in our daily lives since the fastest we move here on earth is maybe at 100 , 200 or at the most 300 km per hr . If you substitute this velocities in the above equations the differences in mass is negligible. However as the speed approaches the speed of light the difference becomes more and more pronounced.

So what does it imply :
1) As a body moves faster it gets heavier.

-If a body becomes as fast as half the speed of light its mass increases by just 50% of the rest mass.

-If a body attains 90% of the speed of light its mass becomes 2.29 times more than the rest mass.

-If a body attains 99% of the speed of light its mass becomes more than 7.1 times the rest mass.

-If a body attains 99.9% of the speed of light its mass becomes 22.366 times the rest mass.

-If a body attains 99.99% of the speed of light its mass becomes 70.71 times the rest mass.

-If a body attains 99.999999999% of the speed of light its mass becomes 22360.67 times the rest mass.

-If a body attains 99.999999999999% of the speed of light its mass becomes 707114.60 times the rest mass of the body.

So from the above data it is clear that at very high velocities approaching the speeds of light a small increase in velocity leads to big increase in mass. Also it would require lot more kinetic energy at high speeds to accelerate the body since the mass is constantly increasing.

We do not come across such speeds in normal life except for certain high energy labs like CERN's  Large Hadron Collider and only subatomic particles which have extremely low mass can be accelerated to this speeds with the technology that we have today.