RELATIVISTIC INCREASE IN MASS
.
Relativity  |  Topics
. This page utilises mass-energy equivalence to show that the mass energy content (or 'Inertia') of a body increases with speed, approaching infinity as  velocities approach that of electromagnetic radiation in vacuo.This interesting and important result may be deduced from a handful of fundamental principles and a simple integration. Albert Einstein addressed this question in his 1905 paper 'Is the inertia of a body a measure of its mass/energy content?' .

---

From the relationships
.

.
we can deduce that
.

.
We now utilise two fundamental physics principles:
.

.
and
.

.
and from these we find that
.

.
Combining this with our first result and integrating,leads to the following result:
.

. Here E is the total energy of the body, E_o is its rest energy and c is the speed of light. From here we use E=mc² again and our first result to obtain, finally a velocity dependent mass. .

.

Conclusions

1. Clearly at rest (v=0) then m = m0 and we identify mo as the 'Rest Mass'.

2.As v approaches c then mass m(v) approaches infinity.

3.If v = c then m(v) is infinite. This is clearly silly , so we deduce that particles with non-zero rest mass cannot attain light speed, as to do so would require an infinite input of  energy.

.
If you have mastered this simple bit of physics, why not try Problems 2?
Back To The Top.