We have discussed the effects of relativistic speeds on time now let's have a look on its effect on mass. To get straight to the point the mass of an object will increase when traveling at relativistic speeds. The equation for calculating the mass as seen by an outside observer is as follows:
m = m0/((1 - v2/c2))1/2
where: m0 = the mass measured at rest relative to an observer traveling with the same velocity as the mass, the "rest mass".
m = the mass measured by the observers on the other reference frame.
v = the speed of the object
c = the speed of light in a vacuum
Look at the following example:
A particle is accelerated to a speed of .95c relative to an observer in a laboratory, the "lab" frame. If the particle was originally measured to have a mass of 5 grams, what is the mass that is observed in the laboratory?
m0 = 5 g
v = .95c
m = ?
solving: m = (5 g)/(1- (.95c)2/c2)1/2
m = (5 g)/(.312)
m = 16 g
Hint: When working these problems be sure to think about what the answer should look like. That is in this case I knew that the mass measured in the lab had to be larger than the rest mass. So if I got m and m0 confused I would have realized it when I got a smaller number. Just understand the concept and then think about your answer!
Now once again notice that at small speeds the quantity v2/c2 approaches 0 and m = m0, but at high speeds the quantity approaches ∞ (but never reaches it) therefore causing m to become larger and larger! This is why you can never travel faster than the speed of light in a vacuum. Once again think about it!
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