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sylas
#10
Jun7-09, 11:47 AM
Sci Advisor
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Quote Quote by Shyan View Post
I still don't understand.because for getting to c you don't need an impossible acceleration.the same goes for force.so how does the energy gets infinite?
The momentum of a particle with non-zero rest mass m and velocity v is
[tex]\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]
The total energy is
[tex]\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]
As you show in your first post, this diverges to infinite values as v approaches c.

Note that F = ma is only true at sub-relativistic velocity. But [itex]F = \frac{dp}{dt}[/itex] is always true. As you apply arbitrarily large forces, you can get momentum as large as you like... but never infinite.