## Odd Force Equation

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

Moderators: gmalivuk, Moderators General, Prelates

### Odd Force Equation

I was reading a book, and I ran into this odd equation:

F=\frac{d}{dt}(\frac{mv}{(1-\frac{v^2}{c^2})})

Where does this equation come from and what does it represent?
foxgloves

Posts: 6
Joined: Fri Dec 26, 2008 2:47 am UTC

### Re: Odd Force Equation

It's the relativistic version of Newton's second law. If the velocity v << c, where c is the speed of light, the denominator vanishes and you obtain the Newtonian version F=ma. However, as an object approaches the speed of light the denominator approaches zero, and the force required to further speed it up approaches infinity. So this always enforces the universal speed limit of c for massive objects and is consistent with other relativistic effects such as time dilation and length contraction, all of which contain the Lorentz factor in some form, as seen here also (only squared).
bosonicyouth

Posts: 90
Joined: Sat May 01, 2010 8:59 am UTC
Location: Brisbane, Australia

### Re: Odd Force Equation

Yeah, the “real” version of Newton’s 2nd law, as in the version that’s true and generally applicable, is “Force equal rate of change of momentum”, or symbolically F=dp/dt. That is the definition of “force”. You’ll never see a proof of Newton’s 2nd law, because it is not a theorem but actually a statement of definition.

So, once you know that force is defined as F=dp/dt, then calculating force just means taking the derivative of momentum. And as it turns out, in special relativity the momentum of an object is p=γmv, where γ is the Lorentz factor γ=dt/dτ=1/√(1-v2/c2).
Small Government Liberal

Qaanol

Posts: 2234
Joined: Sat May 09, 2009 11:55 pm UTC

### Re: Odd Force Equation

The thing is, the lorentz factor has a square root in it so what foxgloves has actually written is very odd (and will only hold at rest). I guess they made typo/transcribed it incorrectly.
Gear wrote:I'm not sure if it would be possible to constantly eat enough chocolate to maintain raptor toxicity without killing oneself.

eSOANEM

Posts: 1916
Joined: Sun Apr 12, 2009 9:39 pm UTC
Location: Grantebrycge