Show that m varies with v in theory of relativity

AI Thread Summary
The discussion centers on the relationship between mass and velocity in the context of relativity, particularly the derivation of the equation involving force, momentum, and mass change. Participants express confusion over the implications of taking the derivative of mass with respect to velocity (dm/dv) and the appearance of a term (m') that complicates the equation. The conversation highlights the importance of recognizing that the rest mass (m0) is constant, while also addressing the role of acceleration (a) in the equations. There is a consensus that the derivation should consider the direction of force relative to velocity, as this affects the resulting relationship between force and acceleration. Overall, the participants are seeking clarity on the correct application of these principles in their calculations.
Feodalherren
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Am I supposed to take dm/dv? That means m0 is constant, correct?

If I do that I end up getting a m' on the Left hand side... What the heck does that mean?! Also where the crap is the "a" coming from?!
 
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Consider: F = d/dt (p) = m dv/dt + v dm/dt = m a + v dm/dt
Now introduce your idea of taking dm/dv in coming up with dm/dt as a function of a and dm/dv.

Warning: I have not succeeded myself in deriving this result. And I know it's correct, dadblame it!
Somebdy - help!
 
Feodalherren said:
image.jpg

image.png


Am I supposed to take dm/dv? That means m0 is constant, correct?

If I do that I end up getting a m' on the Left hand side... What the heck does that mean?! Also where the crap is the "a" coming from?!

a = dv/dt.
 
Feodalherren said:
That means m0 is constant, correct?
Correct.
If I do that I end up getting a m' on the Left hand side... What the heck does that mean?!
Since there is no m' in the problem, the m' means whatever you said it meant when you wrote it down.
Also where the crap is the "a" coming from?!
Read the problem again.

You'll also get a better response if you control your frustration and avoid even mild profanities here.
 
rude man said:
Consider: F = d/dt (p) = m dv/dt + v dm/dt = m a + v dm/dt
Now introduce your idea of taking dm/dv in coming up with dm/dt as a function of a and dm/dv.

Warning: I have not succeeded myself in deriving this result. And I know it's correct, dadblame it!
Somebdy - help!
It does work.
 
tms said:
It does work.

Yeah, I know it has to, I just could not get the result.
 
I think the problem should have stated that the force is assumed to act parallel to the velocity. Perhaps that was meant to be evident by the lack of vector notation. But, anyway, it's worth noting that if the force does not act parallel to the velocity, then you will get a different result for the relationship between the force and acceleration. (In fact, the acceleration is generally not even in the same direction as the force).
 
I'm still not getting it right. There must be something I'm missing.

The constants are m0 and c, correct?

when I do d/dv I end up with [ -2m0vc^(-2) ] / (1-(v^2/c^2))^3/2
 
F=d(mv)/dt.

dm/dt=dm/dv dv/dt = a dm/dv .

Your formula for dm/dv is not correct. The first "2" should be 1/2.

ehild
 

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