Show that m varies with v in theory of relativity

[Feodalherren]

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?!

 

[rude man]

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!

 

[rude man]

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.

 

[tms]

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.

 

[tms]

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.

 

[rude man]

It does work.

Yeah, I know it has to, I just could not get the result.

 

[TSny]

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).

 

[Feodalherren]

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

 

[ehild]

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