A QUESTION ABOUT SR (DERIVATION OF E=MC^2-M0C^2)

[love sersh]

I've just met a problem when I differentiated the mass-velocity equation.

In m²(c²-v²)=m0²c² because the right one is a constant

after differentiation , i got d [ m²(c²-v²) ] = 0

which means c² d (m²) = d(m²v²)

i don't think it makes sense, hope someone can help me point out the wrong step，thanks a lot！

Edited October 13, 2014 by love sersh

[xyzt]

I've just met a problem when I differentiated the mass-velocity equation.

In m²(c²-v²)=m0²c²

You should get [math]2mc^2dm-2m^2vdv-2v^2 mdm=0[/math] or, alternatively: [math]2c^2mdm=d(m^2v^2)[/math] or [math]c^2d(m^2)=d(m^2v^2)[/math]

Edited October 13, 2014 by xyzt

[love sersh]

You should get [math]2mc^2dm-2m^2vdv=0[/math], i.e. [math]c^2dm=0.5md(v^2)[/math]

I knew that , but it's the next step ,c² d (m²) = d(m²v²) ,

c² 2mdm=2mvdmv , I m just a little confused about the first one

[xyzt]

I knew that , but it's the next step ,c² d (m²) = d(m²v²) ,

c² 2mdm=2mvdmv , I m just a little confused about the first one

 

 

[math]c^2 d(m^2)= d(m^2v^2)[/math] is perfectly correct.

Edited October 13, 2014 by xyzt

[elfmotat]

Just as a little aside, nobody uses the concept of relativistic mass anymore. It's not very useful and tends to confuse people.

[love sersh]

Just as a little aside, nobody uses the concept of relativistic mass anymore. It's not very useful and tends to confuse people.

so what concept should we use to deal with the prediction of lorentz transformation？

 

 

[math]c^2 d(m^2)= d(m^2v^2)[/math] is perfectly correct.

thanks，i am just not sure about it at first

[elfmotat]

so what concept should we use to deal with the prediction of lorentz transformation？

 

Just use rest mass in all of your equations.

[swansont]

!

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