Mass and velocity, thank you for your help

[UglyNakedGuy]

Dear all,

I am a lover in astrophyics, however, I have not got much knowledge in it. Recently, I read a book and it says " the mass (of an object) increases as its velocity goes up", I don't think my brain works for this sentence...

I seem to remember that P=M*V, so literally, if velocity increases mass should decrease?

Please don't laugh and enlighten me :P

 

[jedishrfu]

p=m*v is from Newtonian mechanics whereas the statement on increasing mass with increasing speed is related to special relativity theory and applicable for speeds approaching the speed of light.

 

[UglyNakedGuy]

so may I know the equation for p under SR? thank you for your reply :)

 

[DrGreg]

This is the concept of "relativistic mass" which was once quite popular but rarely used nowadays amongst professional physicists, who prefer to stick with a non-varying "rest mass".

I hope you are familiar with the concept of kinetic energy -- "the energy (of an object) increases as its velocity goes up" -- and also with E = mc² relating mass to energy. The idea of relativistic mass was to treat kinetic energy as part of an object's mass

 

[DrGreg]

In relativity we have momentum p and energy E given by$$\begin{align} \textbf{p} &= \frac{m\textbf{v}}{\sqrt{1-v^2/c^2}} \\ E &= \frac{mc^2}{\sqrt{1-v^2/c^2}} \end{align}$$where m is rest mass. Relativistic mass was$$\frac{m}{\sqrt{1-v^2/c^2}}$$

 

[UglyNakedGuy]

This is the concept of "relativistic mass" which was once quite popular but rarely used nowadays amongst professional physicists, who prefer to stick with a non-varying "rest mass".

I hope you are familiar with the concept of kinetic energy -- "the energy (of an object) increases as its velocity goes up" -- and also with E = mc² relating mass to energy. The idea of relativistic mass was to treat kinetic energy as part of an object's mass

I see, so that's actually a algebra thing?

(for my own understanding , sorry if I am wrong) the energy of an object and its V have a positive correlation, so E goes up when speed goes up.

and then, since E=mc^2, and c is constant ( assume in vaccum) so we relate E with c .

is this correct?

thank you !

 

[jedishrfu]

if you set v=0 then you get the famous e=mc^2, the energy at rest from the equations above.