# Mass and velocity, thank you for your help!

1. Nov 25, 2012

### 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 dont think my brain works for this sentence...

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

Please dont laugh and enlighten me :P

2. Nov 25, 2012

### Staff: Mentor

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.

3. Nov 25, 2012

### UglyNakedGuy

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

4. Nov 25, 2012

### 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

5. Nov 25, 2012

### 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$$\frac{m}{\sqrt{1-v^2/c^2}}$$

6. Nov 25, 2012

### UglyNakedGuy

I see, so thats actually a algebra thing?

(for my own understanding , sorry if Im 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 !

7. Nov 25, 2012

### Staff: Mentor

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