I was wondering that a change in velocity can change the mass of an object slightly. I thought of this since p=mv so if we rearrange it to be m=p/v. Does this mean that a change in momentum or velocity can actually change the mass?
Asked
Active
Viewed 176 times
0
-
See here. – Charlie Oct 19 '20 at 14:40
-
1What do you have in mind that can change momentum but not change velocity (or vice versa)? – BioPhysicist Oct 19 '20 at 19:38
2 Answers
2
You have this equation, $p = mv$. If you increase the velocity and keep $p$ constant, yes you must have had an increase in mass. The question is, what does it mean for $p$ to be constant? It is defined by the product of mass and velocity. So you have done nothing to make predictions, you have just stated what you would call mass if you increased v and kept p the same. OR since mass and velocity are more readily known as measured quantities to the layman, you have said increasing v and lowering m keeps mv the same. See? you've said nothing of any value
0
Note, for a small change in $p$ (and $v$, as their correlation is 1, or $m$ depending on normalization):
$$ \delta m = \frac d {dp}({\frac p v})\delta p+ \frac d {dv}({\frac p v})\delta v $$
$$ \delta m = \frac{\delta p} v - \frac{p\delta v}{v^2}$$
Since:
$$ \delta p = m \delta v$$
we get:
$$ \delta m = \frac{\delta p} v - \frac{p\delta p/m}{v^2}$$
$$ \delta m = \delta p(\frac 1 v - \frac{v}{v^2})$$
$$ \delta m = \delta p(\frac 1 v - \frac{1}{v}) = 0$$
So, no.
JEB
- 33,420