# Object's Mass Increasing

I just want to verify that I have the right mindset here on the subject:

p=mv

You can increase the momentum as much as you want, but when v reaches the speed of light, it cannot increase any more, but since momentum is still increasing, that means the mass must be the one to increase, for it is the only thing that can.

Hootenanny
Staff Emeritus
Gold Member
Another way to think about it is that the momentum increases faster in special relativity than classically predicted, after all classical mechanics is only an approximation to special relativity. What we should write is,

$$p\approx mv$$

And,

$$p=\gamma mv$$

And just to clarify, an object with mass cannot reach the speed of light.

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allright. Thank you.

I just want to verify that I have the right mindset here on the subject:

p=mv

You can increase the momentum as much as you want, but when v reaches the speed of light, it cannot increase any more, but since momentum is still increasing, that means the mass must be the one to increase, for it is the only thing that can.
v can never reach the speed of light. There is no upper bound for the magnitude of momentum. As v approaches c, p approaches infinity. Therefore if one defines the mass of an isolated object then m = p/v m which approaches infinity.

Pete

Hello leftyguitarjo.

I think you have the mathematics back to front. You may not be able to increase momentum as much as you want because it is restricted by any limitations SR imposes on v and m. Momentum p is the dependent variable and varies when mass m and/or velocity v are changed. For a given mass you can increase the velocity at which it moves and so change the momentum. Of course the velocity is limited to less than c. It is not very practical to achieve the same result by holding v constant and altering m. There are other complications such as mass increasing with velocity.

Matheinste.

v can never reach the speed of light. There is no upper bound for the magnitude of momentum. As v approaches c, p approaches infinity. Therefore if one defines the mass of an isolated object then m = p/v m which approaches infinity.

Pete
That was a bit confusing. I meant to write
Therefore if one defines the mass of an isolated object as m = p/v then m will approaches infinity as v approaches c.

Pete