Relativistic Momentum to Kinetic Energy Conversion

[mayeraus41]

Just consider the following;
A large object, say a sun or neutron star, is traveling through the universe at near the speed of light (let's say 99% of c). This super massive object is on a collision course with a fixed/static super massive object relative to the body in motion. When the eminent impact occurs, the dynamic object will transfer it's momentum to the static body, Newtons third law, almost like astronomical scale Newton balls. The problem is, how is the relativistic mass converted into kinetic energy, assuming that the transfer is not instantaneous and occurs over a span of time. To me it would seem as though energy potential is lost all together as it decelerates because the relativistic mass is not transferred as it dissipates exponentially while the force is not transferred exponentially.

If someone could please help explain how the relativistic momentum/mass is converted to kinetic energy that would alleviate the spitting psyche headache. I know I'm wrong because energy must be conserved, but would like someone to explain how.

Thanks.

 

[DaveC426913]

This seems to be the crux of your argument:

...energy potential is lost all together as it decelerates because the relativistic mass is not transferred as it dissipates exponentially...

Why do you say the [momentum] is dissipated "exponentially"?

 

[mayeraus41]

Because the dynamic object is losing velocity, at least in the incipient stage of impact. And if I know my relativity equations I know that as velocity decreases, Mass does proportionally.

 

[DaveC426913]

Because the dynamic object is losing velocity, at least in the incipient stage of impact. And if I know my relativity equations I know that as velocity decreases, Mass does proportionally.

Ah I see. The object's relativistic mass drops as it slows.

But why do you think the momentum is not being transferred?

You don't measure mass alone in the collision, you measure momentum. That's what gets transferred. The momentum of the object takes into account its relativistic velocity.

 

[mayeraus41]

Ah I see. The object's relativistic mass drops as it slows.

But why do you think the momentum is not being transferred?

You don't measure mass alone in the collision, you measure momentum. That's what gets transferred. The momentum of the object takes into account its relativistic velocity.

So are you saying that standard Newtonian understanding of momentum doesn't or does apply at relativistic velocity? If not how is the relativity factored into momentum? That's a bit off topic but still I'm curious.

My thought is that through the collision speed is lost or at least distributed across the two objects to a level below any significant relativistic speed. therefore momentum is lost.

 

[DaveC426913]

So are you saying that standard Newtonian understanding of momentum doesn't or does apply at relativistic velocity?

The momentum is transferred. How the object gets the momentum it does (whether via its rest mass or its velocity or its relativistic mass) seems to be immaterial.

I confess, I do not have a concise answer, I am just following the logic.

 

[mayeraus41]

The momentum is transferred

I confess, I do not have a concise answer, I am just following the logic.

Irrelevant as it may be, still fascinating to consider. It's difficult for me to quantify as energy is required to attain the relativistic mass and higher velocity. To me the energy almost disapears. And I know that to be impossible, that's why i find it troubling.

 

[jtbell]

So are you saying that standard Newtonian understanding of momentum doesn't or does apply at relativistic velocity? If not how is the relativity factored into momentum?

In non-relativistic mechanics, p = mv. In relativistic mechanics,

$$p = \frac {mv} {\sqrt {1 - v^2 / c^2}}$$

where m in both cases is the "invariant mass" of relativity.

If you prefer to think in terms of what is often called "relativistic mass" (but is not commonly used by physicists nowadays) then p = mv in both cases, and relativity factors into the definition of "relativistic mass."