Does it take work for a rocket ship to lose mass?

Question

A rocket ship in uniform flight has mass, velocity, momentum, and kinetic energy. It has the alien technology to be able to decrease its mass while maintaining its momentum. Does it take work to lose its mass, and, if so, how much work does it take to lose all of it and how fast it will then be going? Use relativistic momentum and energy, not Newtonian.

Gary, this is alien technology, it has the ability to change its own mass at will, instead of blowing it out of its back end.

Answer 1

If you assume momentum conservation, it can be shown that the kinetic energy increases when it loses mass.

Let's suppose initially, mass = m, vel = v
Momentum = mv, KE = 1/2 * mv^2

Then it loses half its mass
So new velocity = 2v ( to maintain momentum)
new KE = 1/2 (m/2) (2v)^2 = mv^2

So the kinetic energy doubles, meaning that it gains energy from somewhere. So I'd say yes, it does require work.

Generally if the new mass if f*m, f < 1
new velocity = v/f
new KE = 1/f * initial KE
Change in KE = (1-f)/f
If it loses all its mass (f --> 0), then the speed will increase indefinitely, assuming that aliens have no speed of light restrictions.
I guess this would be like disappearing and reappearing somewhere else (after they regained their mass).

Answer 2

Yes the Explosion of the moving gases cause a force which moves at a certain velocity and the product of the force time the velocity of the moving force is equal to the power that moves the rocket.
The mass loss of the rocket times the velocity of light
squared is equal to the Kinetic energy of the rocket.
To determine work you need to Use the first and second law of thermodynamics.
The work is proportional to the original mass content of the fuel minus the mass loss to its surrounding.
Ek =change in mass x c^2 ,is the kinetic energy of the Rocket.

Answer 3

Burning rocket fuel is not alien technology, it was developed right here on Earth nearly a century ago. Well, not alien assuming you're from Earth...

=8^)

...and the burning of fuel is the RELEASE of potential energy, used to heat a mass and impart a velocity to it such that its reaction may accelerate the spacecraft.