# Momentum in special relativity

1. Oct 11, 2007

### anon54325345

A spaceship of mass 10^6 kg is coasting through space when suddenly it becomes necessary to accelerate. The ship ejects 10^3 kg of fuel in a very short time at a speed of c/2 relative to the ship.
a. Neglecting any change in the rest mass of the system, calculate the speed of the ship in the frame in which it was initially at rest.
b. Calculate the speed of the ship using classical Newtonian mechanics.
c. Use your results from (a) to estimate the change in the rest mass of the system.

Lorentz momentum: P = (gamma)*m*V

solving momenta from both (A) and (B), I find that the relativistic momentum is higher. But I am a little lost as how to calculate (C) I can find the kinetic energy difference and convert that to (lost) mass?

2. Oct 11, 2007

### learningphysics

I think you should use energy conservation to do part c) using the speed you got in part a)...

set initial energy = final energy... solve the equation for final rest mass of the ship...