Momentum in special relativity

AI Thread Summary
The discussion focuses on calculating the speed of a spaceship after it ejects fuel, using both special relativity and classical mechanics. In part (a), the relativistic speed is determined using Lorentz momentum, which yields a higher momentum than classical calculations in part (b). For part (c), the change in rest mass is estimated by applying energy conservation principles, where the initial energy equals the final energy. The kinetic energy difference can be converted to lost mass, indicating a decrease in the ship's rest mass due to fuel ejection. The calculations illustrate the significant differences between relativistic and classical mechanics in high-speed scenarios.
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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?
 
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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...
 

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