Momentum in special relativity

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SUMMARY

The discussion focuses on calculating the momentum and speed of a spaceship of mass 106 kg that ejects 103 kg of fuel at a speed of c/2. Using Lorentz momentum, the relativistic speed of the ship is derived, demonstrating that relativistic momentum is greater than classical momentum. The discussion also emphasizes the importance of energy conservation in determining the change in rest mass after fuel ejection, suggesting that the initial energy equals the final energy to solve for the final rest mass of the ship.

PREREQUISITES
  • Understanding of Lorentz transformations and relativistic momentum
  • Familiarity with classical Newtonian mechanics
  • Basic knowledge of energy conservation principles
  • Concept of rest mass and its relation to energy
NEXT STEPS
  • Study Lorentz transformations in detail
  • Explore the implications of relativistic momentum in high-speed scenarios
  • Learn about energy-mass equivalence and its applications in physics
  • Investigate the differences between relativistic and classical mechanics
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Physics students, aerospace engineers, and anyone interested in the principles of special relativity and momentum calculations.

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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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