Relativity Problem: How much work must be done on a spaceship to bring it to a certain speed?

Question

42,000 kg spaceship is to travel to a star 6 light years from earth. passengers on the ship want the trip to last no more than a year. how much work must be done on the spaceship to bring it to the speed necessary for this trip?

To solve this problem, is the kinetic energy of the ship at this particular speed equal to the work needed?

Anonymous · Accepted Answer

Two parts.
gamma of 6 = 1 / sqrt( 1 - (v/c)^2), v = 0.986c

Second part.
Total energy
E^2 = (pc)^2 + (mc^2)^2, with p as a vector p = gamma * m * v

Since "work done" is just the change in energy from v = 0 to v = 0.986c (so the (mc^2)^2 terms cancel out), I think you can do the rest.

Now normally, you'd want to slow down and land at the end, which would increase the amount of work required, but that is not what this problem called for...
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/rocket.html

Anonymous · Answer

This question is flawed in multiple ways. Most obviously, a trip the distance of 6 light years cannot possibly take one year.

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Relativity Problem: How much work must be done on a spaceship to bring it to a certain speed?

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