Calculate the energy needed to accelerate a spaceship of mass 10,000 kg to a speed of 0.3c for intergalactic space exploration. Compare with the projected energy usage of the Earth in a decade 10^22J?

Answer 1

I just answered this a few minutes ago. I used the rest mass here because .3*.3 is just about .1 and not worth calculating beta. However look at the problem below this one if you want to do the relativistic problem.
Posted by Paul on Sunday, September 14, 2014 at 4:30pm.

Calculate the energy needed to accelerate a spaceship of mass 10,000 kg to a speed of 0.3c for intergalactic space exploration. Compare with the projected energy usage of the Earth in a decade~10^22J?
well i don't know how to start the problem


Physics - Damon, Sunday, September 14, 2014 at 4:58pm

(1/2) m v^2
= 5,000 * (.3*3*10^8)^2
= 5*10^3 * .81 * 10^16

= 4.05 * 10^19

Answer 2

The above answer is incorrect by over an entire order of magnitude.

(1/2)mv^2 is not the formula for relativistic momentum. Rather you're looking at mc^2(gamma-1) where gamma is (1/(1-(v^2/c^2))^.5). plugging in all of the numbers from the problem gives us:

10000c^2*(0.048)

Which is about 9*10^20 Joules.