Thanks for the reply. So for the first case I start by solving for gamma:
## \gamma = \sqrt{\frac{1}{1-(.9965)^2}} = 11.96 ##
Now I can find the kinetic energy:
##KE = (11.96-1)(20,000kg)(c)^2 , c = 3*10^{8} m/s##
KE = 2.138*10^{22} J
Now for the other method using total energies, I first...
Homework Statement
How much energy does it take to accelerate an object of mass 20,000 kg from rest to 0.9965c?
m = 20,000 kg
v0 = 0 m/s
vf = 0.9965c
Homework Equations
##
E^{2} = \sqrt{(pc)^{2}+(mc^{2})^2} \\
E_{KE} = (\gamma - 1)mc^{2} \\
\gamma = \sqrt{\frac{1}{1-(v/c)^{2}}} \\
p = \gamma...