- #1
Robert23
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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 mv
##
The Attempt at a Solution
I was unsure if I should use an initial energy and a final energy then take their difference or simply evaluate the relativistic kinetic energy. In doing so I would use the first equation listed for an initial case of v0 = 0 so it's just the objects rest mass energy. The final energy would have vf instead. Then the difference I found was 1.968*10^(22) Joules. However I thought it would also make sense that I can just say the energy to accelerate it from rest is simply the relativistic kinetic energy. Now I evaluated this and found an energy of 2.15*10^(22) Joules. What I don't understand is why these methods do not both work. Is it simply sig-figs or am I missing something? Please let me know if there are any mistakes and which equation is appropriate and why. Thanks!