Conversion of Mass to kinetic energy.

[theshanthan]

Homework Statement

A lump of uranium has a mass of 2.0 kg, and begins at rest. Half of the lump’s mass is going to be totally converted into kinetic energy of the other half. After this is done, how fast is the remaining half going?

a. 0.60 c
b. 0.80 c
c. 0.87 c
d. 1.0c

Homework Equations

gamma = 1/ sqrt(1-(v^2/c^2)
KE = (gamma - 1)mc^2
(KE + mc^2)initial = (KE + mc^2)final

The Attempt at a Solution

0 + 2c^2 = C^2 + KE
KE = C^2

(gamma - 1)mc^2 = c^2
gamma = 3/2

V = 0.745

But according to the answer I am wrong. I have a final and I am trying to study for it, but this is not making any sense. as I posted above the answer is C. Any help would be appreciated!

 

[Filip Larsen]

Solving (γ-1)m₁c² = m₂c² with m₁ = m₂ does not give γ = 3/2.

 

[theshanthan]

Thank you! Thanks a lot! I feel smart and dumb at the same time. Smart because I figured out the way to solve it all by myself and dumb because I just can't do super simple algebra!