# internal and center of mass energies

**1. The problem statement, all variables and given/known data**

An object with kinetic energy K explodes into two pieces, each of which moves with twice the speed of the original object.

Compare the internal and center-of-mass energies after the explosion.

**3. The attempt at a solution**

Let K_{1} be the kinetic energy of the main object before the explosion. k_{2} and k_{3} be the kinetic energies after explosion.

K_{1} = k_{2} + k_{3}

Let K_{1} = 0.5m_{1}v_{1}^{2} = K

Then

0.5m_{1}v_{1}^{2} = 0.5m_{2}v_{2}^{2} + 0.5m_{3}v_{3}^{2}

and since each pieces has twice the velocity of the original piece befor explosion

0.5m_{1}v^{2} = 0.5m_{2}(2v)^{2} + 0.5m_{3}(2v)^{2}

∴ 0.5m_{1}v^{2} = 0.5(4v^{2})(m_{2}+m_{3})

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