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 K1 be the kinetic energy of the main object before the explosion. k2 and k3 be the kinetic energies after explosion.

K1 = k2 + k3

Let K1 = 0.5m1v12 = K


0.5m1v12 = 0.5m2v22 + 0.5m3v32

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

0.5m1v2 = 0.5m2(2v)2 + 0.5m3(2v)2

∴ 0.5m1v2 = 0.5(4v2)(m2+m3)

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