If two particles collide on a linear track and coalesce. Where the mass of each particle is 1kg, and before the collision one particle has a velocity of 2m/s and the other is stationary. After the collision the total momentum will be the same (2kgm/s).
Yet the total KE has increased from 1/2*1*2^2 = 2 to 1/2*2*1^2 = 1
Where did this extra KE come from?
EDIT:
And if there is a stationary particle of mass 10kg, that splits into two particles A and B travelling in opposite directions with mass 8kg and 2kg respectively. If we give particle B velocity of 4m/s, then to conserve momentum particle A must have a velocity of 1m/s? This all seems correct to me as momentum and mass are both conserved.
However when looking at their KE, particle A has a KE of 4J but particle B has a KE of 16J? Where am I going wrong here? Is there something I'm missing that means that one of either KE or momentum isn't conserved in interactions like these??