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and then the two bodies move off together, then conservation of momentum suggests that the since the combined mass is 2m, the new velocity will be 1/2 u.

Total momentum before collision = mu + m0 = mu

Total momentum after collision = m(1/2u) + m(1/2u) = mu

However energy before collision = 1/2mu

^{2}

and energy after collision = 1/2m(1/2u)

^{2}+ 1/2m(1/2u)

^{2}= 1/4mu

^{2}

So it seems the energy is halved or am I making an error in the calculations ?