I'm new here. this is in reference to the video posted by veritasium on the bullet block experiment. i realise there is already a thread on this but i want to ask a variation of the question. so basically we have two identical blocks and we shoot identical bullets at them one at the centre and another off centre. which one will rise higher? now the answer assuming the collision is inelastic is already discussed. but what if the collision were perfectly elastic? i know this is practically impossible but still we have momentum telling us that both blocks must rise to the same height but since no energy is lost as heat, energy tells us that the rotating one must rise to a lower height. What am i missing??
but still we have momentum telling us that both blocks must rise to the same height
That's not true here. In the first case where the bullet is embedded, the final velocity of the bullet and the block must be identical. Since initial momentum of the two shots were the same, then the final momentum will be the same as well. Because they are connected, the distribution of that momentum cannot change.
But in the elastic case, the final velocity of the bullet and the block are not linked. Conditions may distribute the initial momentum between both objects in different ways. This means that in the two cases, the block may rise to different heights.