Questions about conservation of momentum and energy

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Homework Statement

Ok so a block is suspended by two massless strings. A bullet hits the block and gets imbedded in it and moves. Bullet has speed v block has mass M. Bullet has mass m
A second question if that is a system isolated if gravity acts on it and related to that is if mechanical energy is conserved if a system is not isolated and why?

Homework Equations

Mechanical energy and momentum

The Attempt at a Solution

I understand how to do this problem but my professor said something about we are appoximating something since the mass of the bullet is sufficiently small and if the bullet was very heavy everything would be messed up. I think it has something to do with the bullet not stopping in the block in a short amount of time but I am not sure and I was wondering if anyone knows what goes wrong when bullet is not sufficiently light. On another note, I know that if there is an external work done on a system then E mechanical is not conserved but what if the external works cancel out such as two people exerting equal and opposite work on a system. I hope my paragraph isnt too hard to decipher.

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