Questions about conservation of momentum and energy

[jeremy222]

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 isn't too hard to decipher.

 

[jbsteele]

For the first question, when the bullet strikes the block, it transfers momentum to the block, which causes it to move. The momentum of the bullet before and after the collision is equal, since the bullet is massless. This means that the momentum of the block after the collision is equal to the momentum of the bullet before the collision, multiplied by the ratio of the block's mass to the bullet's mass (M/m). Thus, the velocity of the block after the collision is equal to the initial velocity of the bullet (v) times this ratio (M/m). For the second question, mechanical energy is conserved in an isolated system. If there is an external work done on the system then the total energy of the system will not be conserved. This is because the external work can either increase or decrease the total energy of the system.