# Conservation of Mechanical Energy and Momentum in total inelastic collisions?

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Conservation of Mechanical Energy and Momentum in total inelastic collisions?

In an inelastic collision, such as a bullet getting stuck in a block hanging on a string, has two types of conservations?

-Total Inelastic Collisision Conservations:
(1) Conservation of Mechanical Energy: Uo+Po = U + P

(2) Conservation of Total Momentum: (m_1)(v_1a) = (m_1 + m_2)*v_b

-Questions:
1. Every time (or majority of the time) I am working with a total inelastic collision problem, must I use these two equations or at least consider them first.
2. I read that the conservation of energy is not conserved in total inelastic collisions, then how is it that the total kinetic energy is?
3. How is the conservation of total momentum conserved? Is it by taking into the account the initial momentum of the objects before the collision and the momentum of the objects as they are stuck together? I don't know if I am asking this right. I just want more insight into collisions inelastic/elastic.

Energy is conserved, but specific forms of it need not be as they can be converted to other forms. In an inelastic collision, some kinetic energy is converted to something else, usually heat.
Momentum is conserved - it takes no form other than a kinetic one.
"Instantaneously", the momentum of the bullet becomes shared between the bullet and the block, but subsequently some will pass to the string etc.

I understand the concept of conservation of energy: that it can neither, created nor destroyed...thus in the case of the collision that it has to go to some other system if its not in our system of interest such as the collision itself (thus energy leaving our system in the form of heat). The conversion of energy to other forms, such as heat, when their is an inelastic collision, is this an internal energy of a system (what's the difference between in an external- vs internal- system)? I'm having a hard time relating it to real world situations...

The bullet and block would become hot. This is still a form of kinetic energy in reality, but it's now the random jiggling of molecules. This is not considered mechanical energy since it is not easily used for mechanical purposes.

Ok, thanks for talking physics with me...I need to get this Physics jargon down cus I'm struggling with this. All tips and info help at this point, so thanks again.