Question

if two bodies collided together, and the energy wasn't conserved.
can the linear momentum be still conserved ?!

Answer 1

in other words
does the conservation of momentum depends on the conservation of energy ?

Answer 2

Momentum is often conserved in collisions when energy is not.

Momentum is conserved in a collision if there are no forces other than those acting between the objects in the collision.
This is because of Newton's third law. If you add up all the forces acting on all the objects colliding, all the forces between object colliding add up to zero.
If there are no other forces, the total force is zero so the total momentum doesn't change.

Answer 3

NO, conservation of momentum does not depend on energy. Momentum is always conserved. And actually energy is also always conserved. When we say there is loss of energy, we mean that the energy is lost in the form of heat or light that can not be presented by E=mv.

Answer 4

So if was told that two bodies collided , and there was an energy loss.
can i use the relation (m1u1 + m2u2 = m1v1 + m2v2 ) ?

Answer 5

As long as there are no forces other than the forces between the two objects colliding, you can still use conservation of momentum, \[m _{1, initial} v_{1, initial} + m_{2, initial} v_2\]