Conservation of momentum in an inelastic collision

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The law of conservation of momentum states that all momentum is conserved in a collision. Momentum is defined as p = mv. When a collision occurs, most of the time a lot of velocity is lost and most of the mass remains. For example, a fast moving trolley runs into a brick wall, after hitting the brick wall no mass is lost or gained but a significant amount of velocity is lost. Using the formula p = mv, the final momentum will be lower than the initial momentum.

Also, impulse can be defined as the change in momentum. But isn't momentum always conserved?

This seems to be an obvious paradox but I know that I've got something wrong so can someone please lead me in the write direction. Cheers
 

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Doc Al
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The law of conservation of momentum states that all momentum is conserved in a collision.
The total momentum is conserved in a collision. The individual momenta of the various bodies will certainly change--forces are being exerted on them.

Momentum is conserved in the absence of external forces.
Momentum is defined as p = mv. When a collision occurs, most of the time a lot of velocity is lost and most of the mass remains. For example, a fast moving trolley runs into a brick wall, after hitting the brick wall no mass is lost or gained but a significant amount of velocity is lost. Using the formula p = mv, the final momentum will be lower than the initial momentum.

Also, impulse can be defined as the change in momentum. But isn't momentum always conserved?
No. If something experiences a force--thus an impulse--its momentum will change.

When the trolley runs into the wall, the wall and trolley exert forces on each other. The trolley loses momentum and the wall (and the attached earth) gains momentum. (You won't notice the change in the wall's momentum since the wall+earth is so massive.)
 
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yep makes sense thanks mate
 

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