The Law of Conservation of Momentum

[temaire]

Homework Statement

This is more of a theoretical problem than a practical one. I am having a bit of difficulty understanding the concept of inelastic collisions and conservation of momentum. The law states that during inelastic collisions, total momentum is conserved, but total kinetic energy is not. But then I think to myself: if kinetic energy decreases in an inelastic collision, then the velocity of the colliding objects must decrease, which then means that the total momentum of the system decreases. However, this is contrary to the law. Can someone clear this up for me?

Homework Equations

$$p=mv$$

The Attempt at a Solution

Like I said, this is more of a theoretical problem, so there shouldn't be a need to show any work.

 

[Dick]

Compare your problem to an actual example. A 1kg mass moving at 1m/s to the right collides with a 1kg mass moving at 1m/s to the left and they stick together. The result is a stationary 2kg mass. The velocities decreased, did the momentum? Remember momentum is a vector quantity.