# Is Momentum conserved in this block-wedge system?

There's a block slides downward along a frictionless wedge which sits on a frictionless horizontal surface, when the block leaves the wedge, both of the wedge and the block have a horizontal velocity in opposite direction.

In this situation,can we say the momentum of the system is conserved? How to deal with the vertical motion of the block? If I say the system is conserved, should the system include earth? Since the force of gravity of the block as an external force of the block-wedge system has done work during the motion.

Any idea or hint is appreciated!

• Only the horizontal momentum is conserved, since there is a vertical external force. You can include Earth so that all momentum components are conserved, but it's not helpful for solving the problem (i.e. you get 1 more equation to use, but also 1 more variable). – knzhou Apr 13 '16 at 1:28
• so if I have the horizontal velocity of both of the block and wedge I can say m1v1 = m2v2? (the system initially is at rest) @knzhou – JTing Apr 13 '16 at 1:30