Block on a smooth wedge (wedge on smooth floor):

When a block slides on a wedge that is free to move, both accelerate. The constraint is that the block stays on the wedge surface.

Analysis method:

1. Let wedge acceleration = A (horizontal), block acceleration along wedge = a
2. In ground frame, block has both A (horizontal from wedge) and a (along incline)
3. FBD of block: mg down, N perpendicular to wedge surface
4. FBD of wedge: Mg down, N from block, N' from floor
5. Constraint: block's acceleration perpendicular to wedge surface = wedge's component perpendicular to surface

Result for smooth surfaces: A = mgsin(theta)cos(theta)/(M + msin^2(theta)) a = (M+m)gsin(theta)/(M + msin^2(theta))