Mass sliding down a plane Say we have a mass $m$ sliding down a plane with friction. Will the plane move too if it's mass is finite? Because the force of friction acting on the mass $m$ must react on the plane too but isn't it supposed to dissipate and be unusable.
 A: Yes, the plane will move too by momentum conservation, but there is no contradiction here. Energy gets dissipated, momentum is not.
In fact, it's possible for a system to lose virtually all kinetic energy while still having a large momentum. For example, if $mV$ is large but $V$ is much smaller than 1/large, then $mV^2$ is very close to zero.
A: Yes, assuming the the surface on which the plane rests is frictionless (or has a small enough coefficient of friction such that the static friction between plane and earth is 'small enough' it will move in the opposite direction).
Consider the following sketch:

I drew the FBD for the block and the incline (or the plane, if you will). I assumed no friction between the incline and the surface the incline was on.
Interestingly, if everything were frictionless, you'd still end up with the plane accelerating.  The presence of friction between the block and plane as the block is sliding down will actually decrease the net force force that is responsible for the leftwards push on the incline.
The completely frictionless case is actually an introductory problem in Lagrangian mechanics, where you end up finding the equations of motion of the block and incline. If you know some Calculus and are interested in this topic, I'd recommend you look at the following excellent video: https://www.youtube.com/watch?v=FyslRoCuBdY&ab_channel=FacultyofKhan.
