Inclined Plane Momentum Conservation with Frictionless Horizontal Surface

[leonidas24]

Consider the classical physics problem of a cube sitting atop a frictionless inclined plane. Of course, this cube will accelerate down the plane with acceleration dictated by F = mgsin(theta), where theta is the angle between the inclined plane and the horizontal surface.

Easy enough.

Now, my question is this; if the inclined plane was itself sitting atop a frictionless, horizontal plane, would it too accelerate in some direction as the cube slides down its surface? In order to conserve momentum, for instance?

 

[sophiecentaur]

Just write out the force equation and that should do it. Have faith, my lad! Physics works.

 

[jack action]

The cube would have a simple vertical free fall and the inclined plane would move out of its way as the cube goes down since it doesn't have any restriction.

 

[Doc Al]

Now, my question is this; if the inclined plane was itself sitting atop a frictionless, horizontal plane, would it too accelerate in some direction as the cube slides down its surface? In order to conserve momentum, for instance?

Of course.

The cube would have a simple vertical free fall and the inclined plane would move out of its way as the cube goes down since it doesn't have any restriction.

The cube is not in free fall. The incline exerts a force on it.

 

[sophiecentaur]

The cube and the ramp will move apart horizontally - Newton's Third Law - in addition to the cube moving vertically.