Conceptual Question: Block on a wedge on a frictionless surface

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In the scenario of a block on an inclined plane resting on a frictionless surface, the inclined plane will indeed move if the block has mass. The block exerts a force on the inclined plane that is both downward and sideways due to gravity. If the weight component along the incline exceeds static friction, the inclined plane will slide. Conversely, if static friction is sufficient to counteract this force, the plane will remain stationary. Thus, the movement of the inclined plane depends on the balance between the gravitational force acting on the block and the frictional forces at play.
msun5040
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Homework Statement


This is more of a conceptual question, but say a block was set on top of an inclined plane, which was set on top of a frictionless level surface. Would the inclined plane move? Why or why not

Homework Equations


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The Attempt at a Solution


My thought process was that since the the surface is level, it would mean that the inclined plane would not move. However, I don't know how gravity would play into this situation.
 
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Let's say that the block had mass and the inclined plane had none - or very little.
The block is applying a force to the inclined plane that is normal to its surface. So the block is not pushing straight down on the block - it is pushing down and to the side.

So you tell me what will happen to that inclined plane.
 
You didn’t say the plane was frictionless, so you will need to consider two different cases. Either the component along the incline of the weight of the block exceeds static friction or it doesn’t.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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