What is causing the horizontal acceleration of a ramp with a block on it?

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The discussion centers on a physics problem involving a block on a frictionless ramp, which is placed on a frictionless table. The key issue raised is the inconsistency in forces acting on the ramp, leading to its horizontal acceleration without any opposing force. It is noted that if the block slides down the ramp, the ramp accelerates left while the block accelerates right, creating a paradox. The conversation highlights that the assumption of no friction leads to unrealistic scenarios, as friction is necessary to prevent the ramp from accelerating indefinitely. Ultimately, the problem illustrates the complexities of analyzing motion in systems with multiple interacting components.
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I seem to be a bit stuck on a problem. Consider a block sitting on a ramp, both of which are on a table. Assume that the friction between the ramp and the table is 0. Then, the forces acting on the ramp are gravity, a vertical normal force from the table, and an angled normal force from the block. This would imply that the ramp is always accelerating horizontally, because there is nothing to cancel out the horizontal portion of the normal force from the block. This is simply impossible. What force or bad assumption am I forgetting about?
 
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Why is it impossible? This is a non realistic problem that has no friction on the table.

The block slides down, producing an acceleration of the ramp to the left, while the block accelerates to the right.

Of course, if the block does not slide down, then there is friction between the block and the ramp. The direction of the force of the block on the ramp is down the incline...
 
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