What is the acceleration of the wedge on a slope with a block on top?

AI Thread Summary
The discussion focuses on calculating the acceleration of a wedge on a slope with a block on top, emphasizing that the wedge does indeed accelerate due to the forces involved. When the block is placed on the wedge and released, the normal reaction force from the block creates a horizontal component that acts on the wedge, causing it to accelerate. The key to finding the wedge's acceleration lies in understanding the relationship between the normal force and its horizontal component, which can be derived from Newton's third law. Specifically, the normal force acting on the wedge is related to the weight of the block and the angle of the slope. Overall, the acceleration of the wedge is a result of the forces acting on it due to the block's weight and the geometry of the system.
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A wedge with mass M rests on a fricitonsless horizontal table top. a block with mass m is placed on the wedge. There is no friction between the block and the wedge. The system is released from rest.

q1: calculate the accelration of the wedge

now why would the wedge have any accelration at all? wouldn't just stand still?..

I can't get how I'm suppose to calculate the acceleration of the wedge.
 
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The wedge exerts a reaction force on the thing on the wedge. From Newton's third law there must consequently be a force on the wedge equal to the normal reaction force. As this force is not perpendicular to the horizontal a component of this force is in the horizontal direction, producing an accelleration on the wedge.
 
So if the normal force for the block is n the opposite one which is the one that acts on the wedge will be m*g*cos(aplha).. but how do I get the horizontel component for this force?
 

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