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

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SUMMARY

The acceleration of a wedge on a frictionless surface with a block on top can be calculated using Newton's laws of motion. When the block is placed on the wedge and released, the wedge accelerates due to the horizontal component of the normal force exerted by the block. Specifically, the horizontal force acting on the wedge is derived from the normal force, calculated as n = m * g * cos(α), where α is the angle of the wedge. This results in the wedge accelerating horizontally as a response to the block's weight and the angle of inclination.

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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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