[Physics] Force applied to an inclined plane

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Below is a picture of the problem. Any guidance would be helpful.

This problem isn't actually from any assignment, per se. I'm hoping that, by understanding this, it'll help me to understand a more complicated system where one inclined plane is resting on another inclined plane, and there's a mass on the top of the second plane, and the bottom incline is being accelerated by an applied force–but since I don't understand how this much simpler system works, I don't seem to have a chance at the more complicated system.

Diagrams

Forgot to include what the question is asking for. Since this isn't really a question I've been asked, I guess what I want to know is the acceleration of the system.

Best Answer

A shorter way to do this would be to use the concept of a pseudo-force.

When you observe the motion from the inclined plane's frame, you should be applying a pseudo-force (virtual force in the direction opposite to acceleration) because it is an accelerating frame.

Considering this, there are three forces on the block in this frame (which is seen stationery). One is gravity, downwards. Another is the normal reaction from the plane. Third is the pseudo-force, leftwards.

All you gotta do now is balance these three forces, because they cancel out and keep the block stationery.

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