Can you solve the particle sliding on a movable inclinded plane problem

Machinus
Can you solve the "particle sliding on a movable inclinded plane" problem...

...using Newtonian Mechanics?

No Lagrangians.
 
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Work from the frame of the inclined plane and write the second law for the smaller block by adding an inertial force.

Then consider that center of mass of the two doesn't accelerate and write another equation. Solve the two and you get the accelerations.

This is basically working from two different frames in the same problem but works since working in non-inertial frame and adding an inertial force is the same as taking relative accelerations into account and working from an inertail frame. But this is sometimes simpler.

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