Normal Force Ramps: Solving m's Motion Problem

AI Thread Summary
To determine the minimum horizontal force F needed to move a small block m up a triangular ramp M on a frictionless table, the normal force between the block and the ramp must be analyzed. The normal force is influenced by both the weight of the block and the applied force F, which must be resolved into components acting perpendicular to the ramp. The static friction, characterized by the coefficient u, plays a crucial role in calculating the force required to initiate motion. Clarification on the interaction of forces and the correct application of free body diagrams is essential for solving this problem. A clear understanding of these dynamics will lead to the correct solution.
nothilaryy
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Problem: A small block of mass m rests on the rough, sloping side of a triangular block of mass M which itself rests on a horizontal frictionless table. If the coefficient of static friction is u determine the minimum horizontal force F applied to ramp M that will cause the small block m to start moving up the incline.

I'm pretty sure I know how to go about solving the problem, but after thinking about it so much I'm afraid I'm confusing myself about the normal force between the ramp and the block. Would I be correct in stating that I have to take in account part of the applied force F for the normal force? Or is it just m*g*sin(angle of ramp) for the block? I'm not sure I've ever done a problem that involves looking at both sides of a normal force. Let me know if you need a diagram of the problem or more proof of my thinking/work (believe me, I have plenty)
 
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if you show us your work would be more clear and if you use freedody diagram would be better.
 
I attached my freebody diagrams. Sorry for the iffy MS paint quality.
 

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