What is the least amount of force needed to pull a board out from under a box?

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To determine the least amount of force needed to pull a board out from under a box, one must consider the forces acting on both the box and the board. The box experiences static friction, which must be overcome for the board to be pulled out. The equations of motion include F=ma for both the box and the board, with net forces calculated in both the x and y directions. A proper free body diagram (FBD) is essential for visualizing these forces and ensuring accurate calculations. Understanding the relationship between static and kinetic friction coefficients is crucial for solving the problem effectively.
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Homework Statement


A small box of mass is sitting on a board of mass and length L . The board rests on a frictionless horizontal surface. The coefficient of static friction between the board and the box is . The coefficient of kinetic friction between the board and the box is, as usual, less than .

Find , the constant force with the least magnitude that must be applied to the board in order to pull the board out from under the the box (which will then fall off of the opposite end of the board).


Homework Equations



F=ma

The Attempt at a Solution



im confused for my force body diagrams
box is m1 and board is m2
for the box i have
Fnet y: n-m1g=0
Fnet x: fk=m1a

for the board i have:
Fnet y: n-(m1+m2)g=0
Fnet x: F-fk=(m1+m2)a
 
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Hello, did you try to sketch FBD?

I thing it might be a problem with Your last line.
 

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