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

[Toranc3]

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

 

[mishek]

Hello, did you try to sketch FBD?

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