Answer
The nails must exert at least 2400N of force at A to hold the board in place.
Work Step by Step
We sum the torques about the fulcrum to solve for the force in the nails at A.
$(+ \circlearrowleft) \sum \tau=0$
$F*.75m-.75m*45kg*9.8m/s^2-2.25m*65kg*9.8m/s^2=0$
$F=(.75m*45kg*9.8m/s^2+2.25m*65kg*9.8m/s^2)/(.75m)$
$F\approx2400N$
Therefore, the nails must exert at least 2400N of force at A to hold the board in place.
