Question

The uniform 4.0 m, 80 N plank is shown with a 80 N weight resting on top, 1.0 m from the right
end. The plank is in equilibrium. What is F1 in Newtons?

Answer 1

To find F1, sum moments about F2 to zero

F1 will make a counter clockwise moment a distance 4.0 from F2
The weight of the plank will make a clockwise moment a distance 4.0/2 from F2
The point load will make a clockwise moment a distance of [1.0 ] from F2

F1[4.0] - 80[4.0/2] - 80[1.0] = 0

F1 = (160 + 80) / 4.0

F1 = 60 N

as the result is positive, our assumed direction of upward is correct

If the supports are not located at the ends of the plank, the moment arms might have to be adjusted, but the solution principle remains the same.