Final answer:
To keep the 10 N board in static equilibrium with a 3 N upward force on the left, a person must apply a 7 N upward force 3.5714 meters from the left edge of the board.
Step-by-step explanation:
The magnitude of force needed to keep the board in static equilibrium can be found by applying the principle of moments (or torques), which states that for an object to be in equilibrium, the sum of the clockwise moments about any pivot must equal the sum of the anti-clockwise moments about that pivot.
For the 10 N board of length 5 meters with a 3 N upward force applied at the left, we have an opposing 7 N force to achieve equilibrium. To find the position where the 7 N force must be applied from the left edge, we use the formula:
Setting the sum of anti-clockwise moments equal to clockwise moments:
ΣMoments anti-clockwise = ΣMoments clockwise
0 + 7 N × x = 25 N·m
7 N × x = 25 N·m
x = 25 N·m / 7 N = 3.5714 m
Therefore, the person must place the 7 N force 3.5714 meters from the left edge of the board to maintain static equilibrium.