To find the distance from the woman's center of mass to the edge of the board closest to her feet, an equilibrium equation of torques is set up based on the forces involved and solved for the unknown distance x.
The question asks to calculate the distance between the center of mass (c.m.) of a person and the edge of the board closest to the feet, when the woman is lying on her back on a horizontal wooden board. To solve this, we consider the equilibrium of torques about the pivot point, which is the block of wood under the board. The total downward force due to the woman's weight (W = mg) plus the weight of the board must be balanced by the upward force from the scale. With known distances from the pivot, we can set up the following equation for static equilibrium:
Torque due to board weight + Torque due to woman's weight = Torque due to scale reading
(70 N)(L/2) + (60 kg · 9.81 m/s²)(x) = (220 N)(L), where L is the length of the board and x is the distance from the pivot (block of wood) to the woman's center of mass.
Solving this equation enables us to find the distance x, which represents how far the woman's center of mass is from the edge of the board closest to her feet.