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A woman is lying in a perfectly static position on her back, on top of a horizontal wooden board. The board is resting on a block of wood at one end, and on a weighing scale at the other end. The mass of the person is 60 kg; the length of the board is L = 5.00 m; the weight of the board is 70 N; the reading on the scale placed under the edge of the board closest to her head is 220 N. Calculate the distance between the center of mass (c.m.) of the person and the edge of the board closest to the feet.

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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.

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