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Answer :
The distance from her feet to her center of mass is approximately 2.1 meters.
To find the center of mass, we need to consider the concept of torque. Torque is the force applied at a distance from a pivot point, and it causes an object to rotate. In this case, the pivot point is the center of mass.
To determine the distance of the person's center of mass from her feet, we can use the equation:
Torque = Force × Distance
Let's calculate the torques at the head and feet scales. The distance between the scales is given as 1.69 meters. The force at the head scale is 400 N, and at the foot scale, it is 322 N.
At the head scale, the torque is:
Torque_head = Force_head × Distance
Torque_head = 400 N × 1.69 m
Torque_head = 676 N·m
Similarly, at the foot scale, the torque is:
Torque_foot = Force_foot × Distance
Torque_foot = 322 N × 1.69 m
Torque_foot = 544.18 N·m
To find the distance of the center of mass from the feet, we can equate the torques at the head and feet scales:
Torque_head = Torque_foot
Force_head × Distance_head = Force_foot × Distance_foot
400 N × Distance_head = 322 N × Distance_foot
Distance_foot = (400 N × Distance_head) / 322 N
Plugging in the values:
Distance_foot = (400 N × 1.69 m) / 322 N
Distance_foot ≈ 2.1 m
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