A 75 kg man sits at one end of a uniform seesaw pivoted at its center, and his 24 kg son at the other end. Where would his 55kg wife have to sit to balance the seesaw?
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To balance the seesaw, the torques on both sides of the pivot point need to cancel out. The torque of an object is a measure of the force's ability to rotate the object around the pivot point. The torque is calculated as the product of the force applied and the distance from the pivot point.
In this scenario, the torque on one side of the seesaw is given by the weight of the person multiplied by their distance from the pivot. Let's assume the distance from the center pivot to the ends of the seesaw is equal and has a value of "d".
For the man, the torque is given by:
Torque_man = Weight_man * Distance_man
= 75 kg * 9.8 m/s^2 * d
For the son, the torque is given by:
Torque_son = Weight_son * Distance_son
= 24 kg * 9.8 m/s^2 * d
Since the seesaw is balanced, these torques must cancel each other out. Therefore, the torque of the man should be equal to the torque of the son:
75 kg * 9.8 m/s^2 * d = 24 kg * 9.8 m/s^2 * d
Simplifying this equation, we find:
75 kg = 24 kg * (55 kg * d) / d
Solving for the unknown, we find:
55 kg * d = 75 kg
d = 75 kg / 55 kg
Therefore, the 55 kg wife would need to sit at a distance equal to 75 kg / 55 kg from the center pivot point to balance the seesaw.