After dinner (see Problem 7.21 ), two guests decide to use...

After dinner (see Problem $7.21 ),$ two guests decide to use the same $3.0-\mathrm{m}$ -long 5.0 $\mathrm{kg}$ board as a seesaw, using a small bench as a fulcrum. An 82 -kg man sits on one end and a 64 -kg woman sits on the other end. Where should the bench be located so that the board balances?

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Key Concepts

Torque

Torque is the measure of the rotational force applied to an object, calculated as the product of the force and its distance from the pivot point. Understanding torque is essential in problems involving rotation and balance, as it determines how different forces can cause an object to rotate around a fulcrum.

Rotational Equilibrium

Rotational equilibrium occurs when the sum of all torques acting on a system is zero, meaning there is no net rotational motion. This concept is crucial in balancing problems, as it ensures that clockwise and counterclockwise torques cancel each other out, leading to a stable configuration.

Lever Principle (Principle of Moments)

The lever principle, or principle of moments, states that for a lever to be in balance, the moment (torque) produced by the force on one side of the pivot must equal the moment produced by the force on the other side. This concept is foundational in understanding how different weights and distances can be arranged to achieve balance in systems like seesaws.

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