A person carries a plank of wood 2 m long with one hand pushing down on it at one end with a for

step 1 So here in this problem we are given this plank which is 2 meter long and a person carries this

A person carries a plank of wood 2 m long with one hand...

A person carries a plank of wood 2 $\mathrm{m}$ long with one hand pushing down on it at one end with a force $\mathrm{F}_{1}$ and the other hand holding it up at 50 $\mathrm{cm}$ from the end of the plank with force $\mathrm{F}_{2} .$ If the plank has a mass of 20 $\mathrm{kg}$ and its center of gravity is at the middle of the plank, what are the magnitudes of the forces $\mathrm{F}_{1}$ and $\mathrm{F}_{2} ?$

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Key Concepts

Rotational Equilibrium

Rotational equilibrium occurs when the net torque acting on a system is zero, meaning that all clockwise torques are balanced by counterclockwise torques. This principle is used to determine the relationships between forces applied at different distances from the pivot point.

Center of Gravity

The center of gravity is the point in a body where the entire weight can be considered to act. For uniform objects, it often coincides with the geometric center, and its position is crucial when calculating torques due to gravitational forces.

Static Equilibrium

This concept refers to the condition in which an object remains at rest because the sum of all external forces and the sum of all torques acting on it are zero. It is fundamental in mechanics, ensuring that there is no net translation or rotation when forces are applied.

Torque (Moment)

Torque is the measure of the tendency of a force to rotate an object about a pivot or axis. It is calculated as the product of the force and the distance from the pivot point (lever arm). Understanding torque is essential for analyzing rotating systems and ensuring balance.

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