Final answer:
The force needed on the lighter child's side of a seesaw for balance is determined by the torque equation. The lighter child needs to sit farther from the pivot point to create equal torque to the heavier child's side, ensuring equilibrium.
Step-by-step explanation:
If two children of different weights are on a seesaw, the force that needs to be exerted on the lighter child's side is dependent on the principles of torque and equilibrium. This is because a seesaw is an example of a lever where the pivot point, or fulcrum, is in the middle. Equilibrium occurs when the product of the weight and distance from the fulcrum (i.e., torque) is equal on both sides.
In order for the seesaw to be balanced, the torque on the lighter side must be the same as the torque on the heavier side. Torque is the product of the weight (or force due to gravity on the mass) of the child and the distance from the pivot (r), which is expressed as Torque = Weight × Distance from Pivot. Therefore, the lighter child should sit at a distance from the pivot that creates a torque equal in magnitude to that of the heavier child's weight multiplied by his or her distance from the pivot. This concept is reflected in the formula Torquelighter = Torqueheavier implying that (Weightlighter × Distancelighter from pivot) = (Weightheavier × Distanceheavier from pivot).
If the seesaw is in balance, it means that no additional force needs to be applied on the lighter child's side to maintain the equilibrium position, because their increased distance from the pivot point compensates for their lighter weight.