Final answer:
To determine where seat 1, occupied by the smaller child, should be located on a seesaw to maintain balance, we apply the principle of moments. Torque caused by each child's weight must be equal and opposite. By calculating this, we obtain the distance at which the 20.0 kg child needs to be seated from the pivot.
Step-by-step explanation:
The student's question relates to the principle of moments (also known as torque) in physics, which is essential when dealing with equilibrium situations such as a seesaw. When two children sit on a seesaw at different distances from the pivot (the center point), their weights will create different amounts of torque. To maintain balance, the torques produced by each child must be equal and opposite.
In this case, we have two children of masses 20.0 kg and 30.0 kg sitting on opposite sides of a seesaw, which has a total length of 3.00 m and a pivot point in the center. To calculate the distance from the pivot point where the smaller child should sit to balance the seesaw, we use the formula: weight × distance from pivot (20 kg child) = weight × distance from pivot (30 kg child).
Since the total length of the seesaw is 3.00 m, the distance from the pivot to the end is 1.50 m on each side. If we call the distance from the pivot to the 20 kg child d, then the distance from the pivot to the 30 kg child will be 3.00 m - d. Using the balance equation, we get:
20.0 kg × d = 30.0 kg × (1.50 m - d).
Solving for d, we find that the smaller child should sit at a calculated distance in order to maintain balance on the seesaw.