Question

Two children of mass 18 kg and 31 kg sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of 3 m, at what distance from the pivot point is the small child sitting in order to maintain the balance?

Answer 1

The small child with a mass of 18 kg must sit 1.90 meters from the pivot point to balance the seesaw, using the principle of moments.

Step-by-step explanation:

To solve for the distance from the pivot point where the small child must sit to maintain balance on the seesaw, we can use the principle of moments (also known as the principle of lever or torque). In a balanced seesaw, the product of the mass and distance (moment) from the pivot must be the same for both children.

Let's denote the distance for the child with mass 18 kg as d1 and for the child with mass 31 kg as d2. Because they are sitting on opposite sides, the total distance d1 + d2 is 3 m. We are asked to find d1.

To maintain balance:

• 18 kg * d1 = 31 kg * d2
• Since d1 + d2 = 3 m, d2 = 3 m - d1

Substituting the value of d2 in the balance equation:

• 18 kg * d1 = 31 kg * (3 m - d1)
• 18 kg * d1 = 93 kg m - 31 kg * d1
• d1 (18 kg + 31 kg) = 93 kg m
• d1 = 93 kg m / (18 kg + 31 kg)
• d1 = 93 kg m / 49 kg
• d1 = 1.90 m

Therefore, the small child (18 kg) must be sitting 1.90 meters from the pivot point to achieve balance on the seesaw.