On a seesaw with sliding seats, a child is sitting on one side and an adult on the other side. The adult weighs twice that of the child. The seesaw however is balanced. Draw a figure which depicts this situation showing the distances from the fulcrum where the child and the adult are seated.
For the seesaw to be balanced, the principle of levers states that F₁ × d₁ = F₂ × d₂. Since the adult weighs twice the child (W_adult = 2 × W_child), the child must sit at twice the distance from the fulcrum compared to the adult.
Diagram Description:
- Draw a horizontal beam balanced on a triangular fulcrum at the center.
- On the left side, draw a child sitting at a distance 2d from the fulcrum.
- On the right side, draw an adult sitting at a distance d from the fulcrum.
- Label the distances clearly: "2d" on the child's side and "d" on the adult's side.
For example, if the child sits at 2 m from the fulcrum, the adult sits at 1 m from the fulcrum.
Explanation
Using the lever principle from the context (F₁ × d₁ = F₂ × d₂), when one weight is twice the other, the lighter weight must be placed at twice the distance from the fulcrum to achieve balance. This is demonstrated in Example 7.13 where a 15 kg child at 2 m balances a 30 kg child at 1 m.
Solution Steps
Step 1: Apply the lever principle: F₁ × d₁ = F₂ × d₂
Step 2: Let child's weight = W, then adult's weight = 2W
Step 3: Substitute: W × d_child = 2W × d_adult
Step 4: Simplify: d_child = 2 × d_adult
Step 5: Draw the seesaw with child at distance 2d and adult at distance d from fulcrum