Question 17: Balancing Clowns
Lever Principle:
Each board acts as a lever with a 2:1 ratio. The load acts on the longer arm (length \(2l\)) and the support (clown’s foot) acts on the shorter arm (length \(l\)).
Force Equation: \( F_{load} \times 2l = F_{support} \times l \implies F_{support} = 2 F_{load} \).
Each board acts as a lever with a 2:1 ratio. The load acts on the longer arm (length \(2l\)) and the support (clown’s foot) acts on the shorter arm (length \(l\)).
Force Equation: \( F_{load} \times 2l = F_{support} \times l \implies F_{support} = 2 F_{load} \).
Chain Calculation:
- Clown 1:
Input Load: 30 kg (Initial mass).
Support Required: \( 30 \times 2 = 60 \) kg.
Clown 1 uses 60 kg of his weight to balance Board 1.
Weight passed to Board 2 (Leftover): \( 80 – 60 = 20 \) kg. - Clown 2:
Input Load: 20 kg.
Support Required: \( 20 \times 2 = 40 \) kg.
Clown 2 uses 40 kg.
Weight passed to Board 3: \( 80 – 40 = 40 \) kg. - Clown 3:
Input Load: 40 kg.
Support Required: \( 40 \times 2 = 80 \) kg.
Clown 3 uses 80 kg (his full weight).
Weight passed to Board 4: \( 80 – 80 = 0 \) kg.
Conclusion:
Clown 3 balances perfectly on one leg (supporting Board 3) with no weight left to press down on Board 4. The chain effectively terminates in a stable state at Clown 3. Any further extension would require a clown to support more than their body weight (e.g., input 80 would require 160 support), which is impossible.
Clown 3 balances perfectly on one leg (supporting Board 3) with no weight left to press down on Board 4. The chain effectively terminates in a stable state at Clown 3. Any further extension would require a clown to support more than their body weight (e.g., input 80 would require 160 support), which is impossible.
Answer: 3 Clowns