Lever: 6 kg at 0.2 m, force at 0.4 m

A 6 kg object hangs 0.2 m to the left of the fulcrum of a lever. What force must be applied 0.4 m to the right of the fulcrum to balance the lever? (Take g = 10 N/kg.)

Step-by-step

1. Weight on the left F₁ = mg = 6×10 = 60
   The object's weight provides the effort on the left
2. F₁·L₁ = F₂·L₂ → F₂ = F₁×L₁/L₂ = 60×0.2/0.4 = 30
   Lever balance: effort × effort arm = load × load arm
3. Equivalent mass = 30/10 = 3 kg
   Convert to the everyday "how heavy"

Why it works

A lever is balanced when the effort times its arm equals the load times its arm: F₁ × L₁ = F₂ × L₂. A longer arm therefore needs a smaller force.

Common mistakes

• Multiplying 60 N by 0.4 ÷ 0.2 instead of dividing by it.
• Treating the 6 kg mass itself as the force on the left arm.

Related

lever-fulcrum-two-arms-balance lever-balance-find-right-weight n-phy-lever-balance-1