Lever: force needed on the other arm

On a lever, a 3 kg object hangs 0.4 m to the left of the fulcrum. What force must be applied 0.6 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 = 3×10 = 30
   The object's weight provides the effort on the left
2. F₁·L₁ = F₂·L₂ → F₂ = F₁×L₁/L₂ = 30×0.4/0.6 = 20
   Lever balance: effort × effort arm = load × load arm
3. Equivalent mass = 20/10 = 2 kg
   Convert to the everyday "how heavy"

Why it works

Balancing means the two moments are equal: F₁ × L₁ = F₂ × L₂. The weight of the 3 kg object is 30 N, and the longer right arm needs a smaller force.

Common mistakes

• Reversing the arm ratio and getting 45 N.
• Answering 3 kg directly, as if the two arms were equal.

Related

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