Torque and rigid-body equilibrium

Equipment

• 3D lever-on-fulcrum model (panel 1) and rigid-body balance (panel 2)
• Left/right force sliders F₁, F₂ and lever-arm sliders d₁, d₂
• Load-mass and g sliders; net-torque readout

Procedure

1. Find the lever balance point

   In panel 1 set F₁ = 20 N, d₁ = 5 m, F₂ = 25 N and slide d₂ until the bar levels out. Check $F_1d_1=F_2d_2$: d₂ = 4 m balances exactly — the side with the larger force needs the shorter arm.

2. Inverse force–arm proportion

   Double F₂ to 50 N: predict the new balance arm $d_2'=F_1d_1/F_2'=2$ m before sliding. Verify, then keep the product F·d constant and trade (F₂, d₂) along the hyperbola d₂ ∝ 1/F₂ — illustrating the lever's mechanical advantage.

3. Full rigid-body equilibrium

   In panel 2, vary «Load mass» and «g»: read net torque and net force. Equilibrium needs BOTH $\sum\vec F=0$ AND $\sum\tau=0$ — satisfying only one still gives translation or rotation; record an example of each failure mode.

4. Predict and extend

   Pick any load and g; compute $P=mg$ and the arm needed to offset a fixed opposing force before measuring. Extension: drop g to ~1.6 (the Moon) — the same load needs a different arm; explain why pliers/levers «multiply» force in proportion to the arm ratio.

Simulation

Experiment history

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