LEVER
τ₁ vs τ₂ — slide the mass until the moments agree.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Two masses, one rigid beam, one pivot. Statics asks a single question: do the turning tendencies cancel? Distance matters exactly as much as weight — that trade is the whole trick of the lever.
Forces
Each mass pulls straight down with F = mg. The pivot pushes back, and whichever end rests on a stop gets help there too — vertically, everything balances no matter what. Forces alone cannot tell you which way the beam turns.
Torque
Torque is force times lever arm: τ = F·d, taken about the pivot. m₁ turns the beam one way, m₂ the other, and the larger moment wins — the stop quietly supplies the difference, F_s = τ_net/L.
Balance
Now perform the experiment: slide m₂ outward until the moments agree. The beam lifts off its stop and levels at exactly d₂* = m₁d₁/m₂ — no heavier mass required, just a longer arm.
Advantage
The lever’s bargain, written as one ratio: MA = d₂*/d₁. A small weight on a long arm holds a large weight on a short one, and virtual work shows the books closing — F₁d₁ = F₂d₂* to the last digit.