Presets
Playback
Parameters
Model checks
The science
Torque balance
A lever turns about its fulcrum, so what matters is torque: τ = F d cosθ, the force times its perpendicular arm. The lever is balanced when Feffort b = m g a, which gives F = m g a / b. The ratio b / a is the ideal mechanical advantage: with a 1.60 m effort arm and a 0.32 m load arm it is 5, so a 12 kg crate (weight 117.7 N) is held by 23.5 N.
Distance pays for force
For a small angle the effort end moves b sinθ while the load rises a sinθ. Work in is F × (effort distance) and work out is m g × (load height); with no friction they are equal, so a lever multiplies force by dividing distance and never creates energy. The simulation integrates the rigid-body equation I d²θ/dt² = τnet with I = m a² + Ibeam, including the weight of the beam (a uniform bar about its own centre) and an optional pivot friction torque.
Honest simplifications: the crate is a point mass fixed at the end of the short arm, the force stays vertical, the beam is rigid and the angle is limited by two stops; the film in the 3D page adds captions and a camera, not different physics.
What to try
- Press the Balanced preset: effort exactly equals m g a / b and the lever hovers instead of accelerating.
- Lengthen the effort arm and watch the needed force fall as 1/b on the balance curve.
- Add pivot friction and see that work in exceeds work out: the difference is the loss.
- Give the beam some mass and notice the longer side now helps the effort.