The Little Lift
Try it yourself · One lever, three choices
The 3D lever, captioned forces, distances, mechanical advantage, and equal torques all update from the same ideal model. 3/3 model checks pass.
What the model is showing
A first-class lever lifts a crate when you press down on the longer side. For an ideal balanced lever, the clockwise and anticlockwise torques are equal.
| Load weight, m × g | 117.7 N |
| Long arm, dₑ | 1.60 m |
| Short arm, dₗ | 0.32 m |
| Input work at 0.20 rad | 7.49 J |
| Output work at 0.20 rad | 7.49 J |
The science · equations and honest limits
At the point of ideal static balance, the moment about the fulcrum is equal on both sides:
Fₑ = m · 9.81 · dₗ / dₑ
Ideal mechanical advantage: MA = dₑ / dₗ. When the beam rotates by angle θ from horizontal, each end's vertical travel is exactly h = d · sin(θ) for this rigid, rotating geometry.
Equal ideal work: Fₑ · hₑ = (mg) · hₗ. The example animation ends at θ = 0.20 radians (approximately 11.5°).
Assumptions: rigid massless beam, frictionless pivot, gravity of 9.81 m/s², force applied vertically, a quasi-static idealised comparison of forces and displacements. Force equilibrium for a tilted beam uses perpendicular moment arms d cosθ on both sides, so cosθ cancels for vertical forces.
Limits: real beams bend and have weight; pivots have friction; the contact geometry changes; accelerating the load needs additional force. The crate is visually fixed to the rotating beam rather than hanging vertically. This is a conceptual film, not a structural safety calculator.