Presets
Playback
Machine
Counterweight, arm geometry and efficiency set the launch speed.
Release and projectile
Angle and drag decide how much of the energy becomes range.
Model checks
The science
Energy budget of the lever
The falling counterweight releases about E = η M g hdrop, where hdrop is roughly 1.85 times the short arm length and η lumps all losses (sling, friction, counterweight kinetic energy). The projectile leaves with v0 = √(2E / m) after paying m g h/2 to lift itself.
Flight
In vacuum the range from height h is R = v0 cosθ (v0 sinθ + √(v0² sin²θ + 2 g h)) / g, best near 45° for ground launches. With drag the acceleration is a = -(½ ρ Cd A / m) |v| v - g, integrated by fourth-order Runge-Kutta, so the best angle drops below 45° and range falls.
Honest simplifications: the arm swing is drawn smoothly and not integrated as a double pendulum; η is a single lumped number; no spin, wind or sling release timing. Treat the launch speed as a model input, the flight maths as exact. Educational physics only, with an inert test ball.
What to try
- Raise the counterweight and watch the range grow only like the square root of the energy.
- Set drag to zero (Vacuum ideal): the yellow and dashed curves coincide.
- Compare a light fast ball with a heavy boulder at the same counterweight.