Plan and elevation. One state drives both drawings: magnet position (x, y, z) = (r cosθ, 11.8 - L, -r sinθ) with slew angle θ, trolley reach r and cable length L.
Pull model. Within radius R = 1.55 + 1.75 p the pull acceleration is a = 20 p² (1 - d/R) / max(0.35, m/500). The p² scaling mirrors the real law: lifting force on a flat pole face is F = B²A / (2 μ0) with B proportional to coil current. The linear fall-off in d is a deliberate simplification: a real electromagnet's force drops much faster than linearly with air gap and depends on scrap shape and contact.
Capture rule. A load latches when d < 0.76 + 0.34 p and m ≤ 900 p + 220 kg. For scale, B = 1 T over a 2.5 m² face would hold about 1 MN in perfect contact; practical lifting magnets are rated far lower because of air gaps and non-flat scrap.
Hanging load. The latched load is a damped spring about 0.76 m under the magnet: x'' + 1.45 x' + 10.5 x = -1.6 vmag, so ωd = √(10.5 - 0.725²) = 3.16 rad/s, period 1.99 s.
Fall. Released scrap obeys v' = -g - 0.15 v, so h = (g/k)(t - (1 - e-kt)/k) with k = 0.15 1/s; without drag t = √(2h/g). Bounces use restitution 0.23. Educational model; not affiliated with any crane or magnet manufacturer.