Crane Loader

Simple definition

Work is the energy a force transfers when its component along the motion acts through a displacement.

Example

Pulling a crate 5 m with 200 N of cable tension at 30° to the deck transfers 200 × 5 × cos 30° ≈ 866 J.

The cable pulls with a constant force F held at a constant angle θ, and the jib fixes the haul distance d, so the energy it transfers is exactly W = F d cos θ. Only the component along the deck does work; the vertical component does none, because the crate never rises.

That vertical component is not wasted, though. It carries part of the weight, so the deck only pushes back with N = mg − F sin θ and friction bills you Wf = μN d. Raising θ therefore buys a cheaper haul — right up until F sin θ reaches mg and the crate would lift clear of the deck, which the winch refuses.

Whatever survives the drag is kinetic energy at the moment the jib lets go: ΔK = W − Wf. The crate then coasts, losing μmg per metre, and stops after K / μmg. That is why a greased rail carries a small release energy such a long way.

Two berths add the rest of the chapter. A breaker trips when P = Win / t climbs over the winch ceiling, and a worn gearbox draws Win = W / η out of the charge for every joule that reaches the cable.