Equality of work when using machines
A machine may give a gain in force, but it gives no gain in work. This shows up in experiment: lifting a load directly to a height h requires work A₁ = P · h (P is the weight of the load). If the same load is raised with an inclined plane or a lever, the force is smaller (F < P), but the distance moved by the force is longer (s > h): A₂ = F · s. In an ideal, frictionless machine A₂ = A₁, i.e. F · s = P · h. For example, lifting a 1000 N load 2 m: A₁ = 1000 · 2 = 2000 J; with an 8 m inclined plane F = 250 N, A₂ = 250 · 8 = 2000 J. With a movable pulley the force is half but we pull twice as much rope. For a lever too, F₁ · s₁ = F₂ · s₂ (ideal). In real machines, because of friction and the weight of the parts, the work put in is always greater than the useful work.
Experiment: with a dynamometer lift the same load straight up (F₁, h) and then pull it up a plank (F₂, s). Compare A₁ = F₁ · h and A₂ = F₂ · s: which is a little bigger, and why? Safety: use a small load (200–300 g) and keep hands away from the plank edges.