Chapter III review and final summary
In Chapter III we studied equilibrium of bodies and simple machines. The centre of mass is the point where gravity is applied; types of equilibrium are stable, unstable and indifferent. Moment of force M = F · l (N·m); a lever balances when F₁ · l₁ = F₂ · l₂. Simple machines: a fixed pulley (no gain, direction changes), a movable pulley (2-fold gain), an inclined plane (F = P · h : s), screw, wedge, windlass (R : r). Golden rule: whatever we gain in force we lose in distance. Efficiency η = A_u : A_t · 100 % < 100 %. For example, if a 1000 N load is raised 2 m on an 8 m inclined plane, the ideal F = 250 N; if the real force is 300 N, A_t = 300 · 8 = 2400 J, A_u = 2000 J, η = 2000 : 2400 · 100 % ≈ 83.3 %. To make a body stable, its centre of mass should be lower and its base wider.
“Machine cards”: each pupil gets a picture of a machine (scissors, pulley, axe, screw, wheelbarrow) and names its type, whether it gives a gain in force, and the golden rule.