The golden rule of mechanics. Efficiency of a machine
The golden rule of mechanics: a machine that gives a gain in force by some factor loses the same factor in distance; no machine gives a gain in work. In use a machine does useful work A_u on the load (e.g. lifting: A_u = P · h), but the total work A_t we put in is larger (friction, weight of parts). The efficiency is the ratio of useful work to total work: η = (A_u : A_t) · 100 %. Efficiency is always below 100 %, because A_u < A_t. For example, if 200 J is spent for 160 J of useful work, η = 160 : 200 · 100 % = 80 %. Approximate efficiencies: a fixed pulley 94–98 %, a screw and inclined plane less. To raise efficiency, friction is reduced by lubrication and parts are made lighter. A “perpetual motion machine” with efficiency above 100 % cannot be built.
“Best machine”: groups use three ramps (smooth plank, plank with cloth, plank with sandpaper), measure A_u and A_t and calculate the efficiency; which is highest? Safety: use a light load and pull the dynamometer smoothly without letting go.