Efficiency and Levers

The efficiency and simple machines calculator finds efficiency, useful work and work input, torque, the force and lever arm from the lever rule, and the efficiency of an inclined plane.

Efficiency

η = ^W_out/_Win · 100%

No machine reaches 100%: part of the work is lost to friction and heat.

Lever and torque

Torque M = F · l, where l is the lever arm — the shortest distance from the pivot to the line of action. A lever balances when the moments are equal:

F₁l₁ = F₂l₂

Example. 20 N on a 30 cm arm balances F₂ = 20 · 30 / 60 = 10 N on a 60 cm arm — a twofold gain in force.

Inclined plane

η = ^Ph/_Fl · 100%

Useful work lifts a load of weight P to height h; the work input is the pull F along a ramp of length l.