mechanical efficiency
Summary
Mechanical efficiency is the fraction of the work or energy put into a machine that comes out as useful work, e = Wout/Win. Real machines lose some input as thermal energy through friction, so efficiency is below 100% and cannot exceed it.
Detail
Meaning: Mechanical efficiency compares useful output to input. Energy is conserved, but in a real machine part of the input is dissipated as thermal energy by friction or air resistance, so the useful work out is smaller than the work in. A frictionless ideal machine would be 100% efficient. Simple machines such as ramps, levers and pulleys trade force for distance; they can reduce the force needed but do not reduce the work.
Equation: e = Wout/Win = Pout/Pin, where e is efficiency (dimensionless, often given as a percent), W is work (J), and P is power (W). For a simple machine, e = actual mechanical advantage / ideal mechanical advantage (a dimensionless ratio of the output force to the input force).
On the MCAT: A passage describes a pulley system, incline or lever with friction. You are given the input force and distance and the load lifted, then asked for efficiency, or for the energy lost, Win − Wout. Expect qualitative questions too: more friction lowers efficiency, so the same output needs more input work.
Common confusion: A mechanical advantage greater than 1 does not mean more work comes out than goes in. Conservation of energy requires Wout ≤ Win, so efficiency cannot exceed 100%. Do not mix this with heat-engine efficiency, which is net work divided by heat input and is also limited by the second law of thermodynamics.
Sources
- Physics (Cutnell and Johnson)
- Physics: Principles with Applications (Giancoli)
- College Physics (Serway and Vuille)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.