Engineering Mechanics · Levers and pulleys
Machines trade force for distance
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Machines trade force for distance

No machine gives you energy. Every one of them trades: less force, more distance, and the product stays put. That trade has a name — mechanical advantage.

For a lever, MA=dedlMA = \dfrac{d_e}{d_l}M A equals d-e over d-l. The subscripts are the whole convention, so fix them now: ded_e is the effort arm, pivot to your hands, and dld_l is the load arm, pivot to the load, both in metres. MAMA is a bare ratio — metres over metres, no units — and it says how many times the bar multiplies your pull. An MA of 4 means the effort is a quarter of the load. A lever is just a moment balance wearing work clothes.

A block and tackle does the same trick with rope: F=WnF = \dfrac{W}{n}, where WW is the load in newtons, nn is the number of rope sections actually supporting the moving block (a plain count, no units), and FF is the effort in newtons. Six sections, a sixth of the load — and six metres of rope hauled for every metre the load rises. The energy bill is never discounted.

Then reality takes its cut. η=WoutWin\eta = \dfrac{W_{out}}{W_{in}}eta equals W-out over W-in, with η\eta the Greek letter eta. WoutW_{out} is the useful work delivered and WinW_{in} the work you paid in, both in joules; the ratio is bare, and quoting it as a percentage is a courtesy, not a unit. The shortfall went to friction, heat and noise. An efficiency above 100% is not a good machine — it is an arithmetic error.