Pulleys as a Work Input-Outut Device

In our previous topic we saw how adding extra pulleys resulted in mechanical advantage being doubled, which translates to a 50% decreased lifting effort over a previous scenario.    Pulleys are engineering marvels that make our lives easier.    Theoretically, the more pulleys you add to a compound pulley arrangement, the greater the mechanical advantage — up to a point.   Eventually you’d encounter undesirable tradeoffs.  We’ll examine those trade offs, but before we do we’ll need to revisit the engineering principle of work and see how it applies to compound pulleys as a work input-output device.

Pulleys as a Work Input-Output Device

The compound pulley arrangement shown includes distance notations, d₁ and d₂.   Their inclusion allows us to see it as a work input-output device.  Work is input by Mr. Toga, we’ll call that WI, when he pulls his end of the rope using his bicep force, F.   In response to his efforts, work is output by the compound pulley when the urn’s weight, W, is lifted off the ground against the pull of gravity.   We’ll call that work output WO.

In a previous topic we defined work as a factor of force multiplied by distance.   Using that notation, when Mr. Toga exerts a force F to pull the rope a distance d₂ , his work input is expressed as,

WI = F × d₂

When the compound pulley lifts the urn a distance d₁ above the ground against gravity, its work output is expressed as,

WO = W × d₁